The purposes of this study were as follows: (1) To examine how K-8 prospective teachers’ personal mathematics teacher efficacy beliefs vary when they are measured in the context of four written mathematical teaching scenarios, and (2) To examine the extent to which K-8 prospective teachers’ personal mathematics teacher efficacy beliefs and mathematical knowledge for teaching are aligned. Forty-two prospective teachers participated in the study. Participants were first asked to respond to four written mathematical teaching scenarios that required responding, as a teacher, to student questions about fraction concepts. Prospective teachers then evaluated how effective they believed their responses would be for developing student understanding. Approximately two weeks later, participants were asked to write mathematical explanations for four written mathematical tasks that paralleled the teaching scenarios and were then asked to evaluate their own mathematical understanding of each task. Different patterns emerged based on whether prospective teachers exhibited high or low mathematical knowledge for teaching on a particular task. Additionally, reported self-evaluations of mathematical knowledge for teaching were helpful for understanding the nature of prospective teachers’ personal teacher efficacy beliefs.

• Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407.
• Bandura, A. (1986). Social foundations of thought and action: A social cognitive theory. Englewood Cliffs, N.J.: Prentice-Hall.
• Bates, A. B., Latham, N., & Kim, J. (2011). Linking preservice teachers’ mathematics self-Efficacy and mathematics teaching efficacy to their mathematical performance. School Science and Mathematics, 111(7), 325-333.
• 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(3), 194-222.
• Brodkey, J. J. (1993). Learning while teaching: Possibilities and problems. Teacher Education Quarterly, 20(1), 63-70.
• Charalambous, C.Y. (2010). Mathematical knowledge for teaching and task unfolding: An exploratory study. The Elementary School Journal, 110(3), 247-278.
• Enochs, L. G., Smith, P. L., & Huinker, D. (2000). Establishing factorial validity of the Mathematics Teaching Efficacy Beliefs Instrument. School Science and Mathematics, 100(4), 194-202.
• Guest, C. B., Regehr, G., & Tiberius, R. G. (2001). The life long challenge of expertise. Medical Education, 35(1), 78-81.
• Hacker, D. J., Bol, L., Horgan, D. D., & Rakow, E. A. (2000). Test prediction and performance in a classroom context. Journal of Educational Psychology, 92(1), 160-170.
• Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.
• Huinker, D., & Madison, S. K. (1997). Preparing efficacious elementary teachers in science and mathematics: The influence of methods courses. Journal of Science Teacher Education, 8(2), 107-126.
• Kruger, J., & Dunning, D. (1999). Unskilled and unaware of It: How difficulties in recognizing one's own incompetence lead to inflated self-assessments. Journal of Personality and Social Psychology, 77(6), 1121-1134.
• McCoy, A. C. (2011). Specialized mathematical content knowledge of preservice elementary teachers: The effect of mathematics teacher efficacy. (Unpublished doctoral dissertation.) UMKC, Kansas City, Missouri.
• Morris, A. K., Hiebert, J., & Spitzer, S. M. (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.
• Pajares, M. F. (1992). Teachers' beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(3), 307-332.
• Philipp, R. (2002). IMAP: Integrating Mathematics and Pedagogy to Illustrate Children's Reasoning. San Diego, CA: San Diego State University.
• Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
• Swars, S., Hart, L. C., Smith, S. Z., Smith, M. E., & Tolar, T. (2007). A longitudinal study of elementary prospective teachers' mathematical beliefs and content knowledge. School Science and Mathematics, 107(8), 325-335.
• Swars, S., Smith, S. Z., Smith, M. E., & Hart, L. C. (2009). A longitudinal study of effects of a developmental teacher preparation program on elementary prospective teachers' mathematics beliefs. Journal of Mathematics Teacher Education, 12(1), 47-66.
• Tschannen-Moran, M., & Hoy, A. W. (2001). Teacher efficacy: Capturing an elusive construct. Teaching and Teacher Education, 17, 783-805.
• Wenner, G. (1993). Relationship between science knowledge levels and beliefs toward science instruction held by preservice elementary teachers. Journal of Science Education and Technology, 2(3), 461-468.
• Wenner, G. (1995). Science knowledge and efficacy beliefs among preservice elementary teachers: A follow-up study.Journal of Science Education and Technology, 4(4), 307-315.
• Wheatley, K. F. (2000). Positive teacher efficacy as an obstacle to educational reform. Journal of Research and Development in Education, 34(1), 14-27.

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