The post How to THANK a teacher! appeared first on Sara VanDerWerf.

]]>This week (May 6-11, 2019) is national teacher appreciation this week. There will be lots of pictures of apples and a flurry of effusive general praise sent out in tweets and emails thanking teachers for their work. The superintendent will send an email. So will every building principal. So will the head of teaching and learning. The Assistant principals, school board members, parent group leaders, the local news and more will all follow with short pieces thanking every teacher. If teachers are really lucky there will be a piece of chocolate in their mailbox attached to a flyer with a picture of an apple with a standard thank you – the same one give to everyone. Or if you are really, really lucky – teachers will get a free breakfast of doughnuts and juice (and weirdly no apples – they are always pictured with things having to do with teachers – yet I’ve never once in my 28 years of education eaten one at school unless it was part of my lunch). All of this is great – but I thought I would offer up some ideas of what us teacher really would love for you to do for us this week and really all year. Note: This is purely my opinion – not all of us teachers are the same. If you are a teacher – I’d love to hear your ideas below in the comments.

The general emails and tweets during teacher appreciation week are great – but has meant more to me in my career are the short (1-2 sentences – paragraph at most) emails or conversations where someone has shared a very specific thing I’ve done as a teacher that made an impact. For example…

- Sara, last night my daughter told me that she misses having you as a teacher because even though you made her work hard, you really made her think and she knows she got smarter.
- Sara, I noticed that you attended the the basketball game last night. I saw you seek out a student and tell that how amazing they were. Thank you for taking time away from your own family to invest in the lives of our students.
- Sara, I walked into your room during class and all of your students were up and talking about math. I was only there for a couple of minutes – you did not even see me – I loved how engaged the students were. I asked a student what they were working on and they taught me what a logarithm is.
- Sara, my student is feeling so confident with mathematics this year. I caught him helping his younger brother with math and usually they are fighting about who sits where when they are playing video games. Thank you.

I personally would way rather get a one sentence of something specific about who I am as a teacher and what I am getting right – then a free doughnut. (I like doughnuts too – I’d love both). The general emails of praise sent out this week somehow turn me off, because they don’t feel like you see me as an individual.

**A MESSAGE TO ALL ED LEADERS: ** As teachers we know best practice is to first build relationships with every single student. We are asked to study our students, get to know them as individuals – to know their passions, hopes and dreams. We get to know our student’s cultures. Last year, I had 170 students I studied and built relationships for. On Pi day I wrote every single one of them a personal note with a specific thing I noticed about them and their strengths and assets. I wrote just a sentence or two. I did this multiple other times in the year too. My students need to hear this – read this. If I (and every other teacher I know) can do this – so can you as a leader.

**I dare every building and district official to write a minimum of 170 personal notes to teachers this week. In each write a sentence that proves you know that teacher as an individual – that you see teachers as part of your school community.** District officials (this includes you school board members) – If you can’t do this for 170 teachers because you don’t know them well enough like we know every student – then I’d love for you to spend time this week looking at how you can study your teaching staff and see their assets and build relationships with them. Model for us teachers what you would love to see us doing with our students.

Often we hear students, parents, teachers or leaders saying something really nice about a teacher in our schools. Those things said behind their backs never makes it to the teacher directly. Students may be too shy to say something. Teachers and other leaders may be too busy. What I started doing years ago as a teacher was every time I heard something positive about a teacher being said I would write it down, not name the source and email it or put it in the teachers mailbox. This practice may have changed me more than my teaching peers because it keeps my focus on naming the good in education and I get so many teachers emailing me back saying “Thank you Sara for telling me that. I needed that today. I don’t hear enough of this.”. It is true. Teachers are loved – they just don’t hear it enough.

If you want to do the same as me..here is the template…

Don’t wait to put these thoughts on fancy note cards. Post-it notes work great. Email is great. Just do it.

The timing of teacher appreciation week for math teachers is interesting. Math teachers have the greatest stress of anyone in K-12 education this time of year. We are the only ones responsible for up to 1/2 of the publicly reported metrics in our school and district. Often our leaders have things built into their job performance connected to math metrics. Everyone in the building is expected to contribute to reading assessment performance, but math teachers are left holding math performance on their own shoulders. May is at the end or in the middle of testing season in schools across america. Math teachers during this time are feeling frustrated, overwhelmed, shame, and exhausted. We can be our own harshest critics. Many feel like failures as teachers. Even if testing went well, we tend to focus on what did not. Our emotions are raw. The littlest thing, sometimes even a compliment, can set us off into tears or make us want to quit the profession. The testing culture in America has created anxiety ridden students that we support and love on – but often math teachers own emotional needs during this time are overlooked.

One thing most math teachers would love for Teacher Appreciation Week – would be a removal of the stress and anxiety around testing and scores. What structures in your building can you change change the negative aspects of testing? Start planning now so that testing season 2020 does not carry this weight for students and math teachers. Ask for specific ways to eliminate testing anxiety and stress and work to change those things.

A greatest form of praise for a teacher is when a someone (including those in leadership) say something like * “I noticed your classroom you ________________. Can you tell me how you made this happen?” * If you say something like this to a teacher what you are saying to them is…..

- I noticed something specific you do well.
- I value your expertise and want to do know more. I can learn something from you.
- I see you and want to hear from you.

Even if you think you know how they do the thing you ask about – asking them for advice may reveal something you did not know already. Asking for advice levels the playing field between leaders and teachers and creates community.

Many leaders I’ve worked with as a teacher or now as a leader have done a phenomenal job of seeing and naming teacher’s strengths and assets. One way this is done is after an informal walk through of a classroom a leader immediately sends feedback to the teacher with 2-3 positive things and 1 area to grow in. Sometimes these things get cute names like “Glows and Grows’.

As a teacher, I know how I receive these well meaning emails or notes. I appreciate the positive things for 10 seconds, but quickly forget about what was said and obsessively stew (in my overly busy overwhelmed self) about the noted area of growth. All the work by the leader to note what went well is lost to what they think I don’t do well. (even the cute plant growing out of the ground can’t save my reaction) You could have told me I was the best teacher ever, but I will not see that if I see even one small thing I should work on. I read too much into what they said. At times misjudge what was meant and spin in my head about what they must think of me and fear losing my job. At year 28 – I am not quite this bad, I’ve learned how to take feedback, but every week I am coaching really good young teachers into saying in the profession because they only see the bad and not the good.

Giving and receiving feedback is an important part of our jobs. Do it. But at times, consider giving feedback on what teachers are doing well – show appreciation – outside of also giving an area of growth. If you want teachers to hear what is working. Isolate that message so they don’t skip over it.

Sometimes teacher appreciation week feels for teachers like something that is being checked off of leaders list. In our heads we imagine you saying, ‘Great, I sent out my yearly email thanking teachers. Check. I can check that off the list until our first meeting in the fall.’. Don’t get us wrong, we appreciate anything during teacher appreciation week, but want keeps us in the profession is the gratitude we receive continually throughout the year. We believe your general email of thanks the week set aside to honor us if you have also modeled your thanks with acts of gratitude with a personal touch all year.

At one school I worked at a parent came to me at the start of the year and told me, “I will be here in the building every Tuesday from 9-10:30am. Give me anything you want me to photo-copy, cut, organize, clean…etc. She showed up and did this. **IT WAS THE BEST. I FELT APPRECIATED.**

A community member with no relationship to a school I worked in showed up in the principals office with 10 amazing electronic pencil sharpeners and said “Give these to any teacher you think would love one”. My principal walked into my room later that day and plugged one into the wall for me. **IT WAS THE BEST. I FELT APPRECIATED.**

An assistant principal showed up in my classroom after school one day, stacked all my chairs. Told me to put my feet up and told me what they appreciated about me as they worked. **IT WAS THE BEST. I FELT APPRECIATED.**

A colleague told me what they hear students saying they loved about a project in my class, asked about the project and asked me for my advice. **IT WAS THE BEST. I FELT APPRECIATED & VALUED.**

A district leader walked into my room and dropped a hot white mocha from a nearby coffee shop on my desk while I was teaching with a note that said “Thanks for working hard for South HS students and families”. This person noticed what I was drinking at a meeting months earlier, remembered and showed up unannounced. **IT WAS THE BEST. I FELT APPRECIATED.**

A parent showed up after school one day with cleaning supplies and washed all my classroom tables and boards. **IT WAS THE BEST. I FELT APPRECIATED.**

A parent tweeted out a picture of my play table and said “I wish all teachers made space for play in the math classroom. Look at what I made. **IT WAS THE BEST. I FELT APPRECIATED.**

A student I taught 19 years ago sent me a Facebook message telling me how my class made them feel – all these years later. **IT WAS THE BEST. I FELT APPRECIATED.**

It does not matter what you do. Do something. Do it regularly. Do in unannounced. Small is all we look for. Notice us teachers getting it right. Name it.

Need Ideas? Here are some I’ve collected. In no particular order…..

For those of you with bad 50 year old eyes like me… you can download it HERE: 30 ways to thank a math teacher.

As always, I’d love to hear what you think. If you are a teacher – what makes you feel appreciated or loved? If you are a parent or leader – what do you do? What questions do you have. Tweet at me @saravdwerf or comment below. Also, check out my new Math Teacher Instagram Page HERE. I am currently, out of the classroom. This week I am committed to writing 170 1-2 sentences of specific things I’ve noticed about 170 classroom teachers directly to them. I’ve already done 40. I’m busy….but classroom teachers are busier. If they can find time to give value 170 students each day. I can find time to value 170 or more teachers this week. May you do the same. If 170 is too much pick a number you can do. 1 is good. 10 is better. Thank you to all classroom teachers. You do have the most difficult job in education. I see you. I hope to be a leader that you believe values your humanity and your work.

Lastly, I tweeted out today asking teachers how they would like to be thanked. Check out this thread and read the words from teachers for more ideas. So far their ideas pretty much match the ones I’ve shared above. Click the thread below to read more.

Next week is teacher appreciation week. Lots of people will send tweets & emails full of general praise of teachers. I think we can do better. Teachers, I'd love to hear from you. What makes you feel loved, valued and appreciated? My blog post & ideas will come soon. #mtbos pic.twitter.com/kK08ozIwjo

— Sara VanDerWerf (@saravdwerf) May 4, 2019

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]]>The post Small Change, Big Difference part 1. Why you should eliminate ‘POINT’ from your vocabulary. appeared first on Sara VanDerWerf.

]]>I asked math twitter (#MTBoS) to tell me about small changes they’ve made that resulted in big differences in their mathematics classrooms. I **HIGHLY recommend** you read the tons of responses I received (click the link below to read the entire thread). I promise something in this thread will inspire you.

Reading through all the responses, one thing that surprised me was how many responses had nothing specific to do with math, but had everything to do with building relationships with students. You can’t teach math until students trust you and believe that you believe in them. If you have a small change you love for the math classroom, please comment below.

**My answer to this question!**

I could write a book on small changes in the math classroom that have had a huge impact on student engagement and learning, but I thought I would start with something that will enhance your students conceptual understanding. I selected this small change as the first one to share with you based on observations in classrooms this fall and working with math teachers from all over the country. It is clear to me that some things I took for granted as normal in my own classroom and district are not well known by many secondary math teachers in other places. Small changes I and others in my distract made years ago are new to many teachers I’ve worked with. So what is this small change that can lead to enhanced conceptual understanding?

Let me begin with a question for you.

**What is the goal of K-5 mathematics?**

I’ve asked this question to lots of people. Most secondary math teachers shrug and are unsure. Many elementary math teachers and leaders say ‘* number sense*‘. While I agree number sense is the goal, the definition of the phrase is vastly different depending on who you ask. When many of us hear ‘number sense’ we think, ‘yes! I am doing this’. Unfortunately, some of us hear ‘number sense’ & view this phrase through a faulty lens of what we believe elementary math is, specifically to be good at elementary math is to be fast at arithmetic calculations – this is not what my elementary math leader friends mean when they say ‘number sense’.

So what is a good definition of ‘number sense’? From Wikipedia (they have all the answers, don’t they?) Gersten and Chard say number sense “refers to a child’s fluidity and flexibility with numbers, the sense of what numbers mean and an ability to perform mental mathematics and to look at the world and make comparisons. Here is another definition from Christina Tondevold’s website ‘Build Math Minds‘. (check her site out – she is passionate about not just knowing what number sense is, but how you actually build number sense in your students)

How I talk about the goal of K-5 mathematics…

I don’t say the goal of K-5 mathematics is ‘number sense’ since many have faulty definitions of this phrase. I’ve been blessed in my state to be surrounded by amazing elementary math thinkers and somewhere in my own learning on the topic in the last 10 years I was told the **goal of elementary mathematics to build a flexible understanding of the base-10 number system. **This is the phrase I now say and also informs my own practice. The key words in this statement are **‘flexible**‘ and ‘**base-10**‘. These words have informed my work in the last 10 years more than pretty much anything else. What does flexibility in the base-10 number system mean? Let me give you a few examples (this is literally just the tip of the tip of the iceberg that is K-5 math)…..

A student who is flexible within the base-10 number system would decompose the number 437.

**437 = 400 + 30 + 7 = 4**x**100 + 3**x**10 + 7**x**1**

Students may say ‘** 437 is 4 hundreds, 3 tens and 7 ones**‘ using place value language.

Note: many of us secondary people are comfortable with this example – but not the next…students are flexible if they also see 437 in other ways…for example:

**437 = 430 + 7** ** = 43**x**10 + 7**

**Flexible students** might also say ‘** 437 is 43 tens and 7 ones**‘. Students would represent this understanding using a variety of models.

See what ‘a flexible understanding of the base-ten number system’ also looks like in a few photos below:

So K-5 mathematics is all about building a flexible understanding of the base-10 numbers system. My question now is for every secondary and above mathematics teacher….**What are YOU DOING in your own 6-12th grade classroom to build a flexible understanding of the base-ten number system? **Unfortunately for many of us we are doing very little. It is time to change this. You can begin this change with a small change that will give you immediate results!

