The Pursuit of 100%. Practical Ideas for Engaging Students

This post includes resources/links from a presentation I did for the Global Math Department. (You can watch the recording by clicking HERE!).  I’ve also included additional resources from a day of professional development I did with Minnesota Teachers on 6.21.16.  Enjoy. (If I missed something in this post you were hoped would be here, let me know)

Let me begin by saying a strong word about engagement.  I’ve observed 100’s of math classrooms and thousands of my own lessons over the past 25 years and it is rare for there to be 100% of students engaged for longer than a couple of minutes.  I often observe 100% compliance in math classrooms….but COMPLIANCE IS NOT ENGAGEMENT or at very least not the type of engagement I want for my classroom.  Compliance (passively looking like you are doing what I ask) is often enough to make me look like a highly proficient teacher to others.  I’ve often seen leaders observe a lesson and see students completing 20 problems involving logarithms and been impressed with the engagement.  I think it was because there was the word logarithm on the task.  As I observed the room though I saw zombie like motions to complete a task.  When asked what a logarithm was, students had no idea how to answer this.

The type of engagement I am talking about is related to students engaged in productive struggle in mathematics classroom.  The type of engagement I am looking for results in empowered students who leave my room and extend their learning of math outside the111 classroom.  Engaged students are addicted to the cycle in a math classroom of being ‘puzzled and the catharsis that comes from being unpuzzled’. (this phrase is from a really lovely post by Dan Meyer – you need to read it – entitled ‘Culture beats Curriculum – Worshiping the real world’)  My goal is to create a mathematics classroom where my students are addicted to being puzzled (they are comfortable struggling with math) and trust me and our class to support them so they can feel how good it feels when they understand (become unpuzzled).  This is engagement in mathematics class to me.  Finally, I know students who are deeply engaged in math when I see it.  There is a brightness, a light, in students eyes.  Students are talking out loud about mathematics.  Students look like this:

Before I tell you some of my ideas for HOW to engage 100% of your students in mathematics, stop and take 61 seconds to brainstorm why students are NOT engaged.  I’ll pause my post until you do this…..


are you brainstorming ideas?

seriously, do it.

For me trying how to figure out solving a challenge in my classroom always starts by trying to get in the minds of my students.  I do this by getting to know them, build relationships with them, asking them, reading what the research says….etc.  My list of why my student don’t engage is long, but I will begin with just 3 ideas for this post…1)  Students don’t feel successful in math.  2)  Students don’t have the academic language to engage.  3) Students don’t know how to engage.  For my first 7 tips, I will use ‘students talking about mathematics’ as evidence of engagement (knowing there are lots of other ways to measure engagement).  Sidenote:  I read Steven Reinhart’s NCTM article titled “Never say anything a kid can say’ every year.  You should too.  Here is a link.  So here we go with 7 things that have worked well in my classroom to engage ALL …


 1) I find many math teachers are not well trained in Social/Emotional learning and even if they are trained they do not employ the strategies they’ve learned in their math classrooms. This lack of training or hesitancy to add this to their classroom gets in the way of engagement of their students.   I am a HUGE believer that teaching the Social aspect of school is just as important as teaching the Academic/Math part of school.  If I want students to do well in my class I can not assume they know how to function in my classroom.  I am a big believer in modeling everything in our classroom (how do you do homework, what do you do if you don’t understand, how do you ask a question, how do you manage supplies….etc) I don’t asgroup work day 1 picsume my students know how to work in groups or with a partner.  I see at as my job to model this and teach them how to do this.  I have found an activity that has been pretty fool proof at immediately getting 100% engaged in working and talking to their group members.  At the start of every school year (day 2/3 or 4) I use a task I call the 100’s task.  On day 3 of school – every group looks like the picture to the right.  I’ve blogged about this task in depth (script and all) HERE – the 100 Numbers Task).  Read it and use it this fall in your classroom and more importantly refer to it throughout the school year and watch as more students.  I’ve received lots of great feedback from this task from others that have used it in their own classrooms.  One more thing – make sure you follow this task up with a couple of rich tasks with low floors and high ceilings so students can practice what they learned.  I have several I recommend in my post.  Here is another other blog post about the task from Megan Schmidt @veganmathbeagle ‘Making Groups Work’.

