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Relevant CAT: Conceptual Diagnostic Test
Discipline: Mathematics (also measures essential prerequisite understanding for physical science)
Description:
The Basic Skills Diagnostic Test (BSDT) is a 24-item free-response test on basic mathematics understanding. Eleven questions (two questions have two parts) assess three basic pre-algebra areas: operations on fractions in decimals, area and volume, and proportional reasoning. Eight questions assess basic algebra concepts (concept of a variable, order of operations, simplifying expressions, particularly inappropriate cancellation, linear equations). Three questions assess intermediate level algebra concepts: the concept of a function, the graph of a function, and the concept of a logarithm.
The test has been conducted in a variety of post-secondary settings, and in high schools in the U.S. and Canada. The test has also been used as an assessment tool for the mathematical level of teachers and prospective teachers, often with surprisingly poor results. An example of the kinds of questions asked in the test appears in box, below.
The questions were selected from lengthy experience in a laboratory mathematics and science program designed to bring students from extremely basic levels up to the level of preparation needed for serious college level work. The questions are the type that repeatedly reveal the most basic conceptual misunderstandings -- misunderstandings which are usually very surprising to faculty and administration. The author is especially interested in the use of the instrument for professional development of teachers.
Those interested in using the test should contact the author. There is a package of material (somewhat home-made and primitive) for scoring the test and obtaining a report. The test is not multiple-choice, and an information sheet in this package describes how to assign full, half, or no credit. A computer program can be supplied that allows inputting of the results and the program will generate a report on overall statistics and question-by-question results.
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Example questions similar in format to the BSDT
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Arithmetic:
What is 5 divided by 1/3? (Note: no division sign, “divided by” in words is harder.)
Algebra:
Solve the following equation for x: 0.04x + 3 = 4x
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Tool:
| The tool can be sent to colleges and universities by contacting the author, Jerome Epstein. Authorized representatives of schools and school systems also should contact the author. Security of the test is essential. |
Authors:
Jerome Epstein (Department of Mathematics, Polytechnic University, 6 Metrotech Center, Brooklyn, NY 11201, (718) 260-3572, jepstein@duke.poly.edu).
Selected References:
Epstein, J. "What is the real level of our students? or What do diagnostic tests really measure?" to be published.
Epstein, J.: (1997) Cognitive Development in an Integrated Mathematics Program, J. College Science Teaching, 27, 194–201.
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