**Small Change #1: ** **Outlaw the word ‘point’ in your classroom.**

When you return to your classrooms in January, post a few signs around the room that look like this:

Perhaps you don’t say anything about them for a few days. Put one on your classroom door and between classes while in the hallway greeting students (did you read all the ideas shared in the tweet above? you need to be in the hallway between classes) shrug your shoulders and say ‘I don’t like the word point, it is not allowed in this classroom.’ when they ask about the sign. Have fun with it. If you have fun with it, your students will too.

Note: Here is a sign you can download and use in your classroom:

**Why should you outlaw the world ‘point’? **If you don’t know why yet, then I recommend putting up the following problem for your students on the board:

Say to your class, “*Quick, no calculators, add this as fast as you can, go!*” Watch as tons of students sit there having no idea what to do and others furiously working to get common denominators. After 30 seconds, say to the class, “*Stop. Look up here. <insert student name> read this out loud to the class.*” As the student reads the expression you write 5.307 and listen to the chorus of ‘Ohs!’ ring out in the classroom. Your secondary students are very weak at connecting fractions to decimals.

You should eliminate the word ‘point’ in your classroom, because it is the easiest and fastest way to build students understanding of the base-10 number system past the decimal point in your classroom. Here is how I introduce this word being outlawed to my students.

**Step 1.** Write the following number on the board: **5.45.** Invite your class to say the number out loud. When they say ‘*Five point four five*‘, say “*No, that is not how you say it, who can say it in another way?*” It will take little time for someone in the class to say ‘*Five and forty-five hundredths*‘. When they do, say “Y*ES! From this time forward in this class we will never use the word ‘point’ in this classroom. All decimals will be read using place value language.”*

**Step 2:** Write up 3-6 more decimal numbers and as a classroom practice this together. Read these chorally.

** 3.2 ***‘Three and two tenths’* **7.009 ***‘Seven and nine thousandths’* **16.182 ***‘Sixteen and one-hundred eighty two thousandths’* …and so on….

**Step 3:** After you say each number, write the appropriate fraction.

**TIPS: ** I am not a fan of much on my classroom walls that is not student work, but one poster I think every secondary classroom should have is is a place value poster. As you say these numbers point at the poster. I recommend limiting most examples to the thousandths place. Also, no need to go to billions in your examples either. The goal here is to get your students using place value language.

When you introduce saying decimal numbers without using the word ‘point’ – especially if you do it in a fun and playful way – you will be surprised how easily your students will adapt to this. They start doing this immediately. They catch each other and hold each other accountable. Honestly, more than likely, the person who in your classroom who will have the hardest time with this will be YOU, the teacher. I have been doing this for years and I still find myself saying ‘point’ at times.

Not only will this be an easy transition for your students, you will notice your students understanding of place value improve without you having to do much else. I introduced this idea to middle school teachers at a training I was doing recently. We were training a unit on teaching calculations with decimals. One model in the unit was using the area model to visualize partial products in the expression 2.4 x 1.3.

Teachers were worried in students first experience with decimals that students would not know what do do when they multiplied three-tenths and four-tenths. As we said these decimals aloud (without saying ‘point three’ and ‘point four’) teachers had an A-HA moment and wrote these as fractions. They believed their students could connect multiplying fractions to the decimal work. Teachers asked me, *‘does this always work?*‘

Our teacher PD, where I had outlawed the word ‘point’ for teachers led to teachers themselves making connections between fractions and decimals and making themselves more flexible within the base-ten number system.

Once again, **my challenge to you, is to make a small change in your classroom that will lead to a big difference in students conceptual understanding of the base-10 numbers system. Outlaw the word ‘point’ from your classroom. **One small note, I was religious about this change in my middle school classrooms. When I returned to teach HS three years ago, I got a little lax with this and noticed a difference immediately. This is for MS and HS. We all need to work on our flexibility within the base-10 number system.

In future posts I will reveal 8 additional small language changes I’ve made in my classroom that have resulted in big conceptual understanding differences in my students. For now, start 2019 by not saying ‘point’ and using place value language to name all decimals.

**DOWNLOAD A FREE PDF!****9 language changes that build conceptual understanding.**

If you want a preview to my 9 changes to mathematical language to build conceptual understanding, enter your email below and I will connect you with a one pager you can download of 9 things to say in your classroom (with 9 things to stop saying).

**BONUS MATERIAL for Secondary Math teachers. ** Calling all 6-12+ math teachers. it is time for us to improve our understanding of how to teach elementary mathematics (number sense). Many of us struggle knowing how to teach a student to subtract, who can’t subtract. If that is you, below are some easy ways you can improve your understanding of elementary education from the comfort of your classroom our couch. At minimum commit 34 minutes of your life to doing #1 below. Seriously. If you don’t have 34 minutes to work on your own practice then don’t you dare give your students another homework or project again. We need to learn and practice just like our students.

**What can you do to learn about K-5 Mathematics?**

- Graham Fletcher has five great videos (slightly more than 34 minutes total – don’t tell me you don’t have time to get smarter!) for the progression of learning mathematics in Elementary.
**Watch all of these.**Ideally, watch one video with a teaching peer (How great would it be if you had a group of 2-5 teachers at a coffee shop from various grades to watch each video have this conversation). I recommend watching each video eat least twice. Listen for Graham saying things like ‘model’, ‘efficiency’, ‘flexible’, ‘context’, ‘let’s not rush them’, ‘let students explain’…..- The Progression of Early Number and Counting. (7 min 34 sec) Here are some terms to ‘google’ to learn more after watching the video.
- Subatizing
- Rote Counting
- 1-1 correspondence
- Cardinality

- The Progression of Addition and Subtraction (7 min 20 sec) Here are some terms to ‘google’ to learn more after watching the video.
- 5 Frames
- Unitizing
- 10 Frames
- decompose numbers
- partial sums

- The Progression of Multiplication (5 min 56 sec) Here are some terms to ‘google’ to learn more after watching the video.
- partition
- array
- relational thinking
- area model
- base 10 blocks (10 rods…)
- partial products

- The Progression of Division (7 min 49 sec) Here are some terms to ‘google’ to learn more after watching the video.
- partitioning
- base-10 blocks
- area model
- decompose numbers
- concrete model to representation to written expression
- fair share model
- partial quotients

- The Progression of Fractions. (7 min 26 sec) Here are some terms to ‘google’ to learn more after watching the video.
- partition
- length model
- set model
- area model
- number line
- counting circles
- unit fractions
- common denominator and common numerator
- Benchmark fractions

- The Progression of Early Number and Counting. (7 min 34 sec) Here are some terms to ‘google’ to learn more after watching the video.
**Print out and read**the Common Core progressions HERE, particularly these two:- Check out Christina Tondevold’s website ‘Build Math Minds‘. She has great resources and offers virtual PD on elementary math. Join her Facebook group too.
- Learn about ‘CGI’. CGI stands for ‘Cognitively Guided Instruction’ and comes from research out of the University of Wisconsin Madison. I highly recommend reading ‘Children’s Mathematics’ by Thomas Carpenter to begin your journey in understanding more.
- Check out Pam Weber Harris’ website ‘Math is Figureoutable’. She is the perfect transition resource linking K-5 math to 6-12 math. I love her levels of Algebraic Reasoning. If you don’t know the difference between additive and multiplicative thinking, you have no business teaching proportional reasoning (just sayin).

6. In my home state of Minnesota the godfather of Elementary Mathematics – he has trained almost every great Elementary Leader I know in my state – is James Brickwedde. His PD is a master class for people who want to go deep in their knowledge of how students develop numeracy. Google his name and read things he has written or check out his website, The Project for Elementary Math (note: Jim is the organizer behind this summer’s CGI conference in Minneapolis)

7. The rest….there are lots of other K-5 words you can google and learn mor about….: Fact Families, Additive Thinking , Open Number Lines, Tape Diagrams (bar model) , Rekenrek, Counting On, Direct Modeler, Compensate, Multiplicative Thinking, Relational thinking…..also get familiar with all types of K-5 models. Here are a few places to start.

- Get familiar with elementary models – check out this ‘Progression of Math Models‘ in Eureka K-5 Mathematics for what some common elementary models look like.
- Check out this powerpoint about models in the Engage NY materials too.

Lastly, what do you do to improve your K-5 math understanding. Let me know in the comments below. I highly recommend looking for good K-5 PD in your area this summer and attending it as a 6-12 person. Not sure where the PD is, contact your local NCTM affiliate and ask them. They will know.

**That is all for now – I know, I know – my usual ridiculously long post. Let me know what you think by commenting below or by tweeting me at @saravdwerf. I love hearing from you all.**

The post Small Change, Big Difference part 1. Why you should eliminate ‘POINT’ from your vocabulary. appeared first on Sara VanDerWerf.

]]>The post Using Name Tents throughout the year. Guest Post. appeared first on Sara VanDerWerf.

]]>One reader who took me up on using name tents a year ago introduced herself to me at the NCTM national conference in DC in April and shared her experience. On a whim I asked her to write it up and send it to me. Four months later she did and I received the following in an email from her. Check this out – Thank you to** Erin Stenger** for sharing her experience with name tents below.

As I soak up the highs and lows of last school year, I’ve found that building relationships with students had the most positive impact on my year. Building relationships creates a classroom community that enables students to listen, learn, and do mathematics because they trust that I will be there to support and guide them.

Last year, one of the “first day of school” activities that caught my eye was Sara Van Der Werf’s Name Tents. (Thank you for sharing!!) I used the activity each day for the first week and learned some neat things about my students. Nic for example likes to go fishing, Athena has been to Iceland (wow!), Jack wanted to know when the first test was going to be, and Morgan was nervous about how she has done in math class before and if she will be able to handle Algebra 2. I also quickly identified students who may have a hard time staying on task when I would open up a name tent to comment and it was blank. I found most students were honest and sincere. Sara’s name tent activity provided an outlet where students could ask me about who I was and how my class worked without announcing it to the whole class.

One student who stood out was Selma when she wrote “I’m not good in Algebra and I hope this class changes that a lot.” A few days later she wrote “Do you believe in me and that I can pass this class? Because I don’t.” Wow – talk about some math-failure baggage. I replied as honestly as I could: “ I have no reason to believe otherwise. I believe every one of my students can learn math with practice and effort, including you. Fresh class = fresh attitude. Keep me in the loop if you’re getting overwhelmed.”

Selma continued to work in class and participate but I knew I wasn’t seeing her full potential. By winter break, she was not doing well. She avoided completing missing assignments because she hadn’t spent the time to learn material she had missed. I pulled her name tent off my shelf and handed it back to her with my original comments highlighted and an additional comment, “You can do this. Depends on how much you want to work for it. Your choice.” I didn’t need to say anything else.

Selma came in the next week with a fresh notebook and a fresh attitude. I had built a relationship with Selma so she knew the following: 1) I believed she is capable of learning math in my class, 2) she received specific feedback to know what she needed to improve on, 3) she knew I was there to support her but that she had to take ownership of her work. Selma came in a few times afterschool to learn material and make up her assignments. By the end of the year, Selma passed Algebra 2 and I hope she gained confidence in her ability to do mathematics.

I would highly encourage you to use Sara’s Name Tent activity your first week back, but I have one suggestion. Pull them out in a few months and re-read them. Maya Angelou once said “When someone shows you who they are, believe them the first time.” Once you begin to know your students, you will be surprised at how open they are on that first week. **The best time to lay a foundation for building relationships with students is when you can catch them being their most true and honest selves. **

THANK YOU Erin for sharing your story using name tents! Thank you to every reader that shares their experiences with name tents with me. I’ll add more ideas from other users below here soon. Until then – have a great start to school everyone.

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]]>The post Math Fails 2018 Set #4 – 87 new pictures to download appeared first on Sara VanDerWerf.

]]>Still 5 years later, the best thing I’ve put on my walls that students, other teachers, parents and almost anyone looks at and discusses regularly is my #MathFail wall of fame. For the last 2 years I’ve put 20-30 laminated math fails in my hallway and enjoy watching people regularly stop and try and figure out what is wrong with each picture. I switch out pictures occasionally since I have somewhere between 200-300 pictures I found over the years. Below are some of my favorites from between August 2, 2017 and today, August 1, 2018. If you are looking for a fun idea for the walls of your classroom or school I HIGHLY recommend adding a #mathfail wall to your school.

There is one type of math fail that is found and shared with me each year. I like to call this type the “Here’s a penny, keep the change!” #math fail. Each is a picture of something for sale that as listed should sell for slightly less than a penny each. It is a misconception of parts of dollars ($) vs parts of cents (

I dare you the next time you see one of these photos at a store to purchase an item, walk up to the counter with a penny and say “Here is a penny, keep the change!” and walk away. This year you could have purchased pens, lemons (or DEMONS depending on how you read the sign), boneless wings, pool noodles, Mac & Cheese or peanut butter bars all for less than one penny each.

Bad graphs are make up a ton of the #mathfails I get tagged in. Not only are there a lot of them – they also generate a lot of the conversation in my #MathFail display in my schools hallways….Here are a few from this year…

Confusing hotel room signs seemed to be a theme this year. I feel I was tagged in them at least 5 or 6 times. I only found 2 though when I put the collection of #mathfails together this year.

**Where is room 1111?**

These 2 #mathfails are great conversation starters around percentages…..

First a Lift ad from this year….

And an old comic…

Several fails got at the definition and conventions in mathematics – specifically related to “Is zero a positive or negative?” and “Is one a prime number”

It is not just tweets, advertisements and store pricing where you can find #mathfails. #Mathfails are found in our text books and the work we assign our students. Here are just 3 this year from the #MTBoS community.

**Janell really has lost her marbles!**

**Just no!** Is there a worse context for a math problem this year? I think not. (but if you have one – tweet me at @saravdwerf – I’d love to see it and add it to next years set!

