A structural model of mathematics achievement was tested with 117 male and 108 female high school seniors. Two attitude measures, 3 mathematics self-efficacy scales, and a mathematics achievement test were administered in the same order to all the subjects. Teacher-assigned marks in a selected mathematics course the subjects were taking were also obtained. The covariance matrices of boys and girls were analyzed with a 2-group LISREL procedure. The LISREL model specified mathematics self-efficacy as a mediator between mathematics attitude and achievement. The postulated model for similarly specified parameters was a good fit to the data for both boys and girls.This study examines the role of self-efficacy as a mediator between attitudes and achievement in mathematics. A selfefficacy perspective on the understanding of performance on specific tasks is well documented (

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One of the aims of a mathematics prog- gram is to familiarize the students with the Pythagorean theorem. The result, stated algebraically, is c2 = a2 + b2. Stated geometrically, the Pythagorean theorem refers to squares drawn on the three sides of a right triangle. The theorem states that the square drawn on the longest side has exactly the same area as that of the other two squares combined. Is it possible systematically to dissect the two smaller squares into pieces that will cover the larger square? The answer to this question is the focus of this article, which offers sugges-tions about how the Pythagorean theorem can be introduced to students in the middle school years. Enrichment challenges in the form of proofs suitable for high school geometry students are also included. Finally, three proofs of the Pythagorean theorem based on careful analysis of the puzzles are discussed. Senior high school students can be asked to prove that the pieces actually fit and to use this tessellation as a starting point to provide an alternative proof of the theorem.

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