Math Algorithms
May 13, 2008
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.
Entry Filed under: Education, Elementary Education, Fifth Grade, Fourth Grade, Learning, Math, Middle School, Public Schools, Reform, Second Grade, Secondary Education, Students, Teaching, Third Grade, school, standardized tests. .
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1.
eyeingtenure | May 13, 2008 at 9:55 pm
There’s nothing in the fifth-grade standards that expressly prohibits teaching sixth-grade standards, is there? I mean, if you cover the fifth-grade version briefly, and the class is ready to go on to sixth grade from there, you’ve covered the standard.
Right?
2.
mpullen | May 13, 2008 at 9:59 pm
Yes, you could go on to the 6th grade standards, but you couldn’t disregard the 5th grade requirement to use the product of the denominators, which is a shame. Of course, the tests these 5th graders would face would all have 28/32 as the right answer to that sample problem, too, so you’re faced with that added pressure to conform to the current-year standards alone.
3. Standards for Dummies at &hellip | May 14, 2008 at 10:32 am
[...] confusing, misleading, or get in the way of understanding. A Michigan math standard, courtesy of The Elementary Educator: “N.FL.05.14 Add and subtract fractions with unlike denominators through 12 and/or 100, using the [...]
4.
Robert Pondiscio | May 14, 2008 at 10:36 am
Great post I’m sharing this with the readers of The Core Knowledge Blog.
5.
A. Mercer | May 14, 2008 at 6:58 pm
I wanna do a math jamboree of problems like this one and my “round food” post with middle and high school math bloggers in the summer, you game for it?
6.
cassyt | May 14, 2008 at 8:26 pm
Oh dear, I taught my third graders how to do this (in Arizona). It was a lesson in their third grade Singapore Math books. Maybe the kids in Singapore are genetically more mathematically capable than the ones in Michigan.
7.
mpullen | May 14, 2008 at 8:36 pm
Robert — thanks for the link!
Alice — if I commit to anything else this summer, I’ll never sleep.
Cassyt — third graders could realistically add fractions using this algorithm, as long as understanding was not a concern. As soon as a child can multiply, this algorithm becomes accessible; yet teaching it as a rote method for students to follow is exactly the type of thing that prevents kids from truly understanding math as they advance through school.
8.
Liza Lee Miller | May 14, 2008 at 10:16 pm
That is an idiotically specific standard. I would not teach my kids to use 80 as the common denominator — particularly if they were already seeing that 8 would work. Argh. Besides, in California, 5th graders CAN reduce fractions. Is it something in the water in Michigan? Sigh. Heck. We can teach them to cross-cancel fractions in multiplication. It’s wild times here, I’m telling you!
9.
Karen Smith | January 21, 2009 at 3:02 pm
Good grief – as I read these comments I keep seeing the term “reduce.” That is an archaic misnomer – you are NOT making the fractions smaller- please use “simplify” instead.