Solving a homeschool math problem is only interesting and genuinely satisfying when it is hard. Easy problems are forgettable. Hard problems are the ones that build real mathematical thinking.
One Never Truly Fails to Solve a Math Problem
Solving a math problem requires an approach. If the approach is obvious and correct, the problem is easy. Hard problems do not present an obvious approach. Elegance is rarely the first word that comes to mind when describing a successful approach to a difficult problem, because the best approach is rarely the first one tried. Things are messy.
The beauty of mathematics is that you can brainstorm all kinds of ideas about how to proceed and actually try them out until one works. As Thomas Edison understood, every failure is a step toward success. One never truly fails to solve a math problem. You simply have not solved it yet.
Two Kinds of Intermediate Setbacks May Occur
- You think a dead-end is an obstacle. Until you realize it is truly a dead-end, you keep working at it. That is not entirely wasted effort: useful insights often emerge from that persistence. When you finally recognize it as a dead-end, you are ready to try a different approach.
- You think an obstacle is a dead-end. You try other approaches. When none of those works, you begin to wonder: "Hey, maybe that was not a dead-end after all. Maybe it was an obstacle." You struggle until you make a breakthrough and solve it.
Photo credit: @ofnumbersandstars
How to Support Your Child Through Mathematical Struggle
Self-awareness and the ability to let negative emotions such as frustration and impatience drive positive action will eventually result in success. Encourage your child to ask for help when needed, without letting pride get in the way of seeking guidance from others. By constantly seeking input from peers and colleagues, Albert Einstein ensured his theories were as sound as possible.
The best homeschool math curriculum, for special needs students, gifted learners, and average learners alike, does not simply show students which approaches work best. It teaches them how to think so they can arrive at the best approaches themselves.
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