How Not to Teach Math

Kathy Liu Sun, a former high school math teacher who is now an assistant professor of education at Santa Clara University says too many teachers are having their students work on computers for the entire math lesson.

She writes:

Proponents argue that computer-based lessons allow students to go at their own pace and expose students to content they might not otherwise have an opportunity to see. But these benefits come at a high cost.

One of the most pressing problems is the content and focus of these digital lessons, which are often simply digital replications of traditional lecture based math lessons. (You remember these: teacher at board showing you example after example, followed by practicing a similar problem with different numbers twenty times over.)

Whether delivered digitally or in person, this type of instruction sends the wrong message about mathematics. It teaches students that mathematics is about mastering a set of procedures, rather than viewing mathematics as a creative subject that is about problem-solving and sense-making.

Research has shown that such an emphasis on mathematical procedures is not supportive of student learning and fails to help students to draw connections between key mathematical ideas, think critically, and problem-solve. These skills are particularly important for 21st Century citizenry and long-term achievement outcomes.

While your seventh grader engaging in digital math lessons might be learning pre-calculus procedures, she may not have any understanding of the underlying concepts that will be critical for future success.

Liu Sun may as well have been talking about my 13 year old self. Thanks to my Old School parents, meaning unending hours with flashcards, I had all the necessary math facts etched into my cerebral cortex. Consequently, I could solve equations with the best of them, but I didn’t understand the underlying concepts when the road kicked up. As a result, even my final math class, Algebra 2/Trig, proved difficult.

Liu Sun continues:

. . . consider how technology might genuinely support mathematical sense-making and problem-solving. A recent study conducted at Stanford University found that students who played a game that focused on the relationship between numbers, rather than memorized math facts, led to better learning outcomes.

Good educational technology, implemented at the appropriate time, can enhance math learning. Here are a few things to look for when examining technology to support mathematics learning:

  1. Exploration: The technology should provide opportunities for students to explore by conjecturing, testing out different ideas, and making mistakes. We should avoid digital learning programs that focus only on memorization or funnel students’ thinking

  2. Multiple Solution Strategies. Identify technology applications that have more than one way to solve the problems. For example, rather than using digital flashcards such as 3+4 = ?, we can identify apps that ask students to find pairs of numbers that add to 7. The latter question has many solutions such as 1 & 6, 2 & 5, 0 & 7 and supports students to understand how one whole number (in this case 7) can be broken into parts in multiple ways.

  3. Connections between concepts and procedures. Good educational technology supports students to focus on relationships, not discrete facts. Rather than choose a digital program that solely focuses on doing the same procedure over and over, identify a program that supports students to understand why the procedure works. For example, with regards to the earlier problem 3+4 = ?, a digital program that includes other representations, such as images of objects that students move around can better support to develop meaning of the procedure. Digital math games that focus solely on procedures should only be considered after students have strong understanding between concepts and procedures.

Like a wannabe Maggie Z, humble blog loyalist and middle school math teacher extraordinaire, I’m only going to assign Liu Sun partial credit for her blog post because she stops short of identifying any specific technology applications that check the three aforementioned boxes.

Thus proving blogging is harder than it looks.

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