The Washington Post has a very good piece about math literacy and how it affects minority students. Unfortunately, the column focuses too much on attitudes–which do matter–and not enough on why students can’t do math. That is, what are students deficient in such that they can’t do math very well. This is the only mention of the problem:
Johnson has developed a 10-question diagnostic test that can pinpoint why a student is struggling. Often the problem can be tracked back to some lesson missed in earlier grades. A mathematical term incorrectly defined, a concept not fully comprehended, a fundamental law broken.
“Sometimes, students will be taught how to answer questions as they appear on a test but not learn the principles that will allow them to solve problems wherever and however they appear,” Johnson said.
“Teachers will try to relate to students by using slang instead of sticking to the fundamentals. They’ll refer to parts of a fraction as ‘these bad boys up here’ and ‘those bad boys down there.’ So when the student gets a test that refers to denominators and numerators, he has no idea what they mean.”
What’s frustrating is that there’s no exploration of why some students have difficulty with algebra–it’s just treated as a given and an immutable reality.
In my previous experience as a math tutor (caveats: small n, ‘failing’ high school students), the primary reason students have problems with algebra isn’t algebra per se, it’s arithmetic. Every student had problems with basic arithmetic–every single one had problems with fractions. Watching an older high school student solve 1/2 + 1/3 for 1/5 is heartbreaking. And decomposing 13 x 7 into (10 x 7) + (3 x 7) was like performing magic. But most could figure out ‘if [famous] basketball player scores X points per quarter, how many points per game does he score?’
The problem was a lack of fluency with numbers and very, very basic number theory.
(I’ve been making this point for a while now.)
There are too many students who need remedial education in one or more areas. Until we provide that remedial education one way or another, the various performance gaps will not close.