Math Mistakes: The Road to True Learning

Have you noticed how nearly every math textbook presents math concepts with perfect elegance? The textbook plan is just to follow the path and you will know the math.

Excuse me, but that's just not how kids learn math. Math is messy. Most of it isn't intuitively obvious. And nearly everyone makes lots of mistakes before gaining understanding and mastery.

A student cannot gain true mastery until mistakes are made, discovered, and corrected by the student. If you're an educator (and if you're a parent or a teacher or even a mentoring fellow student, you are an educator) consider that by giving a student who has made a mistake the correct answer you are hindering that student from gaining true mastery. In fact, by even telling a student that a mistake has been made you are guilty of the same.

OK you ask, then what do you do when your five year old tells you that 1 plus 1 is 3 (or when your 16 year old says that 2x is the derivative of 2x2)? The answer is surprisingly simple: Resist the urge to say no and to give the correct answer.

Even resist the urge to explain the process by which to get the right answer. Instead do what business school professors do so well: Lead your children down the path to contradiction so they can discover the error of their ways on their own terms.  Aha, so 1 plus 1 is 3? Interesting! OK, if 1 plus 1 is 3, then what is 2 plus 1? Or, what is 1 plus 1 plus 1? And for our budding calculus student: So 2x is the derivative of 2x2? Then what is the derivative of x2?

As an educator, lead students down the path of their choosing. They'll soon develop an internal compass that will lead them onto the right path - one of their own choosing, not some textbook publisher's - to math success.

As President of ShillerMath and Founder/Executive Director of the Rising Stars Foundation, Larry Shiller seeks to make the US #1 in math. Larry graduated from M.I.T. and the Harvard Business School and is the author of Software Excellence (Prentice-Hall, 1990), and ShillerMath Tidbits (monthly newsletter since 2003).  You can visit his website at

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