education | MathMinds

I have blogged a few times about problem posing using print materials and lately I’ve become really interested and excited about the potential for digital tools in this work!

If you are new to problem posing, below are a few slides from Jinfa and my NCSM presentation for background – each image is linked to an associated research paper.

What is problem posing?

Many activities can easily be adapted to provide opportunities for problem posing by removing task questions (left) and replacing it with different prompt options (right).

How can digital tools enhance problem-posing experiences?

Being relatively new to both problem posing and digital lessons, I have learned so much trying things out in math classes this year. As always, the more I learn, the more questions/ideas I have. Below are two digital lessons that involve different flavors of problem posing.

Lesson 1: Our Curious Classroom

You can click through the lesson screens to see the full flow, but in a nutshell, students answer questions about themselves and explore different data displays.

After answering the first survey question, we asked students for problems they could answer about their class data and recorded their responses (sorry for the blurry image, I had to screenshot from a video clip:).

The students then worked at their table to answer the questions based on their choice of display.

The lesson continues with more survey questions, data display exploration, and ends with students personalizing their own curioso character (see bottom of post for unrelated, cute idea).

Things I learned:

Student responses can be collected and displayed so quickly with digital which saved us more instructional time for posing and solving problems.
The capability to see data displays dynamically change from one to another enhanced the discussion about which display was most helpful to answer the problems and why.
Students were so motivated to answer questions about themselves, learn about their classmates (audio clip below), and ask and answer questions about their own class, not a fictitious one.

“What did you like about the lesson?”

Things I wonder:

While having the teacher record the questions on the board worked perfectly, I wonder if or how younger students might digitally input their own questions w/o wearing headphones for voice to text or having spelling errors that are challenging for others to interpret? Maybe something like a bank of refrigerator magnets to choose from?
During the lesson, could the teacher input student questions onto cards in the Card Sort in Desmos so they could then sort the problems based on structure before solving?

Lesson 2: Puppy Pile

In this lesson, students generate a class collection of animals, are introduced to scaled bar graphs, and create scaled bar graphs. This one has a different problem-posing structure than the the first lesson which was interesting!

In this lesson, students use the Challenge Creator feature. In order to pose their problem to the class, students create their own set of animals (left) and then select a scale and create a bar graph (right).

After submitting their challenge, students then pick up one another’s problems and solve them.

Things I learned:

Students were extremely motivated to create their own problems and solve the problems of others.
This version of problem posing allowed students to have more control over the situation around which they were formulating problems, which they really enjoyed.
Challenge Creator is an amazing tool for repeated practice that is MUCH more engaging than a worksheet of problems.

Things I wonder:

How could this activity structure support or extend the problem posing experience in Lesson 1?
What other K-5 math concepts would be great candidates for a Challenge Creator problem-posing activity?

Final thoughts

I think problem posing is such an important instructional structure whether done in print, digital, or a hybrid of the two. It is important, however, to also consider the math, student motivation, and amount of time students spend engaging in the problem-posing process when choosing the format we use.

I would love to hear about what you try, learn, and wonder whether you try these lessons or adapt other lessons for problem posing!

Unrelated by Adorable Idea…

After Lesson 1, Katie printed out their personalized Curiosos for the wall;)

The Lesson

Last week, it was the first 3rd grade lesson about division. We decided to launch by mathematizing Dozens of Doughnuts to set the stage for the subsequent activities. If you haven’t read the book before, it is about a bear named LouAnn who keeps baking 12 doughnuts to share with a different number of guests who arrive at her door. We read the book and did a notice and wonder, anticipating we would hear something about LouAnn sharing doughnuts and the number of doughnuts, friends, or plates, which we did.

Student Displays

We then asked small groups to record all they ways that LouAnn shared her doughnuts. We purposefully didn’t specify the representation so they could look for different ways during the gallery walk.

As we walked around it was great to see the various ways students were representing the situations, but some small groups seemed to have settled on only one way. We had planned for them to look for similar and different ways during the gallery walk, but that can be so passive, with no opportunity for them to connect those new ideas to their work. So, instead of waiting for the gallery walk at the end, we decided to engage them mid-activity with each other’s ideas and allow time for them to use those ideas.

Taking a page from Tracy’s book, Becoming the Math Teacher You Wish You Had, we opted for a Walk-Around to cross pollinate ideas. We asked students to walk around and look for ideas they wanted to add to their poster. These could be new ideas or just a different way of representing an idea they already had.

You would have thought we gave them a chance to ‘cheat’ as they walked around with such intention to other’s posters. I wish I had captured the before and afters of all of their posters, but here are just a few where you can see the new addition of ideas.

After they finished adding to their posters, we paused to discuss the ideas they found from others – both new ideas they hadn’t thought about and ideas they had, but were represented in different ways.