Math Algorithms

Designed for 5th graders in Michigan, this is the word-for-word text of my least favorite math standard ever:

“N.FL.05.14   Add and subtract fractions with unlike denominators through 12 and/or 100, using the common denominator that is the product of the denominators of the 2 fractions, e.g., 3/8 + 7/10: use 80 as the common denominator.“

It’s almost as if someone is purposely trying to ensure that students cannot possibly understand what they are doing in math class.  (And I love the line that says we’re working with unlike denominators “through 12 and/or 100″ — do we get to pick or something?)  Anyway, I can picture this scene playing out in classrooms around the state:

Teacher: “OK, kids, today we’re going to learn how to add 3/4 + 1/8.  First, let’s find a common denominator for these two fractions.  What could that be?”

Student 1: “Eight.”

Teacher: “No.  Remember what we talked about yesterday?  The State of Michigan says you’re supposed to multiply the denominators of the fractions you’re adding.  So what is the common denominator that we should use?”

Student 2: “Thirty-two.”

Teacher: “Good!  So now, let’s convert both fractions into thirty-seconds.  We can do that by cross-multiplying across the fractions…”  [editor's note: cross-multiplying was required in the previous version of this standard but mercifully is no longer specifically deemed mandatory]

Student 1: “Wait a minute.  Isn’t three-fourths the same thing as six-eighths, so we could just…”

Teacher: “QUIET!!  If we cross multiply we get 3 x 8, which is 24.  So three-fourths is just 24/32.  Then if we cross-multiply the other way, we get 1 x 4, which is 4, so the second fraction is 4/32.  So we add those up and get our answer, 28/32.”

Student 1: ”Isn’t that just seven-eighths, since…”

Teacher: “NO!! Reducing fractions is a 6th grade benchmark.  28/32 is the only correct answer for 5th graders in the State of Michigan.  Does everyone understand what to do?”

I see the algorithm mentality everywhere in math: we borrow, carry, invert and multiply, and cross-multiply our way through math calculations instead of truly understanding numbers and what various problems mean.  It just infuriates me when the benchmarks teachers are told they must teach toward serve to exacerbate this sort of teaching without understanding.