Browse > Article

Exploring How Middle-School Mathematics Textbooks on Functions Provide Students an Opportunity-To-Learn  

Kim, Gooyeon (Sogang University)
Jeon, MiHyun (Graduate School of Education, Sogagn University)
Publication Information
School Mathematics / v.19, no.2, 2017 , pp. 289-317 More about this Journal
Abstract
This study aims to explore how Korean middle-school mathematics textbooks on functions provide students an opportunity-to-learn [OTL]. For this purpose, we investigate 3 textbooks in terms of mathematics content and practice, the level of cognitive demands of mathematical tasks, types of student responses, types of context-based tasks, and connections among the tasks. The findings from the data analysis suggest as follows: a) an opportunity-to-learn to connect procedures to functional concepts and new ideas of functions to the existing one is very limited; b) the textbooks seem to provide students an OTL to understand functions as definitions, rules and conventions and to experience repeatedly procedural executions through worked examples and mathematics tasks; c) students may not experience to explain their own ideas/thinking by using mathematical sentence or justify their own cognitive processes; and d) students can be exposed to get a sense of mathematics as a set of fragmented and isolated facts or procedures, rather than to encourage to expand and deepen their understanding of functions.
Keywords
Opportunity-To-Learn; functions; textbooks; middle school level;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 교육과학기술부 (2009). 2009 개정 수학과 교육과정.
2 교육과학기술부 (2010). 2011년 주요 업무계획: 창의인재와 선진과학기술로 여는 미래 대한민국. Retrieved from http://if-blog.tistory.com/939
3 권지현․김구연 (2013). 중학교 수학 교과서에 제시된 기하영역의 수학 과제 분석. 수학교육, 52(1), 111-128.
4 김구연 (2011a). How teachers use mathematics curriculum materials in planing and implementing mathematics lessons. 학교수학, 13(4), 485-500.
5 김구연 (2011b). The impact of enacted curriculum on student learning in mathematics classrooms. 한국학교수학회논문집, 14(1), 31-42.
6 김대영 . 김구연 (2014). 중등 수학교사의 교과서 수학과제 이해 및 변형 능력. 학교수학, 16(3), 445-469.
7 김미희․김구연 (2013). 고등학교 교과서의 수학과제 분석. 학교수학, 15(1), 37-59.
8 김민혁 (2014). 수학 교사의 교과서 및 교사용 지도서 활용도 조사. 학교수학, 16(3), 503-531.
9 마민영․신재홍․이수진․박종희 (2016). 중학생들의 함수의 그래프에 대한 이해와 발달. 학교수학, 18(3), 457-478.
10 문진수․김구연 (2014). 중등 수학교사의 함수에 대한 지식(MKT)측정 및 분석. 학교수학, 17(3), 469-492.
11 박종희․신재홍․이수진․마민영 (2017). 그래프 유형에 따른 두 공변 추론 수준 이론의 적용 및 비교. 수학교육학연구, 27(1), 23-49.
12 이광상․조민식․류희찬 (2006). 엑셀의 활용이 일차함수 문제해결에 미치는 효과. 학교수학, 8(3), 265-290.
13 이혜림 . 김구연 (2013). 수학교과서 문제에 대한 예비중등교사의 이해 및 변형 능력. 수학교육학연구, 23(3), 353-371.
14 전미현․김구연 (2015). 예비교사들의 수학교수지식(MKT) 측정 및 분석 연구. 수학교육학연구, 25(4), 691-715.
15 홍창준․김구연 (2012). 중학교 함수 단원의 수학 과제 분석. 학교수학, 14(2), 213-232.
16 Ball, D. L., & Cohen, D. K. (1996). Reform by the book: What is-or might be-the role of curriculum materials in teacher learning and instructional reform? Educational Researcher, 25(9), 6-8.   DOI
17 Bell, A. (1993). Principles for the design of teaching. Educational Studies in Mathematics, 24, 5-34.   DOI
18 Charalambous, C. Y., Delaney, S., Hsu, H., & Mesa, V. (2010). A comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning, 12, 117-151.   DOI
19 Collopy, R. (2003). Curriculum materials as a professional development tool: How a mathematics textbook affected two teachers' learning. Elementary School Journal, 103, 287-311.   DOI
