Making Math Moments That Matter – Live

What makes students remember the math they are learning? Is it because you’re using a real world problem that they can relate to? Is it because maybe you used a 3-Act task? Is it because they practiced the content over and over? Is it because you used spaced practice versus massed practice? My good friend Kyle Pearce and I believe it is much more than that.

While at Oame 2018 Kyle and I took a chance and hit record on Facebook Live during our 75 minute workshop title Going Deeper with Math Moments That Matter. If you missed it or want to learn more you can watch the whole thing right here!

Session Description:

What makes a memorable math moment? Is it a real world task? Is it relevant to your students? Is it media-rich or delivered in 3 acts? While many professional development sessions focus on a specific component of an effective math lesson, Jon Orr and Kyle Pearce will model what they believe to be the three key components of an effective mathematics lesson: sparking student curiosity, fuelling their sense making and igniting your next steps. Join them as they lead a task to break each component down and then build it all back up to create a memorable math moment.

What were your moments that you remember from math class?

What do you want your students to remember 5 years from now? Leave comments below. Or jump over to my Facebook Group and you can comment there.

Grab the Making Math Moments Matter Curious Task Template and our file with support resources over at makemathmoments.com

Thanks for being here with us!

Building Resilient & Determined Math Students

Are you frustrated with how easily some of your students just give up while doing a math problem? You know that if they just stick with it that they will learn but they just want to be hand-held through math class every day. In the book How Children Succeed: Grit, Curiosity and the hidden power of character  Paul Tough argues that students succeed not because of intelligence but because of how much stick-to-it-ness, grit, and Determination they have.

It’s not that I’m so smart, it’s just that I stay with problems longer. – Albert Einstein.

Tough says that you can build perseverance in children by playing chess. From the book, “Teaching chess is really about teaching the habits that go along with thinking,” Spiegel explained to me one morning when I visited her classroom. “Like how to understand your mistakes and how to be more aware of your thought processes.” Playing chess over and over builds up a chess player’s level of determination. They have to take risks and learn from those risks in order to succeed. If we want our math students to build up resilience and determination then we also have to push them take risks and learn from the outcome of those risks.

In math class we can build up resilience, grit and stick-to-it-ness if we put students in experiences where they have to persevere through a tough situation. But think of their whole math class experience up to this point. It’s likely that a student would  never have had the opportunity to try to solve a problem before we math teachers show them the examples and how to solve it the math teacher way. Our students need experience persevering through tough situations like the chess player.

Imagine the first time you play chess and your opponent takes your bishop early in the game. You might think the game is pretty much over. Why go on? Or think of the young basketball player who has the right footing for a layup. They definitely weren’t a pro at that the first few times. But over time in each situation players overcome that resistance and persevere. They learn to be successful.

But in math class we assume math students should be good problem solvers and have grit in our math classes immediately. We say “our students give up too quickly” but when did we ever give them time to build those perseverance skills up? When did we teach them how to persevere? We are the ones that have to give them experiences to build that skill up.

3 Tips to Prevent the “Give Up Moments” and Create resilient Problem Solvers

1. Routinely have students solve unfamiliar problems through a supportive productive struggle process.

Use the Hero’s Journey to structure your math class and create productive struggle moments daily for your students. As an example, if I didn’t push my students to solve these problems routinely on their own to start our lesson then they would not only miss gaining the experience to persevere 

but I the teacher would also miss gaining valuable information about what my students know or don’t know. Problem solving must be a regular part of learning not just a once a unit or end of unit thing.

2. Create an environment where risk taking is low stakes.

In order for students to take risks and learn how to persevere the stakes for failure have to be low. It has to be painless to make mistakes. How are we doing this in our math classes? One easy-to-implement technique to make risk-taking low stakes is to bring dry-erase boards into your classroom. The no-permanence of the boards makes risk taking easy and it’s one of my favourite things. Students can attempt strategies quickly and wipe away quickly if needed. You can read more about the research behind non-permanent surfaces from Peter Liljedahl.

3. Show students that you value perseverance:

Create an assessment routine that promotes growth instead grades. Students quickly learn what you value. If we’re saying to them daily that we value the process of their learning over the final answer then how to we prove it to them? Your actions speak loudly. Give your students room to show that they have persevered while solving problems. Learn how you can implement an assessment routine that promotes growth and resilience by watching Conall’s Assessment story:

Read more about promoting growth in your assessment here.

Disclaimer: This transformation won’t happen over night. You yourself have to be resilient and determined. It’s possible that you might not see that change even this semester. But by allowing students to productively struggle through problems, giving them a low stakes risk taking environment and proving to them you value persistence WILL build their resilience and determination in the long term. We also must have a stick-to-it-ness to build great thinkers!

Sum It Up! 

Here is a small strategy I used for our review day today.

In Advanced Functions we were reviewing average rates of change and instantaneous rates of change.

Instead of just doing problems from the book I organized the rate problems in 4 sets, polynomial, rational, trigonometric, and exponential/logarithmic functions. Each set had 3 problems.

