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During the past year and a half, I’ve been engaged in writing math strategies for an education firm. One of the major areas of this work has been researching and compiling effective strategies for building conceptual understanding of fractions from K5. Through researching the progressions of fractional reasoning my go to references were, Battista, Steffe, and Olive. They identified six levels of fractional reasoning or trajectories of mathematical thinking required to develop the ability to reason proportionally. Generally, third grade marks the introduction to multiplication and fractions. Later in the elementary grades, students need to begin developing strategies for understanding fractions, decimals and percents by using manipulatives, drawings and diagrams. Division is the most important concept related to fractions, decimals and percents and all these math concepts require proportional
reasoning.Through the elementary years, students begin experiencing a shift in mathematics concepts from additive to multiplicative situations. Although multiplicative concepts are initially difficult for students to
comprehend, a—
mathematics curriculum must not wait …
to advance multiplicative concepts, such as
ratio and proportion. These principles must
be introduced early when considering additive situations. (Post et al. 1993) This was taken from: Tobias, Jennifer M., Andreason, Janet B., Developing Multiplicative Thinking from Additive Reasoning. “Teaching Children Mathematics,” September, 2013, Vol.2. Issue 2. pp. 1029