. "Test 4: High School Mathematics Proofs, Models, and Problems, Part 1 Test." Testing Teacher Candidates: The Role of Licensure Tests in Improving Teacher Quality. Washington, DC: The National Academies Press, 2001.
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Testing Teacher Candidates: The Role of Licensure Tests in Improving Teacher Quality
• Table of specifications:
What KSAs (knowledge/skills/abilities) are tested (e.g., is cultural diversity included)? The test is intended to focus on problem solving, communication, reasoning, and mathematical connections. “This basic mathematics test requires the examinee to demonstrate an understanding of basic concepts and their applications in constructing a model, writing a proof, and solving two problems” (Tests at a Glance: High School Mathematics, p. 36). The basic mathematics content in this test covers arithmetic and basic algebra, geometry, analytical geometry, functions and their graphs, probability and statistics (without calculus), and discrete mathematics. The test assesses knowledge in at least five of these six areas. Each of these six areas is described in some detail below.
To solve the four problems, examinees must be able to understand and work with mathematical concepts, reason mathematically, integrate knowledge of different areas of mathematics, and develop mathematical models of real-life situations (ETS, June 2000, Test Analysis Subject Assessments Mathematics: Proofs, Models, and Problems, Part 1).
Comment: The topical coverage of the test seems reasonable when considering that it is only one of several tests in a series of mathematics tests (but a content specialist could judge more appropriately the quality and completeness of the content coverage). There is no indication of what percentage of the test is related to each content area or to the broader skills (e.g., work with mathematical concepts).
There is also a caveat in the Tests at a Glance: High School Mathematics that examinees may have to draw on competencies from other content areas to solve problems. It is not clear if this means other areas of mathematics (e.g., calculus) or other content areas such as history.
The absence of a more specific distribution of test content and the potential for the examinees to need skills other than those specified in the preparation materials are problematic. The first problem can lead to validity concerns, especially considering the comparability of scores across forms. The second problem suggests the potential for validity problems in terms of potential contamination of scores due to the need for skills other than those for which inferences from the scores may be desired.
How were the KSAs derived and by whom? The content domain1 was determined by using a job analysis procedure that began in 1989.
This domain was for all tests that might be used to license teachers of mathematics; thus, it is broader than the domain for this test, which is only one test out of six that relate to high school mathematics. The total domain contains 12 major knowledge categories: Basic Mathematics, Geometry, Trigonometry, Functions and Their Graphs, Probability and Statistics, Calculus, Analytical Geometry, Discrete Mathematics, Abstract Algebra, Linear Algebra, Computer Science, and Pedagogy Specific to Mathematics.