Basic Skills Diagnostic Test (BSDT)

Developed by Jerry Epstein

Purpose To assess fundamental skills in mathematics and basic quantitative reasoning.
Format Short answer
Duration 30 min
Focus Mathematics Content knowledge (quantitative reasoning, basic algebra skills, arithmetic skills, measurement basics)
Level Intro college, High school
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Research-based Validation
This is the lowest level of research validation, corresponding to at least one of the validation categories below.

Research Validation Summary

Based on Research Into:

  • Student thinking

Studied Using:

  • Student interviews
  • Expert review
  • Appropriate statistical analysis

Research Conducted:

  • At multiple institutions
  • By multiple research groups
  • Peer-reviewed publication

The questions on the BSDT were developed by the author based on student thinking. They were tested at multiple institutions with many different populations of students. The BDST is discussed in one peer-reviewed article and the results are available in one unpublished article. 


  • J. Epstein, Cognitive development in an integrated mathematics and science program,
    Jour. of Coll. Sci. Teach., 27 (3),  (1997). 

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Typical Results

Overall results on the BSDT for a variety of courses and institutions from (Epstein, 2002). A description of each course represented in this table is given below. 

During the years 1989 - 1992 this test was given to a variety of student populations at Hofstra University. The students there are generally middle class, suburban, with SAT scores close to the national average. The test was given to students in Computer Science 005, 015 and 132. Students in CS-005 were liberal arts majors. Students in CS-015 were Freshman C.S. majors plus a variety of other. These students all had had math at least through pre-calculus. Students in CS-132 were senior C.S. majors and a few engineers. All had had 3 semesters of calculus, differential equations, and calculus-level probability and statistics.

The test was given also to students in Math 298, Math 011, Math 015, Math 10E, Math 009 and in the CSTEP and STEP programs at Hofstra. Math 298 is taken by graduate students, largely in math and science education. Math 11 is a pretty standard pre-calculus course. Math 10E and Math 9 are the required math courses for Business majors, 10E being a one-semester calculus course.  Math 015 is largely taken by liberal arts majors and Education majors. CSTEP students took the test in the summer prior to their regular entrance into Hofstra. These are minority students in a program designed to help them succeed in the professional tracks. The STEP students were high school students all enrolled in "Sequential II", the second year of "integrated" algebra, geometry. Nearly all were 10th graders, all were minority students.

In 1991-92 the test was given to populations of 15 and 18 year olds in Canada, to several populations at Wellesley College, and in 1993-95 to several groups of students at City University of N.Y. The population in Canada was from Lincoln County, Ontario. The students taking the test were selected from classes considered typical cross-section in nature. The grade 10 students were early in their second year of algebra. The grade 13 students in many cases had four years of high school math including pre-calculus. 

At CUNY the test was administered to:

  • Students in non-calculus Physics 166 (N=26) and Physics 167 (N=31) at Lehman College, which is a four-year school in The Bronx. Trigonometry was a prerequisite for this course. 
  • Populations in PHY-201, technology physics, and PHY-301, college physics at Queensboro Community College (10 each). All these also have had math through trigonometry.
  • Students at Lehman taking CORE 106, a required science course for non-science majors (N=18). A group of "Freshman Year Initiative" students at Lehman College in an integrated course of CORE-106 and CORE 108 (N=22). These courses form a mathematics and science "core" at the college which everyone is supposed to take. They are identified above as "FYI".
  • A section of CORE-098 (N=30), students who have passed the CUNY Math Assessment Test but gotten too low a passing score to go into CORE 108.

Wellesley College is a highly selective college for women with mean SAT scores in math of about 625. At Wellesley the test was taken home and returned, while all other classes gave the test in-class. The test was given to 20 students in Writing-125 (Freshmen), 17 students in Chemistry-281 (Sophomore) and 10 students in Math-305 (upper level).

During 1995, the test was given to 3 populations at New York University.

  • An Astronomy course (N=126) where the students were liberal arts, seeking to pass a required science course for a Core requirement,
  • A "General Physics" course (non-calculus level, largely pre-medical students, N=62)
  • A physics course for high school science teachers (N=13).

The General Physics students were in the second semester. They are not representative of the students entering this program since the first semester had about a 20% attrition rate. The high school teachers were mostly biology teachers.

Finally in 1995 the test was given to two sections of calculus based introductory physics at the University of Utah. Here, the test was taken home and returned with not all students returning it. Thus we have the same self-selection problem as above. The test was given to over 200 students. A random sample of 60 was used for the results shown below.

In 1999, the test was given at Polytechnic University to about 100 students in MA-105 (pre-calculus). A random sample of 35 was chosen for the results below.

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The latest version of the BDST, released in 1997, is called v1.