Examining Prospective Primary School Mathematics Teachers’ Algebraic Habits of Mind in the Context of Problem Solving
Yıl 2018,
Cilt: 2 Sayı: 4, 64 - 80, 13.09.2018
Emine Nur Ünveren Bilgiç
,
Ziya Argün
Öz
The
aim of this research is to examine the algebraic mind habits in the context of
problem solving of elementary mathematics teacher candidates within the
pedagogical field. The study which was dominated by qualitative paradigm was done
in the pattern of case study. With this aim, data were gathered from 30
prospective teachers via “Algebraic Habits of Mind Worksheet” and interviews.
The data were analyzed in the light of the components of theoretical title of
algebraic habits of mind and according to the stages of descriptive analysis. The
teacher candidates made solutions based on memorizations without writing what
is given and wanted; however they clearly wrote what is given and wanted in the
last two problems. While this seems to be a form of rules that represent direct
functions in the questions seen as exercises; it causes them to use the
thinking / reverse thinking step more actively when they are perceived as
problems. At the interviews, it
is seen that the fourth grade prospective teachers are more detailed about the
construction on their stunets’ knowledge
than the first grade prospective students and that the first grade only
focuses on solving.
Kaynakça
- Bass, H. (2008). Helping Students Develop Mathematical Habits of Mind. Paper presented at a Project Next Session on Joint Mathematics Meetings, San Diego, CA.
- Cuoco, A., Goldenberg, E. P., & Mark, J. (1996). Habits of mind: An organizing principle for a mathematics curriculum. Journal of Mathematical Behavior, 15(4), 375-402.
- Cuoco, A., Goldenberg, E. P., & Mark, J. (2010). Contemporary curriculum issues: Organizing a curriculum around mathematical habits of mind. Mathematics Teacher, 103(9), 682-688.
- Driscoll, M. (1999). Fostering algebraic thinking: A guide for teachers, Grades 6-10. Portsmouth, NH: Heinemann.
- Goldenberg, E. P., Shteingold, N., & Feurzeig, N. (2003). Mathematical habits of mind for young children. In F. K. Lester & R. I. Charles (Eds.), Teaching mathematics through problem solving: Prekindergarten-Grade 6 (pp. 15-29). Reston, VA: National Council of Teachers of Mathematics.
- GorLGn, M. (2011). Mathematical habits of mind: Promoting students’ thoughtful considerations. Curriculum Studies, 43(4), 457–469.
- Greenes, C., & Findell, C. (1998). Algebra puzzles and problems, grade 6. Mountain View, CA: Creative Publications.
- Harel, G. (2007). The DNR system as a conceptual framework for curriculum development an instruction. In R. Lesh, J. Kaput & E. Hamilton (Eds.), Foundations for the future in mathematics education (pp. 263-280). Mahwah, NJ: Lawrence Erlbaum Associates.
- Hawker, S.; & Cowley, C. (1997). Oxford dictionary and thesaurus. Oxford: Oxford University.
- Herbert, K., & Brown, R. H. (1997). Patterns as tools for algebraic reasoning. Teaching Children Mathematics, 3(6), 340-344.
- Jacobbe, T., & Millman, R. S. (2009). Mathematical habits of the mind for preservice teachers. School Science and Mathematics, 109(5), 298-302.
- Johnson, B.; & Christensen, L. (2014). Educational research: Quantitative, qualitative, and mixed approaches. Thousand Oaks, CA: SAGE.
- Kaf, Y. (2007). Matematikte model kullanımının 6. sınıf öğrencilerinin cebir erişilerine etkisi [Effect of model use in mathematics on algebraic access of 6th grade students] (Unpublished master’s thesis). Hacettepe University, Ankara, Turkey.
- Lim, K. H., & Selden, A. (2009). Mathematical habits of mind. In S. L. Swars, Stinson, D. W., & Lemons-Smith, S. (Eds.), Proceedings of the Thirty-first Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1576-1583). Atlanta: Georgia State University.
