One Basic Problem For Math Literacy

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.”

As I’ve noted before, it’s usually not a cognitive issue, but one of ignorance:

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.

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3 Responses to One Basic Problem For Math Literacy

  1. Eric Riley says:

    While teaching calculus, I had three problems that would gauge the success of a student in my class:

    (1) adding unlike fractions
    (2) long division with a remainder
    (3) a trig problem for 30°, 60°, or 45°

    Generally, failure on either of the first two would also indicate s difficulty with basic algebra, and the third would show that remedial work was needed in trigonometry.

    The most depressing part was students that would argue with my assessment by saying they had gotten an A in their previous classes.

    I was not a popular teacher – but following instructors could identify my students by how well-prepared theyare were, which counts as a win in my book.

  2. John Magoun says:

    I do occasional math work with students (I tutor for the SAT and conduct a general studies curriculum in an institution), and I agree about the lack of core math skills in many high school students. Fractions in particular are a common problem. I think it is because they have been raised on calculators that give decimal answers and offer no easy way to do fraction problems.

    In terms of how students need to progress, Math is a foreign language, like French or Spanish. One doesn’t expect students to read Spanish literature if they don’t have a working vocabulary or understanding of the grammar; at the same time students fluent in Spanish have no place in a classroom where introductory phrases and simple terms are all that are being taught.

  3. kaleberg says:

    Fractions are the big sticking point, but many have trouble with simple arithmetic and order of operations. I’m not sure of how fractions are being taught. We were given little pie slices and taught how to add fractions with them.

    The problem is that math is cumulative, and it hard to BS your way through it. If you didn’t quite get something, even if you got it well enough to pass a quiz at the time, that lack of understanding will bite you later. If you missed something completely due to illness, a move or just horsing around, then that omission will bite you later.

    For a good paper on this that deals with students at community colleges:

    https://www.carnegiefoundation.org/wp-content/uploads/2013/05/stigler_dev-math.pdf

    If you don’t want to read the whole thing, just go to the table of problems that gave students the most trouble.

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