بررسی دانش محتوا و دانش پداگوژی محتوای معلمان ابتدایی و ارتباط آن با توانایی حل مسائل کسرهای ریاضی دانش‌آموزان
الموضوعات : پژوهش در برنامه ریزی درسیابوالفضل رفیع پور 1 , فرهاد کاظمی 2 , محمدرضا فدایی 3
1 - دانشجوی دکترای آموزش ریاضی، دانشگاه شهید باهنر کرمان، کرمان، ایران.
2 - هیئت‌علمی گروه آموزش ریاضی، دانشکده ریاضی و کامپیوتر، دانشگاه شهید باهنر کرمان، کرمان، ایران.
3 - هیئت‌علمی گروه آموزش ریاضی، دانشکده ریاضی و کامپیوتر، دانشگاه شهید باهنر کرمان، کرمان، ایران.
الکلمات المفتاحية: دانش محتوا, حل مسئله, دانش پداگوژی محتوا, کسرهای ریاضی,
ملخص المقالة :
هدف این مطالعه بررسی دانش محتوا و دانش پداگوژی محتوای معلمان ابتدایی و ارتباط آن با توانایی حل مسائل کسرهای ریاضی دانش‌آموزان بود؛ بنابراین 256 معلم پایه پنجم و ششم ابتدایی به‌صورت تصادفی انتخاب شدند و ابزار سنجش دانش محتوا و دانش پداگوژی محتوا روی آن‌ها اجرا شد. همزمان ابزار سنجش توانایی حل مسائل کسر نیز روی 5179 دانش‌آموز همان معلمان اجرا شد. نتایج نشان داد: 1) معلمان مدارس ابتدایی فاقد دانش محتوا و دانش پداگوژی محتوای مناسب و کافی درزمینة کسرهای ریاضی می‌باشند. 2) توانایی حل مسائل کسر دانش‌آموزان بخصوص روی مسائل مفهومی ضعیف است. 3) بین دانش محتوا و دانش پداگوژی محتوا با توانایی حل مسئله کسر دانش‌آموزان همبستگی مثبت معناداری وجود دارد. 4) تحلیل ساختار میانگین‌ها، بین معلمان زن و مرد نشان داد که گرچه میانگین دانش محتوا و دانش پداگوژی محتوای معلمان مرد از معلمان زن اندکی بالاتر است، اما تفاوت معنی‌داری بین آن‌ها وجود ندارد. 5) مشخص شد که بین دانش محتوا و دانش پداگوژی محتوا با شاخص‌های سابقه تدریس و مدرک تحصیلی معلم‌ها همبستگی مثبت و معناداری وجود دارد. نتایج این مطالعه لزوم توجه ویژه به بازنگری در دوره‌های آموزش پیش از خدمت و ضمن خدمت معلمان را مورد تأکید قرار می‌دهد.
Berliner, C. D. (1994). Expertise: The wonder of exemplary performances. In J. N. Mangieri & C. C. Block (Eds.), Creating powerful thinking in teachers and students (pp. 161–186). Fort Worth, TX: Holt, Rinehart & Winston.
Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90, 449-466.
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: what makes it special? Journal of Teacher Education, 59, 389-407.
Ball, D. L., Lubienski, S. T., & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (4th ed., pp. 433–456). Washington, DC: American Educational Research Association.
Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., et al. (2010). Teachers' mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47, 133-180.
Behr, M., Lesh, R., Post, T., & Silver E. (1983). Rational number concepts. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes, (pp. 91-125). New York: Academic Press.
Behr, M. J., Wachsmuth, I., Post, T. R., & Lesh, R. (1984). Order and equivalence of rational numbers: a clinical teaching experiment. Journal for Research in
Mathematics Education, 15, 323-341.