- Mark, J., Cuoco, A., Goldenberg, E. P., & Sword, S. (2010). Developing mathematical habits of mind. Mathematics Teaching in the Middle School, 15(9), 505-509.
- Mason, J., Burton, L., & Stacey, K. (1998). Thinking mathematically (3rd Edition). Edinburgh Gate, Pearson.
- Matsuura, R., Sword, S., Piecham, M., B., Stevens, G., & Cuoco, A. (2013). Mathematical habits of mind for teaching: Using language in algebra classrooms. The Mathematics Enthusiast, 10(3), 735-776.
- Poindexter, C. (2011). Teaching “habits of mind”: Impact on students’ mathematical thinking and problem solving self-efficacy. In L. McCoy (Ed.), Studies in Teaching 2011 Research Digest (pp. 97-102). Winston-Salem, NC: Wake Forest University.
- Rolle, Y. A. (2008). Habits of practice: A qualitative case study of a middle-school mathematics teacher (LGctoral dissertation). Retrieved from https://search.proquest.com/LGcview/304519107. Trybulski, D. J. (2007). Algebraic reasoning in middle school classrooms: a case study of standards-based reform and teacher ınquiry in mathematics (LGctoral dissertation). Retrieved from https://search.proquest.com/LGcview/304837846.
- Turkish Ministry of National Education (2008). Matematik öğretmeni özel alan yeterlikleri [Mathematics teacher specific field competencies]. Ankara: Devlet Kitapları.
- Turkish Ministry of National Education, (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. Sınıflar) öğretim programı [Secondary school mathematics course (5th, 6th, 7th and 8th grades) curriculum]. Ankara: Devlet Kitapları.
- University of Nebraska-Lincoln, (2006, June 3). Collection of Habits of Mind Problems. Retrieved July, 2017, form http://ime.math.arizona.edu/2006- 07/0301_workshop_NB_hanLGuts/Collection%20of%20Habits%20of%20Mind%20Probl ems.pdf.
Examining Prospective Primary School Mathematics Teachers’ Algebraic Habits of Mind in the Context of Problem Solving
Yıl 2018,
Cilt: 2 Sayı: 4, 64 - 80, 13.09.2018
Emine Nur Ünveren Bilgiç
,
Ziya Argün
Öz
The
aim of this research is to examine the algebraic mind habits in the context of
problem solving of elementary mathematics teacher candidates within the
pedagogical field. The study which was dominated by qualitative paradigm was done
in the pattern of case study. With this aim, data were gathered from 30
prospective teachers via “Algebraic Habits of Mind Worksheet” and interviews.
The data were analyzed in the light of the components of theoretical title of
algebraic habits of mind and according to the stages of descriptive analysis. The
teacher candidates made solutions based on memorizations without writing what
is given and wanted; however they clearly wrote what is given and wanted in the
last two problems. While this seems to be a form of rules that represent direct
functions in the questions seen as exercises; it causes them to use the
thinking / reverse thinking step more actively when they are perceived as
problems. At the interviews, it
is seen that the fourth grade prospective teachers are more detailed about the
construction on their stunets’ knowledge
than the first grade prospective students and that the first grade only
focuses on solving.
Kaynakça
- Bass, H. (2008). Helping Students Develop Mathematical Habits of Mind. Paper presented at a Project Next Session on Joint Mathematics Meetings, San Diego, CA.
- Cuoco, A., Goldenberg, E. P., & Mark, J. (1996). Habits of mind: An organizing principle for a mathematics curriculum. Journal of Mathematical Behavior, 15(4), 375-402.
- Cuoco, A., Goldenberg, E. P., & Mark, J. (2010). Contemporary curriculum issues: Organizing a curriculum around mathematical habits of mind. Mathematics Teacher, 103(9), 682-688.
- Driscoll, M. (1999). Fostering algebraic thinking: A guide for teachers, Grades 6-10. Portsmouth, NH: Heinemann.
