Learning to be a Math Teacher: What Knowledge is Essential?


Mary REID , Steven REID


Abstract

This study critically examined the math content knowledge (MCK) of teacher candidates (TCs) enrolled in a two-year Master of Teaching (MT) degree.  Teachers require a solid math knowledge base in order to support students’ achievement.  Provincial and international math assessments have been of major concern in Ontario, Canada, due to declining scores.  Research aimed to investigate the development of TCs’ math capacities for effective teaching is important to teachers, school districts, universities, professional learning associations, and policy makers.  The researchers of this study analyzed the basic numeracy skills of 151 TCs through pre- and post-tests.  In addition, eight TCs took part in semi-structured interviews and shared their experiences in the MT math program.  Test results indicated improvements in many areas, however, not all numeracy skills improved significantly.  Interviews revealed TCs’ perceptions of the math test, courses, and instructors, as well as the importance of teaching math during their practicum placements.  The researchers made recommendations to teacher education programs in areas such as: establishing minimum math competency standards, enhancing coherence between MT math courses and practicum placements, and providing additional support for TCs with low math proficiency.


Keywords

Elementary math teacher education, Teacher candidates, Pre-service teacher education, Math content knowledge, MCK, Teacher learning

Paper Details

Paper Details
Topic Mathematics Education
Pages 851 - 872
Issue IEJEE, Volume 9, Issue 4
Date of acceptance 15 June 2017
Read (times) 248
Downloaded (times) 97

Author(s) Details

Mary REID

University of Toronto, Canada


Steven REID

University of Toronto, Canada


References

Adler, J., & Davis, Z. (2006). Opening another black box: Researching mathematics for teaching in mathematics teacher education. Journal for Research in Mathematics Education, 37(4), 270-296.

Alsup, J., (2004). A comparison of constructivist and traditional instruction in mathematics. Educational Research Quarterly, 28(4), 3-17.

Alsup, J., & Sprigler, M. (2003). A comparison of traditional and reform mathematics curricula in an eighth grade classroom. Education, 123(4), 689-694.

Ambrose, R. (2004). Initiating change in prospective elementary school teachers’ orientations to mathematics teaching by building on beliefs. Journal of Mathematics Teacher Education, 7(2), 91-119. doi:10.1023/B:JMTE.0000021879.74957.63

Amgen Canada Inc., & Let’s Talk Science. (2013). Spotlight on science learning: The high cost of dropping science and math. Retrieved from http://www.letstalkscience.ca/images/SpotlightOnScienceLearning-2013.pdf

Ball, D. L. (1990a). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90(4), 449-466. doi:10.1086/461626

Ball, D. L. (1990b). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21(2), 132–144. doi:10.2307/749140

Ball, D. L., Hill, H. H., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29(3), 14-46.

Ball, D. L., Lubienski, S., & Mewborn, D. (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). New York, NY: Macmillan.

Ball, D. L., Sleep, L., Boerst, T. A., & Bass, H. (2009). Combining the development of practice and the practice of development in teacher education. Elementary School Journal, 109(5), 458-474. doi:10.1086/596996

Ball, D.  L., Thames, M.  H., & Phelps, G.  (2008).  Content knowledge for teaching: What makes it special? Journal for Teacher Education, 59(5), 389–407.  doi:10.1177/0022487108324554

Bartell, T. G., Webel, C., Bowen, B., & Dyson, N. (2013). Prospective teacher learning: recognizing evidence of conceptual understanding. Journal of Mathematics Teacher Education, 16(1), 57-79. doi:10.1007/s10857-012-9205-4

Baxter, L. A. (1991). Content analysis. In B. M. Montgomery, & S. Duck (Eds.), Studying interpersonal interaction. (pp. 239-254). The Guilford Press, NY: New York.

Biddlecomb, B., & Carr, M. (2011). A longitudinal study of the development of mathematics strategies and underlying counting schemes. International Journal of Science and Mathematics Education9(1), 1-24. doi:10.1007/s10763-010-9202-y

Cai, J., & Wang, T. (2010). Conceptions of effective mathematics teaching within a cultural context: Perspectives of teachers from China and the United States. Journal of Mathematics Teacher Education. 13(3), 265-287. doi: 10.1007/s10857-009-9132-1

Conference Board of the Mathematical Sciences. (2012). Issues in mathematics education: Vol. 17. The mathematical education of teachers II. Providence, RI: American Mathematical Society.   

Creswell, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches (3rd ed.). Thousand Oaks, CA: Sage.