Amie tweeted this one out – and she is the daughter of a citrus farmer…. we can do so much better selecting contexts for our math problems…

Nope. #mathfail pic.twitter.com/rWnjyMeEQg

— Amie Albrecht (@nomad_penguin) April 20, 2017

I’ll leave you with this classic Peanuts cartoon…

The vast majority of my collection of math fails has very little to do with Geometry – this year was different and had a few fun ones to offer. One of my favorite came from this story (click link) from England. Look at this picture… What do you notice? What do you wonder?

A quote from the article….

Look at the picture above. What do you think of?

Do you think of the corner of Stanley Park which divides two great football teams?

Do you consider that one mast in the ground as a symbol of the different directions in which two great football clubs have gone?

Do you wonder what would happen if certain players in history had taken the blue path instead of the red, and what might have become of them?

Because if you do then you’re not looking hard enough.

What should really be ticking you off about that bloody picture is the footballs on the sign. They might seem fine to you, white polygons rattled on a brown background, but take a closer look.

This article and these signs all over England set off a national petition found in tweets almost a year ago….

In the era of ‘fake news’ talked about all the time, I’d be lying if I said I did not think some of the #mathfails shared with me were manufactured and fake. I have zero time to track down accuracy on these – but some of them I suspect were put together by someone. For example – I feel like someone put a paper ‘1’ in front of 30% at this Target store and took a picture – if they did -Kudos to them as the font accuracy is great. The height of the ‘1’ is just a touch too long to make me think this is real. If it is real – please let me live by this Target.

Any mathematics on twitter connected to politicians always makes me wonder if the tweet is real or made up or…..for example…this tweet would be a great math hook to start a conversation about measures of center – but may be a bit too political to have a safe conversation – reading the responses to this tweet though was worth my time for a bit to laugh about math….

I would imagine that 50% are below average… that's how math works. The real question is what is average now vs before common core. https://t.co/OnwYhzS7iU

— Donald Trump Jr. (@DonaldJTrumpJr) October 31, 2017

A favorite tweak to tasks I put in front of students is to add the phrase ‘Convince Me’ to a picture, visual or problem. This phrase has opened up a deeper level of discourse in my students as they work to craft convincing arguments for the class. This is a phrase I could see myself using with some of the #MathFails in the set.

For example – I would turn these three #mathfails into ‘**Stand & Talks’** (the best routine I’ve ever used in my classroom – click to read more) to start a conversation.

**#1 ** Mike Flynn tweeted this question out. (click the link to see others responses and additional links about why you can’t walk up the Washington Monument).

What’s the verdict on this? Is it a math fail or a reasonable approximation for a comparison? Photo credit: @Redhdteacher pic.twitter.com/dLY3rQkTOA

— Mike Flynn (@MikeFlynn55) December 11, 2017

I turned this tweet into a stand and talk with the visual and this phrase “** Convince the class that this is a reasonable approximation.” **You can download my Word Doc visual HERE

**#2** This meme made its way around twitter a while back and I was tagged with the hashtag #mathfail by several of you. I think it would make a great introduction math hook to start a unit on exponential vs linear growth.

**#3 **I feel like I could make an entire day long task comparing surface area to volume in different 3D shapes with this #mathfail. Here is what my initial stand and talk looks like….

I would follow up students beginning ideas with time for exploration and calculations and ask them to provide evidence to prove their argument. This also opens up other conversations about why product package design is made the way it is made (transportation, materials used, …..)

You can download all three of the ‘Convince Me’ #mathfails in a word doc HERE: Convince Me Math Fails

I really, really dislike when the equal sign is misused. This screen shot from the last year from a NBC show – Genius Junior (click to see video link) – that marks a contestants mathematics as he calculates really bugs me. This is something I try and stop my students doing in their thinking. This is why so many students have a incorrect conception of an equal sign as a symbol that asks you to calculate whatever is to the left of the symbol. My wondering is how I could use this screen shot – perhaps in a stand and talk – to correct their understanding of an equal sign as meaning ‘is the same as’ or to see each side as equivalent….thoughts? Comment below or tweet me @saravdwerf.

This picture from the back of a bus was tweeted out to me this year! Really – do we need adds like this to keep the status quo of many disliking math? Why must this continue. This is a ‘Math Fail’….Ugh!

I made the sign on the back of the bus a bit larger….check out what it says and what math class is equated to….Ugh, again!

I am currently on a journey to better recognize the structures in my world and in education that center and privilege me as a white middle class educator. Not only do I want to notice structures that leave many others feeling other, outside or not included – I am working on dismantling these structures around me. I have a long long long way to go in this journey – I, like so many of you, have so many unconscious biases from my years of conditioning in a world that privileges me and denies others – but despite this I am on a journey – there are numerous #mathfails we could find that set up our classrooms and schools for the success of some and as not safe places for others. One really small thing I can do is use some of the math fails to spark conversation with educators and/or students about why these visuals are damaging. Here are 2 examples from this year.

The tweet below from the campus of Brigham Young University caused a #mathfail that centered white males as being mathematicians made the Huffpost this year. You can click HERE to read the story and response of the the organizers.

This next #mathfail would be great to talk about not only the content, but why the way the graph is made continues to center white people as privileged. How could you use this visual in your classroom to not just talk about mathematics, but also about the world our students live in and the world we want for them in the future. If this visual sparks your interest – **then you can read a lot more about it HERE.**…

I did not include this photo in the word doc linked below -but thought I’d include it in this post. Last September the Minnesota Council of Teachers of Mathematics sent me balloons on my birthday (to school!). So great! Right? I’m a lucky girl! At the time I was the out-going President of the organization. Can you catch the #mathfail?

September 2017 I turned 49 – not 50! But, I let everyone at my school believe I was 50 last year. When I turn 50 in a month and a half, it will be no big deal. I’ve felt 50 for the last year. Thank goodness I am not sensitive about my age. Despite the wrong year – I will always, always be thankful for anyone thoughtful enough to do kind things. I live in a state full of the kindness and smartest math teachers anywhere. Because of them I am a better teacher leader. May you all have amazing people in your life who make you better too – even if they get your age wrong.

There are 87 total images this year. I’ve only touched on less than 1/2 above. Download the Word Doc or PDF to see all the new ones from this year. I’ve also included links to my previous 3 sets. My collection of #mathfails is now over 300 images. I recommend putting no more than 20 images out at a time if you make a wall of #mathfails for students and others to look at. I also highly recommend switching out 2-3 every few weeks to keep things vibrant and interesting.

Set #4 – new summer 2018 (see descriptions above) WORD DOC : Math Fails 2018 Set 4 or PDF: Math Fails 2018 Set 4

Set #3 – new summer 2017 93+ images

Set #2 – new summer 2016 72+ images

Set #1 – the Originals collected on or before January 2016 80+ images

**Do you have something to add to the math wall of shame? Tweet me @saravdwerf, email me at saravdw@gmail.com or post using hashtag #mathfail. I would love to add more to my collection for summer 2019 (I still don’t believe I’ll be able to find more than 10 for a year from now….we will see)**

The post Math Fails 2018 Set #4 – 87 new pictures to download appeared first on Sara VanDerWerf.

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]]>During the last few years I’ve been observed by others maybe 100 times. I have 2 common comments when people observe my room. #1: “I’ve never been in a math classroom where students move so much.” #2: “*How do you get your students to not use their cell phones in class? **I did not see students on them, unless you asked for them out.**“* Observer comments about cell phone usage in my classroom generated way more questions of education peers than almost anything I do.

In the last month I’ve attended 3 different 2-day PD’s. As part of each PD we’ve been at some point asked to brainstorm common classroom norms or expectations. At each PD session educators from all levels and backgrounds complained about the effects of cell phones in the classroom. Many seem to have given up on trying to keep students off of them. Many complained about their schools lack of control over them. Many longed for the days in the past when cell phones were not prevalent. Many talked about how bad cell phone use was the day ‘* Fortnite*‘ was released for cell phones. In these conversations I felt like I was alone in arguing for cell phones in the classroom. I don’t feel like I have to manage them more than anything else in my classroom and

I went to college with a typewriter. A typewriter. Yes, I’m that old. My first school had a mimeograph machine (google it) for copies. We did have a super slow copy machine too (no fancy stuff – no collating or staples). The TI-81 came out my first year of teaching and I lived through

years of many calling graphing calculators the end of math education. 25 years later you now find TI-8x products in almost every classroom. The first half of my career was all done on an overhead. It has been 10 years since I touched a overhead. (thank god) Imagine if I still taught like I did my first year of teaching and had not adapted to what is new and amazing? Imagine if I was not using my smart-board to create a technology rich classroom?

My job is to adapt to the students I teach and the world they live in and the world I am preparing them for. Adapting to the current realities of 2018 comes with amazing things like Desmos Activity Builder and also comes new challenges to manage – Cell Phones has been one of those things the last several years. How we engage students in the classroom needs to be tweaked. I don’t lament this. 5 or 10 years from now there will be the next thing I need to adapt to . A new group of teachers will be annoyed and calling this new thing the end of education and culture as we know it. Whatever that new thing is, I don’t plan to join the naysayers. I plan to be with the group of educators adapting to the positive aspects of the new technology. I choose to look for the good. **Cell phones allow me to engage learners I’ve never been able to engage in my entire career.**

When I do speak up for my love of using cell phones educators give me lots of excuses for why they can’t do the same. “*Sara, my students are poor, they don’t have cell phones?”* I disagree. That may have been true 5 years ago, but look at the data. I teach at a school with large numbers of students in poverty and high percentages of immigrant students. Do you know what all of them have? A cell phone. I can count on one hand the number of students who do not have a cell phone and all of those students have a parent with a cell phone. This excuse is not an excuse anymore. For the very few students have this issue, I work with my school leaders to supplement technology for these students, but honestly I’ve not had to do this at all in the last 2 years.

“*But Sara, my students don’t have access to **WiFi*.” This excuse is true for some students in rural areas, but in cities, this is so untrue now a days. My experience has been my students are masters of knowing how to get free WiFi (McDonalds, libraries, school…..) everyday. There is still work to do on this, but the number of student without access has decreased exponentially over the last few years. I chose to not base what I do in my classroom for the small number of students who can’t or don’t have. Instead I am investing time into getting resources for these students so all have access.

**The Desmos APP.**It is no secret I love Desmos. I use it often. When I am using Activity Builder, I usually use a set of iPads or Chrome Books. When we are just using the Desmos calculator**I prefer to have students work on the Desmos APP on their personal cell-phone**(we all downloaded it together the first week of school? Why? Simple.**My students (and your students) are way more likely to use Desmos at home if we use it on the platform they will most likely use it outside of the classroom.**My experience is despite using Desmos all the time on computers/tablets in the classroom, there is a fairly large group of students who will not make the jump to the idea that they can also use Desmos on their phone—even if you tell them they can. Telling is not enough. I saw huge increases in at home use of Desmos when I started having students use Desmos on their phones regularly in class. Students do what we model for them. Side note- I have a classroom set of TI-84’s out all the time for student use. We use them but at least 1/2 the time we use our phones and the Desmos APP. Why? What do students have within inches of their body 24/7? Not a tablet, not the TI-84 you made them buy or even their computer. The one thing you are assured all students will have with them all the time is their phone. .- For more of my thoughts on Desmos – I blogged about my love of Desmos HERE (from a Keynote I did for Desmos on ‘Evangelizing Desmos”) and also HERE & HERE (on how I introduce Desmos at he start of the year with resources). I was in the Minneapolis Paper talking about why I love this app HERE and also a news story on the local Minneapolis news HERE.

**The cell-phone camera APP!**– If students did not have cell phones, the thing I would miss more than anything would be their access to the camera on their cell phones. The students ability to take photos of notes on the smart-board or work they they do on white boards or take pictures of a classmates notes has been a game changer for improving students engagement and success in my classroom, particularity for my EL students. Often I will say as we are working on something complex on the board up front – feel free to take a picture of the board. My work on the board has intentional color and I am skilled at creating organized notes – many of my students are not. Many of my EL students and some Special Ed students will engage in classroom discussions more frequently if they are freed from putting all their energy to writing and digesting lots of information quickly. My students take so many pictures each day I sometimes feel a bit famous as they snap pics of all the things we do. My students are paparazzis of math work. All them time I see my students pulling up pictures of math work and zooming in to study what is there. It is a new form of studying for math. Again, guess what my students don’t have with them 24/7 – their notebooks. What they do have with them 24/7 is the pictures they took of math work with the cameral on their phone Here are a few other ways the camera on a cell phone helps my students…- I have had several students with poor vision or broken glasses use their phone to ‘see the board’ they take photos of everything and zoom in on what they can’t see. OR they use their phones camera to zoom in on the board at the front of the room, no pictures needed.
- I have taken myself out of the loop of students getting missed work when they are absent. I teach my students that a norm in our classroom community is that we help each other. One way we do this is to let absent students take pictures of notes/examples they may have missed. No need to borrow someone’s notebook.
- Students take pictures of answer keys to homework assignments all the time. I love it. Why – they actually look at them later and it saves time in class – I don’t need to give 10 minutes to look over answer keys, I can just give a couple of minutes – students take pictures of anything they miss.

**The Google Chrome (or any other search engine) APP.**If you have not read my blog post on why it is important to teach students to ‘google’, stop what you are doing and go read it HERE now! One of the best things I’ve every done is to teach students how to find information they don’t know. In fact, I almost never answer any questions related to math that students should already know. Instead I tell them to take out their cell phones and look it up. (obviously I also build community in the classroom and also recommend using their peers). Why have them search instead of me telling them? One goal in my classroom is to empower students to solve their own issues and find information when they need it. If I answer all questions, I am the sole-keeper of math knowledge and when I am not around they sit there doing nothing waiting for me to appear. My goal is to make my role in their learning of math unnecessary. I of course will always be willing to help them if they go to google and still don’t understand something. I have taught them tips for googling (read my post for more) so they can find great resources…Here are a few of my tips for them.- Be specific – don’t google just google ‘slope’. Instead google ‘
**definition of slope**‘ or ‘**slope formula**‘ or…. - There are lots of words that have different meanings outside of math, so I teach my students to add the word ‘math’ to their google searches. For example search ‘
**slope math definition**‘. - I teach my students to click on Google images. Many of my students are only 30 seconds away from saying “Oh, I get it (or remember it) now” when they see a good image. I’ve found google images to be faster to students solving their math issues.
- I also model how to use/click on the ‘Video’ tab and look for videos to teach/reteach them a skill.
- I have a lot of language learners in my classroom, so I’ve also modeled clicking on the sound icon that pops up in google and listening to the word 7 repeating the word out-loud at least 10 times. You may think they won’t do it, but you’d be amazed. My students want to learn the English language better. I catch many students popping in an earbud to do this more times than you would think. If you model it for them a couple of times in class, they will do it.
- Speaking of EL students. I’ve taught my lowest language learner EL students to add ‘Spanish’ or ‘Somali’ to any web search. Often they can find information and images in their first language. For example: “
**multiplying polynomials spanish**“. - UPDATE: Thank you to Bonnie Basu for reminding me to have students use ‘Google Translate! Yes!

