The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

A construction of a time-speed function in the time-distance function of students with chunky reasoning

덩어리 추론을 하는 학생의 시간-거리함수에서 시간-속력함수 구성에 대한 연구

  • Received : 2023.08.28
  • Accepted : 2023.10.17
  • Published : 2023.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

Previous studies from domestic and abroad are accumulating information on how to reason students' continuous changes through teaching experiments. These studies deal with scenes in which students who make 'smooth reasoning' and 'chunky reasoning' construct mathematical results together in teaching experiments. However, in order to analyze their results in more detail, it is necessary to check what kind of results a student reasoning in a specific way constructs for the tasks of previous studies. According to the need for these studies, the researcher conducted a total of 14 teaching experiments on one first-year high school student who was found to make 'chunky reasoning'. In this study, it was possible to observe a scene in which a student who makes 'chunky reasoning' constructs an output similar to 'a mathematical result constructed by students with various reasoning methods(smooth reasnoning or chunky reasoning) in previous studies.' In particular, the student who participated in this study observed a consistent construction method of constructing the function of 'time-speed' from the function of 'time-distance'. The researcher expected that information on this student's distinctive construction methods would be helpful for subsequent studies.

국내외 선행연구들에서는 교수실험을 통하여 학생들의 연속적인 변화에 대한 추론 방식에 대한 정보를 축적해가고 있다. 이들 연구에서는 연속적인 변화를 매끄러운 추론과 덩어리 추론을 하는 학생들이 교수실험에서 함께 수학적 결과물을 구성해가는 장면들을 다루고 있는데, 이들의 결과를 보다 세밀하게 분석하기 위해서는 특정 방식으로 연속적인 변화를 추론하는 학생이 이전 선행 연구들에서의 과제들에 대하여 어떠한 결과물을 구성해가는지 확인할 필요가 있다. 이러한 연구의 필요에 따라, 연구자는 덩어리 추론을 하는 것으로 확인된 고등학교 1학년 학생 한 명을 대상으로 총 14차시의 교수실험을 진행하였다. 본 연구에서는 덩어리 추론을 하는 학생이 '이전 선행연구에서 연속적인 변화에 대한 추론 방식이 다양한 학생들이 구성하였던 수학적 결과물'과 유사한 산출물을 구성해가는 장면을 관찰할 수 있었다. 특히 본 연구에 참여한 학생에게서 '시간-거리함수에서 시간-속력함수를 구성하는 일관된 구성 방식'이 관찰되었으며, 이러한 학생의 독특한 구성 방식에 대한 정보가 후속 연구에 도움이 될 것이라 기대하였다.

Keywords

References

  1. Castillo-Garsow, C. C. (2012). Continuous quantitative reasoning. In R. Mayes, R. Bonillia, L. L. Hatfield, & S. Belbase (Eds.), Quantitative reasoning: Current state of understanding, Wisdome monographs (Vol. 2, pp. 55-73). University of Wyoming.
  2. Castillo-Garsow, C., Johnson, H. L., & Moore, K. C. (2013). Chunky and smooth images of change. For the Learning of Mathematics, 33(3), 31-37.
  3. Ellis, A. B. (2011). Algebra in the middle school: Developing functional relationship through quantitative reasoning. In J. Cai& E. Knuth (Eds.), Early Algebraization (pp.215-238). Springer. https://doi.org/10.1007/978-3-642-17735-4_13
  4. Ellis, A., Ely, R., Singleton, B., & Tasova, H. (2020). Scaling-continuous variation: Supporting students' algebraic reasoning. Educational Studies in Mathematics, 104(1), 87-103. https://doi.org/10.1007/s10649-020-09951-6
  5. Glasersfeld, E. (1995). Radical constructivism: A way of knowing and learning. Studies in Mathematics Education Series: 6. The Falmer Press. https://doi.org/10.4324/9780203454220
  6. Hauger, G. S. (1995). Rate of change knowledge in high school and college students. p. 49. Washington, D.C. : ERIC Clearinghouse microfiches. ED392598.
  7. Lee, D. G. (2017a). A study on 1st year high school students' construction of average speed concept and average speed functions in relation to time, speed, and distance [Unpublished Doctoral dissertation, Korea National Education University].
  8. Lee, D. G. (2017b). Study of students' perception and expression on the constant of distance function in the relationship between distance function and speed function. The Mathematical Education. 56(4), 387-405. http://doi.org/10.7468/mathedu.2017.56.4.387
  9. Lee, D. G. (2021). A study on the process of constructing speed-time function from distance-time function y=2^x by students with different reasoning methods for continuous change. Journal of Educational Research in Mathematics, 31(2), 153-177.
  10. Lee, D. G., Moon, M. J., & Shin, J. H. (2015). A student's conceiving a pattern of change between two varying quantities in a quadratic functional situation and its representations: The case of Min-Seon. The Mathematical Education. 54(4), 299-315. https://doi.org/10.7468/mathedu.2015.54.4.299
  11. Lee, D. G. & Shin, J. H. (2017). Students' recognition and representation of the rate of change in the given range of intervals. The Journal of Educational Research in Mathematics. 27(1), 1-22.
  12. Lobato, J., Hohensee, C., Rhodehamel, B., & Diamond, J. (2012). Using student reasoning to inform the development of conceptual learning goals: The case of quadratic functions. Mathematical Thinking and Learning, 14(2), 85-119. https://doi.org/10.1080/10986065.2012.656362
  13. Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh & A. E. Kelly (Eds.), Research design in mathematics and science education. Kluwer.
  14. Thompson, P. W. (1994). 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. 179-234). State University of New York Press.
  15. Thompson, P. W., & Carlson, M. P. (2017). Variation, covariation, and functions: Foundational ways of thinking mathematically. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 421-456). National Council of Teachers of Mathematics.