Most 8th grade math teachers make decisions about what and how to teach based on the content of standardized tests administered in their district, according to a study conducted by the National Center for Research in Mathematical Science Education (Romberg et al. 1989). Teachers align their curriculum with the test, but analysis indicates the test is not aligned with the future needs of students.
Of those responding to a random survey of 1,200 teachers from throughout the United States, less than 20 percent reported making no instructional changes as a result of the standardized test administered in their district. Thirty percent reported giving more emphasis to “basic skills” than they would if the test were not given. Twenty-five percent reported giving more emphasis to paper-and-pencil computation, and 24 percent said they spent more time on topics that were emphasized on the tests.
According to Curriculum and Evaluation Standards for School Mathematics, “To become mathematically literate, students must know more than arithmetic” (National Council of Teachers of Mathematics 1989, p. 18). In grades 5–8, “a broad range of topics should be taught, including number concepts, computation, estimation, functions, algebra, statistics, probability, geometry, and measurement” (NCTM 1989, p. 67).
The National Center for Research in Mathematical Science Education has studied the content of the six most widely used standardized tests in mathematics at the 8th grade level (Romberg and Wilson 1992). An average of only 6 percent of the items were from each of the domains of number systems and number theory; algebra; probability; or statistics, geometry, and measurement. A full 71 percent of the items were from one domain: numbers and number relations, that is, arithmetic. This disproportionate emphasis on the arithmetic domain in standardized tests clearly is inconsistent with the recommendations of NCTM.
A similar imbalance is observed when the items are analyzed according to the mathematical process involved. Seventy-nine percent of the items were classified as computation and estimation. Eighteen percent were classified as communication. The important processes of problem solving, reasoning, connections, and patterns and functions together accounted for a total of only 5 percent of the items.
While educators talk about the importance of higher order thinking, only 11 percent of the items were classified as conceptual. Fully 89 percent were classified as procedural. For example, a procedural question might ask a student to perform a computation using long division. A conceptual question might ask students to create a long division problem with a solution between 99 and 199.
Test publishers typically classify the following type of question as a measure of problem-solving ability: “John wants to buy a video that usually sells for $24.95. It is on sale for 20 percent off. About how much will he save if he buys it on sale?” Students facing this type of problem for the first time would indeed have to invent a solution for it. However, the processes for this type of question are commonly taught to and practiced by students. The problem really assesses the procedural knowledge of computation not the conceptual knowledge of problem solving.
In spite of this lack of alignment between standardized tests and the goals of school mathematics, the American public believes that an increased emphasis on standardized testing will improve instructional programs in schools. Over 70 percent of Americans favor the use of standardized tests to compare the achievement of local students to those in other communities. Even more, 85 percent believe standardized tests should be used to identify areas in which students need extra help (Elam et al. 1992).
If these currently available standardized tests are used as the basis for comparing mathematical performance from one district to another, or for identifying areas in which students need extra help, the curriculum in that district will acquire an inappropriate emphasis. It will emphasize rote procedural knowledge of arithmetic computation, and it will de-emphasize or eliminate problem solving and mathematical reasoning. It will de-emphasize or will eliminate measurement, geometry, statistics, probability, and algebra. The curriculum will fail to reflect the mathematics our students need for literacy in the 21st century.
