Titlebook: Developing Deep Knowledge in Middle School Mathematics; A Textbook for Teach Sergei Abramovich,Michael L. Connell Textbook 2021 The Editor(

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,Teaching Middle School Mathematics: Standards, Recommendations and Teacher Candidates’ Perspectiveshool mathematics instruction, to share recommendations for the mathematical preparation of the middle grades teachers, and describe a number of notable perspectives on mathematics education that have been the backbone of the current reform movement of pre-college mathematics teaching worldwide. As w

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Modeling Mathematics in the Digital Era,nds-on experiences with actual objects. This approach will be further developed in Chap. 3 as a means to allow for the development of plausible reasoning and proof even at a concrete operational level. The second perspective is that of modeling real world events using the principles of mathematics.

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Modeling Mathematics with Fractions,n the division of two integers does not results in an integer: the part-whole context and the dividend-divisor context. The division of integers is typically introduced through two modeling contexts: measurement and partition. One can say that the part-whole and the dividend-divisor contexts for fra

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Decimal and Percent Representation of Rational Numbers,ndard base-ten system in use today. This commonly held perception generally reflects a lack of basic numeracy on the part of the students concerning the foundations of number and number representations. This is a problem which must be directly addressed in initial instruction if advancement is to be

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Ratio and Proportion, additive thinking. In other words, instead of describing a relationship between two quantities as being larger by three or smaller by five, the relationship would be described in terms such as triple the size, one fifth the size, four times greater, etc. The ability to use proportional reasoning is

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Combinatorics,tics. For example, knowing from counting experiments that different arrangements of objects in a set do not change their total count (alternatively, changing ordinalities of objects in a set does not change the set’s cardinality) leads to the following big idea of mathematics—integers can be represe

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