- Be specific – don’t google just google ‘slope’. Instead google ‘
**Reminder, Calendar and Messaging APPs.**In an effort to help my students learn to manage their student work and create healthy habits that will serve them in college, I often will have students ask Siri to set a reminder in their phone during class “Siri, remind me at 9pm tonight to do my homework”. I will have them message/text their parents during class to see if they can come in for help the next morning. I have them take out their phones and put due-dates into their calendars. When I conference with students about when they will come in to get help or do a re-assessment of a learning talks, if they select a morning time, I ask them what time they need to get up to get here on time and then have them set the alarm in their phone in front of me. I use these apps a ton of way with students. As I’ve said numerous times above, my students have their cell phones with them always. Teaching and modeling them how to use them to manage their lives as students and communicate with parents and peers is part of creating empowered mathematicians in my classroom. I also model how to set a timer for 20 minutes and then stop when they do homework outside of class (I don’t believe in more than 20 minutes of practice a day, but that is another future blog post).**The rest.**There are lots of great APPs out here for phones that students and you may use – too many to go into in this post. For the most part I don’t have students use or download too many fancy apps. I find the most useful apps are the simple apps mentioned above. Here are a few more ways I have students use their phones regularly….

- I no longer – ever – answer “
*What’s my grade?*” student questions. I teach them how to look up their grade on their phone. Again as above, I could show them how to do this on a computer/tablet – but where will they look it up most often, their phone, so I teach them on the platform they will use. I rarely if ever get asked by students to know about heir assessment or other grades – they usually know moments after I change information online. - My students use their phones to check email from me with resources, websites…etc and/or they use their mail apps to email their families with information. I give students permission to email or text absent student/friends the notes they missed or pictures of the homework assignment or…..Again, I am out of the loop of solving issues I use to have to solve prior to cell phones. I also have decreased the number of emails from students asking for information, they almost always ask a peer since this is how I model it in class.
- We also use google drive for a variety of things. Again nothing to fancy, but all save tons of time and take away excuses for why students can not be working on math outside of class.
- I also love apps for setting timers in class or picking a random number or…..things like that.

If you have a favorite APP that you have students use on their phones, I’d love to know about it. Comment below.

I have lots of apps on my own phone that I use all the time and make me more efficient as a teacher.

- I love, love my camera app. I can take pictures of student work or answer keys or screen shots of ideas I want to steal from twitter or……Love it. I can easily email myself the pictures I find.
- In the last year I’ve found an app I love way more than my camera app.
**If you don’t have****‘CamScanner’**,**stop what you are doing and download it now.**It takes just minutes to set-up and**the jpegs and pdfs you can create are far superior to my phones camera or the scanners at my school**and I can use it from the comfort of my home. No more running down to the copy room to scan something. I love it because I can easily remove backgrounds from photos and eliminate shadows in ‘Auto’ mode. Seriously,**I use this all the time.**I used it at PD last week to take photos of the 40 sheets of chart paper of notes and ideas we generated and created a pdf of all our work for participants. It took me less than 10 minutes (and I’m slow). Its free and the best. Can I gush anymore? - I love to use
**my phones ability to video tape anything**. I video student presentations or a student saying something nice about another teacher and I text these videos to parents or the teachers students are complementing. I use the video feature to video tape myself so I can look at my practice. Seriously, no excuses, when is the last time you video taped your own practice and watched it? Make it a goal to video tape 10 minutes minimum at least once a quarter next school year. - Speaking of improving your practice, Annie Fetter’s tweet to put your
**phone in your pocket and record yourself for 10 minutes**and listen to the questions you ask students and listen to wait time is the easiest self-improvement practice you can start as an educator this year. I don’t know who started this – Annie or perhaps Peg Cagle – both are goddess and if they tell me to do something I will . You should too. Do it and let me know how it goes. - I love the
**Remind101**APP for communicating with students and/or students about classwork, due dates, encouragements….. This is probably the best app right now for connecting me and other teachers easily with families -something I was not good at in the past, prior to cell phones. It is an APP I could have mentioned above for students. - I love to
**set reminders and/or alarms**on my phone when I get an email about something I need to remember in the classroom. For example “Siri remind me at 9:55 that there is a fire drill at 10” or “Siri, remiend me to send Jose at 2pm to the counselors office”. The little bings or buzzes keep me on my game. - I often will
**email/tex****t**a parent from my phone a picture of their students work or thinking or a picture of them working – 95% of these are positive messages to families. - I am currently loving
**Duolingo**. If I am asking my students to be persistent in learning math each day, than I too need to be in a daily habit (for at least 5-10 minutes) of personally being persistent with something difficult for me. I am trying to learn Spanish using Duolingo. - Finally, Id dabble in polling apps like ‘Poll Everywhere’.

There are some APPs that lots of teachers love that I do NOT love. I am on a mission to remove structures in the mathematics classroom that value speed. Too many students define being good at math as being fast at math. I am out to change this. For this reason, even though it is engaging, I am never use things like Kahoot in class.

I get asked about managing cell-phones all them time. There are dozens of things I do to manage cell phones and most of those things are related to managing my classroom overall. I am not sure I am the expert, but I’ll share a few ideas that have world for me.

- One worry some teachers have with phones is ‘I don’t want to embarrasses my students without phones, so unless all students have them I am not going to use them in my classroom’. I have no desire to embarrass any of my students, but if I waited for all my students to have a cell phone in class there would never be a day where this was true. Something that has worked for me though to honor all students and give them a safe way to opt out is to say the following….”
*If your cell phone is charged, take it out and__________________.*“. Saying ‘if your cell phone is charged, gives students a safer out to say to peers vs. I don’t have a cell phone.**If your cell phone is not charged, share with a neighbor** - I have only one rule in my classroom and it is not ‘No Cell phones”. My one and only one rule/expectation for students in my classroom is that WE WILL DO MATH FOR 50 MINUTES IN THIS CLASSROOM EVERYDAY.
- I have the 2nd sign pictured as a sign in my classroom. I teach this expectation. During the first few weeks of school we brainstorm and name together what a classroom with this expectation would look like, sound like…etc. I tell them that anything that gets in the way of us doing math will make me annoyed. Students name things I might be annoyed with – they name phones, tardies, side talking, not having supplies out…..etc. I say ‘YEP’. Here is a word doc with my sign. 50 minutes I use the 2nd one with less words in my own classroom. if your classes are 55 minutes or more, change the number 50 to the full number of minutes of your class.
- I am a big fan of managing my classroom with non-verbals (ENVoY) and predictable routines. If I see a student with a phone out, I catch their attention and don’t say anything, I just point at the sign. If i need to do it again, I’ll get closer to them and point at their phone and shake my head. Once in a great while (once a month maybe), I will ask a student who is not responding to put their cell phone on my desk and they can get it back at the end of the hour. I have not had to involve admin, in years.
- If my expectation is that we do math for 50 minutes, then I model that every day in my classroom. I start class immediately when the bell rings. I We are doing math to within 30-60 seconds of the end of class. I never give ‘work on homework’ time in class. When I fill up class-time with learning experiences – I have less phone or other issues. Students are allowed to use their phones the last 30 seconds or 60 seconds if class if we finish a bit early.
- I do not let students listen to music in class ever. My goal is to build a community of students. Earbuds are isolating always. They have plenty of other hours in the day they can listen to music. I also watched this video from Simon Sinek (see link to my blog and his video in the resource section below) that challenged my thinking on students and technology. I blogged about it too. (again, see below)
- During the first week of school we also brainstorm things we can use phones for in math class (see all the things listed above). I tell them that I will at times ask everyone to take out their cell phones and that for sure is an OK time as long as they are using it for math. We all take out our phones the first week of school and download the Desmos app and a few others. In the first weeks of school we get out cell phones together and google math concepts and skills together. I tell students that I will almost always say yes to using phones if they ask and are using it for something mathy. For the first month or 2 of class I am on them all the time to ask – sometime in the first few months the out-loud asking becomes nonverbal asking with head nods, pointing to their pocket….etc and with me nodding my approval.
- At the start of every class I quickly say in a positive tone “Put your phones and earbuds way. In your pocket or Backpack – not your lap or table”. Being willing to give one quick reminder most days has eliminated most of my issues. I do NOT allow phones on the desk/table or lap ever. Having it out of site, makes it a bit harder to be distracted by them.
- For the most part I then consistently model and enforce the 50 minutes of math every day expectation. This means I am (usually non-verbally) calling out every small thing. I talk to every tardy student every time. I point at phones every time I see them. It sounds like a lot, but really if I am on it the first couple of weeks of school, the rest of the year is a breeze.
- I do not let students charge phones for the most part during class. I do have a few exceptions to this. I tell students that if once or twice this year they have an emergency phone call from a parent they may need to take or an emergency charging situation and they talk to me before class I will most likely say yes. This has eliminated all the students initial concerns like “But what if my mom is going into surgery and I need to call her?”
- I write on my assessments ‘Phones must be put away the entire hour” and do have a policy that any phones out on test days, even if they finish early will be considered cheating and a score of zero on the assessment. Being clear, means that I never notice visible phones on test days. Could it happen, sure, but I am fairly on top of them on these days.
- Do students sneak phones is my class – sure – but observers in my classroom tell me rarely. If students are going to rebel for 2 minutes in my room once a week and look at a phone, I don’t care, rebel away.
- I do not want to waste my time or my students times with all the cool ‘cell phone jail” things all over Twitter and Pinterest. The 1-2 minutes of lost learning time each day would not result in any less students using phones in my room and I also feel like it focuses too much energy on the phones and somehow makes them more visible. Tony Riehl did a post on a distraction box (see below) that I would mildly recommend, but for the most part all of these calculator case phone/jail/charging station things are NOT for me – ever.
- Ultimately, managing cell phones is not stressful to me and I don’t feel like it takes too much of my time. Believing cell phones have a place in my classroom changed my attitude towards them. Having a 50 minutes of math everyday expectation that I model and value with the structures and routines in my classroom makes all the difference. Using non-verbal reminders and permission makes life so much easier.

In 5 or 10 years there will be something new I need to learn to manage that fights for students time and attention. I will adapt and change by finding the assets of the new and building off of those things. Today’s distractions are not new in education and we know that. I choose to embrace what is amazing about cell phones. Frankly, I could cry talking about them becasue for the first time in my 20+ year teaching career my students in poverty have 24/7 access to things that formerly only middle class and wealthy students have. My students in poverty can now access a library (Google) any time they want to teach them anything they need. My students now carry a graphing calculator (DESMOS) with them everywhere. There is always a way for all my students to contact me if they need to outside of class. There is no excuses anymore to doing math outside of my classroom. Cell phones have closed some opportunity gaps that existed the first 20 years of my career. I am lucky to teach in the era of cell phones and am excited for what comes next.

- The amazing Jose Luis Vilson also argued for cell phones in this article
**HERE.**Read his point view as well as someone who argues against cell phones. - Tony Riehl’s cell phone policy got a lot of legs online a year ago thanks to Dan Meyers own blog post on the topic.
- CNN “Smartphones are not a smart choice in middle school”
- Washington Post “Teenage depression and suicide are way up — and so is smartphone use“
- I
**wrote about Millennials and technology HERE**based on a video you should all watch from Simon Sinek on technology’s impact on our students (and adults too). After watching it I have rethought my own beliefs about the role of cell phones in my classroom.

In this post I made an argument for using cell phones in the classroom. I fully expect that some reading this will have different opinions than my own. This blog post is just what I believe as of July 2018. I may change my views. I have zero desire to engage in a debate in the role of technology or cell phones in the classroom. This blog post is my answer to all the observers in my classroom who have asked about my cell phone beliefs. It is totally cool with me if you feel differently.

Technology, like anything else in life is best when it is used in balance with the other things you value in life. This is a picture I keep next to my desk. I want to remember to be like the older woman in this photo more often. I want to put down my own cell phone and be fully present in enjoying the world around me and participating fully with the wonderful people in my life. I want to see my students and not just exist in the same spaces with them. I too need to use technology judicially. I am no different than my students. Perhaps you will join me in posting this photo by your desk. (this photo is one of 31 from a calendar of photos I blogged about HERE.)

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]]>I agreed to present with her (though I was crazy scared that I would be perceived as being that HS person that would blame earlier grades for the ills of math). In a week, I’ll fully blog what we shared – but until then I am posting the resources we shared with Elementary math teachers in our state. If you are not in MN – feel free to check these out too.

**60+ Elementary Math Resources for FREE!** (a google doc linked with tasks, videos, PD….etc) We will add more to this page – If we are missing a great resource let us know. The resources are grouped in the 6 big areas we talked about in our session.

