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Teaching Student-Centered Mathematics: Chapters 5-8
Chapter 5 deasl with the development of fraction concepts based on the use of models and manipulatives. The physical models help students build concepts in their minds of region or area, length, and sets. The "correct shares" activities willl help my students understand that like fractions are congruent, whereas unlike fractions are not equal. Students frequently want to divide a circle into thirds by drawing two straight parallel lines as one would a square or rectangle.
Chapter 6: The development of fraction concepts should follow the same path as the developement of whole numbers. Just as a numeral represents a quantity or value, fractions like wise must be constructed and understood by the student. Haste to teach rules must be abandoned until student conceptualization can bridge the gap between cocept and application of rules that emerge as a natural part of solving problems involving fractions. Van de Walle and Lovin reiterate time and again that traditional algorithms are not to be taught initially. I will need to try all tasks in a variety of ways until I am comforatble and can anticipate strategies and results.
Chapter 7 explores the use of decimals and percentages. Building on the concepts of fractions, students can discover the relationship between fractions and decimals by reviewing the base-10 system. Using the 10 x 10 squares, students can create fractions to represent numbers such as .45. With questions such as, "Is this greater or less than 1/2?" students can begin to construct an understanding of decimals and percentages.
Chapter 8 deals with geometric thinking and geometric concepts. In the work of van Hiele and van Hiele-Geldof, learners progress through 5 developmental stages (not age dependent) as they progress through geometric thinking. Experience with geometric models and activities is the single greatest factor. the more students explore and manipulate objects and models in the suggested exercises, the greater their conceptualization and understanding.
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