Creswell, J. W., & Clark, V. L. (2007). Designing and conducting mixed methods research. Thousand Oaks, CA: Sage.

Darling-Hammond, L., & Youngs, P. (2002). Defining “highly qualified teachers”: What does “scientifically-based research” actually tell us? Educational Researcher, 31(9), 13-25.

Denzin, N., & Lincoln, Y. (2000). Handbook of qualitative research (2nd ed.). Thousand Oaks, CA: Sage.

Education Quality and Accountability Office. (2016a). Highlights of the provincial results: Assessments of reading, writing and mathematics, primary division (grades 1-3) and junior division (grades 4-6): English-language students, 2015-2016. Toronto, ON: Education Quality and Accountability Office.

Education Quality and Accountability Office. (2016b). Programme for international student assessment (PISA), 2015: Highlights of Ontario student results. Toronto, ON: Education Quality and Accountability Office.

Eisenhart, M., Borko, H., Underhill, R., Brown, C., Jones, D., & Agard, P. (1993). Conceptual knowledge falls through the cracks: Complexities of learning to teach mathematics for understanding . Journal for Research in Mathematics Education, 24(1), 8-40. doi:10.2307/749384

Frykholm, J.A. (1999). The impact of reform: Challenges for mathematics teacher preparation. Journal of Mathematics Teacher Education, 2(1), 79-105. doi:10.1023/A:1009904604728

Grover, B. W., & Connor, J. (2000). Characteristics of the college geometry course for preservice secondary teachers. Journal of Mathematics Teacher Education 3(1), 47-76. doi:10.1023/A:1009921628065

Hiebert, J. (1992). Learning and teaching with understanding. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65-97). New York, NY: Macmillan.

Hiebert, J. (1999). Relationships between research and the NCTM standards. Journal for Research in Mathematics Education, 30(1), 3-19. doi:10.2307/749627

Hiebert, J.  (2013).  Conceptual and procedural knowledge: The case of mathematics.  Routledge.

Hiebert, J., Gallimore, R., Garnier, H., Givvin, K. B., Hollingsworth, H., Jacobs, J., … Stigler, J. W. (2003). Understanding and improving mathematics teaching: Highlights from the TIMSS 1999 Video Study. Phi Delta Kappan, 84(10), 768-775.

Hiebert, J., Stigler, J. W., Jacobs, J. K., Givvin, K. B., Garnier, H., Smith, M., … Gallimore, R. (2005). Mathematics teaching in the United States today (and tomorrow): Results from the TIMSS 1999 video study. Educational Evaluation and Policy Analysis, 27(2), 111-132. doi:10.3102/01623737027002111

Hill, H. & Ball, D. L. (2004). Learning mathematics for teaching: results from California’s mathematics professional development institutes. Journal for Research in Mathematics Education, 35(5), 330-351. doi:10.2307/30034819

Hill, H., & Ball, D. L.  (2009). The curious - and crucial - case of mathematical knowledge for teaching. Phi Delta Kappan, 91(2), 68-71. doi:10.1177/003172170909100215

Hill, H., Rowan, B., & Ball, D. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Education Research Journal, 42(2), 371-406. doi:10.3102/00028312042002371

Kagan, D. (1992). Professional growth among preservice and beginning teachers. Review of Educational Research, 62(2), 129-168. doi:10.3102/00346543062002129

Kajander, A.  (2007). Unpacking mathematics for teaching: A study of preservice elementary teachers’ evolving mathematical understandings and beliefs. Journal of Teaching and Learning, 5(1), 33-54.   

Kajander, A. (2010). Elementary Mathematics Teacher Preparation in an Era of Reform: The Development and Assessment of Mathematics for Teaching. Canadian Journal of Education, 33(1), 228-255.

Kamii, C. (2004). Young Children Continue to Reinvent Arithmetic: 2nd Grade (2nd ed.). New York, NY: Teachers College Press.

Kurasaki, K. S. (2000). Intercoder reliability for validating conclusions drawn from open-ended interview data. Field Methods, 12(3), 179-194. doi:10.1177/1525822X0001200301

Lo, J.-J., & Luo, F. (2012). Prospective elementary teachers’ knowledge of fraction division. Journal of Mathematics Teacher Education, 15(6), 481-500. doi:10.1007/s10857-012-9221-4

Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' Understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.

McCormick, R. (1997). Conceptual and procedural knowledge. International Journal of Technology and Design Education, 7(1-2), 141-159.

