Introduction
Research in mathematics education is interdisciplinary. According to Higginson (1980), mathematics, philosophy, psychology, and sociology are contributing disciplines to mathematics education (similar to what Michael Otte called Bezugsdisziplinen; Otte et al. 1974, p. 20). Linguistics and semiotics could be added. Framing of research, by means of theories or methods from these, amounts to different approaches, mathematics itself being one obvious choice. According to one view, mathematics education as a research field belongs to mathematics: at the second International Congress on Mathematical Education (ICME) in Exeter, Zofia Krygowska suggested that mathematics education should be classified as “a part of mathematics with a status similar to that of analysis or topology” (Howson 1973, p. 48). Another view sees mathematics education as an autonomous science (didactics of mathematicsas Hans Georg Steiner in 1968 called the new discipline he wanted to establish; see...
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References
Artigue M (1994) Didactic engineering as a framework for the conception of teaching products. In: Biehler R et al (eds) The didactics of mathematics as a scientific discipline. Kluwer, Dordrecht/Netherlands, pp 27–39
Artigue M, Batanero C, Kent P (2007) Learning mathematics at post-secondary level. In: Lester F (ed) Second handbook of research on mathematics teaching and learning. Information Age, Greenwich, pp 1011–1049
Athen H, Kunle H (eds) (1976) Proceedings of the third international congress on mathematical education. University of Karlsruhe, Karlsruhe
Boaler J (2002) Experiencing school mathematics: traditional and reform approaches to teaching and their impact on student learning, 2nd edn. Lawrence Erlbaum Associates, Mahwah
Bosch M, Gascon J (2006) 25 years of didactic transposition. ICMI Bull 58:51–65
Brousseau G (1997) Theory of didactical situations in mathematics. Didactique des Mathématiques 1970–1990. Kluwer, Dordrecht
Carraher DW (1993) Lines of thought: a ratio and operator model of rational number. Educ Stud Math 25:281–305
Cottrill J, Dubinsky E, Nichols D, Schwingendorf K, Thomas K et al (1996) Understanding the limit concept: beginning with a coordinated process scheme. J Math Behav 15:167–192
De Guzmán M, Hodgson BR, Robert A, Villani V (1998) Difficulties in the passage from secondary to tertiary education. In: Documenta mathematica, Extra Volume ICM III (Proceedings of the International Congress of Mathematician, Berlin 1998, August 18-27), pp 747–762
Freudenthal H (1983) Didactical phenomenology of mathematical structures. Reidel, Dordrecht
Freudenthal H (1991) Revisiting mathematics education. China lectures. Reidel, Dordrecht
Furinghetti F, Menghini M, Arzarello F, Giacardi L (2008) ICMI renaissance: the emergence of new issues in mathematics education. In: Menghini M, Furinghetti F, Giacardi L, Arzarello F (eds) The first century of the International Commission on Mathematical Instruction (1908–2008). Instituto della Encyclopedia Italiana, Roma, pp 131–147
Furinghetti F, Matos JM, Menghini M (2013) From mathematics and education to mathematics education. In: Clements MA, Bishop A, Keitel C, Kilpatrick J, Leung F (eds) Third international handbook of mathematics education. Springer, New York, pp 272–302
Gascon J (2003) From the cognitive to the epistemological programme in the didactics of mathematics: two incommensurable scientific research programmes? Learn Math 23(2):44–55
Goldin G (2003) Developing complex understandings: on the relation of mathematics education research to mathematics. Educ Stud Math 54:171–202
Griesel H (1969) Algebra und Analysis der Größensysteme (Teil I). In: Mathematisch Physikalische Semesterberichte, Band XVI(1), pp 56–93