2For 20+ years I made the mistake of saying pretty much daily, “What questions do you have?”  I can probably count on one had the sum total of any meaningful feed back from asking that question of students.  I also would ask “What are we suppose to do in this problem?”.  Asking this resulted in the same 2-5 students in every class responding.  These were such INEFFECTIVE ways of engaging students in my classroom.  Over the years I have transitioned to questions and prompts that engage many more students, but I feel like at year 25 I have found the trifecta of questions that have started to engage nearly 100% of my students daily in mathematical discourse.  Be fore I say much more….. YOU MUST.. .MUST… MUST STOP and click HERE and take 5 minutes to watch Annie Fetter’s Ignite talk titled ‘Ever notice what they wonder?’.  It is seriously the best 5 minutes of PD for every educator if you want to engage more students.  I watch it over and over again.  So again – STOP reading and watch it now whether it is for the first annie.PNGtime or the 50th…….

Are you watching yet?


Thank you for taking just 5 minutes to watch the video.  This video transformed my classroom and helped me work on a piece of student engagement – helping students feel more successful – so they would talk about mathematics more.  Here two questions What do you notice? and What do you wonder”   (also with countless “What Else” “What Else” What Else’s”) will change what you do in class.  I ask these questions EVERY day in my classroom.  EVERY day.  I create ‘scenarios’ (watch the video to see what these ares) out of tasks I plan to use.  LIFE Changing questions.  Kids start talking.

I have recently transistorized from using ‘Why’ ‘Explain your thinking’ ‘Show your work’ to using the phrase ‘CONVINCE ME’ as my main go to phrase to get more students to engage in explaining their reasoning and informal proof.  Using this phrase out loud and in print has seemed to have a positive effect in more students engaging in mathematical discourse.  Try it.

I am a huge believer in the power of repeated messages/mantra’s with students, so much so that I wear around my neck a laminated copy of my favorite questions/prompts to use in the classroom.  I wear them to remind myself – but I also get asked about them all the time and I use my badge to explain to parents/leaders/other teachers the power of these questions for engaging students.  Soon I’ll blog about my geeky math badges and I’ll put the link here when I do.  Until then – WHAT DO YOU NOTICE?   WHAT DO YOU WONDER? & CONVINCE ME!  are the trifecta of math question/prompts you should be using everyday in your classrooms.  Use them to transform the choices you make in lesson planning & selecting tasks and watch your students start talking more.


I am obsessed, obsessed I say, with the intentional use of color in my classroom.  When I intentionally design the colors I use in lessons – way way more students talk in class.  Students I’ve never heard talk  start talking.  I will say a lot more about this in a future blog post this summer – but until then….here is a small taste….

There are so many great resources in the MTBoS universe.  Mary Bourassa’s great ‘Which one doesn’t belong?’ site is one example.  Here is a prompt from the site – one with color and one in just black and white.

When I started using color when I asked “Which one doesn’t belong”?  way more students responded?  Why?  Many, many of our students (particullarly our students in poverty as well as ELL students) struggle with academic vocabulary.  If I give them the black and white image on the left they struggle to say ‘the one in the upper left….” BUT they are very able to say “The purple one doesn’t belong because…”.  All students have math skills.  All.  It just sometimes appear students struggle with math concepts and sometimes the vocab.pngthing getting in the way is having the words to describe what they know in their head.  The most effective way I’ve found to get them talking is to start using color intentionally.  Again I will say a lot more about this in a future post (with more examples).  I will ask you though to check out this post “How the words ‘annual’ & ‘real’ changed what I do every day in my classroom” if you want to learn more about my journey to take away the lack of academic language as a barrier for my students.  (this is another great passion of mine).


