I have been getting ready for a presentation at AMATYC on the ‘bridge to somewhere’ … Algebraic Literacy. A recent post described how to identify Algebraic Literacy, compared to Intermediate Algebra. This post will look at some nice research on how effective intermediate algebra is, relative to preparing students for the typical kind of course to follow … college algebra, or pre-calculus. #bridgesomewhere #AlgebraicLit #DevMath
ACT routinely does research on issues related to higher education. In 2013, ACT published one called “A Study of the Effectiveness
of Developmental Courses for Improving Success in College” (see http://www.act.org/research/researchers/reports/pdf/ACT_RR2013-1.pdf ) The data comes from 75 different institutions, representing well over 100000 students. I was very interested in their results relating to intermediate algebra and college algebra.
Their methodology involves calculating the conditional probability of passing college algebra, using the ACT Math score as the input variable; this was done for two groups … those who took intermediate algebra and those who did not take intermediate algebra. Their work involved a cutoff score of 19 for placing into college algebra (which seems low, but I trust that it was true). Due to waivers and institutional flexibility, they had enough results below the cutoff to calculate the conditional probabilities for both groups; above the cutoff, only enough data was there for the group not taking intermediate algebra.
As an example, for ACT math score of 18: the probability of passing college algebra was .64 for those without intermediate algebra … .66 for those with intermediate algebra. For that score, taking intermediate algebra resulted in a 2 percentage point gain in the probability of passing college algebra. The report also calculates the probability of getting a B or better in college algebra for the two groups (as opposed to C).
Here is the overall graph:
The upper set (blue) shows the probability of passing (C or better) with the dashed line representing those who did the developmental course (intermediate algebra). For all scores (14 to 18) the gap between the dashed & solid lines is 5 percentage points … or less. In other words, the effectiveness of the intermediate algebra course approaches the trivial level.
The report further breaks down this data by the grade the student received in intermediate algebra; the results are not what we would like. Receiving a C grade in intermediate algebra produces a DECREASED probability of passing college algebra (compared to not taking intermediate algebra at all). Only those receiving an A in intermediate algebra have an increased probability of passing college algebra. [Getting a “B” is a null result … no gain.]
Our intermediate algebra course is both artificially too difficult and disconnected from a good preparation. That’s what I will be talking about at the New Orleans AMATYC conference.
The results for intermediate algebra echo what the MAA calculus project found for college algebra/pre-calculus: ‘below average’ students have a decreased probability of passing calculus after taking the prerequisite (when accounting for other factors).
Our current STEM path (intermediate algebra –> college algebra –> calculus) is a bramble patch. The courses do not work, because we never did a deliberate design for any of them. Intermediate algebra is a descendant of high school algebra II, and college algebra is a descendant of an old university course for non-math majors.
Fortunately, we have sufficient information about the needs of the STEM path to do better. The content of the Algebraic Literacy course is engineered to meet the needs of a STEM path (as well as other needs).
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