Daily Math Thoughts

#1  April 9, 2019.  Growing up I remember a box located by the front door of free booklets titled ‘Our Daily Bread’ given away for free at my church.  Each booklet was approximately the size of a 3×5 index card and contained a 1-page reflection for each day in the next 3 months.  When visiting my grandparents on the farm in South Dakota, they would end each evening with all of us gathered around to read the short reflection of the day from this same booklet.  Each reflection included a few paragraphs, a quote, a verse from the Bible and space to reflect.  The short reflections each evening centered us and challenged us in some way.  It is a great memory of my childhood.

20 years into my career as a math teacher I realized I had adopted this habit of my youth into my practice as a teacher – except instead of a tiny booklet, I had collected tons of visuals that without words helped me reflect on my practice and challenged me to do something better.  I even once blogged about 31 of these visuals I made into a calendar of sorts. You can see those 31 visuals HERE.

Starting today, I plan to regularly (not daily, but regularly) start sharing these visuals with you, with a few short paragraphs meant to help you reflect on your own practice and/or challenge you in some way.  You will find these visuals posted both to my blog, saravanderwerf.com, and on my Instagram account @saravanderwerf.  Let me know what you think. 

# 7 April 15, 2019

The story I’ve made up looking at the woman in this picture is that this powerful woman is working hour and hours everyday to make everyone in her work and personal life better. She is working too many hours and when given the chance to relax she works even more. Tonight she worked a long day and picked up her favorite pizza so when she got home she could continue working. Instead her sheer exhaustion let her fall asleep and not fully enjoy the pizza she spent her hard earned money on. 

To me, this is a picture of too many of the math teachers I know. You all are working too many hours (in an impossible job) to meet the needs of each and every student, to satisfy all the demands put on you by your school, district and state and be everything your family needs you to be. You work doing all these things except you are not taking care of yourself first. And this (small??) mistake means you are not fully present to enjoy your students or take joy in your family interactions. The things you’ve invested in have slipped and become unusable. This is not due to your lack of work, but because of your lack of rest. 

Someone out there needs to hear this today. You will be a better teacher and a better member of your family if you take care of yourself first. Yep, you really don’t seem to have time to do this, but you really don’t have time not to. Put aside something that is not necessary. Say ‘no’ to something you really feel you should say ‘yes’ to. The way you say ‘no’ when asked is to simply say, “No, unfortunately I don’t have time for this right now. I already have an event that evening I can’t get out of.” The person asking does not need to know that what you are busy with is an evening at home in front of silly TV and going to bed early. You don’t have to explain the need for time for you to refresh yourself.

Copy this link and read Greta Bergman’s blog related to this issue: https://countjoy12.wordpress.com/2016/11/01/lets-be-real/

#mtbos #iteachmath#dailymaththoughts #mathvisuals #math #mathematics

# 6 April 14, 2019

Julian Assange was arrested this week in London at the Ecuadorian Embassy.  I caught the news coverage  of the arrest while relaxing at a cabin on Lake Superior.  I probably should have thought about the 1st amendment rights of journalists, but here is the series of thoughts that went through my head when I saw his arrest:

Wow, he looks old.  He is 3 years younger than me, do I look that old?  Seriously, I don’t feel as old as he looks.

At age 47 he has done a lot in his life, have I done as much with my life?

Thank God that I have not had to live the last 7 years of my life a prisoner and potentially have even more years ahead of me.

I would not want to be in his shoes right now.  I am thankful for my life in MN

It is so human to compare ourselves to everyone around us.  For me, at age 50, the thoughts above were fleeting, and don’t affect how I live my life.  At age 15, this was not as true.  At 15, I looked around the spaces in school I inhabited, and I thought “I don’t have anything to share as interesting as my classroom peers”, so I hid in silence in my classrooms saying as little as possible.  Those who know me now would not recognize 15-year-old Sara – I was the poster child of a quite introvert.  I was afraid to use my voice to share what I thought. 