Griesel H (1974) Überlegungen zur Didaktik der Mathematik als Wissenschaft. Zent Didakt Math 6(3):115–119
Higginson W (1980) On the foundation of mathematics education. Learn Math 1(2):3–7
Hill HC, Rowan B, Ball DL (2005) Effects of teachers’ mathematical knowledge for teaching on student achievement. Am Educ Res J 42:371–406
Howson AG (ed) (1973) Developments in mathematical education. Proceedings of the second international congress on mathematical education. Cambridge University Press, Cambridge
Jablonka E, Bergsten C (2010) Commentary on theories of mathematics education: is plurality a problem? In: Sriraman B, English L (eds) Theories of mathematics education: seeking new frontiers. Springer, New York, pp 111–120
Jahnke H, Mies T, Otte M, Schubring G (1974) Zu einigen Hauptaspekten der Mathematikdidaktik. In: Schriftenreihe des IDM Bielefeld, Band 1, pp 4–84
Kilpatrick J (1992) A history of research in mathematics education. In: Grouws D (ed) Handbook of research on mathematics teaching and learning. Macmillan, New York, pp 3–38
Klein F (1908) Elementarmathematik vom höheren Standpunkt aus, Bd 2. Springer, Berlin
Lepik M (ed) (2009) Teaching mathematics: retrospective and perspectives. Proceedings of the 10th international conference, Tallinn University, 14–16 May 2009. Institute of Mathematics and Natural Sciences, Tallinn University
Ma L (1999) Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. Erlbaum, Mahwah
Otte M, Steinbring H (1977) Probleme der Begriffsentwicklung – zum Stetigkeitsbegriff. Didakt Math 5(1):16–25
Otte M, Jahnke HN, Mies T, Schubring G (1974) Vorwort. In: Otte M, Jahnke HN, Mies T, Schubring G (eds) Mathematiker über die Mathematik. Springer, Berlin, pp 1–23
Padberg F (1995) Didaktik der Bruchrechnung, Auflage 2. Spektrum, Heidelberg
Prediger S, Arzarello F, Bosch M, Lenfant A (eds) (2008) Comparing, combining, coordinating-networking strategies for connecting theoretical approaches. ZDM – Int J Math Educ 40(2):163
Schoenfeld A (2004) Math wars. Educ Policy 18(1):253–286
Schreiber A (1983) Bemerkungen zur Rolle universeller Ideen im mathematischen Denken. Math Didact 6:65–76
Schwill A (1993) Fundamentale Ideen der Informatik. Zentralbl Didakt Math 25(1):20–31
Steiner H-G (1966) Vorlesungen über Grundlagen und Aufbau der Geometrie in didaktischer Sicht. Aschendorff, Münster
Steiner H-G (1969) Magnitudes and rational numbers – a didactical analysis. Educ Stud Math 2:371–392
Thom R (1973) Modern mathematics: does it exist? In: Howson AG (ed) Developments in mathematical education. Proceedings of the second international congress on mathematical education. Cambridge University Press, London, pp 194–209
Tietze U-P (1994) Mathematical curricula and the underlying goals. In: Biehler R, Scholz RW, Sträßer R, Winkelmann B (eds) Didactics of mathematics as a scientific discipline. Kluwer, Dordrecht, pp 41–53
Vollrath H-J (1984) Methodik des Begriffslehrens im Mathematikunterricht. Klett, Stuttgart
Vollrath H-J (1988) The role of mathematical background theories in mathematics education. In: Steiner H-G, Vermandel A (eds) Foundations and methodology of the discipline mathematics education (didactics of mathematics). Proceedings of the second time-conference. Berlin/Antwerpen, pp 120–137
Vollrath H-J (1994) Reflections on mathematical concepts as starting points for didactical thinking. In: Biehler R, Scholz RW, Sträßer R, Winkelmann B (eds) The didactics of mathematics as a scientific discipline. Kluwer, Dordrecht, pp 61–72
Vom Hofe R (1995) Grundvorstellungen mathematischer Inhalte. Spektrum Akademischer, Heidelberg
Whitehead AN (1913) The mathematical curriculum. Math Gaz 7:87–94
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Bergsten, C. (2014). Mathematical Approaches. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4978-8_95
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