**Our Google Slides (powerpoint)**

**Thanks to Laura for writing most of this up (several weeks ago) – I am now (Memorial Day) getting around to giving you a taste of our joint session at the Minnesota State Math Conference (MCTM) in Duluth in early May…..enjoy….**

Those of you who submit session ideas and tiles to state and national conferences know our pain when you are submitting an idea at the last minute to speak on something 6 months to a year later. If you are like us – the idea of what you will speak on that far out in the future makes it tough to submit a well thought out title and session summary when the session is just an idea in your head. There are a few of you weirdos out there – we see you Robert Kaplinsky – who have their sessions completed (and practiced) a year a head of time – but we suspect most of us are like Laura and I and are submitting titles and session summaries on sessions yet to be fleshed out. That was the case with Laura and I when we wrote our title “**5 ****W****ays ****Elementary Teachers ****C****an ****S****upport ****L****earning in ****Secondary”** and our session description: ‘*What *

*are 5 things elementary teachers can do to support the mathematics their students will see in high school? An elementary and high school math teacher will share these 5 things with the goal of building confident, successful, sense-making mathematicians.’* We had ideas of what we might share 6+ months later – but it was mostly in hour heads and a napkin of notes we scratched out.

When Laura and I sat down to plan the session – our ‘**5 ways’ became ‘6 ways’. ** We decided to start our session by introducing ourselves to you so you could get as sense of our shared values as educators.

This is the image Laura and I selected to represent our introduction to you. When you look at this image – and think of Laura and I – THINK…

**What is the same? **

**What is different?**

*(Note: One goal Laura and I had with our mostly elementary audience was to leave them with tons of resources they could use in their classrooms & planning – here is an example of our first FREE resource – **‘What is the Same and What is Different? images and questions are curated on the **Same or Different website as a way to support mathematical argument in the elementary classroom.)*

As a way to introduce ourselves we wanted to share our believes and values through some true/false statements.

*True or False? Laura & Sara believe students learn through play.*

**True!** In fact, this is a picture of a pattern created in Sara’s High School Classroom at her play table.

*True or False? We have both taught in another state.*

**False! ** Sara has taught grades 7-12 in MN for 25+ years. She spent 5 years as the K-12 Math Lead in Minneapolis Public Schools. Laura taught in California.

*True or False? Both Sara and Laura have taught 7**th** grade math.*

**True! ** Sara’s favorite grade she has ever taught is 7th grade. Despite currently teaching HS, Sara’s heart is in middle school. Laura also taught 7th grade…

*True or False? We are fans of speed in memorizing facts.*

**False.** Laura and Sara both are committed to removing a culture that values speed in the mathematics classroom. For example, Sara has eliminated hand-raising from her classroom. We both know that many students self-identify as ‘bad at math’ simply because they are not as fast as other students in class. We both know that thinking stops on the classroom by many students when they think others have solutions (hand raised). Our goal is to change the culture of our rooms so that students don’t believe that being good is math means being fast at math.

**True or False? Paper assessments are the best way to monitor student progress.**

**Mostly false** – but saying this does not mean we don’t value paper assessments. Both Sara and Laura know that we know a lot about our students thinking and understanding of mathematics by listening to what they say. We are committed to finding ways for every student to speak out loud about mathematics every day in our classrooms. We get information about students understanding by listening to them, looking at their work via paper and many other modes. Everything our students do and say informs our work with them.

*True or False? We have taught tricks to our students to make our students proficient. *

It is (sadly)** TRUE** that both of us at times in our career have taught tricks to our students. We know better now and choose NOT to teach tricks to our students anymore. We value student understanding of concepts over quick tricks that feel good at the time. **Sara has written about this a ton HERE**. In our list of resources we recommend every teacher downloading the FREE ‘Nix the Tricks’ book and working to eliminate tricks from their own classrooms. We’ve also included a great NCTM article on eliminating teaching ‘rules that end’.

My guess many of you reading this are like Laura and I and are either currently teaching math tricks to your students or use to teach tricks to your students. Laura and I don’t want to shame you. We don’t want you to feel bad. We both have this quote near our work spaces. Always in our career as teachers we are looking to do better. This gives us comfort.

**True or False? Allowing students to share their thinking encourages equity in the classroom **

**TRUE! TRUE! TRUE! ** This may be the one that Laura and Sara want to scream out to anyone who will listen. Our goal in lesson planning, in selecting tasks for the math classroom and in what we want our classrooms to look like is things that value students to make their thinking visible. Not just some students – but all students. We are on a mission to find math resources that make this same value easier for teachers who want to do more of this in their own classrooms.

*True or False? We are fans of Pinterest & Teachers Pay Teachers. *

Mostly False! We are never going to be against these resources and know many of you find them super valuable – we just know there are so many other valuable resources out there for FREE. There is no need to pay anyone for great material. We also are fans of all teachers valuing great content in resources over the ‘cute factor’. Don’t get us wrong – we love ‘cute’ – we just love great mathematical concept development even more.

Laura and Sara find most of their resources for own math classrooms by being part of the online math community on Twitter. If you want to join us there – start by following us @saravdwerf and @laura_wagenman on twitter and search the hashtages #MTBoS (math twitter blog o’sphere – the name of the online math community – anyone can join in the conversation – anyone) or #Iteachmath.

For those of you who don’t want to (or can’t) join Laura and Sara on Twitter – **we’ve put together over 60 FREE resources just for Elementary teachers – these are some of our favorites**! They are grouped by the 6 ideas we will share below for how Elementary Teachers can support the work of Secondary math classroom teachers.

Sara – a HS math teacher – and Laura – an Elementary Teacher Leader – are way more similar than we are different. That said – for some reason in education many people look at Sara as having some authority to speak about mathematics over Laura simply because she teaches higher levels of math and uses words like logarithm and trigonometry regularly. What they don’t know looking at Sara – is that she views the learning of mathematics in K-5 as much more important than the work she does in HS. Sara knows how smart and valuable Elementary Math teachers are. Teaching students how to have a flexible understanding of the base-10 number system can not be underestimated. Sara believes that every HS math teacher should be signing up for a 1 week PD this summer on how to teach elementary mathematics. If they do, it will radically change their work at the HS level. Sara knows we have much to learn from Elementary Math teachers and hopes we can see each other as peers who both have expertise that the other needs and not as peers where someone knows more.

**Sara and Laura are on a journey to learn from one another. What you will find below is the 6 areas Elementary mathematics gets right that supports the work of Secondary Math Classrooms. In this post we hope to show you just a taste of what Elementary does well and how that plays out in the secondary classroom. While we have our differences, we are very similar and look toward each other for best practices and leverage each other’s assets to learn and grow.**

If you had been at our session, we would have had you do a STAND & TALK (a favorite of Sara’s) to get you talking to another teacher. Before reading any further – talk out loud (really do it out loud) about how you would answer this question…

Think about how you solved this task and how you would want your students to solve this task before reading further….

This task is one that changed Sara’s practice 10+ years ago when she looked at the student work of her students from a pretest she was asked to give her 7th grade students at the start of the year. Here is a copy of one students work on this problem. What do you notice?

This student got the problem correct. (although it took me a lot longer than I would have liked to figure this out). Despite their correct solution – look at all the arithmetic this student did to figure this out. Think of all the places they could have easily made a small error that would have resulted in them getting this wrong. As a HS math teacher – Sara looks at his and thinks about this student on the ACT where they have 1 minute per problem to answer questions – Is this really the quickest way to answer this problem? Is this way efficient? Does this work show a depth of understanding of fractions?

Laura and Sara look at this work and it challenges us to do better. We want students who look at the original 4 fractions and have the ability to compare them to benchmarks. We want our students to say things like “5/12 is slightly less than 1/2”. There was no use of benchmark fractions, estimation, any sense making.

**Our #1 wish for Elementary (and HS) mathematics is to value Estimation and Sense Making in the math classroom. So how can we do this? **

What can we do, starting in elementary, so students are estimating and sense making? A favorite resource of ours is Estimation 180. (Thank you Anderw Stadal!) There are 300 images that help build estimation and sense making skills through real-world, engaging pictures. Think about how using visuals like this can increase student discourse in your classroom. Think about how these pictures can be used to increase opportunities for students to estimate and develop number sense in your classroom.

Think about how using a photo like this can help students build on their concept of ‘volume’. How many cans are in this cart?

**SIDE-NOTE****:** For obvious reasons you can’t use the following photo Jessica Strom posted on Facebook this week in the classroom- but imagine what great questions you could explore with this photo.

High School Math Teacher, Megan Schmidt recently spent a lot of time in Elementary Math Classrooms and blogged about her experiences **HERE**. Laura and I love this quote from her blog:

**Our goal is to have mathematics classrooms that value ESTIMATION and SENSE MAKING. **

In the secondary classroom Sara uses this prompt towards the beginning of the year to look at the sense making her students bring to the classroom. She says, “No Calculators – calculate this as quickly as you can. Go.”

What Sara finds year after year – is that students rush to remember how to add fractions. They work furiously to get common denominators – many students make arithmetic errors along the way. Most students struggle to figure this out quickly. After 60 seconds Sara says “STOP.”. She then points at the number and asks a student to read the expression out loud. As they read she points at a place value chart she keeps in your room.

As she points at this chart – students explain “OH!” and quickly work to write an answer. She then talks to students about how our classroom will value sense-making over speeding to do a calculation with rules you have to remember.

One of the tweaks teachers can make in their classroom is to replace the world ‘point’ with the word ‘and’ every time they (or students) read a decimal out loud.

For elementary math teachers – in addition to using resources from Estimation 180 – we totally recommend using a teaching technique we learned from Brian Bushart. If you don’t know who Brian is – you need to visit his blog. He is AMAZING. We asked Brian to say a short greeting to MN Elementary Teachers so you could see he is a real person doing the same great work you are. Check him out & listen to what he says about sense making.

Check out this problem we would present to students. What do you notice? What do you wonder?

Are you are wondering what the question is or what you should figure out? We purposely removed the numbers and and the question from this problem to create what Brian and others call a ‘Numberless Word Problem’. Think about what students will notice and make sense of before they rush to answer a question and how that may change how they interact with the mathematics in this problem.

As students ask for it – we reveal information to them.

Again – we will often delay giving the question for a bit allowing students to make sense of the information they have. We have found that removing numbers and questions in our classroom has invited many more students into the problem solving process that in the past did not engage. They were allowed to make sense of information before the ‘race to solve’ the problem began.

Later in this post we will talk about this task again….but until then – we encourage you to value and build number sense in your classroom by learning about Numberless World Problems and using them in your classroom. They are game-changers.

**5.28.18 2:30pm….I am stopping for now – but more resources are coming soon….**

**60+ Elementary Math Resources for FREE!** (a google doc linked with tasks, videos, PD….etc) We will add more to this page – If we are missing a great resource let us know. The resources are grouped in the 6 big areas we talked about in our session.

**Our Google Slides (powerpoint)**

The post MCTM 2018 5 ways Elementary Teachers can Support the work of Secondary Math Teachers RESOURCES appeared first on Sara VanDerWerf.

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]]>**How do you engage every single – I mean every single student – in mathematics every single day – yes, you heard me – engage them in mathematics? ** I shared some ideas on this at the 2018 NCTM conference in Washington DC April 25-28th in a session titled “Engaging Students in Seeing Mathematical Structure” I’ll give you a taste of my session. At the bottom of the post you will find resources including my power point. Here is the question I started the session with.

**Can you see it?**

Stop. Look at the picture for a few minutes? Can you see it? I’ll answer the question at the end of the post – but you’ll get more out of this post if you look first for your self – read the blog and get the answer at the end (don’t cheat).

**So, Can you see it?**

**#1: **My school year starts with defining mathematics. **Check this post out** if you really want to go deep on this topic.

**#2: ** Students will talk out loud about mathematics everyday in my classroom. This means I will prioritize in my lesson planning instructional routines that support student discourse. If they are not talking about mathematics out loud then I must do something different.

**#3: ** One way I’ve found that values talking is an Instructional Routine I call ‘Stand & Talk‘. Most of the suggestions in this post are how how to give students interesting ideas to discuss. ‘Stand and talks‘ are a mode that encourages even more conversation with what you create to talk about.

I have other values that I bring to lesson planning (many you can find on my blog -but these are the ones most connected to this blog.

I am from Minneapolis, Minnesota. Knowing where I am is integral to my next story. My state math conference is in Duluth (shores of lake superior) each year – again you will need to know this in a minute.

I grew up in a family that went on lots of car trips – as the cost of a family on a plane was prohibitive. In the 70’s and 80’s we did these car trips with maps. I LOVED looking at maps and so did my siblings. We mapped things out and looked at locations that we would love to visit someday.. (By the way – this photo is not me. It can’t be – people my age did not have devices like this to listen to music – we had the radio and at some point cassette tapes)

I am from one of ‘those families’ that plays board games all the time. – especially on holidays. In this picture is my brothers roommate from grad school, Volker. Volker is from Germany and introduced us to cool games from his country a 15 years ago. One of our favorites is Setters of Catan. The first 50+ times I played it it was on a board all in German as that was the only way you could buy it. Now days you can find this game everywhere.

Another game produced by the same company as Settlers of Catan is Ticket to Ride. Another favorite of our family.

Here is how the game works. You get a game board which is a map of Europe. Your task is to build railroads across the country.

You get tickets with cities in Europe. The further the distance between the cities the more points you get if you build the route.

Finding the cities on the European maps is easy if they are from cities like London or Amsterdam. But is a challenge when you need to find cities with names you don’t recognize – for me that was towns like ‘Smyrna’ or ‘Sevastopoi’.

Luckily ‘Ticket to Ride’ is there to help. The route cards have stars showing you where to find the cities on the map.

Some years later I was excited when the USA version of the game came out. Finally I could find all the cities on the map quickly.

Within 5 minutes of opening the board. I was extremely frustrated with the map.

I know you can’t see what frustrated me and blow it up. Do you see it?

Not from Minnesota? Can you see it? Remember the map of my state I showed you earlier?

DULUTH is on the game board in the WRONG location. They put Duluth where I live – Minneapolis. Not up by Lake Superior where it is really located.

Honestly, this annoys me so much that every time I play on this game board I get re-annoyed and need to vent for several minutes. If you look at the board there are other annoying things. For example Chicago looks like it is in Indiana.

Ugh….That got me thinking about the European Game Board again. What cities on that game board are in the wrong location. I’ve played the game 50-100 times and never once did I question the location of the cities. Not once.

