Mathematics Education Collaborative

I used to think that if I randomly called on students it would be fair, discussions would be rich, and everyone’s ideas would be honored.  Then I met the class of introverts. Three-fourths of them were boys – sixth graders – and I couldn’t get any kind of discussion started. And cold-calling made it worse. In fact, cold-calling generates compliance, not learning, and it is especially harmful for multilingual students who often benefit from time to talk through their ideas with a trusted friend before sharing with the whole class. 

My class of introverts inspired a quest – how could I create the conditions in math class that would invite rather than compel students to share their ideas? It started with dumping the cold call practice.  When I told the class of introverts I would quit the cold calls, they cheered. That made a huge difference, especially the next year when I started fresh with a new group of students. They knew from the start they could trust me not to put them on the spot. Adam began raising his hand in April of that year. He told me in the last weeks of school, “This is the first time I have ever spoken up in math class. It’s because I am not scared you are going to call on me.”

Eventually, I met Heather and Maribel, accomplished language acquisition teachers.  I figured if anyone could help me figure out how to support students to share their ideas, it would be teachers who had spent their career thinking about language development. We worked together for a school year on the Number Talk routine, looking for ways to adjust and adapt it to invite the voices of multilingual students to the center of our classrooms.

This article, appearing in the September issue of NCTM’s Mathematics Teacher: Learning and Teaching is the result of our work together. Enjoy!

MTLT_Number Talks and Multilingual Learners

Or maybe you prefer a podcast.

Check out our May 7 episode at Rounding Up from the Math Learning Center

Most learners like it when they can do something novel, but hands-on learning has to develop mathematical understanding for students to stay engaged. That is, concrete materials have to allow students to grapple with mathematical ideas they are in the process of developing. When that happens by design, students’ thinking becomes visible to each other and to their teacher.  When students can see each others’ thinking, community develops, and when hands-on materials make it easy for teachers to see student ideas, being flexible and responsive to developing thinking becomes second nature.

High school teachers recently began a five-day workshop designed to deepen their understanding of functions with a lab involving water and vases.  Their task was to predict the graph of the height of the water in a given vase as they added increments of water, and then test their prediction.

This hands-on math got the workshop off to a very strong start. Everyone, no matter their background, understood water and vases, or measuring, or graphing. No one could accomplish the task alone. Someone had to measure, someone had to fill and another person had to record.  Soon the multi-dimensional nature of the task itself got people talking and laughing and helping each other and puzzling over results.

But more than that, the task’s focus on the relationship between an input and an output, landed participants in the center of grappling with ideas essential to understanding functions. Nearly everyone’s predictions improved as they repeated the task with vases of differing shapes, and issues of accuracy, rates of changes, and the relationship between independent and dependent variables became rich sources of conversation.

In fact, hands-on math can make visible the relationships between quantities, through relationships between people.  This is at the heart of powerful mathematics teaching and learning. Once teachers get a taste of it, they want more.