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An Introduction to College Math Placement Testing

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Dave Moursund


I recently wrote an extensive IAE-pedia document on Exploring the College Math Placement Testing Process. It has two major goals:

  1. Goal 1. To help college-bound secondary school students learn to self-assess their progress in learning math relative to the standards set in higher education. A student may well be getting good (or, at least passing) grades in secondary school math courses and still be making poor progress toward being prepared for the rigor and much higher demands of college math courses.
  2. Goal 2. To help secondary school math teachers gain increased understanding of how well they are preparing their students to deal with college-level math courses.

Here is a reference about recent and planned changes to the SAT:

Lewis, Darcy (9/12/2014.) How the New SAT Is Trying to Redefine College Readiness. Retrieved 9/15/2014 from Quoting from the article:

If you are checking out the Best Colleges rankings as a junior or senior, you’re preparing to sit or have already sat for the 2400-point SAT, complete with its fancy vocabulary words and mandatory essay. But members of the class of 2017 will begin prepping next year for a completely overhauled test.

Last March, College Board President David Coleman announced major revisions to the fall 2015 PSAT and the 2016 SAT, saying the SAT had "become disconnected from the work of high schools."

The changes, which include going back to the 1600-point composite score based on 800-point math and "evidence-based reading and writing" sections, and making the essay optional, are intended to better reflect the material students should be learning in high school and improve the SAT’s reliability as an indicator of how prepared applicants are to tackle college work.

High Stakes Math Tests for High School Students

High school students and their math teachers are familiar with high stakes math tests. For example, a math test at the end of a unit, the end of a term, or the end of the year may count substantially towards a student’s grade in the course. Indeed, in some states students do not get credit for the course unless they pass the final exam at the end of the course.

Some what similarily, a number of states make use of high school exit exams. See See also a 2013 article: Exit Strategies: How Low-Performing High Schools Respond to High School Exit Examination Requirements available at

The Advanced Placement tests provide another example. High school students take a final exam for each AP course. Colleges and universities set cut-off scores that determine whether an incoming student will receive college credit for the AP course.

Still another example of high stakes math tests is provided by college entrance exams such as the ACT and SAT. Different colleges and universities use different cut-off scores in determining who is to be admitted. An extensive test preparation industry has developed for the SAT and ACT. Publishers of these tests provide free sample test materials and (non-free) courses designed to help prepare students to do well on the tests. There are many other sources for SAT and ACT test-prep instruction and one-on-one tutoring. For example, click here for free sample SAT tests and materials and here for SAT practice tests.


What Constitutes a Good College Math Placement Test Site?

Here are some of my thoughts about desirable features of a "good" college math placement test site.

  1. The test is openly available and free to anyonenot just students who have been admitted to the specific institution of higher education offering the test. Thus, for example, secondary school students could take that institution's test to determine how well they are doing in their math learning. Students thinking of applying to a particular institution could take that institution's test to see how well they might score on it.
  2. The test is comprehensive and well balanced. It includes a significant emphasis on the various aspects of math maturity.
  3. The test provides analysis and feedback to the student. This feedback points out a student’s relative strengths and weaknesses.
  4. The institution and/or test system makes available comprehensive information about resources that are available free to the student, resources that can provide good quality online instruction for the various areas covered in the test.

In the Web-based research I did while writing the Exploring the College Math Placement Testing Process IAE-pedia document, I did not find a single site that did a good job of meeting all four of these criteria.

Some Examples of College Math Placement Tests

Each college and university is faced by the problem of determining for each individual student and/or helping the student to determine the best math course(s) for that student to begin with. This might range anywhere from a remedial grade school arithmetic course up to a calculus course or a course that has calculus as a prerequisite. For a large college or university, this level of individual screening for each incoming student is a daunting task.

Barton College

Here is some information about the Barton College Math Placement Test. Quoting from the site:

The Mathematics Placement Test (MPT) is administered to all incoming freshman and transfer students who do not bring an advanced placement or college-level transfer credit for a mathematics course to Barton College. The test covers topics from Pre-algebra, Algebra I, Algebra II, and Pre-Calculus. The MPT consists of 40 questions, and students will have 60 minutes to complete the test.

The first 20 questions cover material in a standard Algebra I course. The next ten questions cover material in a standard Algebra II course, and the final ten questions cover material from pre-calculus.

The practice test contains 80 questions, which is twice the number on the actual test. They are all 4-part multiple-choice questions.