The idea that I could not recognize errors on the European board made me think about how we teach mathematics.

Think of ‘Ticket to Ride’ European version as the new mathematics we teach our students.

Because we most of our students struggle with new mathematics and because we are nice teachers who don’t want our students to struggle we jump in and help them with supports to show them the way. We give them cards that show them the location of cities – or in math we write learning targets that give away what the learning for the day will be – ……

and then we map out all the steps to get from one city one by one for them. In math class we map out all the steps for them to solve a problem.

Matt Larson, the past-president of NCTM, talked about how “Caring teachers everywhere jump in and rescue students when they don’t get it.”.

My biggest mistake as a teacher in my career was jumping in and rescuing students when they needed it. We math teachers have good intentions. We want our students to feel successful and so we scaffold to the point of mathematical death most everything we put in front of students. We do the heavy lifting in learning. Students often just copy or mimic what we ask them to do. Then this happens. We ask them to do to different cities on their own (on assessments for example) and they can’t. We’ve handicapped them to do math when they leave our presence.

Worse – not only can they not find the cities and map out a route in math. Students can’t see errors that surround the contexts we’ve given them. Ugh. Something needs to change.

The USA version of the game represents previously learned material.

In this game board of mathematics I can recognize mistakes.

This realization for a board game left me with 2 more questions.

One – I could recognize mistakes on the USA game board because I grew up in a family that looked at maps all the time on car trips in the 80’s and 90’s…..before GPS. What about the students now days who learn directions from a map on GPS that steps out the route for them? Can they see the mistakes I see on maps?

Two if you are a student who enters a course missing prior learning – can you even see anything on the European/New Math game board?

These 2 questions have lead me to a new mantra in how I plan lessons and what I ask students to do in my classroom. Here is the mantra I ask myself over and over again as I plan…..

Since beginning to use this lens, I have seen a radical change in students owning the mathematics they are learning in my classroom. In the past when I rescued them when they struggled, I owned their learning. Now when they see (notice) a pattern and we, the class, discuss it. Their brain has a place to put the math learning, because they prepared a place for it to go in seeing something first. In class we add mathematical vocabulary to what they see and say. We also clean up misconceptions that can come from seeing something incorrectly – even in these times, they own the learning. This is my goal.

The short answer is lots of ways. Here are a few. I shared more in my session.

If you have not yet watched Annie Fetter’s 5 minute ignite talk from several years ago on ‘Noticing and Wondering’ stop reading my blog post and do this now…..

Notice and Wonder is an Instructional Routine we should be doing every single day in mathematics classrooms K-12. It has radically changed students owning mathematical learning in my classroom. Let me give you an example of how I use this.

Look at his equation from my Algebra 2 classroom this year.

How would you find the VERTEX using this equations? You could put the equation into standard form and use this…

In fact, I was at a session at the NCTM national conference this week and a teacher yelled out b/2a for finding the vertex for a problem we were solving. I would argue though that outside of teacher conferences, most of us do not have this information on the tip of our tongues. So, I so no to this as a students first interaction to finding vertices.

What my students do know about the original equation at the Algebra 2 level is that the equation shows us the roots of the equation.

Because of this, I gave them this visual to talk about during a **stand and talk** (more on this below)…. What do you notice?

I know this is a bit hard to read, so let me make the 3 images a bit larger for you. Again, what do you notice? What do you wonder?

My students, without me having to say it or show them, immediately talk about he vertex being in the middle of the 2 roots. They may not always use the word ‘symmetry’ – but our class conversation can add that academic language to their use of ‘middle’ in their initial noticings. They talk about finding the average of the roots before I say anything to them about this. They use the x-value of the vertex and the function to find the y-value – all without me to help them do this. All I did is give them a visual I had made on Desmos to look for patterns – something to notice and ask questions about. **This is the new norm in my class. What can I make that will give students something to notice and wonder about? How can I help them see and talk about a math concept first?**

Here is another example of something I ask students to notice and wonder about:

I love using visuals with noticing and wondering for academic vocabulary. Here is another one- What do you notice? What do you wonder?

I believe the reason MN’s math test scores continue to be at the top of the nations is that our students must be familiar with integers to live here – just sayin….

Here is one last example of something my students notice and wonder about….this one is hanging in my classroom all year. ** You can read all about what I do HERE. Where is this orange golf ball located?**

I do a **‘stand & talk’** nearly every day in my classroom. I HIGHLY recommend you do the same. They have greatly increased the quantity and quality of classroom discourse in my classroom. **I wrote about them HERE** – I recommend reading this post if you plan to do them in your classroom, but here is a short synapses here with an example. Here is what I would say to my class.

“** Put everything down. No pens/pencils, calculators or phones in your hand. When I am done talking I want you to walk across the room and find a partner. Find a partner, not at your table. Partners of 2 only. I am going to give you something to notice. I want you and your partner to notice at least 16 things about what I give you. Then ask yourself, what do you wonder. Ready? Go**.” Here is what I gave them on day 1 of my probability unit.

**What do you notice? What do you wonder?**

I circulate and give partners one copy of this visual for the 2 of them on a 1/2 page of card stock. Here is my original. Intro probability stand & talk marbles & this one is the small one students glue into their notebook zero to 1 prob intro for notebook This is what I see as I walk around the room – every partner looks like this….

Every student, without much work from me is talking out-loud about mathematics. This does not happen with every student when I have them sit and ‘turn and talk’. Stand and talks take the same amount of time and result in more discourse. In the photos they are looking at different visuals – but every day in my class, students are pointing – talking and wondering without me having to stand next to them. After 1-3 minutes, I ask them ‘what do you think the title to this visual is?’ Students say the title before I show them. We do some noticings while they are standing, but then I tell students to come up and grab a smaller copy of what they were looking at and glue it into their notebook. We then annotate the visual.

In 10 minutes we have reviewed a lot of probability’s basics from previous years. I have several students who have interrupted educations and never learned this information before -but even they in 10 minutes had a lot to say about probability. What is important is that students saw it and said it before I did. If you can’t tell, I love, love, love stand and talks. You need to do these. The spring is the perfect time to test the out in your classroom. This fall though, set them as a norm in your classroom from day 1, week 1 and see how the culture of your classroom changes for the better.

In the example above I started with a visual that I found on google images. When I used it first with students though, I removed the labels and and titles. I wanted students to say the title of this visual before I told them – and every class l have ever used this with has named the title – therefore they own the title – before i told them what it was.

The Math Forum people (max, annie, steve, suzanne and others) have been advocating for this for years. they call it ‘Creating Scenarios’. They advocate removing the question and other details so students are not in a race to solve something. I love this so that students will stop and notice mathematical structure before racing towards a solution. As students name things or ask for things we give them the information they need. Brian Bushart does something like this at the elementary level with ‘Numberless Word – Problems’. He has written about this a lot. Check some of it out **HERE.**

Here are a few of the visuals I’ve used where I removed information before using them. ….

When finding measures of center I have used this…

Students notice the numbers on the jerseys and talk about that some students are taller and some are shorter. I ask them what math question we could ask about this picture and students say lots of things, but always someone says, I wonder what the average height of the players on the team is…then I reveal the information we need. to answer this question.

One of my favorite tasks to use week 1 with students is Fawn Nguyen’s Noah’s Ark task. Before giving them the task I remove the question. What do you notice? What do you think the question will be?

What did you notice? I know, I know…you are wondering if you are correct – I can’t do everything for you- to find the answer you need to do a little work so you can see what is out there – either search my site for ‘noah’ or google ‘fawn nguyen noah’s ark’ to find out for yourself.

Here is a visual I use at the start of my systems of inequalities unit. There is no question or directions other than ‘What do you notice?’ Students notice the solid and dashed lines They ask about ‘test points’. They notice regions. Since it is color coded they notice things about graphing each inequality. We glue this into our notebook and write all those things down. Throughout the unit we come back to this visual again and again as we learn new things.

Here is a visual from my quadratics unit. **I remove questions, but then I ask… What math questions could we ask about this visual? Remove and ask students for the question. It is powerful. Y**ou will be amazed at how they look at the structure of the graph first and make sense of this. When a question is asked by another student, they already have seen things that will be useful in answering the question. What math questions could you ask about this picture?

**Here is a real life dilemma from my classroom.** My students – despite using graphs/tables – were continually struggling to see the symmetry and relationship of points on quadratic graph. Some students always saw this – but many did not no matter what I did.

When I became addicted to removing information from graphs I tried something new. I created this visual for day 1 of my transformation unit. I removed axis, curves, lines and numbers and asked students to notice/wonder.

It was amazing. Students noticed all kinds of things. They even drew in curves without me asking them too. Without the distraction of axes and numbers – they saw the pattern in tables throughout he unit in deeper ways. Because we glued this into our notebook – students kept coming back to this over and over again throughout the unit to help them as they transformed equations and graphs of a variety of functions.

Here is what I learned from my students….

It is not the students fault if they do not understand the mathematics I am asking them to struggle with. If they can’t figure things out – of course struggle is good and necessary -but I am talking about the struggle of having no access point -then it is me who must change. It is me who must figure out a way for them to see and say the relationships and concepts we are studying.

I love to turn numbers into visuals for students so they can see the pattern before I tell them. Here is one I use with an introduction to exponents. Students say ‘four to the fourth power’ before I tell them to. These visuals are great for math talks.

Here are a few others I use. This one is my visual multiplication chart connecting multiplication facts to area arrays.

Or this when we are going to talk about he commutative property.

I love starting all units with a **Stand & Talk** – I love to give them something to look at in the unit to get them talking about what we will learn. I am always looking for something that levels the playing field for all students regardless of previous learning. Here is one I use at the start of a Pythagorean Theorem Unit. I love this one, because students think they understand the theorem because somewhere someone has told them a squared plus b squared is c squared. This picture eliminates this memory and starts getting at conceptually what is going on.

Here is another visual – I love love love this one. In one visual my students connect exponential functions to power functions. Look at it. What do you notice – spend some time with this one – there is so much there. Note: I get asked a lot how I make these – often I steal something I find on twitter or google images. **This one I made using this cool site that animates the factors of numbers.**…a few screen shots later I made this.

I also use notice and wonderings to introduce a new concept – like ‘what is a number raised to the zero power?’ or ‘what is a number raised to a negative power?’….love this one too.

To encourage student discourse and to help them see mathematical structure in ways they might not otherwise I have a new favorite phrase i use all the time in class…..’**CONVINCE ME**‘…… For example, with the visual below, I would say, “** Convince me that the equations below are true or false**.” Then i give them a visual that is provocative and gives them something to argue about. I ask them to provide evidence in their arguments.

Try asking a ‘Convince me’ question/statement this week in your classroom and notice how it improves the quality of the discourse. Here is another example I love when teaching or reviewing order of operations. * ‘Convince me which calculator is correct’*.

I love using **Stand & Talks** with notice/wonder to teach new notation. For example.

I use the visual above to introduce Sigma notation to my students. When I use this almost zero percent of my students have ever seen this. Within 4 minutes of noticing with other students they basically tell me everything I want to hear about how this works. For example the words in green are what I hear first.

Then students go on to tell me that we should substitute the starting value into the rule until we get to the stopping value. They then tell the class to add each of these expressions together. Again – my goal has been met. Students tell me how it works before I tell/show them. In total the process took 10 minutes and I have almost no students understand it incorrectly the rest of the year. If they do, they go back to this visual to remind themselves what to do.

I also used this technique with teaching ‘augmented matrices’ and ‘matrix equations’.

Two-way tables is another notation I use this technique with.

After doing some notice wonder with the visual above, I ask students to draw the bag in the 2-way table. Without me showing them, almost every student draws something that looks like this:

I love the ‘same but different’ visuals that have been appearing on #MTBoS twitter – led by Brian Bushart – Here is an example of one I used this week in my class as an introduction to tree diagrams. Take a few moments before reading and ask yourself – **What is the same? What is Different? **

The beauty of this is from what we know from research is best practice. Students need to be comparing and contrasting in mathematics more often. My students were able to name the difference between Independent vs. Dependent events before I told them. Here are 2 other examples – one related to fractions and one related to graphs of quadratic functions. Beautiful, right. I did not create the ones below. They came from twitter and Brian’s site **HERE** and **HERE**.

Here is one I made and use for defining polynomials:

So, you ask, how do I make these? How can you make your own. I ask myself 2 questions….

The arrows below represent my answers to the questions above and also represent what my students said to one another before I told them in class. They were able with this visual to define polynomials without my help.

The students I teach often struggle with the context of the problem vs the mathematics of the problem. I use Stand & Talks with contextual information all the time. For example – this visual..

Instead of me telling my students there are 52 cards, I have them say it. They figure out their are 4 types of cards (I often need to give the academic term ‘suits’). They count 13 of each type….and so on. Again my students say and see it before I tell and show them.

Above are lots and lots of tips for engaging students in seeing structure. I want to end with 3 more tips and as well as some closing thoughts. **Here is extra TIP #1:**

One of the reasons your students are struggling to see structure is they stop thinking once they think someone else has the answer. One structure than many of us need to rethink in our classroom is ‘hands up’. Once a student raises their hand to think – many of your most vulnerable students stop thinking and self-define themselves once again as not smart at math. Many of these students are only 30 seconds or 5 minutes behind their peers yet they feel miles behind. I talked about this fact in **THIS post** recently. Think about what structures in your class enforce the idea of ‘being good at math is being fast at math’ and change these structures. Do it now.

One way I dismantle quickness in my classroom is to teach my students the word ‘Contemplate’. I teach them the meaning of the word and use it often.

I stole this from one of the Instructional Routines David Wee’s uses in his work “Contemplate then Calculate”. Here is an example. In order for students to see how numbers and operations relate to one another I would say “*I want nothing in your hands. Everyone look up here. No hands up. I want you to think about, contemplate, what I am going to show you next. Don’t say anything out loud*” Then I would show this visual…

Giving students adequate think time allows more students to see 135-10 as 125 which is 5 times 5 times 5. It gives them a chance to decompose 36 into 6 times 6. This expression is fairly easy to do, if you stop and think for 30 seconds. If you rush in and try and solve it fast you panic and find it difficult. You could certainly do this same task by saying ‘think’, but something about a fancy word you’ve taught like ‘contemplate’ encourages students to think a little longer giving their brains the chance to see the decomposed parts.