20 Cooney, T. J., Beckmann, 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.
21 Davis, E. A., & Krajcik, J. S. (2005). Designing educative curriculum materials to promote teacher learning. Educational Researcher, 34(3), 3-14.   DOI
22 Day, L. (2015). Mathematically rich, investigative tasks for teaching algebra. Mathematics teacher, 108(7), 512-518   DOI
23 Hill, H. C., & Charalambous, C. Y. (2012). Teacher knowledge, curriculum materials, and quality of instruction: Lessons learned and open issues. Journal of Curriculum Studies, 44, 559-576.   DOI
24 Freeman, D. J., & Porter, A. C. (1989). Do textbooks dictate the content of mathematics instruction in elementary schools? American Educational Research Journal, 26(3), 403-421.   DOI
25 Haggarty, L., & Pepin, B. (2002). An investigation of mathematics textbooks in England, France and Germany: Some challenges for England. Research in Mathematics Education, 4(1), 127-144.   DOI
26 Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-Based Factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524-549.   DOI
27 Kilpatrick, J. (2003). What works? In S. L. Senk & D. R. Thompson (Eds.), Standards-based school mathematics curricula. What are they? What do students learn? (pp. 471-493). Mahwah, NJ: Lawrence Erlbaum.
28 Lappan, G., Phillips, E. D., Fey, J. T., & Friel, S. N. (2014). Connected Mathematics 3: Grade 7. Upper Saddle River, NJ: Pearson.
29 Liu, X. (2009). Linking competence to opportunities to learn: Models of competence and data mining. Springer: New York.
30 Lloyd, G. M. (1999). Two teachers' conceptions of a reform curriculum: Implications for mathematics teacher development. Journal of Mathematics Teacher Education, 2, 227-252.   DOI
31 Lloyd, G. M., Herbel-Eisenmann, B., & Star, J. R. (2011). Developing essential understanding of expressions, equations, and functions for teaching mathematics in grades 6-8. Reston, VA: National Council of Teachers of Mathematics.
32 National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, & B. Findell (Eds.). Washington, DC: National Academy Press.
33 Lloyd, G. M., Remillard, J. T., & Herbel-Eisenmann, B. A. (2009). Teachers' use of curriculum materials: An emerging field. In J. T. Remillard, B. A. Herbel-Eisenmann & G. M. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 3-14). Routledge: New York.
34 National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
35 National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
36 Remilard, J. T. (2005). Examining key concepts in research on teachers' use of mathematics curricula. Review of Educational Research, 75(2), 211-246.   DOI
37 Remillard, J. T., & Bryans, M. B. (2004). Teachers' orientations toward mathematics curriculum materials: Impllications for teacher learning. Journal for Research in Mathematics Education, 35, 352-388.   DOI
38 Reys, B. J., Reys, R. E., & Chavez, O. (2004). Why mathematics textbooks matter. Educational Leadership, 61(5), 61-66.
39 Reys, R. E, Reys, B. J., Lapan, R., Holliday, G., & Wasman, D. (2003). Assessing the impact of Standards-based middle grades mathematics curriculum materials on student achievement. Journal for Research in Mathematics Education, 34, 74-95.   DOI
40 Schmidt, W. H. (2012). Measuring content through textbooks: The cumulative effect of middle-school tracking. In G. Gueudet, B. Pepin, & L. Trouche (Eds.), From text to 'lived'resources; Mathematics curriculum materials and teacher development (pp. 143-160). Dordrecht: Springer.
41 Stein, M. K., Kim, G., & Seeley, M. (2006). The enactment of reform mathematics curricula in urban settings: A comparative analysis. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco.
42 Senk, S. L., & Thompson, D. R. (2003). Middle school mathematics curriculum reform. In S. L. Senk & D. R. Thompson (Eds.), Standardsbased school mathematics curricula: What are they? What do students learn? (pp. 181-191). Mahwah, NJ: Lawrence Erlbaum.
43 Sherin, M., & Drake, C. (2009). Curriculum strategy framework: Investigating patterns in teachers' use of a reform-based elementary mathematics curriculum. Journal of Curriculum Studies, 41(4), 467-500.   DOI
44 Stein, M. K., & Kim, G. (2009). The role of mathematics curriculum materials in large-scale urban reform: An analysis of demands and opportunities for teacher learning. In In J. T. Remillard, B. A. Herbel-Eisenmann & G. M. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 37-55). Routledge: New York.
45 Stein, M. K., Remilard, J. T., & Smith, M. S. (2007).How curriculum influences student learning. In F. K. Lester (Ed), Second handbook of research on mathematics teaching and learning (pp. 319-370). Charlotte, NC: Information Age.
46 Tarr, J. E., Chavez, O., Reys, R. E., & Reys, B. J. (2006). From the written to the enacted curricula: The intermediary role of middle school mathematics teachers in shaping students' opportunity to learn. School Science and Mathematics, 106(4), 191-201.   DOI
47 Tornroos, J. (2005). Mathematics textbooks, opportunity to learn and student achievement. Studies in Educational Evaluation, 31(4), 315-327.   DOI
48 Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn contextbased tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89, 41-65.   DOI