Campbell, F., Nishio, M., Toni M. Smith, Lawrence, M., Clark, Darcy L. Conant, Amber H. Rust, Jill Neumayer DePiper, Toya, F., Matthew J. Griffin and Youyoung Choi(2014) The Relationship Between Teachers' Mathematical Content and Pedagogical Knowledge, Teachers' Perceptions, and Student Achievement.Journal for Research in Mathematics
Education Vol. 45, No. 4 (July 2014), pp. 419-459.
Confrey, J., King, K. D., Strutchens, M. E., Sutton, J. T., Battista, M. T., Boerst, T. A., et al. (2008). Situating research on curricular change. Journal for Research in Mathematics Education, 39(2), 102–112
Cramer, K. A., Post, T. R., & delMas, R. C. (2002). Initial fraction learning by fourthand fifth-grade students: a comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum.Journal for Research in Mathematics Education, 33, 111-144.
Clarke, D. M., & Roche, A. (2009). Students’ fraction comparison strategies as a window into robust understanding and possible pointers for instruction. Educational Studies in Mathematics, 72(1), 127-138.
Depaepe, F; Torbeyns, J; Vermeersch, N; Janssens, D; Janssen, R; Kelchtermans, G; Verschaffel, L; Van Dooren, W. (2015), Teachers' content and pedagogical content knowledge on rational numbers: A comparison of prospective elementary and lower secondary school teachers. Teaching and Teacher Education 47 (2015) 82-92.
Fahimi, Z(2009) comparative study of Curriculum teacher education in Iran, Japan, Singapore, South Korea and America. Thesis in education mathematics in university of Shahid rajaee,1388.
Ghasemi, V. (2012) structural equation modeling in social researches with application of Amos software. Jamee shenasan publisher. Second eddition,1392.
Goos, M. (2009). Investigating the professional Learning and Development of Mathematics Teacher Educators: A theorethical Discussion and Research Agenda. In R. Hunter, B.Bicknell, & T. Burgess (Eds.), Crossing divides: Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia (Vol.1). Palmerston North, NZ: MERGA.
Grossman, P. L. (2008). Responding to our critics: From crisis to opportunity in research on teacher education. Journal of Teacher Education, 59(1), 10–23.
Harbison, R. W., & Hanushek, E. A. (1992). Educational performance of the poor: Lessons from rural northeast Brazil. Oxford, UK: Oxford University Press.
Hattie, J. (2009). Visible learning. A synthesis of over 800 meta-analyses relating to achievement. London: Routledge.
Hill, H. C., Schilling, S. G., & Ball, D. (2004). Developing measures of teachers’ mathematics knowledge for teaching. Elementary School Journal, 105, 11-30.
Hill, H. C., Rowan, B., & Ball, D. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42, 371-406.
Jackson, D. L. (2003). Revisiting sample size and number of parameter estimates: Some support for the N:q hypothesis. Structural Equation Modeling, 10, 128–141.
Kazemi, F. & Rafiepour, A. (2017)developing a scale to measure content knowledge and pedagogy content knowledge of in-service elementary teachers on fractions. International Journal of Science and Mathematics Education,3(15), pp.1-21.
Kleickmann, T., Richter, D., Kunter, M., Elsner, J., Besser, M., Krauss, S., et al. (2013). Teachers' content and pedagogical content knowledge: the role of structural differences in teacher education. Journal of Teacher Education, 64, 90-106.
Kovarik, k. (2008). Mathemetics educators and teachers perceptions of pedagogical content knowledge. the degree of doctor of philosophy.CLOMBIA university.
Krauss, S., Baumert, J., & Blum, W. (2008). Secondary mathematics teachers’ pedagogical content knowledge and content knowledge: Validation of the COACTIV constructs. The International Journal on Mathematics Education. 40:873–892.
Krauss, S., Brunner, M., Kunter, M., Baumert, J., Blum, W., Neubrand, M., et al. (2008). Pedagogical content knowledge and content knowledge of secondary mathematics teachers. Journal of Educational Psychology, 100, 716-725.
