As a middle-school math teacher and later an educational researcher here at the University of Minnesota’s College of Education and Human Development (CEHD), I’ve learned that math teachers must not only have a deep knowledge of math – they need to be able to effectively communicate math concepts so that students can engage in mathematics themselves.
When I began my career as a classroom teacher, I observed a wide variety of pathways to becoming a teacher, including a range of backgrounds in mathematics. This led me to conduct research that has given me insight into some of the knowledge and skills secondary math teachers need – and how we can prepare them to implement classroom activities that will help them better communicate mathematical concepts to their students.
Knowledge vs. Understanding in Math Education
Many people think the primary qualification for being a teacher is knowledge and mastery of the subject matter. By studying secondary math teacher preparation, I’ve found that most teachers come into the field with a deep background in math. The problem is that the understanding of mathematics gained through advanced university mathematics courses is not well-connected to the mathematics in the work of teaching.
For example, most teachers are able to solve any problem in a high school math textbook. But that’s not the same as explaining how to solve those problems in multiple ways so that it’s accessible to many students. It’s really about understanding math in the way that it’s needed for teaching. This understanding is its own complex skill separate from (though connected to) understanding advanced mathematics. A big part of my work is about helping teachers develop the math understanding they need for teaching. Teaching is not simply standing in front of a class to disseminate knowledge; it’s about supporting students to engage in mathematics themselves.
In some ways, teachers must break back down some of the knowledge and skills they’ve developed along the way. For example, if you learned math while studying economics or engineering, you developed a perspective that was best suited to your field. Along the way, you consolidated ideas and concepts to use them more efficiently in your chosen discipline or academic focus. As a teacher, you need to go back and “unpack” these ideas to highlight the underlying mathematical concepts at work, so that students, who are experiencing these concepts for the first time, have multiple access points to make sense of new ideas.
Five Techniques for Better Math Teachers
Improving math education and preparation programs for math teachers is a complicated task, but through my experience and research I’ve learned some general principles and strategies that are effective in helping support all students to engage in mathematics.
- Believe that all students can learn math. You must believe that every one of your students – no matter their background or current level of knowledge – is capable. Look for each student’s individual strengths and how you can leverage those strengths in the classroom. To me, this is the fundamental underlying principle of being a good teacher.
- Use rehearsals as a preparation tool. The most important things that I do in teacher preparation classes is helping my students connect the ideas that we read about to their own practice as teachers. One of the ways I do this is through “coached rehearsals.” One student will lead a discussion while the other members of the class act as the “kids.” During the rehearsal, we have the chance to stop, ask questions, and give feedback, so the discussion leader can get an idea of the kinds of dilemmas they’ll face in a classroom – without the pressure of being in front of a classroom of kids. Later, we use the process of recording video of novice teachers in the classroom and give them the opportunity to analyze their own performance and give feedback to one another.
- Explore multiple solutions to math problems. Doing math with my students is critical. When I’m teaching aspiring math teachers, we’ll do math problems that I would then have them do with their own students. During this process, we analyze the problems, looking for multiple solutions strategies. This helps them gain perspective on how their students might approach a problem. It also highlights that there are often multiple mathematically valid ways to approach a task, and the teacher’s role is to help students make connections among the different solution strategies.
- Listen. Secondary math teachers must be committed to listening to their students and understanding what they have to say about mathematics. By valuing all student contributions and building on them, you’ll help them cultivate a deeper mathematical understanding.
- Understand that there’s no quick fix. With my students, I use multiple strategies to help them learn about teaching. Sometimes it’s rehearsals, sometimes it’s doing math tasks, sometimes we’re watching video or reading and analyzing various aspects of teaching. Having all those touchpoints is critical for me. It’s counterproductive to try and have a quick fix or to think that there’s one technique that will work all the time. Teaching is tough, complex work – but with the right approach I’ve seen my aspiring math teachers – and their pupils – make tremendous strides.
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