Research Article
Year 2019,
Volume: 1 Issue: 1, 1 - 8, 26.07.2019
Abstract
Değişim oranı, fonksiyonların anlaşılmasında
önemli bir konudur. Aslında değişim oranı da bir fonksiyon gibi düşünülebilir.
Çünkü bir niceliğin diğerine göre değişim oranı hakkında muhakeme etmek
fonksiyon kavramının temelini oluşturmaktadır. Bu çalışmanın amacı 8. sınıf
öğrencilerinin değişimin oranı konusunda sahip oldukları düşünme yollarını
belirlemektir. Çalışmanın verileri uygulanan öğretim deneyi süresince elde
edilmiştir. Öğretim deneyinde uygulanan görevler ise öğrencilerin değişimin
oranı konusunda anlayışlarını ortaya koyacak şekilde oluşturulmuştur.
Çalışmanın sonuçlarına göre öğrencilerin düşünme yolları niceliksel olmayan
değişim oranı ve niceliksel değişim oranı şeklinde kategorize edilebilir.
Öğretim deneyinin sonucunda öğrencilerin düşünme yolları, niceliksel olmayan
değişim oranından niceliksel değişim oranına doğru değişim göstermiştir.
Keywords
References
- Bezuidenhout, J. (1998). First‐year university students’ understanding of rate of change. International Journal of Mathematical Education in Science and Technology, 29:3, pp. 389-399, DOI: 10.1080/0020739980290309.
- Carlson, M. P., Smith, N., & Persson, J. (2003). Developing and connecting calculus students' notions of rate-of change and accumulation: the fundamental theorem of calculus. International Group for the Psychology of Mathematics Education, 2, 165-172.
- Carlson, M., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002). Applying Covariational Reasoning While Modeling Dynamic Events: A Framework and a Study. Journal for Research in Mathematics Education, Vol. 33, No. 5, pp.352-378.
- Confrey, J., & Smith, E. (1994). Exponential functions, rates of change, and the multiplicative unit. Educational Studies in Mathematics, Vol. 26, No. 2/3, pp.135-164.
- Cooney, T. J., Beckman, S., & Lloyd, G. M. (2010). Developing essential understanding of functions for teaching mathematics in grades 9-12. Reston, VA: National Council of Teachers of Mathematics (NCTM).
- Ellis, A. B. (2009). Patterns, quantities, and linear functions. Mathematics Teaching in the Middle School, 14(8), 482-491.
- Hauger, G. S. (1995). Rate of change knowledge in high school and college students. Paper presented at the Annual Meeting of the American Educational Research Association. San Francisco, CA, April.
- Herbert, S., & Pierce, R. (2008). An “Emergent Model” for rate of change. International Journal of Computers for Mathematical Learning, 13, 231–249.
- Kalchman, M., & Koedinger, K. R. (2005). Teaching and learning functions. How students learn: History, mathematics and science in the classroom, 351-396.
- Powell, A. B., Francisco, J. M., & Maher, C. A. (2003). An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data. The Journal of Mathematical Behavior, 22(4), 405-435.
- Rowland, D. R., & Jovanoski, Z. (2004). Student interpretation of the terms in first-order ordinary differential equations in modelling on texts. International Journal of Mathematical Education in Science and Technology, 35(4), 505–516.
- Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh & A. E. Kelly (Eds.), Research on design in mathematics and science education (pp. 267–307). Hillsdale, NJ: Lawrence Erlbaum Associates.
- Thompson, P. W. (1994a). Images of rate and operational understanding of the fundamental theorem of calculus. Educational Studies in Mathematics, 26, 229–274.
- Thompson, P. W., & Thompson, A. G. (1992). Images of rate. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, CA, 20-25 April 1992.
- Thompson, P.W. (1994b). The development of the concept of speed and its relationship to concepts of rate. In G. Harel, & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 181–236). New York, NY: State University of New York Press.
- Weber, E.D. (2012). Students' ways of thinking about two-variable functions and rate of change in space. Doctoral Dissertation, Arizona State University.
Year 2019,
Volume: 1 Issue: 1, 1 - 8, 26.07.2019
Abstract
Rate of change is an important
subject for understanding functions. In fact rate of change can be thought as a
function itself. Because reasoning about rate of change of one quantity with
respect to another quantity is the basis of the function concept. The aim of
this research is to determine the 8th graders’ ways of thinking
about the rate of change. The data were gathered using a teaching experiment
methodology. The tasks used within teaching experiment were formed to explain
students understanding rate of change. The results show that students’ ways of
thinking can be categorized as non-quantitative rate of change and quantitative
rate of change. After completing the teaching experiment, the students moved
from non-quantitative to quantitative rate of change.
References
- Bezuidenhout, J. (1998). First‐year university students’ understanding of rate of change. International Journal of Mathematical Education in Science and Technology, 29:3, pp. 389-399, DOI: 10.1080/0020739980290309.
- Carlson, M. P., Smith, N., & Persson, J. (2003). Developing and connecting calculus students' notions of rate-of change and accumulation: the fundamental theorem of calculus. International Group for the Psychology of Mathematics Education, 2, 165-172.
- Carlson, M., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002). Applying Covariational Reasoning While Modeling Dynamic Events: A Framework and a Study. Journal for Research in Mathematics Education, Vol. 33, No. 5, pp.352-378.
- Confrey, J., & Smith, E. (1994). Exponential functions, rates of change, and the multiplicative unit. Educational Studies in Mathematics, Vol. 26, No. 2/3, pp.135-164.
- Cooney, T. J., Beckman, S., & Lloyd, G. M. (2010). Developing essential understanding of functions for teaching mathematics in grades 9-12. Reston, VA: National Council of Teachers of Mathematics (NCTM).
- Ellis, A. B. (2009). Patterns, quantities, and linear functions. Mathematics Teaching in the Middle School, 14(8), 482-491.
- Hauger, G. S. (1995). Rate of change knowledge in high school and college students. Paper presented at the Annual Meeting of the American Educational Research Association. San Francisco, CA, April.
- Herbert, S., & Pierce, R. (2008). An “Emergent Model” for rate of change. International Journal of Computers for Mathematical Learning, 13, 231–249.
- Kalchman, M., & Koedinger, K. R. (2005). Teaching and learning functions. How students learn: History, mathematics and science in the classroom, 351-396.
- Powell, A. B., Francisco, J. M., & Maher, C. A. (2003). An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data. The Journal of Mathematical Behavior, 22(4), 405-435.
- Rowland, D. R., & Jovanoski, Z. (2004). Student interpretation of the terms in first-order ordinary differential equations in modelling on texts. International Journal of Mathematical Education in Science and Technology, 35(4), 505–516.
- Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh & A. E. Kelly (Eds.), Research on design in mathematics and science education (pp. 267–307). Hillsdale, NJ: Lawrence Erlbaum Associates.
- Thompson, P. W. (1994a). Images of rate and operational understanding of the fundamental theorem of calculus. Educational Studies in Mathematics, 26, 229–274.
- Thompson, P. W., & Thompson, A. G. (1992). Images of rate. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, CA, 20-25 April 1992.
- Thompson, P.W. (1994b). The development of the concept of speed and its relationship to concepts of rate. In G. Harel, & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 181–236). New York, NY: State University of New York Press.
- Weber, E.D. (2012). Students' ways of thinking about two-variable functions and rate of change in space. Doctoral Dissertation, Arizona State University.
There are 16 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | July 26, 2019 |
| Published in Issue | Year 2019 Volume: 1 Issue: 1 |
