Monthly Archives: January 2017

Students Know

Students know.

This post was written as part of the 2017 MTBoS Blogging Initiative, in response to the prompt “We all fall down.”  (mtbos stands for math-twitter-blog-o-sphere)

When I was finishing my graduate degree, I was hired to teach my first college art class.  I was really proud of being the “professor.”  I would come to class and say all of the things that I thought the professor should say.  I had had some really wise teachers who showed up to class and gave really wise commentary about art, and I thought that what I was supposed to do was to emulate their behavior, and say wise things.  I remember that there were a lot of students so we had divided up the first formal critique into two days.  On the first day, I acted the part that I thought I had been hired to act.  I said things that sounded like what an art professor should say.

The students saw right through it.  They could tell that I was just playing a part.  It was a miserable day both for them and for me.  I really reflected about this, and was determined for day 2 to be different.  But I was scared too.  If I didn’t say the things that were my idea of what someone in that role should say, what would I have to contribute?  I went to class ready for it to be even worse than the first day.

I don’t know if I said anything wise or deep or even if I gave any meaningful feedback that day, but I was honest.  And students were totally different.  They were actively listening to me and to each other.  They could immediately sense that there was a difference between the two days of critique.  What they wanted was not my idea of an art teacher.  What they wanted was honesty.  As soon as I just acted like myself, they were willing to be on the journey together – even if they had an inexperienced captain.

As a math teacher, I have been so grateful to have made these mistakes in the art classroom.  I had so many art students who were much more gifted artists than I, that I didn’t feel threatened when my math students would catch on to something new before I did, or would think of a more elegant solution than the one I had in mind.  I learned to be comfortable with not knowing as an artist, and have translated these important lessons to my math classroom.  When I catch myself trying to be wise or trying to sound like something I’m not, I remember that first critique day.  Students know.

Read and Share: Some Important Voices in My Classroom

This post was written as part of the 2017 MTBoS Blogging Initiative, in response to the prompt Read and Share.  (mtbos stands for math-twitter-blog-o-sphere)

My math teaching jobs have been at small schools, where I have been the only one teaching my courses.  While I have had great colleagues, I have never had a group of math teachers at my own school to collaborate with.  As a result, the MTBoS has been hugely important to my development as a teacher, and while there are far too many amazing and generous educators who have changed my teaching to list here, I thought that I would share a few of the voices who have had the greatest day-to-day impact in my own classroom, and have linked their name to a recent post that taught me something or caused me to reflect on my practice.  Most of these will not be a surprise to anyone who knows what the letters in MTBoS stand for.

Here’s a student sketching one of Dan Meyer’s Graphing Stories, which has been projected on the whiteboard

Dan Meyer: For me, he is among the most important voices in contemporary math education. I incorporate his ideas about how to make math education meaningful and relevant for my students into my classroom everyday.  But in addition, I follow closely his open minded approach, and his attitudes toward having a productive conversation even with someone who starts from the premise of disagreement, or even a critic who begins by hating on him.

Fawn Nguyen – What can you say about Fawn? Her brash and direct writing give her the room to discuss what it means to really care about your students, and to share he joy of mathematics and the empowerment that comes from learning how to be a problem solver. I will read every word that Fawn writes for us.

A pattern from Fawn’s excellent visual

Nora Oswald – No one can gamify math like Nora. Her activities (or at least the structure of her games) make appearances in my classes at least a couple of times a year. Her structures seem to provoke the healthy kind of competition – where students want to push themselves without keeping the other team down.

The Desmos Team – The desmos team models how to be learners.  They are continually responsive to the community and to improving the calculator and the experience for users.

Kalid Azad – I just recently discovered Kalid’s work when I was looking for a better way to explain the graph of the sine function with radian scale. He has a knack for sharing straightforward examples and ways of thinking about math that focus on conceptual understanding.  The linked post definitely had an immediate impact on my class the next day, and I am making my way through his older work to see where else it might lend new insights for me and for my students.

Ben Orlin – Math with Bad Drawings is insightful, entertaining, and true.  Harder to say exactly what I bring into my classroom, but I find myself thinking of his posts often when I’m with students.

