Placement for a Modern Curriculum: A Fresh Start

The college mathematics profession has been dealing with a number of criticisms of how students are placed in their initial mathematics course.  Even before recent curricular changes, evidence suggested that the tests used for placement were likely to under-place students; a modern curriculum focusing on reasoning as well as procedure increases that placement struggle.  I’ve been working on a fresh start, and I am ready to share an initial version of a new assessment that might help solve both dimensions of the problem.

First, we need to understand the legacy of the current placement tests.  The genetic background of both Accuplacer and Compass is firmly grounded in the basic skills movements of the 1980s.  Specifically, Accuplacer grew out of instruments such as the New Jersey Basic Skills test.  The primary goal during that era was “fix all of the skills that students might lack”; the only reasoning typically included was word problems, with perhaps a bit of estimation.

Our placement needs have shifted greatly since that time.  Courses like Mathematical Literacy (and siblings Quantway [Carnegie Foundation] and Foundations of Mathematical Reasoning [Dana Center]) depend less on procedural skills like those found on placement tests; rather, the issues lie in the answers to this question:

What mathematics is this student capable of learning now?

As a coincidental benefit of the New Life Project, we have information on what these prerequisite abilities should be.  In the design of Mathematical Literacy (ML) and Algebraic Literacy (AL), our teams articulated a list of these prerequisite outcomes:

  • Mathematical Literacy prerequisite outcomes:
    1. Understand various meanings for basic operations, including relating each to
    diverse contextual situations
    2. Use arithmetic operations to solve stated problems (with and without the aid
    of technology)
    3. Order real numbers across types (decimal, fractional, and percent), including
    correct placement on a number line
    4. Use number sense and estimation to determine the reasonableness of an
    5. Apply understandings of signed-numbers (integers in particular)
  • Algebraic Literacy prerequisite outcomes:
    1. Understand proportional relationships in a variety of settings, including paired data and graphs.
    2. Apply properties of algebraic expressions, including distributing, like terms, and integer exponents.
    3. Construct equations and inequalities to represent relationships
    4. Understand how to solve linear equations by reasoning
    5. Understand how to write and use linear and exponential functions

Using these 10 outcomes, I’ve written a “Mathematical Literacy Placement Assessment” (MLPA).  The draft 0.5 of the MLPA has 30 items, with slightly more than half on the AL prerequisites.  Here is the MLPA:

Mathematical Literacy Placement Assessment 2016 version 0.5

Note two things about the MLPA:  (1) the copyright license is Creative Commons by Attribution (you can use it, as long as you state the owner [Jack Rotman] … you can even modify it; (2) the MLPA has not been validated in any way … any use should begin with preliminary validation followed by improvements to the assessment.  In case you are not familiar with the Creative Commons by Attribution license, it allows others to both use and modify the material, as long as the attribution is provided.

The intent of the MLPA is to provide a modern assessment of students who might need a Math Literacy course.  The initial 12 items are prerequisites to that course, so a score on those 12 provides a measure (with reliability and validity to be determined) of a student’s readiness for Math Literacy.  The other 18 items are intended to assess whether the student needs the Math Literacy course; a score on those 18 items would indicate whether the student is ready for an Algebraic Literacy course (or possibly intermediate algebra).

If the MLPA has content validity, we would expect a significant but small correlation with other placement results (Accuplacer, Compass) — because the MLPA is intended to measure different properties than those assessments.  The content validity would need to be established directly, possibly by use in Math Literacy courses (as a pre-test and post-test).  Variations in the two sections of the MLPA should be highly correlated to the students’ work in the Math Lit course.

My goal in developing the MLPA version 0.5 is to provide a starting point for the community of practitioners — both mathematics faculty and companies involved in testing.  Ideally, people involved in this work would collaborate so that an improved MLPA would be available to others.  The hope is that many different institutions and organizations will become involved in developing– and using — a useful modern placement test, which would benefit both colleges and students.

If you would like an MS Word document of the MLPA, please send me a direct email; you are also free to work from the “pdf” version posted above.


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