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http://dx.doi.org/10.7468/mathedu.2019.58.1.79

A case study on students' expressions in solving the limitations of functions problems  

Lee, Dong Gun (MunJeong High School)
Publication Information
The Mathematical Education / v.58, no.1, 2019 , pp. 79-99 More about this Journal
Abstract
This study is a study to collect information about 'Limitations of functions' related learning. Especially, this study was conducted on three students who can find answers by algebraic procedure in the process of extreme problem solving. Students have had the experience of converting from their algebraic procedures to graphical expressions. This shows how they reflect on their algebraic procedures. This study is a study that observes these parts. To accomplish this, twelfth were teaching experiment in three high school students. And we analyzed the contents related to the research topic of this study. Through this, students showed the difference of expressions in the method of finding limits by using algebraic interpretation methods and graphs. In addition, we examined the connectivity of the limitations of functions problem solving process of functions using algebraic procedures and graphs in the process of converting algebraic expressions to graph expressions. This study is a study of how students construct limit concepts. As in this study, it is meaningful to accumulate practical information about students' limit conceptual composition. We hope that this study will help students to study limit concept development process for students who have no limit learning experience in the future.
Keywords
teaching experiment; limit; algebraic solution; graph; lesson; limit of function;
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Times Cited By KSCI : 3  (Citation Analysis)
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1 Kwak, Y.S. (2014). Teacher and qualitative research. Seoul: Kyoyookbook.
2 Park, I.S. & Kim, H.K. (2002). A Study on Teaching and Learning of the Limit Concept in High School. The Journal of Educational Research in Mathematics. 12(4), 557-582.
3 Lee, K.W. (2012). Elementary Social Studies Teacher? Curriculum Expertise in the Practice of Reorganizing Curriculim Materials on Economic Eduation. Research in Social Studies Education. 19(4), 45-60.
4 Lee, K.H. & Shin, B.M. (2005). High Achieving Students' Understanding of Continuity of Function. The Journal of Educational Research in Mathematics. 15(1), 39-56.
5 Lee, S.H., Jang, H.S., & Lee, D.W. (2018). A study of the in-service teachers' and pre-service teachers' recognition the domain in the problem of the continuity of a function. The Mathematical Education. 57(4), 477-499.   DOI
6 Lee, D.G. (2017). 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 dissertaion. Korea National University of Education.
7 Lee, D.G. (2018a). A Study on Expression of Students in the Prosess of Constructing Average Concept as Mathematical Knowledge. The Mathematical Education. 57(3), 311-328.   DOI
8 Lee, D.G. (2018b). A Case Study on Student's Thoughts and Expressions on various Types of Geometric Seies Tasks. The Mathematical Education. 57(4), 353-369.   DOI
9 Lee, D.G. & Kim, S.H. (2017). A Case Study on the Change of Procedural Knowledge Composition and Expression of Derivative Coefficient in Exponential Function Type Distance. School Mathematics 19(4). 639-661.
10 Lee, D.G., Yang, S.H., & Shin, J.H. (2017). A Study on the Process of Constructing the Instantaneous Rate of Change of Exponential Function y=2^x at x=0 Based on Understanding of the Natural Constant e. School Mathematics 19(1). 95-116.
11 Adu-Gyamfi, K. (2007). Connections among representations: The nature of students' coordinations on a linear function task. Unpublished doctoral dissertation, North Carolina State University.
12 Creswell, J. W. (2018). 연구방법, (정종진, 김영숙, 성용구, 성장환, 류성림, 박판우, 유승희, 임남숙, 임청환, 허재복 역), 서울: 시그마프레스. (원저 2014년 출판)
13 Elia, I., Gagatsis, A., & Gras, R. (2005). Can we "trace" the phenomenon of compartmentalization by using the implicative statistical method of analysis? An application for the concept of function. In R. Gras, F. Spagnolo, J. David (eds.), Proceedings of the third international conference I.S.A. Implicative Statistic Analysis, pp. 175-185, Palermo, Italy.
14 Glasersfeld, E. (1999). 급진적 구성주의 (김판수, 박수자, 심성보, 유병길, 이형철, 임채성, 허승희 역). 서울 : 원미사. (원저 1995년 출판)
15 Hatch, J. A. (2008). 교육 상황에서 질적 연구 수행하기 (진영은 역). 서울: 학지사. (원저 2002년 출판)
16 Knuth, E. J. (2000). Student understanding of the Cartesian connection: An exploratory study. Journal for Research in Mathematics Education 31(4), 500-507.   DOI
17 Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33-40). Hillsdale, NJ: Erlbaum.
18 Markovits, Z., Eylon, B. S., & Bruckheimer, M. (1986). Functions today and yesterday. For the learning of mathematics 6(2), 18-28.
19 Stacey, K. & Turner, R. (2014). Assessing mathematical literacy: The PISA experience. Heidelberg: Springer.
20 Merriam, S. B. (1994). 질적 사례연구법 (허미화 역). 서울: 양서원. (원저 1988년 출판)
21 Thompson, P. W. (1994). Images of rate and operational understanding of the Fundamental Theorem of Calculus. Educational Studies in Mathematics 26(2-3), 229-274.   DOI
22 Vinner, S. (1992). The function concept as a prototype for problems in mathematics learning. In E. Dubinsky & G. Harel (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 195-214). United States: Mathematical Association of America.
23 Yin, R. K. (2009). Case Study Research: Design and Methods(4th ed). Thousand Oaks, CA: Sage.
24 Zandieh, M. (2000). A theoretical framework for analyzing student understanding of the concept of derivative. CBMS Issues in Mathematics Education 8, 103-127.   DOI
25 Hiebert, J. & Carpenter, T. (1992). Learning and teaching with understanding. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65-97). New York: Macmillan.