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

By Edgar L Edwards; Mathematics Education Trust

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Example text

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. Students need opportunities to experiment with the use of algebraic skills and problem-solving strategies without always being told which to employ.

They should approach algebra with confidence that they have the ability to understand those reasons. 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 implications for the lower group are overwhelming. We typically are concemed with managing these students, for whom it is easier to stress instrumental leaming and dispensary methods of teaching. We must take the time to implement the recommended curriculum with these students, who require our most expert teaching. If the content and instruction require student activities, thinking, discussion, and explanation first, then the argument is even more acute for these students at risk of not taking algebra.

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