McDougall, D., Ross J., & Jaafar, S. (2006). PRIME ten dimensions of mathematical education: Research study. Toronto, ON: Nelson.

Morris, A., Hiebert, J., & Spitzer, S. (2009). Mathematical knowledge for teaching in planning and evaluating instruction: What can preservice teachers learn? Journal for Research in Mathematics Education 40(5). 491-529.

National Council of Teachers of Mathematics (NCTM). (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics (NCTM).  (2000). Principles and standards for school mathematics. Reston, VA: Author.

Ontario Ministry of Education. (2005). The Ontario Curriculum, Grades 1-8: Mathematics. Toronto, ON: Ontario Ministry of Education.

Ontario Ministry of Education. (2014). Achieving Excellence: A Renewed Vision for Education in Ontario. Toronto, ON: Ontario Ministry of Education.

Parekh, G. (2014) ‘Social citizenship and disability: Identity, belonging, and the structural organization of education’. PhD Thesis, York University, Toronto.

Philipp, R., Ambrose, R., Lamb, L., Sowder, J., Schappelle, B., Sowder, L., . . . Chauvot, J. (2007). Effects of early field experiences on the mathematical content knowledge and beliefs of prospective elementary school teachers: An experimental study. Journal for Research in Mathematics Education, 38(5), 438-476.

Polit, D. F., & Hungler, B. P. (1999). Nursing research: Principles and methods (6th ed.). New York, NY: J.B. Lippincott Company.

Ponte, J. P. & Chapman, O. (2008). Preservice mathematics teachers’ knowledge and development. In L. D. English (Ed.) Handbook of international research in mathematics education: Directions for the 21st century (2nd Edition, pp. 225 - 263). New York: Routledge.

Reid, M. (2013). Mathematics Content Knowledge, Mathematics Teacher Efficacy, and Pedagogy: An Examination of the Three Constructs in Mathematics Preservice Elementary Education (doctoral thesis). University of Calgary, Calgary, Canada.

Rittle-Johnson, B. & Koedinger, K. (2002). Comparing instructional strategies for integrating conceptual and procedural knowledge. In Mewborn, D.S., Sztajin, P., White, D.Y., Wiegel, H.G., Bryant, R.L. & Nooney, K. (Eds.) Proceedings of the 24th annual meeting of the North American Chapters of the International Group for the Psychology of Mathematics Education (pp. 969-978). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

Rowan, B., Chiang, F., & Miller, R. J. (1997). Using research on employees’ performance to study the effects of teachers on students’ achievement. Sociology of Education, 70(4), 256–284. doi:10.2307/2673267

Sandelowski, M. (2001). Real qualitative researchers do not count: The use of numbers in qualitative research. Research in Nursing & Health, 24(3), 230-240. doi:10.1002/nur.1025

Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher15(2), 4-14. doi:10.3102/0013189X015002004

Shulman, L.  (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22. doi:10.17763/haer.57.1.j463w79r56455411

Sowder, J. T. (2007). The mathematical education and development of teachers. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 157 – 224). Reston, VA: National Council of Teachers of Mathematics. doi:10.1234/12345678

Stigler, J.W., & Hiebert, J. (1997). Understanding and improving classroom mathematics instruction: An overview of the TIMSS video study. Phi Delta Kappan, 79(1), 14-21.

Tabachnik, R. B., & Zeichner, K. M. (1984). The impact of students teaching experience on the development of teacher perspectives. Journal of Research in Teacher Education, 35(6), 28-36. doi:10.1177/002248718403500608

Tella, A. (2008). Teacher variables as predictors of academic achievement of primary school pupils mathematics. International Electronic Journal of Elementary Education, 1(1), 16-33.

Thames, M., & Ball, D. L. (2010). What math knowledge does teaching require? Teaching Children Mathematics, 17(4), 220-229.

Tirosh, D. (2000). Enhancing prospective teachers' knowledge of children's conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5-25.

Vistro-Yu, C. P. (2013). Cross-national studies on the teaching and learning of mathematics: Where do we go from here? ZDM Mathematics Education, 45(1), 145-151. doi:10.1007/s11858-013-0488-4 

Yackel, E., Underwood, D., & Elias, N. (2007). Mathematical tasks designed to foster a reconceptualized view of early arithmetic. Journal of Mathematics Teacher Education10(4-6), 351-367.DOI 10.1007/s10857-007-9044-x

Yin, R. K. (2009). Case study research: Design and methods (4th ed.). Thousand Oaks, CA: Sage.