FAQ: The Value of Math Rebellion

I’ve been getting questions about my Math Journaling Adventures books:

“I’m so excited to try math journaling! We bought your Logbook Alpha, and my 11-year-old math-averse son is trying to be a math rebel at every turn.

“But I feel uncomfortable with the idea of rebellion. Doesn’t he need to learn how to solve math problems the right way?”

One of my favorite things about math is that there really is no “right” way to solve math problems.

As I pointed out in my ongoing Mental Math series, even a problem as basic as 6+8 can be approached from many directions. So perhaps I should say, the “right” way is however the student wants to make sense of the problem.

In math, sense-making and reasoning are always the most important things.

Math Rebels Learn More

The math rebellion is not anti-authority. Rather, it encourages creativity and understanding.

Math Rebels try to answer homework problems in a way the textbook would not expect. As I explain in my books:

Math rebels write any true answer except what the textbook expects. For example, if the textbook answer is 57, a rebel might write:

100 − 43

Or (120/2) + (−3)

Or “The total number of mushrooms in the basket, if three hobbits each picked nineteen ’shrooms (not counting the ones they ate).”

Math rebels can make the answer as crazy as they like. Have fun!

We rebel against the rigidity of textbook rules and procedures because we know that math is a vast landscape with many paths. The farther we explore this landscape, the broader our knowledge grows.

Math Rebels fight for three principles: Truth, Justice, and Creative Reasoning.

• Truth: We learn to make sense of mathematics so we can make true statements and avoid false ones.

• Justice: We value justification, the ability to explain our reasoning.

• Creative Reasoning: We understand equivalence, that there are many ways to state a mathematical truth, and we take delight in the unexpected answer.

These principles make a math rebel’s learning much deeper than that of a student who merely reads a textbook and follows the procedures.

Follow the Two Rules

Master teacher W. W. Sawyer explained the two rules of the math rebellion in his book, Vision in Elementary Mathematics:
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“In the beginnings of arithmetic and algebra, the main purpose is not to get the pupil making calculations. The main purpose is to get him into the habit of thinking, and to show him that he can think the problems out for himself.

“Pupils ask ‘Am I allowed to do this?’ as if we were playing a game with certain rules.

“A pupil is allowed to write anything that is true, and not allowed to write anything untrue!

“These are the only rules of mathematics.”

—W. W. Sawyer

If your son follows those two rules, he will be well on his way toward success in math.