Abstract
The purpose of this chapter is to provide a broad view of the state of the field of history of mathematics in education, with an emphasis on mathematics teacher education. First, an overview of arguments that advocate for the use of history in mathematics education and descriptions of the role that history of mathematics has played in mathematics teacher education in the United States and elsewhere is given. Next, the chapter details several examples of empirical studies that were conducted with elementary (or, primary) and secondary mathematics prospective teachers. Finally, the chapter outlines examples of research from the “next generation” of infusing history in mathematics education, by providing accounts of practicing teachers who incorporated history of mathematics in teaching at the primary, secondary, and tertiary levels.
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Notes
- 1.
Although various locations around the world may use “primary” and “secondary” differently, in this chapter, “primary” level corresponds to the school years or grade levels for pupils aged 5–11 and “secondary” level corresponds to years or grade levels for pupils aged 12–18.
- 2.
This mnemonic device, SohCahToa, is employed by school mathematics teachers (and their students) to remember the basic right triangle ratios of sine = opposite (side)/hypotenuse; cosine = adjacent (side)/hypotenuse; and tangent = opposite (side)/adjacent (side).
- 3.
One such mnemonic device in the form of a “cutesy” anecdote is: “Mr. C, who drives around Mrs. A, and tells her how nice his two pies are (C = 2πr) and how her pies are square (A = πr 2)” (Lockhart 2008, p. 9).
- 4.
This observation is made with mathematics education in the United States in mind. France is an existence proof for greater opportunities for teachers to engage in history of mathematics in this way.
- 5.
For example, in 1989, NCTM asked for students to have “numerous and varied experiences related to the cultural, historical, and scientific evolution of mathematics,” which could have entailed learning mathematics from historical methods or reinventing such methods from guided explorations using historical problems. In 2000, however, the language was simplified to focus on the appreciation of mathematics.
- 6.
In the NCATE/NCTM program standards, “content standards” represent the different strands of mathematical knowledge teachers are responsible for knowing for teaching, such as knowledge of number and operation and knowledge of geometries.
- 7.
This is language of the NCATE/NCTM program standards, where “middle level” is understood as grades 6, 7, and 8 (pupils aged 12–14) and “secondary level” is understood as grades 9–12 (pupils aged 15–18). Many consider this redundant (including the author) since two divisions seem sufficient (e.g., elementary and secondary, or primary and secondary).
- 8.
In the NCATE/NCTM program standards, an “indicator” is a specific objective within a given content standard, such as, “Exhibit knowledge of the role of axiomatic systems and proofs in geometry” in the knowledge of geometries content standard.
- 9.
Although many consider middle grades mathematics to be included in “secondary,” these are the terms that NCTM uses.
- 10.
The number of replication sites as of May 2013. Also, since faculty called upon to teach “Perspectives” are often historians of science, the course privileges a “history of science” perspective. Consequently, the breadth of the historical implications of school mathematics or nature of mathematics that students take away from such a course is in need of further research.
- 11.
I am grateful to Christopher Thompson, my graduate research assistant, for his invaluable assistance in collecting and analyzing this information in 2011.
- 12.
The Carnegie basic classifications are RU/VH = Research Universities (very high research activity); RU/H = Research Universities (high research activity); DRU = Doctoral/Research Universities.
- 13.
These Carnegie basic classifications are Master’s L = Master’s Colleges and Universities (larger programs); Master’s M = Master’s Colleges and Universities (medium programs); Master’s S = Master’s Colleges and Universities (smaller programs).
- 14.
Only initial teacher certification programs at the undergraduate level were considered.
- 15.
CollegeBoard College MatchMaker database (http://collegesearch.collegeboard.com/search/index.jsp) was last accessed on 10 October 2010. The database has been replaced with a much more student-friendly website, BigFuture (https://bigfuture.collegeboard.org/), last accessed 27 December 2012.
- 16.
For the purposes of this chapter, we only consider initial teacher preparation programs, that is, undergraduate (tertiary) at the university or college level or postgraduate programs.
- 17.
Only European countries were discussed in the analysis with regard to the first and second types of country identified in the ICMI Study.
- 18.
The ICMI Study defined countries on the periphery as those “where, comparatively recently, historians of mathematics, or mathematics educators with a strong interest in mathematics history, have achieved an academic position where they are able to introduce mathematics history courses into teacher training” (Schubring et al. 2000, p. 94).
- 19.
There exists variability in the importance placed on teaching these subjects in France.
- 20.
The author is grateful to Manfred Kronfellner for providing this information.
- 21.
The author is grateful to Abdellah El Idrissi for providing this information.
- 22.
The author is grateful to Sang Sook Choi-Koh for describing the South Korean context.
- 23.
The European Summer University on the History and Epistemology in Mathematics Education (ESU) was held every 3 years from 1993 until 2010. Subsequent ESUs will be held every 4 years (e.g., the Seventh ESU will be in 2014), but not in years when ICME meetings are held.
- 24.
For a more comprehensive list, see Jankvist (2012).
- 25.
In general, the terms “primary mathematics teachers” and “elementary mathematics teachers” are used interchangeably to describe teachers of pupils aged 5–11 years of age. And, regardless of the term used, such programs are those that prepare generalists, or teachers who teach most if not all of the academic subjects.
- 26.
At the University of Cyprus, entrance into the preservice teacher program is highly competitive and students must take four entrance exams: one in language and three others in different subject areas of their choice.
- 27.
In qualitative research, a purposive sample is one in which a particular participant population is targeted, especially when there is a special nature of the study or participants are difficult to find. This was the case of Alpaslan’s and his colleagues’ research, where new reforms were in place in Turkey’s higher education institutions.
- 28.
- 29.
Lower division courses are courses taken during the first and second year at universities and colleges in the United States.
- 30.
In the United States, Maryland represents an example of this. Prospective elementary teachers are required to take a sequence of mathematics courses, though these may vary by institution. At the University of Maryland, Baltimore County, for example, prospective teachers take Statistics, Mathematics for Elementary Teachers I, and Mathematics for Elementary Teachers II.
- 31.
In some contexts the preparation of mathematics teachers entails an undergraduate degree in mathematics, as in the case of Italy (Furinghetti 2000).
- 32.
Of course, it is possible to see both types represented in the same publication.
- 33.
Three modes of using history in teaching mathematics were given in Clark (2011): history as anecdote, history as biography, and history as interesting problems.
- 34.
Furinghetti noted that she served as the historian “guide” for students, providing “historical information…needed to interpret authors” (2000, p. 47).
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Clark, K.M. (2014). History of Mathematics in Mathematics Teacher Education. In: Matthews, M. (eds) International Handbook of Research in History, Philosophy and Science Teaching. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7654-8_24
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