By Edgar L. Edwards

ISBN-10: 087353297X

ISBN-13: 9780873532976

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**Sample text**

When exploration and reasoning do not lead to the expected results, students must be willing to go back and resolve the differences between their results and the expected results. They may have to start over again, or they may have to seek help. They should recognize that trial and error is a valid mathematical technique. They should not allow fear of errors to deter them from making attempts. Some students may be studying hard but still not be learning; those students probably need to study smarter rather than harder.

The purpose of this chapter is to address a key component for students’ success in algebra: the mathematics curriculum prior to algebra, in the middle school years. Immediately, a problem arises because of our traditional management of students and cuniculum by courses. We usually think of algebra as a course, compartmentalized in a sequence of traditional courses. Worse, we think of the preparation for algebra as a course, or a sequence of courses, called prealgebra. Even the title of this chapter implies that something exists between arithmetic and algebra, some content bridging a gap between the arithmetic of the elementary school and the junior high school or high school course in algebra.

Discussing conclusions and implications of current research in mathematics education, Peterson (in Grouws and Cooney [1988] ) claims that the challenge for educators in the next decade will be to improve students’ leaming of higher-order skills in mathematics. Recent research and theory suggest that the following classroom processes might facilitate that relational understanding of mathematics: (a) Focus on meaning and understanding. (b) Encourage students ’ autonomy, independence, self-direction, and persistence in learning.

### Algebra for Everyone: In-Service Handbook by Edgar L. Edwards

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