Doing the Math - JHU Mathematics - Johns Hopkins University

APPENDICES
Analysis
In general, the VSC and the Accuplacer exams are not well aligned. Of the 14 total indicators for the VSC, only
about three or four appear to be relevant to the Accuplacer. This corresponds to less than 30 percent of the VSC.
The Accuplacer corresponds to traditional material covered in an algebra I course. It is largely concerned with the
abstract manipulations required to solve equations and covers the basic mathematical skills necessary to do so.
These skills include arithmetic skills, as well as formal manipulations of arithmetic and algebraic expressions. The
student is expected to be able to apply these skills to solve problems. There are a few problems that deal with
real-world applications and interpretations, but most problems are stated in purely mathematical terms.
The VSC, in general, does not focus on basic mathematical skills. The curricular approach centers on making the
material relevant to the student rather than the acquisition of basic algebraic skills. For example, a simply stated
skill such as solve a linear equation with rational coefficients is buried in the VSC under general material on lines.
The “Assessment Limits” and “Skill Statement” do not adequately explain how proficient a student is expected to be
at this skill.
The VSC has two Core Learning Goals, and one of them, concerned with data analysis, is entirely missing from the
Accuplacer exam. The CLG 1 for the VSC also includes many topics that are not required for the Accuplacer exam,
such as graphing nonlinear functions, and equations for lines. Of the nine indicators for CLG 1, only three appear
to be directly applicable to the Accuplacer. Conversely, the Accuplacer exam assesses facility with arithmetic
expressions and with formal manipulations of algebraic expressions, particularly polynomials, and much of this
material is not included in the VSC.
The three sections of the Accuplacer are analyzed separately below. In general terms, the VSC and the HSA do not
prepare students to do well on this test. Of the three categories of Accuplacer questions, only one of the
categories, Solving Equations, Inequalities, and Word Problems, has any true alignment with the VSC. The other
two categories involve operations with rational numbers and abstract manipulation, and are not covered in the
VSC.
There are two broad ways in which Accuplacer differs from the VSC and the questions included in the HSA.
Arithmetic
The Accuplacer is designed to be taken without a calculator (though it may offer a calculator in situ on certain
problems). It assumes and requires a certain level of arithmetic fluency. For example, the problem 4- (-6) =
should not require a -5
calculator; only the most basic arithmetic is involved. However, the VSC and the HSA do not include any indication
that students should be expected to build upon and fully master the arithmetic skills they learned in elementary
and middle schools. Thus, students may have long forgotten how to perform elementary calculations by hand.
This sort of mastery is required for a traditional algebra class emphasizing abstract manipulation. However, given
that the VSC seems to favor a more applied approach depending on technology, it may be possible to perform well
in a VSC-based algebra class without full mastery of basic arithmetic.
Level of Abstraction
The problems on the Accuplacer are generally stated in a purely abstract fashion, and they emphasize mastery of
particular mathematical skills. This is in direct contrast to the problems on the HSA, where nearly every problem is
situational. Generally, the level of mastery of a particular mathematical skill required to solve an HSA problem is
minimal. The VSC also seems to de-emphasize mathematical skills in favor of more applied contexts. It is, in fact,
difficult to interpret the VSC in terms of mastery of the abstract skills that are required for the Accuplacer.
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