#4 is probably the easiest tweak that will have the fastest impact on more students talking of anything else in this post.  12 years ago I started working with an amazing math teacher named Allison Rubin Forester.  Ali is not only a math teacher, she is also a dancer and a dance teacher.  In fact she is the only person in the state of MN with both a math and dance teaching license.  Ali is the person who convinced me that students need to MOVE in the math classroom.  I am planning on her doing a guest post on  my blog this summer to share all her amazing ideas with you – but until then I will tell you one thing she taught me that is so easy.  Research says that students need to be up and active at least every 25 minutes.  This tweak is at least a small way to get kids to move for a moment every day in class.

This tweak makes the THINK PAIR SHARE classroom routine better.  Giving students zprivate think time or private think time is integral to student engagement.  I’ve been doing it well for years.  When students have time to think – when you take away the competition of the race to be the first one to figure something out – you will always engage more students. Where I’ve struggled in the past with the think/pair/share routine was when I said ‘turn to your neighbor and tell them what you have noticed’.  Some students did this and some did not.  When this routine to be think/STAND/pair/share and after some private think time I said, “Everyone STAND. Quickly find a partner from another group and tell them what we learned to day.  Go”  Suddenly kids were moving (yea! for movement0 and talking about math.  Every student was talking.  Every students.

Since this moment I’ve used ‘stand and talks’ pretty consistently.  They take no more time than a sit and talk to your neighbor/group.  In fact, sometimes they are more efficient.  While students are talking I walk around and listen in to whatever students are saying.  I rarely join a conversation.  Stand & Talks last 1-3 minutes.  As soon as I notice most students are done sharing I say, “Finish your thought and take your seat” and continue class.


A couple of quick tips on ‘stand and talks’:

  1. Say ‘Stand’ and wait for everyone to stand before giving directions.  If you give directions first, some students will fight standing up.
  2. If students are particularly tired that day, I will have them do a quick stretch after I say stand or make some type of function with their body.
  3. Demand 100% compliance with standing.  Every student – unless they have some type of IEP/504 that says otherwise – stands every time in my classroom.  The first few times I have to spend a bit of time making sure 100% stand, but after the first few times students don’t fight me on this.  If I hear grumble I just say – ‘you’ll be fine.  this is just for a minute.  you will survive’.  The fact that stand and talks are quick, makes a huge difference in getting students to join in. I generally don’t allow leaning or half standing either.
  4. After I say ‘stand’ sometimes I have them pick up their notebook to go find another person to share with and sometimes I have them go to that person empty handed.  I may have them bring a computer/ipad and describe what they are doing on desmos or….
  5. I usually let students select their partner.  It has worked well for my ELL students who often select someone who has a similar home language and they are often helping each other out in ways I can not as a native English speaker.
  6. Most of my stand and talks are just to talk to one person and then sit down.  BUT sometimes I want them to share with multiple people so I will start the same and then call out “SWITCH” and have them switch to a new partner to share something.
  7. I had having empty time at the end of class so If I finish several minutes early I will have students do a quick write of what we learned today and then to a stand and share to debrief that day’s learning.
  8. Finally, I use stand and shares as a way to practice saying new vocabulary out loud.  Too often in math students never hear mathy words like ‘parabola’ roll off their own tongues.  They only hear me or a few other students say those words, so I will put up 5-10 math vocab words occasionally and tell students to STAND and then go find a partner and use at least 3 of the words from the list and tell them what each word means.  This has been a GREAT vocab builder in my room.


I LOVE, LOVE, LOVE having my students work with PARTNERS!  Love it.  Another way to get all students engaged in my classroom was to start crafting quality partner tasks.  Why you ask?


Groups are great – I still use them.  Maybe you can pull of having group roles and modelingadd em up featured and teaching group work better then I can, but in my classroom it seems groups often have 2 or 3 of the 4 people working well together while 1 or 2 students are hiding in the group doing very little mathematical thinking.  There are exceptions to this – depending on the tasks I craft.  One exception is a task I call ‘Add-Em-Up’.  I blogged about this task here.  It is AMAZING  I get 100% engagement from all students for entire class periods every time I use it.  Read the post.    Use it 3-5 times next school year.  Guaranteed engagement for those days.zzz

Back to partner work.  Most of my tasks in class are done with partners.  Why?  It is really difficult to hide in a group of 2.  I have found more students talk about math and engage in mathematical thinking when I have them work with just one other person.

