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.

[UPDATE] – Facebook has removed our video — maybe we were too awesome?? So I’ve included three short snippets from other live workshops here:

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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!

How Can We Anticipate to Fuel Sense Making? Stretching Trees

Are you looking to avoid “Lesson Flops” and bring on a “Lesson Successes?” I sure do. That’s why I plan with anticipation of student thinking in mind.

I want to share a lesson I co-created with Brian McBain and teachers at Wallaceburg Secondary School and how anticipating student thinking helped avoid those flops!

Let’s run through the lesson first, then I’ll give you a window into how we planned it.

In random groupings students went to their wall space and were presented this first task.

I have to admit when we planned it we anticipated everyone to draw Christmas trees but after showing the image they all drew a variation of the one above.

Drawing the trees was no biggie since our new amazing whiteboards from Wipebook.ca (wipebook.com) has grids on them. Students counted up 20 units and drew their very best tree! Onto the next part of the lesson.

Draw another tree that has a height that is less than 50% of the first tree’s height.

Here is a typical drawing from my students.

In small groupings and also as a whole class I asked and discussed “How do you know the height is less than 50% of the original tree?”

And then we moved onto this…

Draw a tree with a height that is more than 50% of the original tree’s height.

With this prompt we wanted to dive into the answers a bit more. “How do you know it’s more than 50%?” “How can we verify that 16 units high is more than 50%?” Also with this we had students drawing trees higher than 100%. We paused the class and verified and shared out the different tree heights around the room.

I prompted them to draw a tree that was exactly 30% of the original tree’s height.

This is where I was super interested to see how they would solve this. Their solutions were going to fuel the discussion going forward (Check below to see how we anticipated what they would do).

Most groups of students used the grid and found a unit rate. Can figure out this strategy?

This group knew that 10 units would be 50% so they took the 50% and divided it up into 10 units giving 5% per unit. Then they counted up by 5s until they reached 30% and got 6 units high. Other groups took the whole 100% and divided it by 20 to get 5%/unit. As a class we gathered around these solutions and explained the strategy. Any group that was stuck went back to their boards to use this newly presented strategy and the other groups pushed forward with this new prompt.

Groups progressed through this prompt at different times, but when they were ready I gave them this one: “Draw a tree with a height that is exactly 62% of the original tree.”

This is where the struggles happened. Again we were interested in HOW students solved this problem. Most new that 60 was going to be 12 units high….and then just estimated from there how high the tree would be. Some did guess and check to narrow down how high exactly 62% was. This was exactly what we had planned. We had wanted and led the students here to create this struggle so that we could step in and teach them a strategy!!

We used a double number line: One side showing percent from 0 to 100 and the other side showing the heights of the tree. But instead of a horizontal number line we tipped it up and made it vertical!

We had a discussion on proportions: “Is this a proportional relationship?” “How do we know?” Yes….so we can apply a proportional strategy to solve this. After that the students had a new and improved strategy to try the next few prompts:

Draw a new tree that has a height that is 17% of the original tree’s height.

and then,

And then we switched to a new “starting” tree.

And kids drew this.

After I felt that groups were comfortable, their next task was given out (which stretched into day 2). We changed the scenario from trees to colouring.

Want to get the PDF with all the image prompts and handouts? Click Here.

When reflecting back this lesson was not one of the “flops” it was a “success” and most of the credit has to go to planning with anticipation in mind.

Anticipating to Fuel Sense Making

When Brian, the team, and I set out to design this lesson we were looking for a way for students to feel like they weren’t learning something new. That they could take the idea of percent and just use it like they have already solved proportion problems. We also wanted students to follow the Hero’s Journey and feel that there was a definite need to use a proportion strategy.

Here is what the early stages of the planning process looked like. Yep, scribbles in a journal. We spent a lot time thinking about the right progression of prompts so that we could maximize student work and use their strategies to push learning forward.

We also spent a great deal of time planning out the different strategies we thought students would use to solve the original prompt “Draw a tree that is 30% of the original tree’s height”

We outlined the strategy of finding the unit rate of 5% per unit, we thought many students would already know the “rule”: Turn the % to a decimal and multiply (But no one did do that in my class). We thought it was possible for them to create a proportion. We thought some groups would try a guess and check strategy. Like: “I think the height is 7. Let’s see if 7 out of 20 is 30%.” Only a few groups did this.  We ranked each strategy in order of most likely to least likely.

Anticipating their solutions and strategies puts me in a better position to understand their thinking and help shape that thinking. For each possible attempt I need to be ready to provide feedback to help them achieve our goals.