Little, T. D., Cunningham, W. A., Shahar, G., & Widaman, K. F. (2002). To parcel or not to parcel: Exploring the question, weighting the merits. Structural Equation Modeling, 9, 151–173.
Lamon, S. J. (2005). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers (2nd ed.). Mahwah: Lawrence Erlbaum Associates.
Ma, L. (1999). Knowing and Teaching Elementary School Mathematics. Mahwah, NJ, Lawrence Erlbaum Associates.
Mack, N. K. (1990). Learning fractions with understanding: building on informal knowledge. Journal for Research in Mathematics Education, 21, 16-32.
Marsh, H. W., Hau, K. T., Balla, J. R., & Grayson, D. (1998). Is more ever too much? The number of indicators per factor in confirmatory factor analysis. Multivariate Behavioral Research, 33, 181–220.
McCaffrey, D., Lockwood, J. R., Koretz, D., Louis, T. A., & Hamilton, L. (2004). Models for value-added modeling of teacher effects. Journal of Educational and Behavioral Statistics, 29(1), 67-101.
Mullens, J. E., Murnane, R. J., & Willett, J. B. (1996). The contribution of training and subject matter knowledge to teaching effectiveness: A multilevel analysis of longitudinal evidence from Belize. Comparative Education Review, 40(2),139–157.
Mortazi Mehrabani, N(2014) mathematics teacher education: a field needs with deep researches. Journal of mathematics cultural and thinking, volume8, pp.137-157.
Newton, K. J. (2008). An extensive analysis of preservice elementary teachers' knowledge of fractions. American Educational Research Journal, 45, 1080-1110.
Park, S., & Oliver, S. (2008). Revisiting the conceptualisation of pedagogical content knowledge (PCK): PCK as a conceptual tool to understand teachers as professionals. Research in Science Education, 38, 261-284.
Park, Y. (2004). Mathematics teacher education in East Asian countries from perspective of Pedagogical content knowledge. www.math.ecnu.edu. cn/earcome3/pl/earcome3(teacher education).doc
Senk, S. L., Tatto, M. T., Reckase, M., Rowley, G., Peck, R., & Bankov, K. (2012). Knowledge of future primary teachers for teaching mathematics: an international comparative study. ZDM Mathematics Education, 44, 307-324.
Shulman, L. S. (1986). Those who understand: knowledge growth in teaching. Educational Researcher, 15, 4-14.
Tirosh, D. (2000). Enhancing prospective teachers' knowledge of children's conceptions: the case of division of fractions. Journal for Research in Mathematics Education, 31, 5-25.
Timperley, H. (2011). Realized the Power of Professional Learning. Open University Press.
Turnuklu, E. B., & Yesildere, S. (2007). The pedagogical content knowledge in mathematics: pre-service primary mathematics teachers' perspectives in Turkey. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1, 1-13.
Usiskin, Z. P. (2007). The future of fractions. Arithmetic Teacher, 12(7), 366–369.
Vamvakoussi, X., Christou, K. P., Mertens, L., & Van Dooren, W. (2011). What fills the gap between discrete and dense? Greek and Flemish students' understanding of density. Learning and Instruction, 21, 676-685.
Vamvakoussi, X., Van Dooren, W., & Verschaffel, L. (2012). Naturally biased? in search for reaction time evidence for a natural number bias in adults. The Journal of Mathematical Behavior, 31, 344-355.
Waller, L.I. (2012) Math Intervention Teachers' Pedagogical Content Knowledge And Student Achievement. Published dissertation in Eastern Kentucky University.
Zehetmeier, S., Krainer, k. (2011). Ways of promoting the sustainability of mathematics teachers’professional development. ZDM Mathematics Education. pp. 875-887.
Zhou, Z., Peverly, S. T., & Xin, T. (2006). Knowing and teaching fractions: a crosscultural study of American and Chinese mathematics teachers. Contemporary Educational Psychology, 31, 438-457.
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