One of my favorite times to do this is on the first day of a new unit.  I give each partner ONE computer and one sheet of paper and tell them to write down everything they know about the new unit’s topic.  The picture to the right is from a day I did this in class with the word ‘quadratics’.  In 10-15 minutes students had self-reviewed what they had learned in the past, recorded tons of vocab we would need in this unit.  Rather than me telling them what they should have remembered from the past – students, in pairs searched this information out for themselves and frankly remembered it better than if it had come from me.

aaa partnersI love using partners with Desmos.  One device for each pair of students.  Students have to work together on tasks built in activity builder.  They just naturally start talking about math.  To the left is a photo of one such task at the end of the school year.  Students started with a sheet of paper (before using Desmos) and tried to figure out which equatins I had used to create our schools name – South .  We were finishing up a conics unit and I had created the word using functions they had just recently learned. After questing the equations, they signed on to Desmos to create the image for themselves.  Students talked/worked together with little help from me.  It was amazing.

Another of my favorite review activities that resulted in 100% engagement for long periods of times – AND where students worked in groups is pictured above.  Sometime this summer I will blog about the activity and post the link here when I do.  It had such a simple tweak (I sat the entire hour and students came to me vs. me going to them).  More soon….


If you want 100% engagement in mathematics then you the teacher need to demand it.  Getting all students to engage is hard work.  Too often we are the ones who let students of the hook of engaging through our actions.  I don’t say this to blame at all.  I struggle with this just like you.  I say this as a challenge to us all.  When I put in the work – especially in the month of September – to create a norm of 100% on task behavior – it pays off in spades.

5 practicesThere are somethings I do though that make this WAY easier.  I work to create a safe in my room to be wrong and succeed.  The first way I do this is with my choice of tasks.  I look for tasks with multiple entry points (low floor/high ceiling) for all students to grow from.  I choose tasks that students can have success on parts of the task if not the whole and I name & celebrate students as they solve even parts of tasks.  The description of how I do this would require its own post – OR – just read the bible on this….Peg Smiths ‘5 practices for orchestrating mathematical discussions’ book.  OR you can read about what I call my MAGICAL TEACHING SWEET SPOT and how that played out with my favorite task in the classroom from a couple of years ago (when 100% of students were engaged).

22 words

Demanding 100% also means students don’t opt out when you call on them.  I’ve moved away from cold calling on students using methods like popsicle sticks.  If I want a safe space in my classroom for my students will talk about math – this can lead to fear.  One way I do cold calling is after a stand and talk (see above) I will start cold calling students to report out.  Students think this is random, but it is not.  During the stand and talk I walked around the room trying to catch students being right/correct.  These are the students I call.  I listen in particullarly to students who never talk in class and catch them saying good things to partners and then call on them.  I have found that once they’ve been called on and they have good stuff to say they are more likely to contribute in future conversations on their own.  Sometimes I tell students I am going to call on them – especia100 percentlly if I know they are super fearful – and say ‘oh, that is good – i am going to call on you – say that’.

Finally, no opt out in my classroom means if I do call on you and you say “I don’t know” or “I wasn’t paying attention”, this does not excuse you from talking about math.  I simply say the phrase to the right and come back to them in a few minutes to answer the same or a similar question.  No one gets to choose to not engage in my classroom.


As you know – Mindset/Grit/Perseverance/Productive Struggle/Effort/Growth Mindset – has been all the rage in educational journals for 5+ years now.  I like the rest of you have downloadread the work of Dweck, Boaler, Willis and more.  We’ve put up bulletin boards.  We have ‘Mindset Monday’s’.  We are passionate about changing the negative scripts in our students heads that they can get smarter at math.  We’ve taught them about how their brains work.  All this stuff is great.  Really….but… Recently, Grit & Effort has been receiving some push-back as blaming students for not working hard enough.  Ultimately, what has happened, in my opinion, is good stuff can play out lots of different ways in our classrooms – some good and some bad.