We take for granted how much time is needed to prepare and anticipate adequately. It takes time to make this happen, but that time is worth every minute. Especially if it puts me in a better place to understand what my students are thinking.

This has been my assessment goal: Understand their thinking in order to push them further. That’s it! That’s the main idea.

Anticipating their thinking will always put me in a better position to fuel their sense making.

Read More: Fuel Sense Making & Black Box Defrost

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!

Instant Pot, Lego Kits, and Teaching Together

Trying to cook with my new Instant Pot it brought up some thinking I wanted to share:

Join me over on Facebook or on Twitter or in the comments below to connect. We can do this better together.

Course Outlines:

Transcript of the Video:

So I consider myself a pretty good cook. After years of cooking for my family I feel like I can look in the fridge and whip up a pretty good stir fry or any other dish from scratch. So then I got this instant pot for Christmas….. And I felt like all my cooking instincts went out the window. I pretty much know how a frying pan works and my experience helps me determine how much time to cook the vegetables for so they’re not too mushy in the stir fry or I know how long to cook chicken in the oven so it’s not too dry, but this instant pot was a mystery. I had never used pressure cooker before…..I felt lost…Right now every time I cook with it I have to follow those mom blog recipes on Pinterest. Or the step by step recipes that come with it. I have no experience with how the timing works. I could cook dinners….but have no real understanding of how I did it!

It reminds me of the time I taught Accounting a couple of years ago. Here I am a math teacher with a bunch of pedagogical strategies on how to teach math that I love using….. Like I was with cooking I felt I was a pretty confident math teacher.  I wanted to teach that accounting class like I taught my math classes (great thinking happening, great discussions, kids struggle through concepts and we chat strategies; all the great stuff I know make kids better learners….but I felt that I couldn’t do that in the accounting class. I just didn’t know the content. I didn’t know the curriculum! I needed help and the only thing I felt like I could do was follow the step by step instructions in the teacher resource guide of the textbook. And there I was teaching accounting with not really knowing accounting…all because I was blindly following the steps.

It was so clear to me right then that Knowing the curriculum matters so much if we want to get creative with our course content quickly. It took me 8 years as a traditional math teacher before I felt I was comfortable enough to start playing around with different pedagogical strategies and deviating from the way the textbook ordered its units. Think about Lego too! If you want to just build lego go for it and try things out, build a masterpiece. Master lego builders spent a lot of time learning how the pieces fit together, And they did that by creating! Lego provides step by step kits so we can all build masterpieces but do we really know how to build that Death Star? Or Lego Friends dream house? I felt like I was just good at following instructions.

When we start our math lessons off with “today we will learn about the Pythagorean theorem” and then write this thing on the board and go through examples we are just giving kids the Lego Step-by-step guide, or the instant pot recipe book. And I now have to wonder, “Are they like me with the instant pot?” It looks like they know what they are talking about but do they really understand? I have to dig deeper, I have to get more info.And I believe teaching through problem solving is one of the best ways to get that information from our students.

Letting students work through problems through their own strategies shows me so much thinking. It’s then that we can consolidate as a group to share each others strategies or I can present new ones if needed. It’s a journey! And it’ll take time for our students to become great thinkers.

Like our students we too are learning through problem solving. We’re problem solving right now how best to teach our students. We’re learning by doing. And sometimes it takes a guide to show a strategy or a different way of doing things for us to go “aha!! Then our minds change. It’ll take time for us to become better. As a beginning teacher I thought I needed a plan to follow so that I could become comfortable with the curriculum. I thought I needed a plan to follow when I started teaching accounting for the first time. What I really needed was more people to talk to so that I could become comfortable with the curriculum and classroom management, and schedules, and assessment, and learning styles, and more and more. My first plan was the textbook and my first people were my math department.

Now there are many plans we can start with, many plans we can learn from and adapt as we grow. But let’s not follow those plans blindly like I followed the accounting teacher resource guide or how absent mindlessly I follow the instant pot recipes. Let’s interact with the creators of those lesson guides, let’s figure out what works best in our classrooms for our students.

You can download my course plans if you want a starting place. But then let’s not let that interaction stop there. Let’s continue the conversation. Let’s adapt those plans together.  Join me over on Facebook or on Twitter or in the comments below to connect. We can do this better together.

By the way I joined a facebook group to learn how to cook with the instant pot…so that soon I’ll be able to create my own dinners with it.

Course Outlines: