Whose problems? Whose game? Whose puzzle?

TRU Math (Teaching for Robust Understanding) a few years ago shared their thoughts about what makes for a “Powerful Classroom”. Here are their 5 dimensions:

Looking through the dimensions here, it is obvious that some of these dimensions are discussed in detail in professional development sessions and in teacher resources. However, the dimension of Agency, Authority and Identity is often overlooked – maybe because it is much more complicated to discuss. Take a look at what this includes:

This dimension helps us as teachers consider our students’ perspectives. How are they experiencing each day? We should be reflecting on:

• Who has a voice? Who doesn’t?
• How are ideas shared between and among students?
• Who feels like they have contributed? Who doesn’t?
• Who is actively contributing? Who isn’t?

Reflecting on our students’ experiences makes us better teachers! So, I’ve been wondering:

Who created today’s problem / game / puzzle?

For most students, math class follows the same pattern:

This pattern of a lesson leaves many students disinterested, because they are not actively involved in the learning – which might lead to typical comments like, “When will we ever need this?”. This lesson format is TEACHER centered because it centers the teachers’ ideas (the teacher provides the problem, the teacher helps students, the teacher tells you if you are correct). In this example, students’ mathematical identities are not fostered. There is NO agency afforded to students. Authority solely belongs to the teachers. But there are ways to make identity / agency / authority a focus!

STUDENT driven ideas

Today as a quick warm-up, I had students solve a little pentomino puzzle.  After they finished, I asked students to create their own puzzles that others will solve.  Here is one of the student created puzzles:

Here you can see a simple puzzle. The pieces are shown that you must use, and the board is included (with a hole in the middle). Now, as a class, we have a bank of puzzles we can attempt any day (as a warm-up or if work is finished).

You can read about WHY we would do puzzles like this in math class along with some examples (Spatial Reasoning).  

What’s more important here is for us to reflect on how we are involving our own students in the creation of problems, games and puzzles in our class.  This is a low-risk way to allow everyone in class do more than just participate, they are taking ownership in their learning, and building a community of learners that value learning WITH and FROM each other!

How to involve our students?

The example above shows us a simple way to engage our students, to expand what we consider mathematics and help our students form positive mathematical identities. However, there are lots of ways to do this:

• Play a math game for a day or 2, then ask students to alter one or a few of the rules.
• Have students submit questions you might want to consider for an assessment opportunity.
• Have students look through a bank or questions / problems and ask which one(s) would be the most important ones to do.
• Give students a sheet of many questions. Ask them to only do the 3 easiest, and the 3 hardest (then lead a discussion about what makes those ones the hardest).
• Lead 3-part math lessons where students start by noticing / wondering.
• Have students design their own SolveMe mobile puzzles, visual patterns, Which One Doesn’t Belong…

Questions to Reflect on:

• Who is not contributing in your class, or doesn’t feel like they are a “math student”? Whose mathematical identities would you like to foster? How might something simple like this make a world of difference for those children?
• Does it make a difference WHO develops the thinking?
• Fostering student identities, paying attention to who has authority in your class and allowing students to take ownership is essential to build mathematicians. The feeling of belonging in this space is crucial. How are you paying attention to this? (See Matthew Effect)
• How might these ideas help you meet the varied needs within a mixed ability classroom?
• If you do have your students create their own puzzles, will you first offer a simplified version so your students get familiar with the pieces, or will you dive into having them make their own first?
• Would you prefer all of your students doing the same puzzle / game / problem, or have many puzzles / games / problems to choose from? How might this change class conversations afterward?
• As the teacher, what will you be doing when students are playing? How might listening to student thinking help you learn more about your students? (See: Noticing and Wondering: A powerful tool for assessment)

I’d love to continue the conversation about students’ identities in mathematics.  Leave a comment here or on Twitter @MarkChubb3

Math Games – building a foundation for mathematical reasoning

In 2001, the National Research Council, in their report Adding it up: Helping children learn mathematics, sought to address a concern expressed by many Americans: that too few students in our schools are successfully acquiring the mathematical knowledge, skill, and confidence they need to use the mathematics they have learned.

Developing Mathematical Proficiency
The potential of different types of tasks for student learning, 2017

As we start a new school year, I expect many teachers, schools and districts to begin conversations surrounding assessment and wondering how to start learning given students who might be “behind”. I’ve shared my thoughts about how we should NOT start a school year, but I wanted to offer some alternatives in this post surrounding a piece often overlooked — our students’ confidence (including student agency, ownership and identity). If we are truly interested in starting a year off successfully, then we need to spend time allowing our students to see themselves in the math they are doing… and to see their strengths, not their deficits.

[The] goal is to support all students — especially those who have not been academically successful in the past — to develop a sense of agency and ownership over their own learning. We want students to come to see themselves as intellectually capable and competent — not by giving them easy successes, but by engaging them as sense-makers, problem solvers, and creators of meaningful and important ideas.

MathShell – TRUMath, 2016

When we hear ideals like the above quote, what many of us see is as missing are specific examples. How DO we help our students gain confidence becomes a question most of us are left with. Adding It Up suggests that mathematical proficiency includes an intertwined mix of procedural fluency, conceptual understanding, strategic competence, adaptive reasoning and productive disposition. Which again sounds nice in theory, but in reality, these 5 pieces are not balanced in classroom materials nor in our assessment data. Not even close!

Adding It Up: helping children learn mathematics, 2001

So, again we are left with a specific need for us to build confidence in our students. There is a growing body of evidence to support the use of strategy games in math class as a purposeful way to build confidence (including student agency, authority and identity).

To be helpful, I’d like to share some examples of possible strategy games that are appropriate for all ages. Each game is a traditional game from various places around the world.

• Dara – Western Africa
• Five Field Kono – Korea
• Mū Tōrere – New Zealand
• Pong Hau K’i – China
• Shisima – Kenya
• Peg Solitaire – Western Europe

*The above files are open to view / print. If you experience difficulties accessing, you might need to use a non-educational account as your school board might be restricting your access.

How to Play:

Each link above includes a full set of rules, but you might also be interested in watching a preview of these games (thanks to WhatDoWeDoAllDay.com)

A few things to reflect on:

• Some students have missed a lot of school / learning. Our students might be entering a new grade worried about the difficulty level of the content. Beyond content, what other aspects of learning math might be a struggle for our students? How might introducing games periodically help with these struggles?
• How do you see equity playing a role in all of this? Pinpointing and focusing on student gaps often leads to inequities in experiences and outcomes. So, how can the ideas above help reduce these inequities?
• One of the best ways to tackle equity issues is to expand WHAT we consider mathematics and expand WHO is considered a math person. How might you see using games periodically as a way for us to improve in these two areas?
• If you are distance learning, how might games be an integral part of your program? How do you see including games that are not related to content helpful for our students that might struggle to learn mathematics? (building confidence, social-emotional learning skills, community, students’ identities…)
• If you are learning in person this year, but can not have students working together, how might you adapt some of these strategy games?
• What might you notice as students are playing games that you might not be able to notice otherwise?
• How might we see a link between gaining confidence through playing strategy games and improvement in mathematical reasoning?
• Why do you think I choose the games above (I searched through many)? Hopefully you can see a benefit from seeing mathematics learning from various cultures.

If interested in more games and puzzles? Take a look at some of the following posts:

• New Skyscraper Puzzle templates
• One-Hole Punch Puzzles templates
• Cuisenaire Cover-up templates
• Skyscraper Puzzles for relational rods
• Zukei Puzzle templates
• Skyscraper Puzzles (original templates)

As always, I’d love to hear your thoughts.  Leave a reply here on Twitter (@MarkChubb3)