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http://dx.doi.org/10.7468/jksmee.2018.32.3.407

A discursive approach to analysis of definition of graph in first year middle school textbooks  

Kim, Won (Korea University Graduate School)
Choi, Sang-Ho (Korea University)
Kim, Dong-Joong (Korea University)
Publication Information
Communications of Mathematical Education / v.32, no.3, 2018 , pp. 407-433 More about this Journal
Abstract
In order to analyze textbooks from a discursive approach, the purpose of this study is to structuralize an analytic framework based on previous literature review and apply it to analyzing the meanings and their syntheses developed by words and visual mediators appeared in the definition of graph in first-year middle school textbooks. The discursive approach consists of the communicational approach developed by Sfard(2008) and the systemic functional linguistics developed by Halliday(1985/2004). In this study, ideational meta-functions for ideational meanings and interpersonal meta-functions for interpersonal meanings were employed to analyze the meanings produced by words and visual mediators in textbooks, whereas textual meta-functions for textual meanings were used for analyzing the synthesized relationships between words and visual mediators. Results show that first, density in mathematical discourse was very high and subjects in mathematical activities were ambiguous in the ideational meanings of words, and behavior aspect was more emphasized than thinking aspect in the interpersonal meanings of words which request student participations. In the case of ideational meanings of visual mediators, there was a lack of narrative diagrams, whereas there were qualitative differences in the case of offer. Second, there was a need for promoting a wide range of diverse synthetic relationships between words and visual mediators for developing enriched mathematical meanings through the varying uses like specification, explanation, similarity, and complement. These results are so important that they provide a new analytic framework from a discursive approach to textbook analysis because not only words, but also visual mediators are analyzed as tools for producing meanings in mathematics textbooks and their synthetic relationships are also examined.
Keywords
communicational approach; social semiotics; discursive approach; textbook analysis; definition of graph;
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1 An, K. Y. & Kwon, O. N. (2002). Error analysis and treatment in function graph task, J. Korea Soc. Math. Ed. Ser. E: Communications of Mathematical Education, 13(1). 337-360.
2 Yang, S. H. (2017). A View on the Diversity of the Word and Mathematical Notation Expression Used in High School Mathematics Textbooks, Journal of the Korean School Mathematics Society, 20(3), 211-237.
3 Lee, J. A., Maeng, S. H., & Kim, C. J. (2007). The Socio-semiotic Analysis of Visual Images in Elementary Science Textbooks: Focused on Weather and Forecast, The Journal of The Korean Earth Science Society, 28(3), 277-847.   DOI
4 Lee, C. H. & Kim, B. M. (2003). Analysis of the Error-Remedial Effect and Change of the Students' Misconception on the Learning of Linear Function, School Mathematics, 5(1), 115-133.
5 Lee, J. Y. et al. (2018). Middle School Mathematics 1, Seoul: Chun Jae Textbook Publishers.
6 Chang, H. et al. (2017). A Comparative Analysis of Ratio and Rate in Elementary Mathematics Textbooks, Journal of Elementary Mathematics Education in Korea, 21(1), 135-160.
7 Kim, S. H. & Paik, H. S. (2016). An exploration of the direction of a graph in middle school mathematics education, Journal of Learner-Centered Curriculum and Instruction, 16(6), 445-468.
8 Kim, S. H. et al. (2015). A study to reform the mathematics textbooks that enhance the understanding of terms and symbols, KOFAC BD16010002.
9 Kim, W. K. et. al. (2018). Middle School Mathematics 1, Seoul: Vi sang Textbook Publishers.
10 Kim, C. & Shin, J. (2018). A Case Study of Students' Constructions and Interpretations of Informal Graphs, School Mathematics, 20(1), 107-130.   DOI
11 Lew, H. C. et. al. (2018). Middle School Mathematics 1, Seoul: Chun Jae Textbook Publishers.
12 Park, S., Byun, H., & Ju, M. (2011). Study on the Mathematics and Learning Characteristics of Middle School Students, KOFAC RRI 2011-5.
