Mental Math: Three Basic Principles

Doing mental math on the couch

“We know that algorithms are amazing human achievements, but they are not good teaching tools because mimicking step-by-step procedures can actually trap students into using less sophisticated reasoning than the problems are intended to develop.”

— Pam Harris, Math Is Figure-Out-Able Podcast

Whether you work with a math curriculum or take a less-traditional route to learning, do not be satisfied with mere pencil-and-paper competence. Instead, work on building your children’s mental math skills, because mental calculation forces a child to understand arithmetic at a much deeper level than is required by traditional pencil-and-paper methods.

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Musings: Mental Math Is the Key to Algebra

Painting by Nikolay Bogdanov-Belsky, public domain

“If you stay with meaningful mental arithmetic longer, you will find that your child, if she is average, can do problems much more advanced than the level listed for her grade. You will find that she likes arithmetic more.

    “And when she does get to abstractions, she will understand them better.

      “She will not need two or three years of work in primary grades to learn how to write out something like a subtraction problem with two-digit numbers. She can learn that in a few moments of time, if you just wait.”

      —Ruth Beechick, An Easy Start in Arithmetic

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      FAQ: The Necessity of Math Facts

      Ah, math facts — the topic that just won’t stop giving grief to students and anxiety to their parents. So it happened that I got another question, but this one leaned in a more philosophical direction…

      “I enjoyed your podcast interview on Cultivating Math Curiosity and Reasoning in Kids. I love the idea that we don’t have to make our children memorize everything in math. We can give them freedom to make mental connections for themselves.

        “But on the other hand, we don’t have unlimited time for them to figure things out on their own, do we? What about children who can’t make these connections for themselves?

          “For example, what about the math facts? If my kids aren’t picking them up, don’t they just have to memorize them?”

          Continue reading FAQ: The Necessity of Math Facts