Abstract
This chapter aims to demonstrate the need for linkages between textbook content and the pedagogical ideas underpinning current standards for middle school 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 will be demonstrated through multiple citations of the standards and other educational materials (available in English), there is a true congruency of the ideas of mathematics pedagogy recorded in Australia, Canada, Chile, China, England, Japan, Korea, Singapore and the United States. Throughout the chapter, the authors will share both solicited and unsolicited (over the years) comments by middle school teacher candidates about their learning to teach the subject matter at that level, indicating the candidates’ interest in acquiring deep understanding of grade-appropriate mathematical content and methods towards gaining much needed professional expertise. Some comments will also include reflections on the candidates’ own experience of learning mathematics as youngsters. In all, the comments will show that positive attitude towards knowledge acquisition stems from the candidates being passionate in helping their future students to be better mathematical thinkers.
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Notes
- 1.
Collateral learning, while being a powerful educational idea in general, may be seen as one of the big didactical ideas of mathematics education because of innate connectivity of mathematical concepts due to which a student, indeed, learns more than “only the particular thing he is studying at the time” (Dewey, 1938, p. 49).
- 2.
Pythagoras (ca. 570 B.C.—ca. 495 B.C.)—a Greek philosopher.
- 3.
Pierre de Fermat (1601–1665)—a French mathematician and lawyer.
- 4.
As follows from formula (9.5), Chap. 9, when its right-hand side is a prime number then n = 2.
- 5.
Christian Goldbach (1690–1764)—a German mathematician.
- 6.
Mediating mathematical learning by visual thinking may be seen as another big idea of mathematics education. In the United States, it is most notably brought into being by the Common Core State Standards (2010) through the use of the so-called “tape diagram” (p. 87) and other drawings.
- 7.
- 8.
Leonhard Euler (1707–1783)—a Swiss mathematician, the father of all modern mathematics.
- 9.
Leonardo Fibonacci (1170–1250)—the most prominent Italian mathematician of his time, credited with the introduction of Hindu-Arabic number system in the Western world.
- 10.
Euclid—the most prominent Greek mathematician of the third century B.C.
- 11.
This automatic cancellation practice can lead to unexpected outcomes when, after several misguided cancellations the numbers 2 and 1 become connected with an equal sign (see Chap. 2, Sect. 2.5).
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Abramovich, S., Connell, M.L. (2021). Teaching Middle School Mathematics: Standards, Recommendations and Teacher Candidates’ Perspectives. In: Developing Deep Knowledge in Middle School Mathematics. Springer Texts in Education. Springer, Cham. https://doi.org/10.1007/978-3-030-68564-5_1
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DOI: https://doi.org/10.1007/978-3-030-68564-5_1
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