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Overlearning for Automaticity

June 2, 2009

This is going to be my motto for next year! I’m especially going to drill into their heads (i.e. venting from this year):

  • Pythagorean triples — on the last day of school, students should not still have to think through 3^2+4^2=5^2!
  • If x^2=a, then x=\sqrt{a}
  • Understanding why it makes sense to solve the equation 25=\frac{1}{2}(75-x) by multiplying both sides by 2 first. (Not to mention, how to multiply both sides by 2.)
  • Learning to see right triangles in problems.
  • Identifying the hypotenuse of a right triangle.
  • Understanding the difference between angle measure and lengths on triangles.
  • Linear pairs and vertical angles — without my having to say, “Notice the straight line …”
  • Area, circumference, and volume formulas
  • The arcs of a circle add up to 360°
  • The difference between perimeter and area — especially on a rectangle

I may come up with more later, but these are the ones that are especially frustrating for me right now. I know it’s not all the kids’ fault — I haven’t (apparently) taught it enough or in such a way that it has sunk into their heads, but it’s still annoying to have more than one student stare at a right triangle with legs of 3, x, and 5, and not realize that the missing leg is 4.

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