David Wees – In addition to the contributions of the New Visions work to my own Algebra curriculum, reading this blog regularly adds a tweak to one of my instructional routines, or adds depth to my formative assessments.

Jo Boaler – her work with youcubed is a really important voice in promoting equity in math education.  As a feminist, my goal to promote equity, uncover unconscious bias, and create opportunities for ALL students is at the core of why I became a teacher, and in fact at the core of my personal values outside of being a teacher.

Whose voices are most important to your teaching, and how do they show up in your classroom?

MTBoS 2017 Soft Skills: My Grade 8 Exit Trip

Here is an excerpt from something I read to students before we get on the bus to leave for our end of middle school overnight trip.  It comes from Joe Ehrmann, a former NFL football star and volunteer coach for the Gilman high school football team .  This comes from the book Season of Life, which I originally read about at Delancey Place.

” ‘What is our job?’ Biff asked on behalf of himself, Joe, and the eight other assistant coaches.

” ‘To love us,’ most of the boys yelled back. The older boys had already been through this routine more than enough times to know the proper answer. The younger boys, new to Gilman football, would soon catch on.

” ‘And what is your job?’ Biff shot back.

‘To love each other,’ the boys responded. “

This post was written in response to Sam Shah’s week 2 mission from the 2017 MTBoS Blogging Initiative: #MTBoSBlogsplosion (mtbos stands for math-twitter-blog-o-sphere). Sam suggested that we focus this week on “soft skills” – the things that we do to help kids grow that aren’t necessarily directly teaching math.  I’ve written here about an overnight trip that I organize at the end of the grade 8 year, including some specifics of the activities that we do to help bring us together.

I believe that as a teacher, helping kids to be confident, and to care about and respect each other is equal in importance to any math skills.  I try to design many lessons to provide opportunities for both of these things – a balance between problem solving, individual reflection, and social behaviors.  These are typically not at odds with each other – teaching problem solving and math skill building does help to boost confidence, and opens more doors for a whole student, however I try to be deliberate about also choreographing social opportunities.  I also include lots of small things in our classroom routines that are there just to build relationships – things which are not specifically math, but which are directed at helping kids to understand how to treat each other, and how to be self-fulfilled, and how to reach their “personal best.”  The Grade 8 exit trip is designed with this in mind.

I am deliberate about using the words field “work” rather than field “trips” when I am off campus with students.  This language makes it clear that we are not passive observers, but instead that we are purposeful in our activities.  I tried to design this trip with this in mind, and had to articulate what I want students to get out of this trip:

  • I want to mark the end of middle school, and entrance to high school as an important benchmark.  This is a big deal for students, and I want to honor this.
  • We should make sure to look back.  They should have some opportunities to reflect on their time as middle schoolers, and to celebrate their personal successes, and the successes of their peers.
  • We should make sure to look forward.  What are they looking forward to?  What fears do they have?
  • We should make opportunities for them to showcase their content skills – writing, performing, problem solving.
  • We should showcase that we value students as whole people – young adults who have idiosyncratic strengths.
  • We should have fun so we have a positive framework to look back on.

We start the day by gathering around a metal can.  Students are given a slip of paper, and asked to write down something that they want to leave behind from middle school.  I tell kids that the move to High School is an opportunity to re-invent yourself, and that we all have things that we want to leave behind and change about ourselves or about our feelings toward some others.  We then toss our slips into the can, and set them on fire – metaphorically “burning our baggage.”  While we are in our circle around the baggage can, I read the rest of the anecdote quoted above to the group.  The message is that whatever ideas we have about each other, we can also find positives, and for this trip, we set aside any issues, and focus on loving each other, and showing that love to each other.

Next, we all draw names from a hat, which contains everyone’s name from the class.  During the bus ride, students are asked to think of something that they appreciate about the person whose name they have drawn.  When we get off of the bus, we begin with an “appreciation circle” where students are asked to share these acknowledgements of their peers.  Our next task is a hike.  I like to find a place where we have to climb up a trail to get to the top of a mountain.   We choose a hike that is as difficult as we feel we can manage for our least in-shape student (or teacher chaperone).  This gives us a metaphor to discuss when we get to the summit.  How climbing the mountain felt like a big deal, and there was complaining, but that we felt accomplished after we got to the top, and about how we helped each other to make it all the way there.  We make some explicit parallels to their middle school experience here, and then we have our second appreciation circle, where students are asked to reciprocate the appreciation that they received at the base of the hike.