- Goldenberg, E. P., Shteingold, N., & Feurzeig, N. (2003). Mathematical habits of mind for young children. In F. K. Lester & R. I. Charles (Eds.), Teaching mathematics through problem solving: Prekindergarten-Grade 6 (pp. 15-29). Reston, VA: National Council of Teachers of Mathematics.
- GorLGn, M. (2011). Mathematical habits of mind: Promoting students’ thoughtful considerations. Curriculum Studies, 43(4), 457–469.
- Greenes, C., & Findell, C. (1998). Algebra puzzles and problems, grade 6. Mountain View, CA: Creative Publications.
- Harel, G. (2007). The DNR system as a conceptual framework for curriculum development an instruction. In R. Lesh, J. Kaput & E. Hamilton (Eds.), Foundations for the future in mathematics education (pp. 263-280). Mahwah, NJ: Lawrence Erlbaum Associates.
- Hawker, S.; & Cowley, C. (1997). Oxford dictionary and thesaurus. Oxford: Oxford University.
- Herbert, K., & Brown, R. H. (1997). Patterns as tools for algebraic reasoning. Teaching Children Mathematics, 3(6), 340-344.
- Jacobbe, T., & Millman, R. S. (2009). Mathematical habits of the mind for preservice teachers. School Science and Mathematics, 109(5), 298-302.
- Johnson, B.; & Christensen, L. (2014). Educational research: Quantitative, qualitative, and mixed approaches. Thousand Oaks, CA: SAGE.
- Kaf, Y. (2007). Matematikte model kullanımının 6. sınıf öğrencilerinin cebir erişilerine etkisi [Effect of model use in mathematics on algebraic access of 6th grade students] (Unpublished master’s thesis). Hacettepe University, Ankara, Turkey.
- Lim, K. H., & Selden, A. (2009). Mathematical habits of mind. In S. L. Swars, Stinson, D. W., & Lemons-Smith, S. (Eds.), Proceedings of the Thirty-first Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1576-1583). Atlanta: Georgia State University.
- Mark, J., Cuoco, A., Goldenberg, E. P., & Sword, S. (2010). Developing mathematical habits of mind. Mathematics Teaching in the Middle School, 15(9), 505-509.
- Mason, J., Burton, L., & Stacey, K. (1998). Thinking mathematically (3rd Edition). Edinburgh Gate, Pearson.
- Matsuura, R., Sword, S., Piecham, M., B., Stevens, G., & Cuoco, A. (2013). Mathematical habits of mind for teaching: Using language in algebra classrooms. The Mathematics Enthusiast, 10(3), 735-776.
- Poindexter, C. (2011). Teaching “habits of mind”: Impact on students’ mathematical thinking and problem solving self-efficacy. In L. McCoy (Ed.), Studies in Teaching 2011 Research Digest (pp. 97-102). Winston-Salem, NC: Wake Forest University.
- Rolle, Y. A. (2008). Habits of practice: A qualitative case study of a middle-school mathematics teacher (LGctoral dissertation). Retrieved from https://search.proquest.com/LGcview/304519107. Trybulski, D. J. (2007). Algebraic reasoning in middle school classrooms: a case study of standards-based reform and teacher ınquiry in mathematics (LGctoral dissertation). Retrieved from https://search.proquest.com/LGcview/304837846.
- Turkish Ministry of National Education (2008). Matematik öğretmeni özel alan yeterlikleri [Mathematics teacher specific field competencies]. Ankara: Devlet Kitapları.
- Turkish Ministry of National Education, (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. Sınıflar) öğretim programı [Secondary school mathematics course (5th, 6th, 7th and 8th grades) curriculum]. Ankara: Devlet Kitapları.
- University of Nebraska-Lincoln, (2006, June 3). Collection of Habits of Mind Problems. Retrieved July, 2017, form http://ime.math.arizona.edu/2006- 07/0301_workshop_NB_hanLGuts/Collection%20of%20Habits%20of%20Mind%20Probl ems.pdf.