I think about the students that we teach in mathematics classrooms everywhere in 2019.  How as teachers do we help students embrace their identities as mathematicians willing to take risks as they make meaning out of the problems and tasks we put in front of them.  I fear too many of our math students do not engage their brains because they’ve compared their mathematical worth to those around them and found themselves to be lacking, so they disengage.  What as a math teacher can I do to not let their natural comparisons impact their actions in class? 

#mtbos #iteachmath #dailymaththoughts #mathvisuals #math #mathematics

# 5 April 13, 2019

A few days ago social media celebrated siblings.  I did not post a pic that day, but my mom did (the one shown here).  I have a younger sister and brother. We were all one year apart in school. One story told over and over again in my life goes like this.

Question posed to my sister Amy:  “Who is the smartest in your family?”

Amy: “Sara, then Paul, then me.”

Sara (me, in response): “No, no that is not right, it is Paul, then me then Amy”.

Amy: “Well, we don’t know who the smartest in our family is, but we know who the dumbest is.”

If you measured our smartness by HS GPA’s, then perhaps my ranking would have rung true.  But is a HS GPA a good measure of smartness? The truth is by any measures we are all smart and we have all succeeded in our chosen professions.  Today though, my sister is defending her doctoral thesis and will become Dr. Amy Carroll.  The amount of work & dedication it takes for anyone to achieve this, is astounding.  Today, the question, based on the measure of highest degree – will put to rest who the smartest VDW sibling is – it will be my sister Amy Sue!  I am so proud of you.  Congratulations!

In my classroom and in my language with my education peers I’ve worked on eliminating labeling any student with words like ‘low’, ‘high’, ‘smartest’….all these words group students based on academic measures that benefit some and exclude others.  Words like ‘low’ keep my focus on deficits.  This is not how I want to see students.  I want to see their assets.  EVERY SINGLE ONE OF my students bring strengths and assets to the table that make them amazing.  I want to see my students past a state testing score or their GPA. Building off of student’s strengths is going to create empowered mathematicians quicker than focusing on addressing their deficits.  The highest GPA dose not predict a student’s future potential. 

My sister did not have the highest GPA in our family, but today she has far exceeded any of us in her degrees post high school.  She has always been talented.  She brings joy to all she meets.  May I see in my students the strengths they already possess and find space to honor these strengths in my mathematics classroom. 

#mtbos #iteachmath #dailymaththoughts #mathvisuals 

#4 April 12, 2019

There has been a freak April snowstorm in Minnesota the last several days (so, so annoying – I refused to put my big puffy coat on again, it is in hibernation until late 2019). Driving to the grocery store, I drove past sign after sign with snow completely obscuring the words and symbols beneath.  YET – every car stopped and waited for a moment as they approached this sign.  I too stopped.  I could not see ‘red’ or read the word ‘STOP’ – yet I knew I should stop.  The octagon shape was enough to signal my actions.

I’ve seen countless stop signs my whole life.  I’d never thought about the 3 forms of communication in the sign until today: COLOR, TEXT and SHAPE.  All communicate an action I should take.  This made me think about my mathematics classroom.

  • How am I communicating to students in several different ways/modes the same message?
  • If something obstructs my students view in some way – is there something else there they recognize to support them in their learning?
  • All kids of signs have a rectangular shape and I have no idea what those signs say – the octagon is so powerful because it is reserved for only one sign – STOP!  Am I reserving some forms of communication for what is most important?
  • What are the most important messages that I want to send to students?
  • Are words necessary?  Are shape and color enough?
  • ‘stop’ is a message I’ve seen as a driver countless times – so much so it has been something I have engaged in unconsciously until its color and text were covered in snow.   Is there some common message in my classroom like ‘show your work’ that would get more attention from students if I ‘covered’ it up somehow? 
  • Note to self – is today’s snow covering traffic signs a street version of mathematics ‘smudged math’?  (google it – good stuff!)