Picture4Over the last few years I’ve learned that doing a few things well – when it comes to Mindset – is better than using everything out there.  You can read a full post on what I love most in this work in this blog (with tons of links) titled “Growth Mindset: the challenges and what has worked for me”.  Read it HERE.  

I have 5 or 6 videos/quotes I use over & over throughout the year.  I focus on persistence and productive struggle (I rarely talk about growth vs. fixed mindsets).  My faves include a scale of persistence I post in my room ranging from a video of a guy on an escalator to a video of a beagle trying to get a chicken mcnugget.  (Read my earlier post HERE to get links to those videos).  

My favorite thing I added this year though was related to how I could encourage students to keep working even if things were difficult.  At the start of 2nd quarter (and this is a really great time for this – better than the start of the year). I introduced a Malcom Gladwell quote:Picture1

I have students read the quote first to themselves and annotate over it.  I had them stand and talk to a partner on what Malcom was trying to say.    I then challenged my class that in 2nd quarter we were going to practice working for 22 minutes at a time without stopping to see what would happen (side note: I tell my students that they only have to spend a maximum of 20 minutes per evening on homework, so this amount of time worked well).  Students really agreed that they often give up too early.  I said, the only way we can get better at this is to practice this.  I don’t know what happened, but something about the #22 resonated with my students.  I set timers in class for 22 minutes and said I was not going to help students during that time.  Sometimes I set a timer for 22 minutes and gave 3 question cubes their groups could use to ask questions.

Sidenote:  Someone shared this video of NYC newscast that talked about ‘You give us 22 minutes, we’ll give you the world”.  I may add this into what I do next year.

The next day after this quote – I did several days in a row of tasks with multiple entry points and had groups and/or partners work on them for 22 uninrupted minutes.  I would set the task up with notice and wondering questions – and then they worked to solve the tasks.  In my advanced algebra class, the first task I used was the painted cube problem.  (see Dan Meyer’s write up of this task here and here and he got the pic above from Nicole Paris and her post is here).  I also started giving 22 minute homework assignments of fairly difficult tasks with the directions – ‘Set a timer for 22 minutes and simply write down everything you tried in this problem during those 22 minutes.  Don’t worry if you can’t solve it.  I just want to see what you tried’. I was amazed how naming a specific number connected to a quote changed how many students engaged in class.


During my global math department presentation, I did not have time to use the slide above.  To get good at working on engaging more and more students, you need to practice using some of the strategies I mentioned.  Above is a great task that I love using related to exponents from Andrew Stadel (see more about his task HERE).  How could I tweak this task using the strategies above?  I will leave this as an open question here (but for sure color could help and a tand and talk and….)  It is a great task to start with – but there is always more I can tweak in my pursut of 100% engagement.

Here is the power point from my Global Math Department Presentation: 6_21_16 Global Math Dept The Pursuit of 100% Engagement

What follows are some additional ideas from a PD session I did with Minnesota teachers earlier that day over a 3.5 hour period of time.

A lot of my engagement ideas from this year came from the time my coworker, Morgan, Picture5and I spent on our backwards bike.  I HIGHLY RECOMMEND you watch this 8 minute video on the backwards bike from Smarter Everyday.  We built a backwards bike and worked on learning how to ride it this school year.  IT WAS THE BEST THING I HAVE EVER DONE AS A MATH EDUCATOR.  If you want to know why or read more about how the backwards bike changed me as a teacher or how it increased student engagement – read my blog post HERE.  Seriously, this is the best – THE best thing I’ve done in my career.  For me to change the success of my students I need to change myself.  The bike did that for me and continues to make me a better educator.

In addition to the things way at the start of this post, I have a few things that guide me in making decisions for my classroom:Capture

  1. This picture was the goal of my Professional Learning Community this year.  It was amazing how when you use this lens to plan lessons and classroom experiences how a side benefit is engaged students.
  2. The biggest mistake I’ve made in the classroom the last 25 years was rescuing students thinking I was helping them.  This is typical of most urban teachers.  It is something I have sought to break the habit of and instead empower students to be able to do things when I am not around.  I no longer want to feel like I am handicapping students once they leave my classroom.  What is less important is can students perform in my classroom, what is more important – and the lens I use to make decisions – can my students do math when they are not in my classroom?  Will students have the knowledge and tools to be life long learners of mathematics?

