The Math Wars: What's Most Important in Math Instruction?

Since the dawn of time (or roughly thereabout), people have debated what is most important in a math class. Whether you're talking about the 1920s, the 1950s, the 1980s, or today, the substance of the debate hasn't changed much. It essentially comes down to the question of what to prioritize in math and, by extension, the best way to teach math. The two sides are (1) deeply exploring concepts through inquiry as a path to build strong problem-solving skills or (2) clear, step-by-step instruction that leads to fluency with procedures.

The impact of this back and forth is that school math instruction regularly swings back and forth between two extremes: step-by-step instruction of procedures and inquiry-based exploration of concepts. This creates a problematic situation for students because the way they're learning math and the messaging about what is important can change every few years, sometimes from one year to the next. 

In an attempt to settle this debate, the National Research Council commissioned a panel of the top researchers in math education to review and synthesize the available research on how students learn math and the best practices for teaching math and training math teachers. Their findings are available in a report titled, Adding It Up: Helping Children Learn Mathematics, and their answer to what is most important in math education is this:

"A claim used to advocate movement in one direction is that mathematics is bound by history and culture, that students learn by creating mathematics through their own investigations of problematic situations, and that teachers should set up situations and then step aside so that students can learn. A countervailing claim is that mathematics is universal and eternal, that students learn by absorbing clearly presented ideas and remembering them, and that teachers should offer careful explanations followed by organized opportunities for students to connect, rehearse, and review what they have learned. The trouble with these claims is not that one is true and the other false; it is that both are incomplete. They fail to capture the complexity of mathematics, of learning, and of teaching.  [...] Mathematics is invented, and it is discovered as well. Students learn it on their own, and they learn it from others, most especially their teachers. If students are to become proficient in mathematics, teaching must create learning opportunities both constrained and open."

Essentially, Adding It Up's summary of the research indicates that time to explore concepts and clear explanations of procedures are important. This is because being truly proficient in mathematics isn't as simple as having one set of skills, such as strong conceptual understanding or strong procedural fluency. Rather, it is made of five interwoven components. Adding It Up defines and explains the five interwoven and interdependent strands of mathematical proficiency, and I'll dive into those in next week's newsletter. (Sign up for my newsletter here.)

In the meantime, your takeaway about the Math Wars should be this: Anyone who is talking about math instruction and saying, "This is the most important part of math," or "Math instruction should always look like ______," is likely oversimplifying math instruction. The Math Wars are, at best, discussing math in terms that are incomplete. At worst, these narrow views of math instruction are actively harming the students caught in the back and forth.