Download Algebra for everyone by Edgar L Edwards; Mathematics Education Trust PDF

By Edgar L Edwards; Mathematics Education Trust

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Extra resources for Algebra for everyone

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The sketch should help the student determine the reasonableness of the solution. 44 ALGEBRA Fon Evrsnromz INTEGRATING IDEAS Practice situations need to provide for ongoing review, application, and integration of previously learned ideas. Mixed practice needs to include opportunities for students to transfer learning to new situations. Consider the following example: In a right triangle, the hypotenuse and the long leg differ by l unit. Find an expression for the other leg. P X Q Solution: Given: p — q = 1 x2 + q2 Z P2 X2 Z P2 _ q2 2 X = x/p - q2 x =\/(p+q>(p-q) = x/(p+q>><1=x/12+4 This problem could be used to integrate several skills and concepts learned earlier, such as factoring and the Pythagorean theorem.

The teacher offers guided practice in class to ensure that students can successfully complete their assignments independently. Then the assignment should result in the students’ having a successful experience applying the knowledge that was presented in the lesson. All too often, the assignment is made before the students have intemalized the new material to be leamed; then the teacher needs to explain the lesson while going over the previous day’s homework. In the process, students begin with an unsuccessful experience that can contribute to lowered expectations by both the students and the teacher.

An essential aspect of algebra is developing skill with algebra as a language with symbols and syntax that can be used to represent a situation, manipulate the representation, and yield new information about the situation. Students need meaningful practice activities to help their development of algebra as a language. DEVELOPING AND MAINTAINING SKILLS IN THE LANGUAGE, SYMBOLS, AND SYNTAX OF ALGEBRA Teachers need to offer practice experiences that go beyond the mechanical tasks usually associated with algebra as a language.

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