The exam site includes information about the scores needed on various parts of the test to qualify for placement in various math courses. I think this type of "disclosure" is quite useful to students; unfortunately, it does not seem to be common practice.

University of Washington

Click here to learn about the University of Washington Practice Math Tests. They make use of the Academic Placement Test Program. A 55-question lower-level and a 45-question higher-level sample test are available. Quoting from the website:

The Academic Placement Testing Program (APTP) is a cooperative program of Washington State public colleges and universities. Faculty from participating institutions have created the Mathematics Placement Test (MPT) to help students, with the assistance of their academic advisers, select first-year mathematics courses for which they are best prepared. The program is managed by the Office of Educational Assessment on behalf of participating institutions.

University of British Columbia, Canada

Here is an example in which the university provides some help, but the student is treated like an adult and is expected to make a decision by him or her self. Quoting from the College Math Placement Tests site:

The example given here is from the University of British Columbia, Canada. UBC makes use of a self-assessment instrument to help a student determine whether to enroll in Math 001 or Math 002. These are both considered to be remedial courses.

Using a self-assessment math placement test is an interesting idea. The stated prerequisite for course Math 002 is course Math 001. However, a student can decide to go directly to course Math 002. To help a student decide whether to do this, a self-assessment exam is available. Quoting from the website:

Test Instructions

Open the exam below in the format you prefer (same test, different formats). [This is a 80-question (not multiple choice) test. The test begins with a number of ninth-grade questions and ends with two trigonometry 12-grade questions.]

Adobe format pdf (.pdf) (146 kb) Click here for the PDF version.

Microsoft Word format (.doc) (246 kb) Click here for the Microsoft Word version.

Write the exam within 2 hours.

Scoring Your Test

Mark your test using the answer key pdf (each question is worth 1 mark).

Total your marks (test is out of 89 questions).

90% is equal to 80 questions answered correctly out of 89.

Goal is 80 questions answered correctly or better.

If you score lower than 80 out of 89, Math 002 may be too difficult for you; consider taking Math 001 first.

Notice the openness of this process. A student is trying to decide whether to enroll in Math 001 or Math 002. The test is taken by and scored by the student. The student uses the test results to help make a decision on whether to enroll in 001 or 002. The student is assumed to have a level of maturity and knowledge of self to be able to make a decision. A teacher, advisor, or counselor does not intervene in the process.

California Institute of Technology

California Institute of Technology’s Computer Science Department makes use of a somewhat similarly open placement process. Caltech’s Computer Science Placement Exam consists of two questions that a student can work on over a period of time. Quoting from a CS Department document:

We shouldn't have to say this, but we will: All of your code must be written by you and you alone. You are not allowed to get any kind of help from anyone else while writing the placement exam. You can consult on-line or printed documentation for the language(s) you use, but you are not allowed to ask questions about the problems either in-person or online before submitting your placement exam. If we find out that you have violated this rule, you will fail the placement exam.

The legendary California Institute of Technology offers a few hundred hardcore and overwhelmingly male nerds the opportunity to tackle a generally crippling curriculum. The mandatory core courses include a load of math and the hard sciences (as well as humanities and physical education requirements). Caltech does not grant credit for AP, IB, or similar tests. However, every student takes a math and physics placement exam before enrolling. If you do well enough on that test, you can get automatic credit for some lower-level Caltech courses. [Bold added for emphasis.]

What You Can Do

You and your students can work together to build an extensive collection of sample questions from College Math Placement and other tests. Students can learn to use them for self-assessment.

Teach your students the rudiments of math maturity, such as learning for understanding, transfer of learning, and math-oriented habits of mind. Help them to spend some time each math period working on these ideas and habits.

IAE References

Moursund, D. (2011-2014). Math education digital filing cabinet. IAE-pedia. Retrieved 6/9/2014 from

Moursund, D. (12/25/2012). Algebra 1 as a remedial college math course. IAE Blog. Retrieved 6/9/2014 from

Moursund, D. (2012). Math maturity. IAE-pedia. Retrieved 6/9/2014 from

Moursund, D. (1/19/2013). College and career readiness. IAE Blog. Retrieved 6/9/2014 from

Moursund, D. (2013). Good math lesson plans. IAE-pedia. Retrieved 6/9/2014 from

Moursund, D. (1/28/2014). Good learners. IAE Blog. Retrieved 6/9/2014 from

Moursund, D. (10/31/2014). Transfer of learning. IAE Blog. Retrieved 6/9/2014 from

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Guest - JonFlippen on Wednesday, 29 November 2017 17:12

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