**Here is extra TIP #2:**

Seriously secondary teachers – especially those of us that teach high school – we need to use more visual representations of student thinking. When is the last time you used open number lines with your students? Open number lines are not just for arithmetic. I use them with expressions and variables (but that is an entire post in itself). Are you using area models and bar models (don’t know what these are, google them and learn)? Are you daily connecting graphs to tables to equations to academic vocabulary? Are you having students make these connections first? This is so easy to do today on my favorite way to graph – Desmos.

**Here is extra TIP #3:**

Again, this could be a post all by itself. Ask yourself, what mathematics is visible to me, but invisible on the paper to students? Ask yourself, how can I make the invisible, visible. The hidden zeros and ones are just a start. There is so many other hidden structures students don’t see that we do.

I know, I know. This was the worlds longest blog post. Can you believe I did all of the above and more in an hour? Whew. I hang the following visual by my desk. I use it to remind me of how I don’t want to teach….

I think all of us have at one time or another valued teaching skills over concepts. I think every teacher gets into the profession because we want to help students. Some of your help of students though is causing them to not be the owners of their learning. We jump in and rescue them – give them answers -scaffold too much – when we see them struggle. This has been my biggest mistake as a classroom teacher in my career.

I could beat myself up about his – I get things wrong all the time – but the frequent readers of my blog already know how I handle the negative thoughts in my head. I always go back to a quote from Maya Angelou….

After reading this post, you know better, so I expect me and you to do better moving forward. Please do me the honor of using these 2 questions to guide your lesson planning.

**QUESTION #1**

**QUESTION #2**

These 2 questions get at the 2 part goal I shared at the start of this post. Print this goal out and hang it by your desk.

Lastly – remember this photo I started the entire blog with? If you still can’t see it. Take 2 minutes to look at again…..

Can you see it? Did you cheat and look down below for the answer? If you can’t see it, I’ve highlighted what is right in front of your face in yellow…

Sticking out perpendicularly from the wall is a cigar. Crazy right? it was there the entire time. Right in front of you. Here is my last thought and the good news of valuing students seeing structure in mathematics. **Once you see the cigar – once students see the structure in mathematics for themselves, one can never unsee it again.** It is now obvious and right in front of you….remember that. Use this fact to encourage yourself. Helping students see and talk about mathematics first is hard work. It takes planning. You will not get it right the first time, maybe even the first several times, but you will get it right. Students deserve your efforts. It is worth it, I promise.

Let’s start with my **POW****ER POINT** Note: I am not sure how helpful it will be for those of you who did not attend because my slides are way more visuals and less writing – but for everyone please note that some slides have links in the notes with more information.

As always, I love hearing from you. Please comment below with thoughts or questions. If you were at my presentation and I am missing something, please let me know and I will update the post as soon as I can. Thanks, my new friends. I appreciate everyone that gave me such kind feedback when I presented.

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]]>The post My favorite question I ask strangers at conferences. appeared first on Sara VanDerWerf.

]]>**What I love most about conferences is meeting new math teachers and expanding my mathematics community.** I say this as in introvert. If you know me, you may doubt this as I present as an extrovert. I present as an extrovert because from my first days of teaching I imagined myself putting on an invisible suit of confidence and outgoingness. I faked my way through my first years of teaching that I was a bigger version of myself. I was tapped to lead at an early age and I took deep breaths, stood taller and relaxed my shoulders as I told my inner self that ‘I could do this’. I’ve practiced being outgoing so long, that it now feels normal. That said, when I return to my home at night, I crash exhausted from being engaged to people for so long – then I know for sure I am an introvert.

Despite my natural introverted tendencies, I know that I can not grow as a teacher without being in relationship with a community of mathematics teachers. My community keeps me emotionally healthy. My community challenges me. My community gives me ideas. My community stops me from isolating myself and depending solely on my own ideas.

The great news in 2018 for introverts like myself is there is a math community anyone can join any day of the year online. If you are not on twitter do that and search hashtags #MTBoS and #iteachmath and start following people tweeting using these hashtags. Even if you never tweet – you are now in this online community. I am so happy to call you a part of my community.

This post is not about the online math community though. This post is about building your community with 3-dimensional human beings. Although I feel like I know people I interact online, meeting them in person is a game changer for me. So what do I do at conferences to build my math community even larger with people not online? I do many things, but let me share just one….

**I introduce myself to strangers.** If I am standing in line with someone, I introduce myself. When I sit in a session, I don’t look for someone I know and sit by them, I sit down near others that I don’t know – often looking for someone sitting alone. After saying **“ Hi, I’m Sara, what’s your name?”** and talking about where we are from (as we awkwardly squint read each others chests/name badges) and what we teach…,

Yes, yes I know – there are 3 questions above, but they are all the same question. Sometimes I ask one, sometimes I am repetitive and ask all 3 at the same time. 2/3 of the people I ask, immediately smile and their face lights up. They start talking in multiple sentences and paragraphs. I rarely have anyone say just a word and stop talking. About a 1/3 of the time people hesitate and then apologize saying, “*You know, that is a deep question. I am going to have to think about that*.” I can see they are trying to get out of answering my question, but I just wait them out and I love the moment when their face lights up a bit and the precede to tell me about something great about their current practice.

I love hearing what they have to say, because often I learn about something new that I want to learn more about later or I am reminded of something I’ve wanted to do more of in my own practice. I love the question, because people in our profession tend to be our own harshest critics and we are always thinking about what needs to be improved. We rarely spend enough time celebrating what is going well or what energizes us in our work. I always, always learn something.

If you are at a math conference – try this question out with at least 5 strangers. See what happens. See how it changes your conference experience. Watch how it builds your math community.

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]]>The post Why I always carry a $1 bill and 4 quarters when I teach. (aka ’30 seconds to Oh!-) appeared first on Sara VanDerWerf.

]]>Despite the differences in their test scores, my students have way more in common than their test scores would tell. All arrive with many assets that allow them to grow as mathematicians while they are in my classroom. My job is to see their assets and use these assets to build off of. The students with lower test scores have one thing in common – all have had interruptions to their education due to some reason that means that they were not currently achieving at the level of their age–alike peers on most assessments.

This school year I have the largest proportion of students I’ve ever had that had major interruptions in their mathematical career before arriving in my classroom. Most of these students are my EL students who may have not been in a math classroom for multiple years for whatever reason. They are 17 & 18 year olds in Algebra 2. Some have math skills at the elementary level. Most have multiple things they were never taught or never had the time to learn well in prior grades. They are brilliant and the most hard working group of students I have ever taught. When some question why students so far behind are in Algebra 2 – I fight to keep them in my class (vs putting them in courses as seniors that teach only middle school material). I believe I can both teach grade level material and also catch them up. In a month I am doing a session at my state math conference on the 50+ things I do in my classroom to accomplish this goal. **This post though, is a short glimpse into my work with my students with the stories of 2 of my current students and what I learned about them (but mostly about me) in the past week.**

In addition to teaching Algebra 2, I spend one hour a day in my schools math center. A place where students come to take tests or receive tutoring in math. Each day 5-10 of my own students show up during 1st hour when I am in the math center (along with students from other teachers courses). I have had the privilege of seeing these students math journey at a much deeper level. Most days these students are working on homework. Every day I see growth in these students and also learn about the depths of the holes left to fill in these students.

This is the story of ‘Fartun’. Fartun is in the top 5 of my hardest working students this year. I suspect she spends a minimum of 2-3 hours a day on math homework. (Note: this is NOT my expectation of her – I want her to do less) Her goal is to catch up on everything she is missing. She is very quiet and smiles with joy frequently. She arrived in this country a little over 2 years ago and I suspect she talks little due to confidence in her language skills.** **She entered class not knowing how to solve simple equations (2x+3=14) and needs a calculator for most simple arithmetic (I am OK with this). She is a strong mathematician, despite not yet having a flexible understanding of the base 10 number system.

We are currently solving systems of equations. To support all my students I give them what I call ‘green sheets’. These are one page (sometimes front and back) of material learned in 8th/9th grade algebra courses that they need to know to be successful in Algebra 2. In our current unit students have 2 green sheets. One for solving equations (6a Daily Practice with Green Sheet) and another for graphing inequalities (Unit 6 Inequality Green Sheet). Everyday in class you hear me say ** ‘get out your green sheets’** as we work. In the math center, students know we will not help them until they’ve first looked at their green sheets and/or googled on their phones the topic we are studying. AS a result, you will always find students with resources out with their homework. Much of the time they answer their own questions about math without having to ask me or my student teacher for help. Fartun is able to figure out all kinds of things on her own at this point of the year. She goes home and watches videos. She asks her peers for help. She uses the resources I give her to help her learn the material she missed in the past.

Last week, this was the problem she was working on in my classroom.

Think of all the skills students need to graph this system. This was the first system that I had given students with non-integer coefficients. Fartun was not shaken. She got to work. About 10 minutes into the problem she caught my attention with a smile and pointed and quietly said – “*this does not make sense.”*

Before I tell you how I answered her – check out her work to this point. Here is a student who struggles with basic arithmetic. She uses a calculator for everything. Without any help from me, she has accurately found intercepts – graphed them – found test points and worked to identify the region of the graph that represents the solution. All without my help. In many classrooms – high school teachers will shake their heads at students like Fartun as they watch her use her calculator to multiply 8 times 4 or subtract 7 from 10. Many High School math teachers say – she should not be in an Advanced Algebra classroom with out basic arithmetic skills. But look at the question Fartun asked me – she has number sense enough to ask a question when something does not make sense to her. She is not blindly using a calculator to do her work – she demands understanding of what she does.

Back to Fartun’s question…..she asked….”* Why is the answer larger than what I started with when there is a decimal? I don’t get it.*”

I had heard a similar question from several of my students in the last day. Their understanding and fluency with decimals is low. To answer her question I took a $1 bill and 4 quarters out of my pocket and said, “How many quarters are in a dollar?” She said 4. I then wrote the following down….

I said, “* How many groups of 0.25 are in 1*?” Fartun said, “

**Fartun is usually only 30 seconds away from an “OH!” and understanding.** In my ideal world I would have Fartun for a 2nd hour of math each day and could slow down and have her and her peers build a fluency with arithmetic and numbers she missed in elementary and middle school. Unfortunately, I only have 50 minutes with her each day. For this reason I am always looking for quick ways for her to fill the holes in her prior education. Using money to help make sense of decimals is a go to for me.

Also -I have immersed myself in reading and learning about how to teach elementary mathematics. Now when I talk about division with students I talk about ‘numbers of GROUPS’, when I talk about subtraction I talk about the ‘distance’ between the numbers. Us High School teachers to the most complaining about students lack of arithmetic skills, but we are the weakest at knowing how to teach these skills this needs to change….NOW….what are you doing to become smarter as a teacher at not only teaching HS standards but also supporting students lack of numeracy skills?

At the start of the school year Fartun was a student I identified as being the most behind in mathematics. Notice I did not say ‘low skilled’. Fartun is a learner. She is bright and hardworking. By unit 3 she was turning in tests that looked like this. Her grade level skills were on par with her peers. Despite this her pre-grade level math skills & continue to unearth conceptual holes. We work hard everyday to fill those. The challenge now is that her brain is saturated and she seemingly at times loses things she’s gained. She is not losing anything -but a lot of her learning is fragile and need of ongoing reinforcement. She is amazing. I hope her next teacher sees this. I hope she believes this about herself.

‘Imran’ is outgoing and positive every time I see her. She is friends with everyone. When someone enters the math center, she greets them by name (regardless of their grade, race…..). She grasps new material quickly. She will forgo doing her own work to tutor anyone in need. She is gregarious, kind and willing to work hard. I’ve been working hard to convince her to become a teacher – despite the challenges she has of only arriving in this country 2 years ago, learning English and still having lots of holes in her mathematics. She would be an amazing teacher – I hope she pursues this path. She is the first to say she was never taught 6-9th grade math. She has good basic arithmetic skills. Because she learns new material quickly, I often think she is stronger than she actually is until she asks me a question that reminds me of the holes that remain.

This is the problem that Imran asked me a question about this week….As you look at this – ask yourself – what will Imran struggle with in this problem? In addition to graphing the system of inequalities, students were asked to identify the corner points in the feasible region.

What would your students struggle with? What would a student of yours whose education was interrupted for multiple years ask? Imran was able to do everything on her own – but she did have one question.

Imran pointed to this and said “**Is there a one in front of x?**” I asked her to read the inequality out loud with a 1 and see if it makes sense. She says “one times x minus 2 times y…..* OH! I get it*“. I said, “

Again, Imran is usually less than 30 seconds from “Oh, I get it“. I need to be prepared to help her get there that fast. I could have said ‘Yes, there is a 1”. Instead I choose to ask questions that hopefully she can answer her own question. I am training her and all my students to answer questions for themselves when they work at home or anywhere I am not. I am not going to college with the and it is my goal to empower them to teach themselves if necessary. Look at her work – Imran is on par with her peers. All I helped her with was giving her the confidence that there was an invisible one in equation 2.

Imran’s question also shows how important it is for us HS teachers to make the invisible ones and zeros in our work visible. I ask myself everyday when I am planning – **HOW CAN I MAKE THE INVISIBLE, VISIBLE?**

One way I do this is by never saying “Cancel the 3’s” in the example above. Instead I write a big 1 and talk about creating factors of 1. I also write in the invisible 1’s and zeros into equations often in class -but that is an entirely another blog post.

I only have 50 minutes a day for 1 school year to catch up Fartun & Imran and their peers on 6+ years of mathematics. This is a seemingly impossible task. I can either choose to focus on what they still don’t know or I can focus on what they do know and the growth they make each day. I can either make decisions about what future courses they have access to based on the fact that they need a calculator to add 7 to -3…..OR….I can believe that they have the ability to learn new material at the same rate (if not greater) than their peers who have had interrupted educations and give them access to high levels of mathematics and watch them flourish.