I’d love to hear what it is for you. Comment below.  See all my daily thoughts located on my Instagram Site. #mtbos #iteachmath #dailymaththoughts #mathvisuals


#3  April 11, 2019

I know what you are thinking….’Sara, ick, what does a picture of a toilet have to do with my mathematics classroom?’.  Stay with me.  Take a look at the photo again.  Check out the totally inconvenient distance between the toilet and the toilet paper.  Think about it – to get a hold of toilet paper you either need to have planned ahead and grabbed it before you sat down OR you have to lean forward and chance getting a bit messy OR you have to skip it all together (which is so not right, TP is something one should not skip).  Seriously, who planned this and thought this was something that would work for those using this bathroom?

This photo made me think of the arrangement of things in my classroom.  What have I not fully thought through in my own classroom that will benefit only those that plan ahead OR are those willing to have to stand up at an inconvenient time? 

One thing that comes to mind in my own classroom was the location of my classroom calculators.  I am currently against using a calculator storage system attached to the wall where students come up and check out a calculator.  I believe that unless I am teaching a topic related to building numeracy, students should have access to calculators always.  This means that my students who can not add 5 and 12 without a calculator can still engage in learning grade level standards.  For this reason I have a bin of calculators at every table in my classroom, within hands reach of students always.  I do this so that students who did not plan ahead at the start of class to grab a calculator do not have to reveal their need for a calculator by having to stand up to go get one.  When I’ve stored calculators anywhere else other than on a students table, those students who need them the most will not use them.  Having to stand up to get one would reveal their perceived low status in the classroom.  Putting calculators at each table and having them there always has been a game changer for my students who need them the most. 

BONUS Hot Tip!  Because I want my students with the most fragile numeracy skills to use calculators I daily say the phrase “EVERYONE, grab a calculator and type into it ‘3 times 14’”. (obviously, what I have them type in changes from day to day based on what we are learning in class).  I say ‘everyone’ and wait to until I see everyone grab a calculator to make a safe space for my students who need to use this tool to begin using it. 

I challenge you to look around your classroom with new eyes.  What item is in a location inconvenient to students, particularly the students that need these things the most?  For me it was calculators.  I’d love to hear what it is for you.  Comment below. 

#mtbos #iteachmath #dailymaththoughts #mathvisuals

Read all my Daily Math Thoughts on my Instagram page at www.instagram.com/saravanderwerf/

#2  April 10, 2019

Last week I was in San Diego for the annual National Council of Mathematics Teacher conference. My first 2 mornings there I was lucky to be invited out for breakfast by two different math mentors of mine. 

Day 1 I met my mentor in the lobby of my hotel.  He has been to SD often and leads me as we walk to breakfast.  We arrive and he recommends something to eat (Dutch pancakes – a favorite of my Dutch heritage).  I follow his lead, arrive safely and start my conference with a full stomach.

Day 2 I get a text from my other mentor to meet at Richard Walkers Pancake House.  I look-up the restaurant on my phone and realize that it is the exact same place as I went the day before.  The day prior. even though I had walked past restaurant signage and looked at the restaurants menus, I never registered the name of the establishment.  Here is the other thing – even though I had walked a very simple route the previous morning  I had no idea how to get to the same exact restaurant and had to enter my destination into the Google Maps App on my phone. 

As I walked the eight-tenths of a mile I thought about how many of us teach math each day.  We lead our students in the math skill of the day.  Our students follow us and mimic our every movement arriving safely at our destination (learning goal) of the day.   We eat (practice the skill) and are satisfied.  Later we ask students to go to the same destination (perform the skill shown the day/week prior) on their own and they fail. 

My wondering for us all today is what would have happened if day one at breakfast I had been forced to figure out how to go where I was going?  Would have I been able to get to breakfast the next day on my own? Would I have actually registered the name of the restaurant.  My guess is, yes I could and would have.

My challenge for myself (and you) is to consider how much of my teaching is leading students so that they are unable to do the mathematics on their own without me.  How does this change how I plan my instruction?

#mtbos #iteachmath #dailymaththoughts #mathvisuals

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