13 Ma, M. & Shin, J. (2016). Gifted Middle School Students' Covariational Reasoning Emerging through the Process of Algebra Word Problem Solving, School Mathematics, 18(1), 43-59.
14 Park, K. S. (2013). An Analysis on Real State of Using Terms in Grade 1-2 Math Textbook/Workbook in Korea: Centered on 'Product', 'Place Value', 'Multiplication Stairs', 'Numeral', School Mathematics, 15(4), 833-846.
15 Park, K. S. & Yim, J. H. (2005). A Critical Examination of Undefined Mathematical Terms Used in Elementary School Mathematics Textbooks of Korea, The journal of educational research in mathematics, 15(2), 197-213.
16 Park, J. H. (2007). A Study on Teaching-Learning for Linguistic Realization in Informative Speech, Journal of Speech Communication, 10, 143-166.
17 Pang, J. S., Kwon, M., & Kim, J. W. (2017). Analysis of the Adequacy of Vocabulary in Elementary Mathematics Textbooks and Workbooks for Grades 5 and 6, The journal of educational research in mathematics, 27(3), 329-350.
18 Jeon, Y. O. (2006). A Study on Unit of Spoken Language, Korean Language Research, 19, 271-299.
19 Jeon, S. K. (2017). A Systemic Functional Linguistic Study on Analyzing the Structure of Teaching Practice of High School Mathematics Lessons from the Perspective of Mathematical Objects(PhD Thesis), Department of Mathematics Education, Graduate School Yeungnam University.
20 Jeon, S. K. & Cho, C. S. (2015). A Study on the Written Texts of a High School Mathematics Textbook and Teacher's Classroom Discourse, Journal of Educational Research in Mathematics, 25(4), 525-547.
21 Choi, Y. S. (2014). Critical discourse analysis, Seoul: Hankookmunhwasa.
22 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
23 Alshwaikh, J. (2011). Geometrical diagrams as representation and communication: A functional analytic framework (PhD Thesis). Institute of Education, University of London, London.
24 Alshwaikh, J. (2016). Investigating the geometry curriculum in Palestinian textbooks: towards multimodal analysis of Arabic mathematics discourse. Research in Mathematics Education, 18(2), 165-181.   DOI
25 Hong Kong Special Administrative Region Government. (2015). Mathematics curriculum and assessment guide (Secondary 4-6). Hong Kong: HKSARG. Retrieved from http://www.edb.gov.hk/ attachment/en/curriculum-development/kla/ma/curr/Math_CAGuide_e_2015.pdf
26 Hersh, R. (1997). What is mathematics, really? New York, NY: Oxford University Press.
27 Kress, G. & Van Leeuwen, T. (2006). Reading images: The grammar of visual images. London: Routledge.
28 Dimopoulos, K., Koulaidis, V., & Sklaveniti, S. (2003). Towards an Analysis of Visual Images in School Science Textbooks and Press Articles about Science and Technology. Research in Science Education, 33, 189-216.   DOI
29 Bezemer, J. & Kress, G. (2008). Writing in multimodal texts: A social semiotic account of designs for learning. Written Communication, 25(2), 166-195.   DOI
30 Department for Education. (2013). National curriculum in England: Mathematics programmes of study - key stage 3. Retrieved from https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/239058/SECONDARY_national_curriculum_-_Mathematics.pdf
31 Halliday, M. A. K. (1961). Categories of the theory of grammar. Word, 17(3), 242-292.
32 Halliday, M. A. K. (1975). Language as social semiotic: towards a general sociolinguistic theory. Columbia: Hornbeam Press.
33 Halliday, M. A. K. (1978). Language as social semiotic: The social interpretation of language and meaning. London: Edward Arn.
34 Halliday, M. A. K. (1985/2004). An introduction to functional grammar, 3rd edition. Revised by Matthiessen, M. I. M., London : Hodder Education.
35 Halliday, M.A.K. & Martin, J. R.(1993). Writing Science: Literacy and Discursive Power. London: the Falmer Press.
36 Halliday, M. A. K. & Matthiessen, C. M. (1999) Construing Experience through Meaning: A Language Based Approach to Cognition. London: Cassell.