I choose to believe my students can do grade level mathematics no matter how far behind they may appear to be when they arrive in my class. I believe all students want to do well in math no matter how resistant they may appear. I choose to see assets. I believe it is my job to do something different if students are not successful and not blame students.

I am not going to lie – teaching the students I teach is damn hard work. Fartun and Imran grapple with feeling like the understand very little all the time. As soon as they mastered one thing in math – 5 other things they’ve yet to master appear. The seem to never have a chance to feel like they are not behind. The rarely feel ‘caught up’. To counteract this we celebrate the mini-moments of Aha’s and Oh, I get its. I frequently remind them of what they were able to do the first week of school and what they can do now so they can see the huge growth they have made. If I don’t show them the growth – they only focus on the things they don’t know yet today. They are now at the point that they are addicted to the struggle of not knowing because they know coming soon is the catharsis of understanding. They see their hard work resulting in understanding and are empowered with tools of how to learn on their own – even if I don’t follow them to college.

I want to close with one more story about ‘Imran’ followed by a challenge to you. Right before winter break I wanted my students to solve and write-up a problem that they could not solve easily a few moments. I selected the classic Painted Cube Task. I knew many of my students had language issues and interrupted geometry experiences so we started by each holding a cube and recording terms like face, vertices, edges. We counted the number of each term. Students explored the task in groups by building cubes, counting and recording information they collected. In doing this the noticed patterns that emerged and world to generalize rules.

Imran and her peers persisted and worked hard. When students were convinced they did not understand I would tell them to go back and build cubes again. I remember overhearing Imran saying to friends on day 2 – “Ms Van was right, if we just build and look for patterns it starts to make sense”. Imran was confident in a solution. On day in the math center she was working on writing up her work. While working she shouts out to me “Ms. Van, what is a vertex?”. I shouted back my answer “A corner” to her. Several minutes later she caught my attention again and said “What is a a corner?”

Here was a student that written beautiful rules for the number of cubes with 0, 1, 2 or 3 sides painted. She understood these rules and had made beautiful diagrams to support her mathematics. Despite all of this – she is still in need of support. She had no idea what ‘corner’ meant. I picked up the kleenex box nearby and pointed at one of the vertices and told Imran ‘this’. She said “**Oh, yeah! ** Thanks.” Again, Imran was 30 seconds away from understanding.

This is her 6 page write-up for the Painted Cube Task. She did this all on her own. I hope her future teachers don’t see her deficits and instead see her amazing potential.

**Here is my challenge to you (and as always me) based on what I learned from Fartun and Imran this week:**

- Noticing the small things students ask about more radically changes my teaching that almost anything else. How can I make space for students to ask questions? How will I make sure I stop and listen to what students are saying?
- Will you see students struggling with elementary mathematics as students who are ‘low’ or as students who are powerful problem solvers who can achieve mastery of grade level standards? How will this view impact what you teach and how you support students?
- What are you doing as a secondary math teacher to improve your skills of teaching elementary math concepts?
- How will you help students with holes in the math background feel success with grade level mathematics in your classroom today? Do the tasks you select have multiple entry points for students?
- What assets do your students bring to the table?
- Are you focusing on proficiency or growth?
- Lastly – most students are only 30 seconds away from “Oh, I get it”. In a classroom that validates speed in answers (answering the first raised hand for example) – students who are only 5 seconds or even 5 minutes behind their peers often feel like they are years behind and have no hope of catching up. How can you change the culture of your classroom to eliminate gaps in understanding that are only minutes away for most students?

One of the challenges of writing this post was worrying about talking about ‘low’ vs. ‘high’ students and all the baggage that comes with this. I hesitated to even push send on this post because like others I hate calling students ‘low’. There are lots of great posts on why I and others hate the term ‘low’. Here are a few for further reading.

- Kristen Gray’s ‘RTI for Adults‘.
- Brian Bushart’s ‘What we Presume‘
- Tracy Zagar talks about this a lot in ‘How not to start class in the fall’.

All of these are great – but from an elementary perspective. Do you know other posts written by secondary math people? If so, let me know.

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]]>The post Why I hang orange plastic golf balls from the ceiling of my classroom. A favorite teaching moment. appeared first on Sara VanDerWerf.

]]>I wait until March to reveal the reason behind the orange plastic golf balls hanging because this is when my districts Algebra 2 Advanced Solving Unit falls in the calendar. In this unit we solve systems with more than 2 variables as well as systems of inequalities. Since I teach a large number of students with interrupted educations I do take a day or two (and some homework assignments) to review solving systems with 2 variables (for many they are learning this for the first time). One of the goals of this review is for students to describe what the solution to a system of equations looks like graphically. The homework the night prior to this lesson is this one – 6M What do solutions look like in 2D homework. This homework refers to a ‘GREEN SHEET’ – every unit I give students 1-3 pieces of cardstock with reference material on them – this is entirely different post I need to do sometime -but the green sheet referenced in this homework is found in this document I give at the start of the unit 6a Daily Practice 2017 v2 if you are interested.

I start this unit with this visual made up from lots of pictures I’ll use in the unit and ask students to predict what we will learn about this unit. I do this in every unit to get students predicting what we will do. Several students notice the orange golf ball and associate it with the ones we’ve had in the classroom all year.

OK – that is enough background – my lesson with my suspended golf balls around my room has resulted in some of my favorite classroom moments ever. I have 5 questions I use in my personal planning of lessons. 2 of them are related to why I use golf balls…..

During a Algebra 2 team meeting a couple of years ago I was wondering aloud how I could have students think about graphing in 3 dimensional space. In the past I’ve done a pretty decent job using these 3D models from this post – but then my colleague – Rob Rumppe (he teaches pre-calculus to our students) – said, “Well, I hang a ping pong ball from my ceiling and ask students to describe where it is located”. I looked at my friend Morgan and this is the lesson we put together from his short sentence to us….

This was the prompt for my students as they walked into my classroom.

I waited for every student to write something. While they were writing I was watching what they were doing – where they where looking. I was looking for students to call on later in our discussion. Some students struggle to begin writing, but I just keep saying “You can describe it however you like”. During this time they also were looking at solutions to the homework linked above.

I then do a 60-90 second review of previous work and remind them what solutions in 2D look like. Then I ask them what they think a solution in 3D space looks like? I use a system we have already solved in class. We had started solving systems with 3 variables at this point, but had not yet talked about what the solutions we were finding looked like on a graph. Students shout out some answers, but for the most part they have no idea. The most common thing they shout out is the intersection of 3 lines. I don’t let this discussion go too long…..then…

I take 4 minutes to define ‘dimensions’. The conversation goes something like this…

- I stand on a point (circle of paper) I’ve attached to a line on the floor of my classroom. “
*Imagine I have no height, width or length. Where could I move if all I had in my world is this circle?*” Students say ‘no-where’. “*Could I reach Jose (seated in the back of the room) and give him a high five?*” Students say ‘no’.

- I then show the next visual and tell my students I now live in a 1 dimensional world like the line on the floor. I model shifting left and right across the line. I say “
*I am inordinately short – what directions can I move?” “Can I give Jose a high-five yet?*” I hold up a meter stick as a representation of a line. We talk about the fact to be a line it would need to go on forever on both directions. We talk about the first dimension is doubling the size of the previous dimension and connecting vertices. - I quickly move on to the next visual. “
*I’ve added a 2nd dimension. This is the dimension you’ve done most of your mathematics in before today*” I hold up a piece of paper and we talk about it being a representation of a plane (though a plane would go on infinitely in all directions – we talk about the paper cutting through the ceiling and floor and through the core of the earth….) Students notice again that we doubled the line segment from 1 dimension to 2 dimensions and connected the vertices. “What directions can I now go?”, I say as I shuffle left and right across the line and jump up and down? “*Can I give Jose a high-five?*” – Nope, not yet. - On to 3 dimensions…. If we take two 2D shapes and connect all 4 vertices we get a 3D shape. I say ‘
*What directions can I do now?*” “*Can I reach Jose*?” YES! I move left right – up down and forward and back. I say “.”**this is the 3D world we live in in real life….but most of the math you’ve done has existed in books or a piece of paper – in math you’ve become use to only 2D world and have yet to visualize algebra in 3D. That is what we will be doing today** - I then have students visualize the fourth dimension. We talk about a hypercube (teseract). I tell them that the movie that freaked me out the most in life was one that tried to use computers to visualize the 4th and 5th dimension. My 3D mind could not wrap its head around it (I always have some of my top student and most creative students ask me at the end of class about this video – that I have no idea where it is). Here is a copy of this visual that students glue into their notebook. 4 DIMENSIONS
- I then show them the 4 dimensions a second time with a few GIFS like these….
- We then look at these GIFS and pictures and connect them to solutions in mathematics. This looks something like this….2D is connected to their homework and finding a coordinate point that is the intersection of 2 lines in a plane. I then ask what they think the solution to system in 3D would look like? Students still struggle to answer this – though some are now thinking it might be intersections of planes.
- I say ‘
*Well we need to do some graphing in 3-dimensions. Let’s start from the beginning*“. I say get out what you wrote at the start of class (10 minutes ago). I have them stand up (we do something called ‘stand and talks‘ everyday in my classroom) with their notebooks and read what they wrote out loud to a classmate. I then have them sit and give them 30 seconds to fix what they’ve written so far. I then call on students to read what they wrote. I point at the orange golf ball in the middle of the room and say, “*Give me directions on how to get there*“. I then act out what they read. Their descriptions are horrible. Students laugh together as I fail. I never reach the ball. I get close sometimes but what they write is not good. I’ve done this many times and not yet has anyone given me a good description of where to go the first time. I then call on the student who I noticed at the start of class doing something interesting. This student(s) is the one who either looked at the ceiling in my classroom. I ask this student to read what they wrote and it usually goes something like this. “*Start in that corner of the room (pointing at one of the 4 corners of my room) and go 4 ceiling tiles forward, 2 left and 1 down…*.” I have yet to quite get there with these directions but I get really close. Students always express audible awe with this students idea. - I then say “
*Let’s try again. This time I want all of us to write the same exact directions to get there. I will answer only 3 questions before you begin. Think carefully – what do you want to know?*” Some student usually asks ‘Where are we going to start?”. I say “*Great question – you mean the origin*.” I whip out a yellow wiffle ball I’ve attached 3 meat skewers to and spin it around in a location. I say “*What other questions do you have?*” Students ask “*What direction do the axes go?*” (or what direction is positive x, y and z). I stop spinning the origin and define this. (Note, for ease sake – I point the y-axis up and down – we do talk about that traditionally in math text books the z-axis will point up and down) I have a student stand up and say “*Look at Amber’s head. Her head is all positive – x, y and z are positive – this octant is where all 3 variables are positive. I then say Look at Isabel. What other questions do you have*?” They then usually ask, “What unit will we measure in.” I then tell them to look at our classroom floor. Our floor is made up of 1 foot by 1 foot tiles. I hold up a 6 foot meter stick next to the origin and say, “*OK, you’ve asked your 3 questions. Write where the orange ping-pong is located. Stand up if you need to*.” Students get up and furiously write. I call on a student to read what they wrote. Usually what they write is an ordered triple (even though I did not tell them to do this). We define ‘ordered triple’ and start over another time with another ball in my room. (I have 3 hanging around the room). - By this time students are feeling good about 3D and I have them get up with a partner and hold a 3D model for graphing I’ve made. You can read more about how to make this with resources HERE. I have students start with their pencils at the origin and graph the following ordered triples.
- We then move to talking about what the graph of x + 2y + 4z = 24 would look like. In the past I’ve used string, push pins and a cardboard box cut open to form an octant and covered in graph paper to do this – but in this class we just imagined this set of points forming plane. What I do does depend on time.
- We go back to the system from earlier in class and talk about the solution to a 3 variable system being the ordered triple – point where 3 planes intersect.
- Here are some visuals students glue into their notebook the next day. (and the word doc What do solutions look like for notebook
- I have LOVED the discussion with my students teaching this lesson. Everyone of them is engaged the entire time. I also have loved how much they understand about solving systems with 3 variables once we have this. They have a visual model to tie solutions to.

I filmed a quick video of my room so you can see my set-up in something closer to 3D than what I’ve talked about above.

Whew – that is a lot in this post. I am going to push send right now (6pm 4.8.18) and clean up mistakes or things I forgot later. Forgive me if this post is a bit messy. I am pushing send now though since I might not do it and I’ve not blogged since September and it is time to get back into it again. Until next time…..

**Additional 3D Resources**

- GeoGebra’s 3D applet
- Mathpix 3D online graphing
- CPM 3D Plotter
- Books: Flatland, A Romance of many dimensions of by Edwin A. Abbott by and Flatterland by Ian Stewart
- How to imagine the 10th dimension Youtube video
- Understanding 4D – the Tesseract Youtube video
- Imagining the Fourth Dimension Youtube video
- 4D world explained Youtube video
- A beginners guide to the 4th dimension Youtube video
- Matt Parker on Youtube Things to do and see in the 4th dimension and his book of the same title.

**Note: ** If I taught middle school I would still do this lesson with a few tweaks when we learn to solve systems in 2 dimensions. I’ve had the best discussions about 3D and 4D graphing with middle schoolers in my career….even more than HS. They can handle this at that age and it sets them up beautifully for HS.

**A final Note: ** I’d love to say I had intentionally hung up the 3 plastic golf balls all school year to add a sense of mathematical intrigue and curiosity into my classroom but in reality they were hanging up all year because I was too lazy to take them down from the previous school year. That said, I HIGHLY recommend you intentionally hang them up in your classroom at the start of the year – torturing the students with ambiguous answers for 1/2 the school year is well worth the enjoyment and created a sense of engagement when we did get to answering their questions I had not seen in previous years.

The post Why I hang orange plastic golf balls from the ceiling of my classroom. A favorite teaching moment. appeared first on Sara VanDerWerf.

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