State Testing and Mathematics Teaching in New Jersey: The Effects of a Test Without Other Supports
Roberta Y. Schorr, William A. Firestone, Lora Monfils
Conflicting findings about the effects of state testing on mathematics teaching have a number of roots, including the strong ideological positions of advocates and opponents of state tests and the fact that state policies vary such that one is likely to find different results in different states. The pressure that students, teachers, and administrators may feel toward high test scores and the opportunities that teachers and administrators may have regarding related professional development can also confound findings on the effects of tests on actual classroom teaching. This article describes the teaching practices of fourth-grade teachers in New Jersey, a state with a fourth-grade mathematics test designed to be aligned with state and national standards. The intent of this test is to challenge conventional practice. However, there is a lack of strong pressure to produce high test scores or effective guidance on the kinds of learning opportunities that must complement those tests in order to lead to fundamental change in teaching. Through interviews and observations of 63 teachers, we found that the teachers reported that they changed their practices in ways compatible with state and national standards and the test. For example, they reported asking their students to solve more open-ended problems and to explain their thinking. However, direct observations suggested that teachers have adopted specific strategies without changing their basic instructional approach. The results from our investigation suggest that in the absence of effective professional development, testing leads to minimal changes in teaching practice.
The Use of Symbols, Words, and Diagrams as Indicators of Mathematical Cognition: A Causal Model
Curtis L. Pyke
This article reports on the results of a study that investigated the strategic representation skills of eighth-grade students while they were engaged in a set of tasks that involved applying geometric knowledge and using algebraic equations. The strategies studied were derived from Dual Coding Theory (DCT) (Paivio, 1971, 1990), and they were elicited with task-specific prompts embedded in an assessment developed for the study. The purpose of the study was to test a model that highlights strategic representation as a mediator of the effects of reading ability, spatial ability, and task presentation on problem solving. The proposed model was tested using the linear structural equations modeling approach to causal analysis and the data did not reject the model. The results showed that students' use of symbols, words, and diagrams to communicate about their ideas each contribute in different ways to solving tasks and reflect different kinds of cognitive processes invested in problem solving.
A Meta-Analysis of the Effects of Calculators on Students' Achievement and Attitude Levels in Precollege Mathematics Classes
Aimee J. Ellington
The findings of 54 research studies were integrated through meta-analysis to determine the effects of calculators on student achievement and attitude levels. Effect sizes were generated through Glassian techniques of meta-analysis, and Hedges and Olkin's (1985) inferential statistical methods were used to test the significance of effect size data. Results revealed that students' operational skills and problem-solving skills improved when calculators were an integral part of testing and instruction. The results for both skill types were mixed when calculators were not part of assessment, but in all cases, calculator use did not hinder the development of mathematical skills. Students using calculators had better attitudes toward mathematics than their noncalculator counterparts. Further research is needed in the retention of mathematics skills after instruction and transfer of skills to other mathematics-related subjects.