By Sepideh Stewart
This ebook addresses students' susceptible beginning in algebra, its motives, and strength ideas to enhance their long term good fortune and knowing in arithmetic as a complete. The authors, who're specialists in a large choice of fields, emphasize that those problems are extra advanced than simply forgotten ideas, and provide strategic techniques from a few angles that may bring up the probabilities of scholar figuring out. teachers who're annoyed with their scholars’ loss of talents and information in school point will locate this quantity important, because the authors confront the deeper the explanation why scholars have problems with Algebra and show the right way to treatment the issue.
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Additional info for And the Rest is Just Algebra
While not factoring the difference in squares, he made the Fig. 6 A typical question in finding the mean and the variance in statistics 14 S. Stewart and S. Reeder Fig. 7 Student’s algebra errors and its consequences in the statistics final exam Fig. 8 The algebra was left to the reader to complete (Rice, 2007, p. 208) classic error of cancelling (b þ a) with (b2 þ a2), assuming (b2 þ a2) ¼ (b þ a) (b þ a), and hence forced his way to the correct result. In findingh the variance,ihe did not start the calculations with the correct formula VarðY Þ ¼ E ðY À EðY ÞÞ2 and carried out on the wrong path for a while and made sign errors while multiplying À(a þ b)(b À a) before giving up simplifying the fraction (Fig.
In an expression with more terms to put together, the problem may become more complicated. When given f(x) ¼ x2 À 3x þ 5, find f(À3); a College Algebra student explained his work as follows: “I used up the negative sign. I have to do parentheses first” and wrote: f(À3) ¼ À32 À 3 (À3) þ 5 ¼ 9 þ 9 þ 5 ¼ 23 followed by: 9 þ 5. “Now I have to do this (indicates the À32), “but I can’t remember if it’s negative nine or just nine. ” He wrote down À9 and stopped. “There’s no sign in front of this (pointing at 9 þ 5), so I need to multiply,” writing À9(14) ¼ 136.
To help students gain a more flexible, deeper understanding of arithmetic and algebra requires much more than computational or symbolic fluency. The National Council of Teachers (1989, 1991, 2000), Cohen (1995), National Research Council (2000, 2001), Conference Board of the Mathematical Sciences (2001), American Mathematical Association of Two-Year Colleges (2004), and the Common Core State Standards Initiative (2010) have all published recommendations for teachers, whether elementary, secondary, or postsecondary, directing instructors to: • Design and implement every instructional activity guided by informed decisionmaking to actively engage students in the learning of mathematics • Integrate technology appropriately into teaching to enhance students’ understanding of mathematical concepts and skills • Use results from the ongoing assessment of student learning in mathematics to improve curriculum, materials, and teaching methods The Curriculum Foundations Project: Voices of the Partner Disciplines echoes these recommendations.