37 Morgan, C. (2016). Studying the role of human agency in school mathematics. Research in Mathematics Education, 18(2), 120-141.   DOI
38 Lemke, J. L. (2003). Mathematics in the middle: Measure, picture, gesture, sign, and word. In A. Saenz-Ludlow, S. Sellweher, & V. Scifarelli(Eds.), Educational perspectives on mathematics as semiosis: From thinking to interpreting to knowing (pp. 215-234). Ottowa: Legas Publishing.
39 McKenzie, D. L. & Padilla, M. J. (1986). The construction and validation of the test of graphing in science(TOGS). Journal of Research in Science Teaching, 23(17), 571-579.   DOI
40 Morgan, C. (1996). Writing mathematically: The discourse of investigation. London: Falmer Press.
41 Morgan, C. & Sfard, A. (2016). Investigating changes in high-stakes mathematics examinations: a discursive approach. Research in Mathematics Education, 18(2), 92-119.   DOI
42 Morgan, C. & Tang, S. (2016). To what extent are students expected to participate in specialised mathematical discourse? Change over time in school mathematics in England. Research in Mathematics Education, 18(2), 142-164.   DOI
43 O'Halloran, K. L. (2005). Mathematical Discourse: Language, Symbolism and Visual Images. London: Continuum.
44 O'Halloran, K. L. (2015). The language of learning mathematics: A multimodal perspective. Journal of Mathematical Behavior, 40, 63-74.   DOI
45 Park, J. (2016). Communicational approach to study textbook discourse on the derivative. Educational Studies in Mathematics, 91(3), 395-421.   DOI
46 Queensland Studies Authority. (2013). Year 7 mathematics - Australian curriculum in Queensland. Brisbane: Queensland Studies Authority.
47 Solomon, Y. & O'Neill, J. (1998). Mathematics and narrative. Language and Education, 12(3), 210-221.   DOI
48 Schleppegrell, M. J. (2007). The linguistic challenges of mathematics teaching and learning: A research review. Reading & Writing Quarterly, 23(2), 139-159.   DOI
49 Sfard, A. (2000). On reform movement and the limits of mathematical discourse. Mathematical Thinking and Learning, 2(3), 157-189.   DOI
50 Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge: Cambridge University Press.
51 Van Leeuwen, T. (2005). Introducing social semiotics. London: Routledge.
52 Vygotsky, L. S. (2011). 생각과 말, (배희철, 김용호 역). 서울: 살림터. (러시아어초판은 1934년, 영어초판은 1986년 출판).
53 Wagner, D. (2004). Silence and Voice in the Secondary Mathematics Classroom. unpublished doctoral dissertation. University of Alberta, Edmonton, Canada.
54 Wagner, D. (2007). Students' critical awareness of voice and agency in mathematics classroom discourse. Mathematical Thinking and Learning, 9(1), 31-50.   DOI
55 Wittgenstein, L. (1953/2003). Philosophical investigations: The German text, with a revised English translation(3rd ed., G. E. M. Anscombe, Trans.). Malden, MA: Blackwell.
56 Kim, N. H. et al. (2016). Study of mathematics curriculum and teaching materials for pre-service teachers and in-service teachers, Seoul: Kyungmoonsa.
57 The Ministry of Education (2015). Mathematics curriculum, Se Jong: The Ministry of Education.
58 National Institute of Korean Language (2018). Standard Korean Language Dictionary(web version), National Institute of Korean Language. Retrieved from http://stdweb2.korean.go.kr/main.jsp#
59 Kwon, S. & Park, K. S. (2011). A Critical Analysis on Usage and Defining Methods of Terms in Elememtary Mathematics Textbooks in Korea Centered on Some Examples, Journal of Elementary Mathematics Education in Korea, 15(2), 301-316.
60 Kwon, Y. M. & An, B. G. (2005). The Analysis on Students' Understanding of Mathematics Terms Being Used in Elementary School Mathematics Textbooks, Journal of Elementary Mathematics Education in Korea, 9(2), 137-159.