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A Problem Solving Course Case: Examination of Preservice Mathematics Teachers’ Perceptions

Year 2019, , 74 - 92, 31.12.2019
https://doi.org/10.22596/2019.0402.74.92

Abstract

Addressing all students’ needs is important for effective teaching. In teacher education programs, it is vital to introduce reform-based instructional approaches to preservice teachers (PST) while emphasizing the essence of subject matter knowledge, pedagogical content knowledge and knowledge about diverse students. This study represents preservice mathematics teachers’ perceptions about distinctively designed Mathematical Problem Solving course. The design of the course basically had an emphasis on problem solving, diversity, and equity consciousness and framed by a hypothetical learning trajectory. The data were gathered through semi-structured interviews. PSTs’ responses were analyzed by thematic analysis. PSTs’ perceptions about the Mathematical Problem Solving course were grouped under four themes and these were efficacy, awareness, shortcomings, and problem sets as challengers. In general PSTs pointed that the course was effective on improving their previous content knowledge, belief about being a better educator, learning heuristics in problem solving, and creating an awareness on diversity and equity while it had some shortcomings such as time management or lack of guidance needed by PSTs. Problem sets were one of the main component of the problem solving and posing structure of the course and these problems were non-routine problems which many PSTs found it difficult as well.

References

  • Braun, V. & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77-101. https://doi.org/10.1191/1478088706qp063oa.
  • Brown, I. A., Davis, T. J., & Kulm, G. (2011). Pre-service teachers’ knowledge for teacing algebra for equity in the middle grades: A preliminary report. The Journal of Negro Education, 80(3), 266-283.
  • Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). Thousand Oaks, CA: Sage.
  • Creswell, J. W. (2016). 30 Essential skills for the qualitative researcher. Thousand Oaks, CA: Sage.
  • Ellis, M. W. (Ed.) (2008). Mathematics for every student: Responding to diversity, grades 6-8. Reston, VA: National Council of Teachers of Mathematics.
  • Emenaker, C. (1996). A problem-solving based mathematics course and elementary teachers’ beliefs. School Science and Mathematics, 96(2), 75-84.
  • Hart, L. C. (2002). Preservice teachers’ beliefs and practice after participating in and integrated content/ methods course. School Science and Mathematics, 102(1), 4-14.
  • Ladson-Billings, G. (1994). The Dreamkeepers: Successful teachers for African American children. San Francisco: Jossey Bass.
  • Ladson-Billings, G. (1998). Just what is critical race theory and what’s it doing in a nice field like education? International Journal of Qualitative Studies in Education, 11(1), 7–24.
  • Ladson-Billings, G. (2011). Is meeting the diverse needs of all students possible? Kappa Delta Pi Record, 48(1), 13-15.
  • Lamberg, T., & Middleton, J. A. (2009). Design research perspectives on transitioning from individual microgenetic interviews to a whole-class teaching experiment. Educational Researcher 38(4), 233-245.
  • MacLaughlin, M. W., Shepard, L. A., & O’Day, J. A. (1995). Improving education through standards-based reform: A report by the National Academy of Education Panel in Standards-Based Reform. Stanford, CA: National Academy of Education.
  • McKenzie, K. B., & Skrla, L. (2011). Using equity audits in the classroom to reach and teach all students. Thousand Oaks, CA: Corwin Press.
  • Polya, G. (2004). How to solve it: A new aspect of mathematical method. Princeton University Press: Princeton, NJ.
  • Ponte, J. P., & Chapman, O. (2008). Prospective mathematics teachers' knowledge and development. In L. English (Ed.), Handbook of international research in mathematics education (2nd ed., pp. 225-263). New York: Routledge.
  • Quinn, R. (1997). Effects of mathematics methods courses on the mathematical attitudes and content knowledge of preservice teachers. The Journal of Educational Research, 91(2), 108-113.
  • Schoenfeld, A. J. (1998). Reflections on a course in mathematical problem solving. In A. H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), CBMS issues in Mathematics Education (Vol.7, pp. 81-113). Rhode Island: American Mathematical Society.
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57, 1-22.
  • Simon, M. A., & Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical Thinking & Learning, 6(2), 91-104.
  • Sleeter, C. E. (2001). Preparing teachers for culturally diverse schools: Research and the overwhelming presence of Whiteness. Journal of Teacher Education, 52(2), 94-106.
  • Watson, D., Charner-Laird, M., Kirkpatrick, C., Szczesiul, S., & Gordon, P. (2006). Effective teaching/effective urban teaching: Grappling with definitions, grappling with difference. Journal of Teacher Education, 57, 395-409.
  • Wilkins, J. L. M. & Brand, B. R. (2004). Change in preservice teachers’ beliefs: An evaluation of a mathematics methods course. School Science and Mathematics, 104(5), 226-232.

