# Infusing assessment into mathematics content courses for pre-service elementary school teachers

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## Abstract

The present study aims to explore the use of assessment in mathematics content courses for future elementary school teachers. Analysis of self assessment data on mathematical understanding and peer assessment data on oral mathematical presentation showed that pre-service teachers had a balanced understanding of procedural knowledge and problem solving. Conceptual understanding was not in the structure of pre-service teachers’ mathematical knowledge. Understandings of conceptual knowledge, procedural knowledge, and problem solving had no meaningful effects on gains in mathematics performance. Aspects of oral mathematical presentation were associated with improved understanding of procedural knowledge and in particular conceptual knowledge. The result of the study calls for a conceptual approach to mathematical knowledge and sufficient mathematical problem solving in college-level mathematics content courses and in particular the infusion of assessment into college-level mathematics education for pre-service teachers.

## Keywords

Pre-service teacher education Structure of mathematical knowledge Infusion of assessment into mathematics content courses## Preview

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## References

- Ball D.L. (1990a) The mathematical understandings that prospective teachers bring to teacher education. Elementary School Journal 90: 449–466CrossRefGoogle Scholar
- Ball D.L. (1990b) Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education 21: 132–144CrossRefGoogle Scholar
- Ball D., Lubienski S., Mewborn D. (2001) Mathematics. In: Richardson V. (eds) Handbook of research on teaching, 4th edn. American Educational Research Association, Washington, DC, pp 433–456Google Scholar
- Black P.J., Wiliam D. (1998) Assessment and classroom learning. Assessment in Education: Principles, Policy and Practice 5: 7–73CrossRefGoogle Scholar
- Borko H. (2004) Professional development and teacher learning: Mapping the terrain. Educational Researcher 33(8): 3–15CrossRefGoogle Scholar
- Borko H., Davinroy K.H., Bliem C.L., Cumbo K.B. (2000) Exploring and supporting teacher change: Two third-grade teachers’ experiences in a mathematics and literacy staff development project. The Elementary School Journal 100: 273–305CrossRefGoogle Scholar
- Borko H., Eisenhart M., Brown C.A., Underhill R.G., Jones D., Agard P.C. (1992) Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily?. Journal for Research in Mathematics Education 23: 194–222CrossRefGoogle Scholar
- Borko H., Putnam R.T. (1996) Learning to teach. In: Berliner D.C., Calfee R.C. (eds) Handbook of ducational psychology. Simon & Schuster Macmillan, New York, pp 673–708Google Scholar
- Edge, D., & Yeap, B. H. (Eds.) (2002). Mathematics education for a knowledge-based era. In
*Proceedings of the Second East Asia Regional Conference on Mathematics Education and Ninth Southeast Asian Conference on Mathematics Education*. Singapore: National Institute of Education.Google Scholar - Even R. (1993) Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education 24: 94–116CrossRefGoogle Scholar
- Fan L., Wong N., Cai J., Li S. (2004) How Chinese learn mathematics: Perspectives from insiders. World Scientific, SingaporeGoogle Scholar
- Frykholm J.A. (1999) The impact of reform: Challenges for mathematics teacher preparation. Journal of Mathematics Teacher Education 1: 79–105CrossRefGoogle Scholar
- Frykholm, J. A. (1999b, January).
*Elementary mathematics: A missing piece in secondary mathematics teacher education*? Paper presented at the annual meeting of the Association of Mathematics Teacher Educators. Chicago, IL.Google Scholar - Lloyd G., Wilson M.R. (1998) Supporting innovation: The impact of a teacher’s conceptions of functions on his implementation of a reform curriculum. Journal for Research in Mathematics Education 29: 248–274CrossRefGoogle Scholar
- Long C.T., DeTemple D.W. (2005) Mathematical reasoning for elementary teachers (4th ed). Addison Wesley, Boston, MAGoogle Scholar
- Ma L. (1999) Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Erlbaum, Mahwah, NJGoogle Scholar
- Mathematical Sciences Education Board. (1996).
*Mathematics and science education around the world: What can we learn from the survey of mathematics and science opportunities (SMSO) and the Third International Mathematics and Science Study (TIMSS)*? Washington, DC: National Research Council.Google Scholar - McTighe, J., & Wiggins, G. (2004).
*Understanding by design: Professional development workbook*. Alexandria, VA: Association for Supervision and Curriculum Development.Google Scholar - Meyer J.H.F., Parsons P., Dunne T.T. (1990) Individual study orchestrations and their association with learning outcome. Higher Education 20: 67–89CrossRefGoogle Scholar
- Morris H. (2001) Issues raised by testing trainee primary teachers’ mathematical knowledge. Mathematics Teacher Education and Development 3: 37–47Google Scholar
- National Council of Teachers of Mathematics. (1989).
*Curriculum and evaluation standards for school mathematics*. Reston, VA: Author.Google Scholar - National Council of Teachers of Mathematics. (2000).
*Principles and standards for school mathematics*. Reston, VA: Author.Google Scholar - Quinn R.J. (1997) Effects of mathematical methods courses on the mathematical attitudes and content knowledge of preservice teachers. Journal of Educational Research 91: 108–119CrossRefGoogle Scholar
- Rech J., Hartzell J., Stephens L. (1993) Comparisons of mathematical competencies and attitudes of elementary education majors with established norms of a general college population. School Science and Mathematics 93: 141–44CrossRefGoogle Scholar
- Rowland, T., Martyn, S., Barber, P., & Heal, C. (2001). Investigating the mathematics subject matter knowledge of pre-service elementary school teachers. In M. Van Den Heuvel-Panhuiz (Ed.),
*Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education*(Vol. 4, pp. 121–128). Utrecht, Netherlands: Freudenthal Institute, Utrecht University.Google Scholar - Simon M.A. (2006) Key developmental understandings in mathematics: A direction for investigating and establishing learning goals. Mathematical Thinking and Learning 8: 359–371CrossRefGoogle Scholar
- Skemp R.R. (1977) Relational understanding and instrumental understanding. Mathematics Teacher 77: 20–26Google Scholar
- Southwell, B., & Penglase, M. (2005, July).
*Mathematical knowledge of pre-service primary teachers*. Paper presented at the 29th conference of the International Group for the Psychology of Mathematics Education. Melbourne: Australia.Google Scholar - Taylor P.M. (2002) Implementing the standards: Keys to establishing positive professional inertia in preservice mathematics teachers. School Science and Mathematics 102: 137–142Google Scholar
- Trochim W.M.K., Donnelly J.P. (2007) The research methods knowledge base (3rd ed). Cengage Learning, Mason, OHGoogle Scholar
- U.S. Department of Education. (1997).
*From college to first-year teaching: How the United States compares with several other countries*. Washington, DC: Author.Google Scholar - Wilson M.R. (1994) One preservice secondary teacher's understanding of function: The impact of a course integrating mathematical content and pedagogy. Journal for Research in Mathematics Education 25: 346–370CrossRefGoogle Scholar
- Wilson S., Ball D.L. (1996) Helping teachers meet the standards: New challenges for teacher educators. Elementary School Journal 97: 121–138CrossRefGoogle Scholar