Engagement starts the first week of school.  It is so important to build relationships with students and tell them about myself and do math that makes students feel successful in math.  I will blog this Capturesummer on my first week of school tasks – probably in August – and will attach links here when I do…but until then, I will give you a couple of things to download from our day together:

Engagement is about Empowering students to know how to advocate for themselves when they struggle.  If your goal is to empower students to seek help in math and have the skills to work on math when they are not around their math teacher – then here are two other blogs to read with more ideas.

  1. Modeling Googling – If you want students using the internet to learn (on a computer or their phones) read this post.
  2. The #1 thing I did in my support classes – although this post is about a student’s 2nd math class – the #1 idea is perfect for any math class.  Read how I got students to advocate for themselves.

Here is my larger power-point from the 3.5 hour training.  I could have spent 2-3 days on this topic.  I will post more later or do another training soon.  June 2016 Engaging Students <===Power Point

Closing thoughts:

  • Start your journey by asking yourself why students are not engaged in your classroom.  Select one of these reasons first – the one that concerns you the most – and start there.  Brainstorm ways to tackle this reason.
  • Model everything.   Don’t assume students know how to do what you ask of them.  Model the social and academic aspects of your classroom.  Model groups.  Model what it means to ‘show your work’.  Model everything.
  • Ask yourself, “How can I remove competition from your math classroom?”  By ‘competition’ I mean the race to be first with an answer.  I’ve personally tried to limit the raising of hands.  As soon as one hand goes up – thinking around the room stops.  How can you give more private think/work time?  How can you solicit answers without it feeling like a race to an answer.  If you can answer these questions you will have increased engagement from students.
  • My list of ideas for engagement in the math classroom in this blog is not exhaustive.  I have lots more.  For example – we know we need to work on students lack of numeracy skills.  To do this you need to start doing number talks.  That is 3-4 blog posts all by itself.  I also love Desmos for engagement – again, I could do lots of posts on this.  I also have not talked at all about the role of race, my white privilege and how this connects to engagement.  I guess I will need to keep blogging.
  • One of the things getting in the way of math classrooms making gains with students who are significantly behind is the idea of being good at math is being able to find the correct answer as quickly as possible.  How can you stop honoring quickness?  How can you change the definition of math and being a mathematician to something more powerful?  I start the year – every year – having students define math (MATHEMATICS IS THE STUDY OF PATTERNS)  and defining what mathematicians do every day (MATHEMATICIANS NOTICE PATTERNS. MATHEMATICIANS DESCRIBE PATTERNS.  MATHEMATICIANS GENERALIZE PATTERNS).  I then tell my students that everyday in this class we will be mathematicians.  We will notice, describe and generalize.  Generalizing will make us efficient (I’ve found this to be a better word than fast or quick).  I craft classroom experiences that allow my students to practice these skills.
  • If students are not talking, it is my, the teacher’s, job to switch things up in the classroom.  Don’t blame the students.  I can guarantee that will never change the level of your engagement in your classroom.  I can guarantee that the small tweaks you make in your classroom will start to have an impact on your students engagement.goal

For those that attended the day long session with me.  Don’t forget the goals you set for yourself this year.

For everyone else – Please tweet me @saravdwerf or Email me at saravdw@gmail.com or comment below.  I’d love to hear your ideas for how you engage your students in productive struggle in mathematics class.  Happy Summer!  Use this time to set some goals for your classroom.

Sara VanDerWerf

I am Sara Van Der Werf, a 24-year mathematics teacher in Minneapolis Public Schools. I have taught math in grades 7-12 as well as spent several years leading mathematics at the district office. I currently teach Advanced Algebra at South High School and I'm also the current President of the Minnesota Council of Teachers of Mathematics (MCTM). I am passionate about encouraging and connecting with mathematics teachers. I'd love to connect via twitter.  Join the community.  Tweet me @saravdwerf.

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