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How to teach math
David Woodside, a seventh-grade math teacher at Taft Junior High in Oklahoma City, reviews a problem on the smart board. Credit: Ron Feemster

This is an exciting time to be a mathematics teacher-educator.

In the past two decades, we have developed a much better understanding not only of how children learn math, but also of how to teach math – and how to prepare teachers to teach math. A short (though incomplete) list of teaching practices that we know work to support student learning includes posing challenging tasks that connect to children’s prior understandings and out-of-school experiences, providing opportunities for children to make sense of and talk about mathematics, and promoting the use of mental mathematics based on patterns in our number system.

Yet it is also a challenging time to be a mathematics teacher educator because these teaching practices are not being used in most classrooms and schools. Further, there are many constraints limiting the use of these practices — ranging from high-stakes testing to crumbling schools.

Related: Stop all the testing in math and set free a generation of American mathematicians

Here, I am advocating for an approach to mathematics teacher preparation that takes seriously our responsibility to support novice teachers in making small changes in the status quo of mathematics teaching while working together with teachers to create more transformational changes.

“The best mathematics teachers will be the ones who have been prepared to empower their students as mathematicians and to teach students that mathematics makes sense.”

At the level of the individual teacher, we have found that preparing teachers to make small changes in status quo practices and tools can be a successful approach that is both manageable for teachers and meaningful for their students. In my work with novice teachers, the small changes I emphasize most include:

1) Ask students “why” at least once every day. Why did that strategy work? Why does that strategy make sense? Why would this work for all numbers?

Related: Memorizers are the lowest achievers and other common core math surprises

2) Instead of looking only for whether a student’s answer was right or wrong, focus on what was right in the student’s work. Then build on what the student did understand in your next discussion and next task.

3) Use your textbook as a tool. Find meaningful tasks in the materials — or tasks that could be meaningful and accessible for students with small changes in numbers or contexts.

4) Provide at least one opportunity each day for students to solve and explain problems mentally (without pencils, paper, calculators, or computers). This promotes students’ sensemaking, creativity and, most importantly, their sense that they are mathematicians.

At the heart of all of these changes is the idea that children learn best when they have opportunities to explore and make sense of mathematics and when teachers have opportunities to hear and respond to children’s ideas.

Related: Catch them before they fall: A summer math program aims to improve odds for success in algebra

While these kinds of small changes can help teachers develop their teaching practices and can lead to increased learning for their students, classroom-level changes will ultimately only lead to, at best, incremental change in the status quo of the larger systems of mathematics education in the United States. However, expecting teachers to have the sole burden for changing these systems is not only ineffective, but also ethically problematic.

Thus, as teacher educators, we must also work together with teacher candidates and teachers to advocate for systematic changes in systems that continue to perpetuate oppression in mathematics education, that allow for the same groups of students to be denied opportunities to learn rigorous mathematics year after year, and that are silent in the face of crumbling and unhealthy school buildings.

To this end, teacher educators and teacher preparation programs must engage together with prospective and practicing teachers in work that: values advocacy skills and a sense of agency as important aspects of teaching; insures all students have access to relevant high-level curriculum; utilizes assessments that reflect the content and practices that we want all students to know and be able to do and supports students in reaching those goals; and understands schools are just one part of communities and that schools and students cannot be healthy unless and until their communities are healthy.

Related: Why is this Common Core math problem so hard? Supporters respond to quiz that went viral

I began this essay noting that this is both a challenging and exciting time to be preparing teachers to teach mathematics. The challenge is that the goal of providing meaningful and equitable mathematic education to all students has been a persistent, yet elusive, goal in the United States for many decades.

The excitement comes from the knowledge that we know what to do — in both K-12 and higher education — to prepare teachers to teach mathematics in meaningful and equitable ways. It should go without saying that the kinds of work described above require teachers who know their mathematics content well. However, the best mathematics teachers will be the ones who have been prepared to empower their students as mathematicians and to teach students that mathematics makes sense.

We know how to do this, but we need to be willing to work together across all of our communities to make the kinds of instructional practices and systemic changes described above accessible to every teacher and every student in the United States.

Corey Drake is associate professor of teacher education and director of teacher preparation at Michigan State University’s College of Education. She would like to thank Tonia Land, Tonya Bartell, Erin Turner, Julia Aguirre, Mary Foote, Amy Roth McDuffie, and Terry Flennaugh for pushing her thinking and work in mathematics teacher preparation.

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  1. Being a science teacher for twenty years, I agree and disagree with some parts of the article at the same time. It is true that the teaching of maths and science should be related to students’ lives, by giving them examples of where we can use this certain knowledge in real life to benefit ourselves. On the other hand, math tests are necessary because understanding of mathematics is like a chain reaction – to succeed it needs every single ring of the chain- therefore a student must certify that is eligible to proceed to the next math level. I think that nowadays one of the reasons that students find hard to understand maths and science is because they are used so much to the computer’s environment, which is very easy to use and doesn’t require much thinking. Comparing my students today with the students I had 20 years ago, I think that the last had more imagination in finding ways to solve problems and more creativity. Maybe that is the reason why although most young people can use a computer easily, few become programmers – perhaps because programming requires mathematical logic (i.e. algorithms) . I really don’t know how the educational system works in Canada and the U.S. , but from what i see in Greece, changes have to take place, but we should not forget that whatever the changes will be, the teaching of maths requires precision, clarity in definitions and a large variety of examples used by the teacher, that will work as a spark in an attempt to challenge students’ minds.
    With regards, Kostas Zournas, physicist in DeLaSalle High school, Thessaloniki, Greece

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