Korean Teachers’ Mathematical Knowledge for Teaching in Algebraic Reasoning

다국어 초록 (Multilingual Abstract)

To collect information about teachers concerning mathematical knowledge for teaching and find out what needs to be considered in developing a curriculum to teach it, the current study surveyed 137 secondary teachers and interviewed thirteen of them in Korea. The survey and interviews used the assessment of mathematical knowledge for teaching about algebra I, which was developed as part of the Measures of Effective Teaching project. The correct response rate of Korean teachers was very high, but there were some differences found in the areas of algebraic reasoning. Furthermore, mathematical analysis is important in assessing students’ algebraic reasoning, and each teacher’s typical teaching method is formidable in evaluating students’ reasoning. Implication is discussed for the improvement of teachers’ mathematical knowledge for teaching algebra.

참고문헌 (Reference)

1 Delaney, S., "“Mathematical knowledge for teaching”: Adapting U.S. measures for use in Ireland" 11 (11): 171-197, 2008

2 Sherin, M. G., "When teaching becomes learning" 20 (20): 119-150, 2002

3 Chazan, D., "What kind of mathematical knowledge supports teaching for "conceptual understanding"? Preservice teachers and the solving of equations" Technion Printing Center 2 : 193-200, 1999

4 Sato, M., "What is the underlying conception of teaching of the edTPA?" 65 (65): 421-434, 2014

5 Ng, D., "Using the MKT measures to reveal Indonesian teachers’ mathematical knowledge: challenges and potentials" 44 (44): 401-413, 2012

6 Shulman, L. S., "Those who understand: Knowledge growth in teaching" 15 (15): 4-14, 1986

7 Koellner, K., "The problem-solving cycle: A model to support the development of teachers' professional knowledge" 9 (9): 273-303, 2007

8 Haimes, D. H., "The implementation of a “function” approach to introductory algebra: A case study of teacher cognitions, teacher actions, and the intended curriculum" 27 (27): 582-602, 1996

9 Norman, A., "The concept of function: Aspects of epistemology and pedagogy (Vol. 25, MAA Notes)" Mathematical Association of America 215-232, 1992

10 Belfort, E., "Tertiary algebra and secondary classroom practices in number and algebra : Closing the gap" The University of Melbourne 79-86, 2001

11 Hiebert, J., "Teaching, rather than teachers, as a path toward improving classroom instruction" 63 (63): 92-102, 2012

12 Ball, D. L., "Teaching as the learning profession: Handbook of policy and practice" Jossey-Bass 3-32, 1999

13 Cohen, D. K., "Teaching and its predicaments" Harvard University Press 2011

14 Lynch, K., "Teachers’ views about multiple strategies in middle and high school mathematics" 16 (16): 85-108, 2014

15 Attorps, I., "Teachers’ images of the ‘equation’ concept" 3 : 1-8, 2003

16 Hitt, F., "Teachers’ difficulties with the construction of continuous and discontinuous functions" 16 (16): 10-20, 1994

17 Hill, H. C., "Teacher quality and quality teaching: Examining the relationship of a teacher assessment to practice" 118 (118): 489-519, 2012

18 Lloyd, G. M., "Supporting innovation: The impact of a teacher's conceptions of functions on his implementation of a reform curriculum" 29 (29): 248-274, 1998

19 Even, R., "Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept" 24 : 94-116, 1993

20 Stein, M. K., "Subject-matter knowledge and elementary instruction: A case from functions and graphing" 27 (27): 639-663, 1990

21 Postelnicu, V., "Student difficulties with linearity and linear functions and teachers' understanding of student difficulties" Arizona State University 2011

22 American Educational Research Association, "Standards for educational and psychological testing"

23 Tirosh, D., "Simplifying algebraic expressions: Teacher awareness and teaching approaches" 35 (35): 51-64, 1998

24 Stump, S., "Secondary mathematics teachers’ knowledge of slope" 11 (11): 124-144, 1999

25 Lewis, J., "Reading between the lines: Teaching linear algebra" 44 (44): 515-536, 2012

26 Chinnappan, M., "Prospective teachers’ perspectives on function representations, In Numeracy and beyond" 155-162, 2001

