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Appendix B: Concepts of Measurement
Pages 359-362

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From page 359...
... For example, if children are shown two equal length rods aligned, they usually agree that they are the same length. If one is moved to project beyond the other, children 4½ to 6 years often state that the projecting rod is longer (at either end; some maintain, "both are longer"; the literature is replete with different interpretations of these data, but certainly children's notion of "length" is not mathematically accurate)
From page 360...
... Additivity is the related notion that length can be decomposed and composed, so that the total distance between two points is equivalent to the sum of the distances of any arbitrary set of segments that subdivide the line segment connecting those points. This is, of course, closely related to the same concepts in composition in arithmetic, with the added complexities of the continuous nature of measurement.
From page 361...
... It creates stable patterns of mental actions that an individual uses to link sensory experiences, rather than the sensory input of the experiences themselves. Such spatial structuring precedes meaningful mathematical use of the structures, such as determining area or volume (Battista and Clements, 1996; Battista et al., 1998; Outhred and Mitchelmore, 1992)
From page 362...
... , Proceedings of the 18th Annual Meeting of the North America Chapter of the International Group for the Psychology of Mathematics Education (vol.

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