The effects of a test preparation guide in problem-solving in improving students' achievement on the New York math 'A' Regents Examinations.

摘要

This investigation explored the effects of a test preparation guide in problem-solving to improve students' achievement on the New York Mathematics 'A' Regents Examinations. The design took the form of a quasi-experiment. The sample consisted of a control group and a treatment group, representing 4th-semester 10th graders. The sample size was 40 students (19 control; 21 treatment).; The major activity of the experiment was the instructor's construction of the Test Preparation Guide based on the problem-solving techniques pioneered by Dewey (1910) and Polya (1945), and the performance standards for problem-solving from New York State/New York City Departments of Education; 10 problem-solving lesson plans (work backwards; find pattern; adopt different viewpoint; solve simpler analogous problem; consider extreme cases; visual representation; guess-and-check intelligently; account for all possibilities; organize data and logical reasoning). The guide encompassed motivational and model problems; classroom practices; key notes and homework schedules; and an additional set of problems prepared by the Brooklyn Superintendency for High Schools.; Teacher-made pre-test and post-test each with 10 open-response questions (mostly from past Mathematics 'A' Examinations) were administered to both groups. Control group was taught problem-solving via traditional instruction (extensive chalk-and-talk, algebraic solutions, formula application, minimal questioning techniques, teacher-dominated sessions). Treatment group received non-traditional instruction with the guide (teacher-facilitator, minimum chalk-and-talk, student-centered classroom). Each treatment session entailed short motivational problems to recall basic computation knowledge, review of problem-solving steps, model problems practice, homework review, student presentations with inter-group support, and summary/feedback of day's activities. Treatment group completed a 17-item questionnaire and written project evaluation.; Means and standard deviations of pretest/posttest were compared with an analysis of covariance (pretest was covariate). The F ratio, compared with critical F values, indicated a significant increase in posttest mean scores of Treatment group over posttest means of Control group (0.05 or 0.001 level). Questionnaire responses indicated that most participants improved confidence as problem-solver, which can better their chances of success on forthcoming Mathematics 'A' Regents Examinations. In addition, the favorable comments of three mathematicians who reviewed the guide validated its contents. Findings suggested an important relationship between acquisition and appropriate use of mathematical problem-solving strategies and achievement on the New York Mathematics "A" Regents Examinations.