Mathematical Content Understanding for Teaching: A Study of Undergraduate STEM Majors

Affiliation(s)

^{1}
Graduate School of Education, University of California, Berkeley, CA, USA.

^{2}
Cal Teach Program, University of California, Berkeley, CA, USA.

ABSTRACT

This paper investigates the nature of mathematical understanding that is needed to teach three foundational early algebra topics. These three topics include dividing fractions, linear equation in two variables and its graph, and quadratic function and its graph. Data from a sample of undergraduate STEM majors in a major research university affirm the importance of developing what Shulman (1999) calls “far more effective mathematics courses in U.S. undergraduate program” in order to equip future mathematics teachers with profound mathematical content understanding for teaching fundamental mathematics (Ma, 1999).

This paper investigates the nature of mathematical understanding that is needed to teach three foundational early algebra topics. These three topics include dividing fractions, linear equation in two variables and its graph, and quadratic function and its graph. Data from a sample of undergraduate STEM majors in a major research university affirm the importance of developing what Shulman (1999) calls “far more effective mathematics courses in U.S. undergraduate program” in order to equip future mathematics teachers with profound mathematical content understanding for teaching fundamental mathematics (Ma, 1999).

Cite this paper

Newton, X. and Poon, R. (2015) Mathematical Content Understanding for Teaching: A Study of Undergraduate STEM Majors.*Creative Education*, **6**, 998-1031. doi: 10.4236/ce.2015.610101.

Newton, X. and Poon, R. (2015) Mathematical Content Understanding for Teaching: A Study of Undergraduate STEM Majors.

References

[1] Adams, P. E., & Krockover, G. H. (1997). Beginning Science Teacher Cognition and Its Origins in the Pre-Service Secondary Science Teacher Program. Journal of Research in Science Teaching, 34, 633-653.

http://dx.doi.org/10.1002/(SICI)1098-2736(199708)34:6<633::AID-TEA6>3.0.CO;2-O

[2] Ball, D. L. (1990). The Mathematical Understanding That Prospective Teachers Bring to Teacher Education. Elementary School Journal, 90, 449-466.

http://dx.doi.org/10.1086/461626

[3] Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing Mathematics for Teaching: Who Knows Mathematics Well Enough to Teach Third Grade, and How Can We Decide? American Educator, 29, 14-17, 20-22, 43-46.

[4] Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content Knowledge for Teaching: What Makes It Special? Journal of Teacher Education, 59, 389-407.

http://dx.doi.org/10.1177/0022487108324554

[5] Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., Klusmann, U. et al. (2010). Teachers’ Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress. American Educational Research Journal, 47, 133-180.

http://dx.doi.org/10.3102/0002831209345157

[6] Borko, H., Eisenhart, M., Brown, C., Underhill, R., Jones, D., & Agard, P. (1992). Learning to Teach Hard Mathematics: Do Novice Teachers and Their Instructors Give up Too Easily? Journal for Research in Mathematics Education, 23, 194-222.

http://dx.doi.org/10.2307/749118

[7] Cochran-Smith, M. & Lytle, S. L. (1999). Relationships of Knowledge and Practice: Teacher Learning in Communities. Review of Research in Education, 24, 249-305.

[8] Goldhaber, D. D., & Brewer, D. J. (1997). Why Don’t Schools and Teachers Seem to Matter? Assessing the Impact of Unobservables on Educational Productivity. The Journal of Human Resources, 32, 505-523.

http://dx.doi.org/10.2307/146181

[9] Goldhaber, D. D., & Brewer, D. J. (2000). Does Teacher Certification Matter? High School Certification Status and Student Achievement. Educational Evaluation and Policy Analysis, 22, 129-145.

http://dx.doi.org/10.3102/01623737022002129

[10] Harel, G. (1994). On teacher Education Programs in Mathematics. International Journal for Mathematics Education in Science and Technology, 25, 113-119.

http://dx.doi.org/10.1080/0020739940250114

[11] Lortie, D. (1975). Schoolteacher: A Sociological Study. Chicago, IL: University of Chicago Press.

[12] Ma, L. (1999). Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Assoc.

[13] Rowan, B., Chiang, F.-S., & Miller, R. J. (1997). Using Research on Employees’ Performance to Study the Effects of Teachers on Students’ Achievement. Sociology of Education, 70, 256-284.

http://dx.doi.org/10.2307/2673267

[14] Schoenfeld, A. H., & Kilpatrick, J. (2008). Toward a Theory of Proficiency in Teaching Mathematics. International Handbook of Mathematics Teacher Education, 2, 1-35.

