By Marjorie M. Petit, Robert E. Laird, Edwin L. Marsden, Caroline B. Ebby
A spotlight on Fractions is the 1st booklet to make cognitive study on how scholars improve their knowing of fraction thoughts comfortably obtainable and comprehensible to pre- and in-service ok– eight arithmetic educators. this significant source assists lecturers in translating study findings into their lecture room perform through conveying special information regarding how scholars increase fraction understandings in addition to universal scholar misconceptions, mistakes, preconceptions, and partial understandings that can intervene with scholars learning.? utilizing wide annotated samples of scholar paintings, in addition to vignettes attribute of school room academics’ reports, this e-book equips educators with wisdom and instruments to bare scholars’ pondering as a way to regulate their educating to enhance scholar studying of fractions concepts.? distinct positive aspects: finish of bankruptcy Questions supply academics the chance to investigate scholar considering and view educational suggestions for his or her personal scholars. tutorial hyperlinks support lecturers relate innovations from the bankruptcy to their very own directions and courses. enormous rules and study reports body the chapters and supply a platform for significant exploration of the instructing of fractions. solution Key published on-line deals vast reasons of in-chapter questions. a spotlight on Fractions bridges the space among what arithmetic schooling researchers have stumbled on concerning the studying of fraction options and what academics want to know to make powerful educational judgements.
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A spotlight on Fractions is the 1st booklet to make cognitive learn on how scholars improve their realizing of fraction strategies quite simply available and comprehensible to pre- and in-service ok– eight arithmetic educators. this crucial source assists lecturers in translating study findings into their school room perform through conveying specific information regarding how scholars enhance fraction understandings in addition to universal pupil misconceptions, error, preconceptions, and partial understandings which could intervene with scholars studying.
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Additional info for A Focus on Fractions: Bringing Research to the Classroom
The large outer square represents one whole unit. It has been partitioned into pieces. Each piece is identified with a letter. What fractional part of the whole is each piece? 16) illustrates diﬃculties that students may encounter when they lose “sight” of the whole as they are solving the problem. Matt correctly wrote the fraction 18 in the part labeled A. Matt incorrectly wrote the fraction 14 in the part labeled I. Here part I contains 14 of the area of the square in the lower right corner comprised of parts H and I, not 14 of the whole square.
16 • Modeling and Developing Understanding of Fractions However, researchers have found that using manipulatives does not guarantee success (Baroody, cited in Clements, 1999; Fennema, cited in Clements, 1999), nor “are manipulatives suﬃcient to guarantee meaningful learning” (Clements, 1999, p. 46). To maximize the impact of using manipulatives to build concepts, researchers suggest that: • • teachers guard against using manipulatives in a rote manner (as Mr. Smith did with the fraction circles); and teachers make clear connections to the mathematical ideas embodied in the manipulative and do not “assume that the concepts can automatically be read oﬀ the manipulative”.
29) and then ask questions that will focus on the mathematical point being made: • • • How are Keisha’s and Leslie’s models alike? How are they diﬀerent? Using Keisha’s model, it appears that 34 > 23. Using Leslie’s model 34 and 2 3 appear to be equal. What feature of the models led to a diﬀerent conclusion? Models are Not the Only Way to Reason with Fractions In the vignette at the beginning of this chapter we found Mr. Smith’s students having a diﬃcult time comparing 37 and 78. The students were relying on the pre-made fractions circles.
A Focus on Fractions: Bringing Research to the Classroom by Marjorie M. Petit, Robert E. Laird, Edwin L. Marsden, Caroline B. Ebby
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