27 Huang, R., "Prospective middle grade mathematics teachers’ knowledge of algebra for teaching" 31 (31): 417-430, 2012

28 Caglayan, G., "Prospective mathematics teachers’ sense making of polynomial multiplication and factorization modeled with algebra tiles" 16 (16): 349-378, 2013

29 National Council of Teachers of Mathematics, "Principles and standards for school mathematics" National Council of Teachers of Mathematics 2000

30 Tanisli, D., "Pre-Service Mathematics Teachers' Knowledge of Students about the Algebraic Concepts" 38 (38): 1-18, 2013

31 Schmidt, W. H., "Opportunity to learn in the preparation of mathematics teachers: its structure and how it varies across six countries" 40 (40): 735-747, 2008

32 Wilson, M. R., "One preservice secondary teacher's understanding of function: The impact of a course integrating mathematical content and pedagogy" 25 (25): 346-370, 1994

33 Chazan, D., "On teachers’ mathematical knowledge and student exploration: A personal story about teaching a technologically supported approach to school algebra" 4 (4): 121-149, 1999

34 Asquith, P., "Middle school mathematics teachers' knowledge of students' understanding of core algebraic concepts: Equal sign and variable" 9 (9): 249-272, 2007

35 Izsák, A., "Metarepresentation in an algebra I classroom" 18 (18): 549-587, 2009

36 Moses, R. P., "Math literacy and civil rights" Beacon Press 2001

37 McCrory, R., "Knowledge of algebra for teaching: A framework of knowledge and practices" 43 (43): 584-615, 2012

38 Kim, Y., "Interview prompts to uncover mathematical knowledge for teaching: focus on providing written feedback" 13 (13): 71-92, 2016

39 Blömeke, S., "Getting the fish out of the water: Considering benefits and problems of doing research on teacher education at an international level" 24 (24): 2027-2037, 2008

40 National Mathematics Advisory Panel, "Foundations for success: The final report of the National Mathematics Advisory Panel" US Department of Education 2008

41 Heid, M. K., "Factors that influence teachers learning to do interviews to understand students’ mathematical understandings" 37 (37): 223-249, 1999

42 Hill, H. C., "Effects of teachers' mathematical knowledge for teaching on student achievement" 42 (42): 371-406, 2005

43 Cai, J., "Early algebraization: A global dialogue from multiple perspectives" Springer 2011

44 Stump, S., "Developing preservice teachers’ pedagogical content knowledge of slope" 20 : 207-227, 2001

45 Phelps, G., "Developing content knowledge for teaching assessments for the Measures of Effective Teaching study" Educational Testing Service 2014

46 Ball, D. L., "Content knowledge for teaching: What makes it special?" 59 (59): 389-407, 2008

47 Ball, D. L., "Combining the development of practice and the practice of development in teacher education" 109 (109): 458-474, 2009

48 Mosvold, R., "Challenges of translating and adapting the MKT measures for Norway" 2009

49 Rockoff, J. E., "Can you recognize an effective teacher when you recruit one?" 6 (6): 43-74, 2011

50 Chazan, D., "Beyond formulas in mathematics and teaching: Dynamics of the high school algebra classroom" Teachers College Press 2000

51 Strauss, A. L., "Basics of qualitative research: Techniques and procedures for developing grounded theory" Sage Publications 2008

52 Cole, Y., "Assessing elemental validity: the transfer and use of mathematical knowledge for teaching measures in Ghana" 44 (44): 415-426, 2012

53 Chazan, D., "An analytic conception of equation and teachers’ views of school algebra" 27 (27): 87-100, 2008

54 Zazkis, R., "Advanced mathematical knowledge in teaching: perceptions of secondary mathematics teachers" 12 : 263-281, 2010

55 김연, "A Comparison Study of Curricular of Teacher Education for Elementary Teachers in South Korea and the United States: Focusing on Opportunities to Learn Teaching Mathematics" 대한수학교육학회 24 (24): 555-572, 2014