I organized the class in groups of 3 and gave each group a set. They were to complete the problems and check the answers.

The kicker here was that the sum of the 3 answers in a set was written on the board.

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If the group got all questions correct their sum of their answers would match correctly. But…… If one was wrong they had to check all solutions and decide which needed fixing.

First, this small change made all groups work more carefully than usual. And second, when they had to double back, you could see them rationalizing which answers “had” to be correct and which answers were “toss ups”.

It was a great tool for students to self assess and evaluate their own readiness.

double desks

After each group completed a set they would swap with another group… Eventually completing all sets.

Promote Struggle – A Hero’s Journey in Math Class

While in Miami for the Apple Distinguished Educators Institute we saw a speaker from Pixar (I can’t recall his name) discuss the aspects of Story. More specifically he spoke about the Hero’s Journey. That talk really hit home for me. Below is how I interpreted his message and how it relates to my classroom.

A Hero’s Journey

All of these characters take a hero’s journey….

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Since I’m a math teacher describing the Hero’s Journey is best done with……a graph (English teachers will know it’s shown as a cycle).

On a time vs. Tension graph the Hero’s Journey looks like this: Time is the length of the journey….or story. The tension is felt by the audience. 

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In the beginning the hero is introduced, the main conflict is introduced, his/her world starts to change. As the story continues the hero must battle the forces of evil & go through struggle. They must experience conflict. It’s the conflict that the hero learns about themselves. They learn their strengths and weaknesses. It’s the struggle that makes the ending awesome. Its the struggle that make the hero see the solution. It’s the lessons they’ve learned in the struggle that let’s them go aha! I know what I need to do! The story would mean nothing to the hero and the audience if the climax was much earlier in the timeline. As the story ends the character returns to a NEW normal. They take their learning and come out stronger on the other side. 

This curve we see above is nothing new to us. This curve is what learners go through. It’s a Learner’s Journey too.

Now, if we take a look at our traditional math classrooms we have a format much like this:

Photo credit: Kyle Pearce

Photo credit: Kyle Pearce

Let’s look at that structure on the Time Tension graph. 

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After we take up homework, we introduce the new lesson or topic or problem to work on. It’s unfamiliar so tension in our students starts to increase.  But what happens is that as the tension rises it immediately falls back down. And my good buddy Kyle Pearce mentioned to me that the tension doesn’t fall all the way back to the axis….a good number of our students feel that tension permanently. 

Why does the tension fall immediately?

We make that happen. We relieve students of their pain by immediately telling them HOW to solve the problem.

Screen Shot 2015-11-17 at 9.59.24 PMIt’s Our examples & solutions. Students don’t get a chance to struggle & discover, Therefore the math formula, strategy or algorithm means nothing to them! The memorizers will memorize and do ok, and the non-memorizers lose again. The ideas and strategies have no real value to them. 

I think students should feel the need for the math they learn. They should experience struggle ….just like the hero.Screen Shot 2015-11-17 at 10.20.30 PM

Let’s take the old model of our lessons and change it to match the Hero’s Journey. It’s the struggle that adds value to their learning. Let’s move the reveal of math rules etc farther in the timeline. Let’s let the students productively struggle through problems. The reveal of the “math” will mean so much more after students see and/or feel the need for it. 

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An example in my class this week came when I wanted to teach students how to determine an equation of a quadratic function when given some key points.

I gave them this simple Desmos Activity Builder slide.

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Students already knew about vertex form of a quadratic function so I knew they could put in most of this equation. It’s the “a” value that they really didn’t know how to get efficiently. So I saw a lot of this…

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Students used trial and error to find -1/4 as the right “a” value. But we then asked “How do we know that’s the right one?” We then discussed plugging in a point to check to see if the right side equals the left side. They had a few more slides just like this but with different points. By the end of the last slide you could see that they really wanted a more efficient way of determining the “a” value than guessing and checking. This is where I stepped in and we discussed the idea of using one of the points and the equation to solve for the “a” value. Everyone was on board! They all had struggled before we discovered an efficient strategy. They all wanted it. If I had started class by showing them the first slide and then just telling them how to do it, I would see lack of understanding of why and bored faces.

It’s the struggle that makes the math worth it! Let’s let our students be Heroes. How are you promoting struggle in your classroom? I would love to hear of your ways. Leave a comment below.

Click here to grab the Desmos Activity Builder Activity I showed above.

[Update: April 2018]

To help you wrap your mind around this lesson model I’ve created a Hero’s Journey Lesson Template. The exercise is to choose a lesson you have coming up in your class. How can you modify that lesson so that the flow follows a hero’s journey? Use the template below to help plan your lesson out.

Exemplar: I used the template to model how I use the Pentomino Puzzles activity to teach solving linear equations.

You can see that we slowly build up the need for a helpful efficient strategy to solve the puzzles. When my students have struggled and persevered 3 or 4 times to solve a tough puzzle, the timing is now perfect for us to step in and help them develop that skill of solving equations.

Download your copy of the Hero’s Journey Lesson Template.