After a snack, students are asked to write a short story in their journals, using the gathered group as the characters in their story.  The story includes a favorite memory from middle school,  a fear about High School, and something that they’re looking forward to in High School.  These always manage to include some of the inside jokes of the group, and highlight some of the idiosyncrasies that we love about each other.  We share back some of these, and then have a late lunch.  I always make sure to prepare some of the food for lunch.  Even if I just make a fruit salad or something, this is how we show love in my family – by feeding each other.  I let students know that this is one way that I am letting them know that I love them.

We give the kids some free time after we get to our hotel before dinner, and finish the evening with some problem solving tasks and reflection.  On day 2, we choose a site and organize some drama and analytical Social Studies activities around where we are.  After lunch, and before heading back to school, we include a closing circle where we reflect on the trip, on our time together, and on what lies ahead.

Preparing to do a Shakespeare reading in an ancient amphitheater!

In considering my students, I am most proud of those who leave my class having gained respect for themselves and for each other, and demonstrate this respect.  This does often go hand in hand with gaining confidence as problem solvers or as math thinkers, but I admit that I have had students who have totally blown it as math students (one or two who have even failed my class), but who still come to have lunch with me sometimes.  I still find some success in having built relationships, and I hope that maybe they’ll learn some math later when they’re ready.

MTBoS 2017: My favorite… tool for teaching transformations

My favorite tools for teaching transformations from parent functions are the Desmos Marbleslides. This is the first year that I have been able to use these activities to cement our learning across function families in our Algebra 2 classes. While these aren’t exactly skill and drill practice, they do seem to give students similar opportunities to do the repetitive work that is needed to build procedural fluency.

Just a few of the reasons I love these marbleslides…

  • They are consistently motivating, fun, and engaging
  • There are opportunities for creative solutions
  • They present open problems with multiple solutions, battling the idea that all math problems have exactly one answer that is in the back of the textbook!
  • As a teacher, I am always interested in and surprised by student solutions – very different from much of my grading
  • Students demonstrate perseverance through these challenges – they really want to come to solutions, and will keep working until they succeed

I made my first custom Marbleslide for students to practice transforming absolute value functions. My activity is basically an exact copy of the Desmos team’s work, but with Absolute value equations. The custom activity was very easy to build, and I am turning over some more creative ideas to explore now that I have done this.

I am pretty sure that part of our success with our understanding of transformations has come from the course map this year. We are basing this year’s sequence of topics around families of functions. We began with an informal study, just looking at shapes and appearances of graphs, and what kids of situations might be modeled by different function types, and have been adding formal analysis of each family with each new unit.  Starting with this big picture has given students a framework to fit each family into – they are connecting what is similar and what is different as they dive into each new kind of function.

It has been amazing to see – we have just gotten into trigonometry, and by the time we got to the sine function, kids were so comfortable with shifting graphs around the plane that I didn’t need to do any explicit instruction – they knew to play with the constants to get their graphs to shift in different ways, and with very little prompting from me, they argued out the differences between period and amplitude shifts.

I am excited to see how these understandings will transfer to the Desmos Drawing project this year. Last year’s students set a pretty high bar, but this year’s 10th graders are already demonstrating a deeper understanding – and 3 months earlier.  Stay tuned!

MTBoS 2017 Blogging Initiative

Happy New Year! Time to share back and collaborate again. Looking forward to seeing ideas from new bloggers and to checking in with old friends.  Note: this post originally appeared on the ExploreMTBoS site.


Welcome to the Explore the MTBoS 2017 Blogging Initiative! With the start of a new year, there is no better time to start a new blog! For those of you who have blogs, it is also the perfect time to get inspired to write again! Please join us to participate in this years blogging initiative! […]

via New Year, New Blog! — Exploring the MathTwitterBlogosphere