How to Succeed in Math: Answer-Getting vs. Problem-Solving

You want your child to succeed in math because it opens so many doors in the future.

But kids have a short-term perspective. They don’t really care about the future. They care about getting through tonight’s homework and moving on to something more interesting.

So how can you help your child learn math?

When kids face a difficult math problem, their attitude can make all the difference. Not so much their “I hate homework!” attitude, but their mathematical worldview.

Does your child see math as answer-getting? Or as problem-solving?

Answer-getting asks “What is the answer?”, decides whether it is right, and then goes on to the next question.

Problem-solving asks “Why do you say that?” and listens for the explanation.

Problem-solving is not really interested in “right” or “wrong”—it cares more about “makes sense” or “needs justification.”

Homeschool Memories

In our quarter-century-plus of homeschooling, my children and I worked our way through a lot of math problems. But often, we didn’t bother to take the calculation all the way to the end.

Why didn’t I care whether my kids found the answer?

Because the thing that intrigued me about math was the web of interrelated ideas we discovered along the way:

  • How can we recognize this type of problem?
  • What other problems are related to it, and how can they help us understand this one? Or can this problem help us figure out those others?
  • What could we do if we had never seen a problem like this one before? How would we reason it out?
  • Why does the formula work? Where did it come from, and how is it related to basic principles?
  • What is the easiest or most efficient way to manipulative the numbers? Does this help us see more of the patterns and connections within our number system?
  • Is there another way to approach the problem? How many different ways can we think of? Which way do we like best, and why?

What Do You think?

How did you learn math? Did your school experience focus on answer-getting or problem-solving?

How can we help our children learn to think their way through math problems?

I’d love to hear from you! Please share your opinions in the Comments section below.

CREDITS: “Maths” photo (top) by Robert Couse-Baker. “Math Phobia” photo by Jimmie. Both via Flickr (CC BY 2.0). Phil Daro video by SERP Media (the Strategic Education Research Partnership) via Vimeo.

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5 thoughts on “How to Succeed in Math: Answer-Getting vs. Problem-Solving

    1. There are so many great learning resources online, aren’t there? When I was a child, we’d make trips to the library and bring home stacks of books — but now, I can visit a whole world of libraries through this magic portal on my desk. 🙂

      You and your daughter might enjoy some of the resources on my Online Math Adventures page.

  1. There is room for both learning maths and getting the right answer.
    I learnt to subtract using the borrow and payback method, but as a child I never understood how it worked. When I was 9, someone in the class asked the teacher where the “ten” was borrowed from. I remember thinking, “That’s a good question”. They must have been doing a calculation related to money, because the teacher answered, “From the bank”. I remember thinking, “She’s not answered the question”. I contented myself with knowing that I didn’t need to know where the “ten” had come from, as long as I followed the algorithm (a word I hadn’t yet learnt) I’d get the right answer. Thereafter, I never questioned where the “ten” came from until my daughter was being taught how to subtract and engaged with a cluttered assemblage of “tens” being subtracted from the next column.
    One doesn’t always need to know exactly how arithmetic processes work.

    1. So true, James. One doesn’t need to know how the subtraction algorithm works to use it, just as one doesn’t need to know how a car works to drive it.

      The whole point of an arithmetic algorithm is that it can be done without thinking. Crank it through, follow the steps, and you’ll get the right answer. In that way, algorithms are more like magic rituals than like mathematics.

      The mathematical philosopher Alfred North Whitehead said:

      “It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them.”

      Civilization may advance as Whitehead claims. But for the purpose of education, I think the “why?” is much more important than following the steps. I want my children to learn to think about what they are doing — and to be able to put those thoughts into words and explain why they got that answer.

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