Browse > Article
http://dx.doi.org/10.30807/ksms.2019.22.4.001

An Analysis of the Types of Slope Concepts in Math Textbooks of Middle School  

Kang, YoungRan (Gyeongsangbukdo Gyeongju Office of Education)
Cho, CheongSoo (Yeungnam University)
Publication Information
Journal of the Korean School Mathematics Society / v.22, no.4, 2019 , pp. 351-367 More about this Journal
Abstract
Slope is an important mathematical concept that is connected to advanced mathematics as well as a basic concept as an indicator of the steepness of a straight line. The purpose of this study is to see how the concept of slope is presented in mathematics textbooks of middle school. For this study, we analyzed the types of slope concepts in the textbooks. In particular, we analyzed motivation activity, definition, examples of slope in them and used a concept framework of slope by Stump(1999, 2001), Moore-Russo, Connor & Rugg (2011). As a result, it was shown that middle school mathematics textbooks use the types of slope concepts to be biased when explaining the slope or presenting the slope problems. In addition, the real contexts of slope is poorly presented, and the concept types change from visual aspect to analytical aspect in the processes. This study provides suggestions on how to present the slope concepts in mathematics curriculum and middle school textbooks.
Keywords
Slope; Concept definition; Concept image; Middle school mathematics textbook;
Citations & Related Records
연도 인용수 순위
  • Reference
1 도종훈 (2008). 직선의 대수적 표현과 직선성(直線性)으로서의 기울기. 수학교육논문집, 22(3), 337-347.
2 안숙영 (2005). 기울기의 개념 분석과 일차함수의 이해를 돕는 기울기 지도. 서울대학교 대학원.
3 양기열, 장유선 (2010). 고등학생들의 함수단원 학습과정에서 나타나는 오류유형 분석과 교정. 한국학교수학회논문집, 13(1), 23-43.
4 우정호, 조영미 (2001). 학교수학 교과서에서 사용하는 정의에 관한 연구. 수학교육학연구, 11(2), 363-384.
5 이헌수, 김영철, 박영용, 김민정 (2015). 일차방정식과 일차함수에 대한 중학생들의 인식과 오류. 한국학교수학회논문집, 18(3), 259-279.
6 Carlson, M., Oehrtman, M., & Engelke, N. (2010). The precalculus concept assessment: A tool for assessing students' reasoning abilities and understandings. Cognition and Instruction, 28, 113-145.   DOI
7 Clapham, C., & Nicholson, J. (2009). Oxford concise dictionary of mathematics, gradien. Retrieved from http://web.cortland.edu/matresearch/OxfordDictionary
8 Confrey, J., & Smith, E. (1995). Splitting, covariation, and their role in the development of exponential functions. Journal for Research in Mathematics Education, 26, 66-86.   DOI
9 Foreman, S. (1987). Algebra: First course. Boston, MA: Addison-Wesley Educational Publishers.
10 김진숙 (1998). 문제해결과 교과서 문제의 교육과정적 의미. 교육과정연구, 16(2), 205-226.
11 Freudenthal, H. (1991). Revisiting mathematics education. Dordrecht, The Netherlands: Kluwer.
12 Kaufmann, J. E. (1992). Intermediate algebra for college students. Belmont, CA:Brooks.
13 Knuth, E. J. (2000). Student understanding of the cartesian connection: An exploratory study. Journal for Research in Mathematics Education, 31(4), 500-507.   DOI
14 Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching, Review of Educational Research, 60(1), 1-64.   DOI
15 Li, Y. (2000). A comparison of problems that follow selected content presentations in American and Chinese mathematics textbooks. Journal for Research in Mathematics Education, 31(2), 234-241.   DOI
16 Moore-Russo, D., Conner, A., & Rugg, K. I. (2011). Can slope be negative in 3-space? Studying concept image of slope through collective definition construction. Educational Studies in Mathematics, 76(1), 3-21.   DOI
17 Mudaly, V., & Moore-Russo, D. (2011). South African teachers' conceptualisations of gradient: A study of historically disadvantaged teachers in an advanced certificate in education programme, Pythagoras, 32(1), 27-33.
18 Nagle, C., & Moore-Russo, D. (2012). A comparison of college instructors' and students' conceptualization of slope. In Van Zoest, L., Lo, J. J., & Kratkey, J. L. (Eds). Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (p. 1010). Kalamazoo, MI: Western Michigan University.
19 Noble, T., Nemirovsky, R., Wright, T. & Tierney, C. (2001). Experiencing change: The mathematics of change in multiple environments. Journal for Research in Mathematics Education, 32, 85-108.   DOI
20 Semadeni, Z. (2008). The triple nature of mathematics: Deep ideas, surface representation, formal models. In M. Niss (Ed.), Proceedings of the 10th international Congress on Mathematical Education, (pp.4-11). Roskilde: Roskilde University Press.
21 Stanton, M., & Moore-Russo, D. (2012). Conceptualizations of slope: A look at state standards. School Science and Mathematics, 112(5), 270-277.   DOI
22 Stump, S. (1999). Secondary mathematics teachers' knowledge of slope. Mathematics Education Research Journal, 11(2), 124-144.   DOI
23 Stump, S. (2001). Developing preservice teachers' pedagogical content knowledge of slope. Journal of Mathematical Behaviour, 20(2), 207-227.   DOI
24 Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference on limit and continuity. Educational Studies in Mathematics, 12(2), 151-169.   DOI
25 Vinner, S. (1991). The role of definition in the teaching and learning of mathematics. In D. Tall (Ed.), Advanced mathematical thinking (pp. 65-81). Dordrecht: Kluwer Academic Publishers.
26 Zaslavsky, O. (2002) Being slopy about slpoe: The effect of changing the scale. Educational Studies in Mathematics, 49(1), 119-140.   DOI