Bir Problem Çözme Dersi Vakası: Matematik Öğretmen Adaylarının Düşüncelerinin İncelenmesi

Year 2019, , 74 - 92, 31.12.2019
https://doi.org/10.22596/2019.0402.74.92

Abstract

Etkili bir öğretme için
bütün öğrencilerin ihtiyaçlarının karşılanması önemlidir. Öğretmen eğitimi
programlarında, konu alanı bilgisi, pedagojik içerik bilgisi ve çeşitlilik
hakkında bilginin önemi vurgulanırken öğretmen adaylarına reform temelli
öğretimsel yaklaşımların tanıtılması can alıcıdır. Bu çalışma, öğretmen
adaylarının özel bir biçimde tasarlanmış Matematikte Problem Çözme dersi
hakkındaki algılarını sunmaktadır. Dersin tasarımı temelde problem çözme,
çeşitlilik ve eşitlik bilinci üzerinde odaklanmış ve Hipotetik Öğrenme Yolu
tarafından çerçevelenmiştir. Veri seti yarı yapılandırılmış görüşmelerden elde
edilmiştir. Öğretmen adaylarının cevapları tematik analiz ile incelenmiştir.
Öğretmen adaylarının Matematikte Problem Çözme dersi hakkındaki algıları dört
temada toplanmıştır ve bunlar fayda, farkındalık, eksiklikler ve meydan okuyucu
olarak problem setleridir. Genel olarak öğretmen adayları dersin, var olan
içerik bilgilerini ve daha iyi bir matematik öğretmeni oldukları hakkında
inançlarını geliştirdiğini, problem çözmede kullanılan sezgisel yaklaşımı
öğrenmelerini, eşitlik ve çeşitlilik hakkında farkındalık yarattığını
belirtmişlerdir fakat bunun yanında zamanlama ya da rehberlik eksikliği gibi
problemlere de değinmişlerdir. Problem setleri dersin problem çözme ve kurma
yapılarından biri olan temel parçalardan bir tanesidir ve bu problemler rutin
olmayan problemlerdir ve öğretmen adayları tarafından zor olarak görülmüştür.

References

  • Braun, V. & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77-101. https://doi.org/10.1191/1478088706qp063oa.
  • Brown, I. A., Davis, T. J., & Kulm, G. (2011). Pre-service teachers’ knowledge for teacing algebra for equity in the middle grades: A preliminary report. The Journal of Negro Education, 80(3), 266-283.
  • Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). Thousand Oaks, CA: Sage.
  • Creswell, J. W. (2016). 30 Essential skills for the qualitative researcher. Thousand Oaks, CA: Sage.
  • Ellis, M. W. (Ed.) (2008). Mathematics for every student: Responding to diversity, grades 6-8. Reston, VA: National Council of Teachers of Mathematics.
  • Emenaker, C. (1996). A problem-solving based mathematics course and elementary teachers’ beliefs. School Science and Mathematics, 96(2), 75-84.
  • Hart, L. C. (2002). Preservice teachers’ beliefs and practice after participating in and integrated content/ methods course. School Science and Mathematics, 102(1), 4-14.
  • Ladson-Billings, G. (1994). The Dreamkeepers: Successful teachers for African American children. San Francisco: Jossey Bass.
  • Ladson-Billings, G. (1998). Just what is critical race theory and what’s it doing in a nice field like education? International Journal of Qualitative Studies in Education, 11(1), 7–24.
  • Ladson-Billings, G. (2011). Is meeting the diverse needs of all students possible? Kappa Delta Pi Record, 48(1), 13-15.
  • Lamberg, T., & Middleton, J. A. (2009). Design research perspectives on transitioning from individual microgenetic interviews to a whole-class teaching experiment. Educational Researcher 38(4), 233-245.
  • MacLaughlin, M. W., Shepard, L. A., & O’Day, J. A. (1995). Improving education through standards-based reform: A report by the National Academy of Education Panel in Standards-Based Reform. Stanford, CA: National Academy of Education.
  • McKenzie, K. B., & Skrla, L. (2011). Using equity audits in the classroom to reach and teach all students. Thousand Oaks, CA: Corwin Press.
  • Polya, G. (2004). How to solve it: A new aspect of mathematical method. Princeton University Press: Princeton, NJ.
  • Ponte, J. P., & Chapman, O. (2008). Prospective mathematics teachers' knowledge and development. In L. English (Ed.), Handbook of international research in mathematics education (2nd ed., pp. 225-263). New York: Routledge.
  • Quinn, R. (1997). Effects of mathematics methods courses on the mathematical attitudes and content knowledge of preservice teachers. The Journal of Educational Research, 91(2), 108-113.
  • Schoenfeld, A. J. (1998). Reflections on a course in mathematical problem solving. In A. H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), CBMS issues in Mathematics Education (Vol.7, pp. 81-113). Rhode Island: American Mathematical Society.
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57, 1-22.
  • Simon, M. A., & Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical Thinking & Learning, 6(2), 91-104.
  • Sleeter, C. E. (2001). Preparing teachers for culturally diverse schools: Research and the overwhelming presence of Whiteness. Journal of Teacher Education, 52(2), 94-106.
  • Watson, D., Charner-Laird, M., Kirkpatrick, C., Szczesiul, S., & Gordon, P. (2006). Effective teaching/effective urban teaching: Grappling with definitions, grappling with difference. Journal of Teacher Education, 57, 395-409.
  • Wilkins, J. L. M. & Brand, B. R. (2004). Change in preservice teachers’ beliefs: An evaluation of a mathematics methods course. School Science and Mathematics, 104(5), 226-232.
There are 23 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Ayse Tugba Oner

Publication Date December 31, 2019
Published in Issue Year 2019

Cite

APA Oner, A. T. (2019). A Problem Solving Course Case: Examination of Preservice Mathematics Teachers’ Perceptions. Harran Maarif Dergisi, 4(2), 74-92. https://doi.org/10.22596/2019.0402.74.92