How high school mathematics teachers use the history of functions into their teaching

Document Type : Mathematical history Paper

Authors

1 Department of Mathematics, Education Faculty of Mathematics and Computer Shahid Bahonar University of Kerman,

2 Kerman - Zarand - Zarand Education Department

Abstract

The concept of a function is one of the fundamental concepts in school mathematics, serving as a unifying idea throughout mathematics. Functions are the primary tools for describing the real world in mathematical language. Almost all students who go through units of mathematics in their academic curriculum become familiar with the concept of a function. However, various research studies indicate that many students have a weak understanding of the concept of a function. The main objective of this article is to depict the historical development of the concept of a function over time and then examine how a group of mathematics teachers in Kerman province teaches it. In other words, this article seeks to address the question of how high school mathematics teachers teach the concept of a function and whether their teaching approach aligns with any historical perspective. The participants in this study are 20 high school mathematics teachers in Kerman province who were selected purposively. The results obtained from classroom observations showed that the participating teachers mostly did not incorporate the historical development and formation of the concept of a function into their teaching. They typically began teaching functions with a formal definition and after presenting a few examples, enumerated the properties of functions. Additionally, the analysis of the study's data indicated that the concept of a function was presented based on the latest recognized representation of functions, namely based on the correspondence approach between sets (ordered pairs).

Main Subjects

[1] Z. Parhizgar, students' understanding of the main concept of function, Ms. Thesis, Shahid Beheshti University, 2017.

[2] M. Towfighi, investigating the misunderstandings of the second grade students of experimental and mathematical fields about the concept of function in Estahban in the academic year 2017-2018, Ms.Thesis, Shahid Rajaee Teacher Training University, 2018.

[3] A. Heydari, subject knowledge and pedagogical content knowledge of future teachers from the concept of function, Ms. thesis, Shahid Rajaei University, 2019.

[4] A. Rayhani, function training, some approaches and challenges, published in the collection of selected articles of the 9th Iranian Mathematics Education Conference, September 2016, Zahedan, Iran. 118--111.

[5] S. Gholam Azad, Rethinking High School Algebra Program, Development of Mathematics Education, No. 63, 2010 12--4.

[6] H. Akkoc and D. Tall, The Simplicity, Complexity and Complication of the Function Concept, In A. D. Cockburn and E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematic Education, 2 (2002) 25–32.
[7] Ch. Insook, Mathematical and Pedagogical Discussions of the Function Concept, Research in Mathematical Education, 3 (1999) 35–56.
[8] I. Kleiner, Evolution of the Function Concept: A Brief Survey, The College Mathematics Journal, 20 (1989) 282–300.
[9] I. Kleiner, Functions: Historical and pedagogical aspects, Science and Education, 2 (1993) 183-209.
[10] M. V. Polaki, Working with functions without understanding: an Assessment of the Perceptions of Basotho college mathematics specialists on the idea of function, Eurasia journal of mathematics, Science and Technology Education, 1 (2005).
[11] J. P. Ponte, The History of the Concept of Function and Some Educational Implications, The Mathematics Educator, 3 (1992) 3-8.
[12] D. Tall and M. Bakar, Students’ Mental Prototypes for Functions and Graphs, International Journal of Mathematics Education in Science and Technology, 231 (1992) 39-50.
[13] D. Tall, Functions and Calculus, In A. J. Bishop et al (Eds.), International Handbook of Mathematics Education, (1997), 289–325.
[14] D. Tall and Sh. Vinner, Concept Image and Concept Definition in Mathematics with Particular Reference to Limit and Continuity, Educational Studies in Mathematics, 12 (1981) 151–169.
[15] A. P. Youschkevitch, The concept of function up to the middle of the 19th century, Archive for History of Exact Sciences, 16 (1976) 37–85.

References

[1] Z. Parhizgar, students' understanding of the main concept of function, Ms. Thesis, Shahid Beheshti University, 2017.
[2] M. Towfighi, investigating the misunderstandings of the second grade students of experimental and mathematical fields about the concept of function in Estahban in the academic year 2017-2018, Ms.Thesis, Shahid Rajaee Teacher Training University, 2018.
[3] A. Heydari, subject knowledge and pedagogical content knowledge of future teachers from the concept of function, Ms. thesis, Shahid Rajaei University, 2019.
[4] A. Rayhani, function training, some approaches and challenges, published in the collection of selected articles of the 9th Iranian Mathematics Education Conference, September 2016, Zahedan, Iran. 118--111.
[5] S. Gholam Azad, Rethinking High School Algebra Program, Development of Mathematics Education, No. 63, 2010 12--4.
[6] H. Akkoc and D. Tall, The Simplicity, Complexity and Complication of the Function Concept, In A. D. Cockburn and E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematic Education, 2 (2002) 25–32.
[7] Ch. Insook, Mathematical and Pedagogical Discussions of the Function Concept, Research in Mathematical Education, 3 (1999) 35–56.
[8] I. Kleiner, Evolution of the Function Concept: A Brief Survey, The College Mathematics Journal, 20 (1989) 282–300.
[9] I. Kleiner, Functions: Historical and pedagogical aspects, Science and Education, 2 (1993) 183-209.
[10] M. V. Polaki, Working with functions without understanding: an Assessment of the Perceptions of Basotho college mathematics specialists on the idea of function, Eurasia journal of mathematics, Science and Technology Education, 1 (2005).
[11] J. P. Ponte, The History of the Concept of Function and Some Educational Implications, The Mathematics Educator, 3 (1992) 3-8.
[12] D. Tall and M. Bakar, Students’ Mental Prototypes for Functions and Graphs, International Journal of Mathematics Education in Science and Technology, 231 (1992) 39-50.
[13] D. Tall, Functions and Calculus, In A. J. Bishop et al (Eds.), International Handbook of Mathematics Education, (1997), 289–325.
[14] D. Tall and Sh. Vinner, Concept Image and Concept Definition in Mathematics with Particular Reference to Limit and Continuity, Educational Studies in Mathematics, 12 (1981) 151–169.
[15] A. P. Youschkevitch, The concept of function up to the middle of the 19th century, Archive for History of Exact Sciences, 16 (1976) 37–85.

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History

  • Receive Date: 27 July 2019
  • Revise Date: 22 January 2020
  • Accept Date: 22 January 2020
  • Publish Date: 23 August 2019

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