[15] Shulman, L. S. (1986). Those Who Understand: Knowledge Growth in Teaching. Educational Researcher, 15, 4-14.

http://dx.doi.org/10.3102/0013189X015002004

[16] Shulman, L. S. (1999). Forward. In L. P. Ma (Ed.), Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.

[17] Wu, H. (2010a). The Mathematics School Teachers Should Know. Talk Given at Lisbon, Portugal, on January 29, 2010.

http://math.berkeley.edu/~wu/Lisbon2010_2.pdf.

[18] Wu, H. (2010b). Introduction to School Algebra.

http://math.berkeley.edu/~wu/Algebrasummary.pdf

[19] Wu, H. (2011a). The Mis-Education of Mathematics Teachers. Notices of the American Mathematical Society, 58, 372-384.

[20] Wu, H. (2011b). Understanding Numbers in Elementary School Mathematics. Providence, RI: American Mathematical Society.

[1] Adams, P. E., & Krockover, G. H. (1997). Beginning Science Teacher Cognition and Its Origins in the Pre-Service Secondary Science Teacher Program. Journal of Research in Science Teaching, 34, 633-653.

http://dx.doi.org/10.1002/(SICI)1098-2736(199708)34:6<633::AID-TEA6>3.0.CO;2-O

[2] Ball, D. L. (1990). The Mathematical Understanding That Prospective Teachers Bring to Teacher Education. Elementary School Journal, 90, 449-466.

http://dx.doi.org/10.1086/461626

[3] Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing Mathematics for Teaching: Who Knows Mathematics Well Enough to Teach Third Grade, and How Can We Decide? American Educator, 29, 14-17, 20-22, 43-46.

[4] Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content Knowledge for Teaching: What Makes It Special? Journal of Teacher Education, 59, 389-407.

http://dx.doi.org/10.1177/0022487108324554

[5] Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., Klusmann, U. et al. (2010). Teachers’ Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress. American Educational Research Journal, 47, 133-180.

http://dx.doi.org/10.3102/0002831209345157

[6] Borko, H., Eisenhart, M., Brown, C., Underhill, R., Jones, D., & Agard, P. (1992). Learning to Teach Hard Mathematics: Do Novice Teachers and Their Instructors Give up Too Easily? Journal for Research in Mathematics Education, 23, 194-222.

http://dx.doi.org/10.2307/749118

[7] Cochran-Smith, M. & Lytle, S. L. (1999). Relationships of Knowledge and Practice: Teacher Learning in Communities. Review of Research in Education, 24, 249-305.

[8] Goldhaber, D. D., & Brewer, D. J. (1997). Why Don’t Schools and Teachers Seem to Matter? Assessing the Impact of Unobservables on Educational Productivity. The Journal of Human Resources, 32, 505-523.

http://dx.doi.org/10.2307/146181

[9] Goldhaber, D. D., & Brewer, D. J. (2000). Does Teacher Certification Matter? High School Certification Status and Student Achievement. Educational Evaluation and Policy Analysis, 22, 129-145.

http://dx.doi.org/10.3102/01623737022002129

[10] Harel, G. (1994). On teacher Education Programs in Mathematics. International Journal for Mathematics Education in Science and Technology, 25, 113-119.

http://dx.doi.org/10.1080/0020739940250114

[11] Lortie, D. (1975). Schoolteacher: A Sociological Study. Chicago, IL: University of Chicago Press.

[12] Ma, L. (1999). Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Assoc.

[13] Rowan, B., Chiang, F.-S., & Miller, R. J. (1997). Using Research on Employees’ Performance to Study the Effects of Teachers on Students’ Achievement. Sociology of Education, 70, 256-284.

http://dx.doi.org/10.2307/2673267

[14] Schoenfeld, A. H., & Kilpatrick, J. (2008). Toward a Theory of Proficiency in Teaching Mathematics. International Handbook of Mathematics Teacher Education, 2, 1-35.

[15] Shulman, L. S. (1986). Those Who Understand: Knowledge Growth in Teaching. Educational Researcher, 15, 4-14.

http://dx.doi.org/10.3102/0013189X015002004

[16] Shulman, L. S. (1999). Forward. In L. P. Ma (Ed.), Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.

[17] Wu, H. (2010a). The Mathematics School Teachers Should Know. Talk Given at Lisbon, Portugal, on January 29, 2010.

http://math.berkeley.edu/~wu/Lisbon2010_2.pdf.

[18] Wu, H. (2010b). Introduction to School Algebra.

http://math.berkeley.edu/~wu/Algebrasummary.pdf

[19] Wu, H. (2011a). The Mis-Education of Mathematics Teachers. Notices of the American Mathematical Society, 58, 372-384.

[20] Wu, H. (2011b). Understanding Numbers in Elementary School Mathematics. Providence, RI: American Mathematical Society.