# The Relationship between Teacher Efficacy, and Students’ Trigonometry Self-Efficacy and Achievement

## Abstract

The purpose of the present study is to investigate the relationship between teacher efficacy to student trigonometry self-efficacy and student trigonometry achievement. The study included 16 high school teachers and their tenth grade students (n=571). Teacher efficacy was studied in terms of general teaching efficacy, mathematics teaching efficacy, and trigonometry teaching efficacy. No significant relationship was found between general teaching efficacy or mathematics teaching efficacy and student-related variables. The t-test results show that students of teachers who had high trigonometry teaching efficacy got higher scores on the trigonometry self-efficacy scale than students of teachers with low trigonometry teaching efficacy. Between these two groups of students’ achievement test scores, on the other hand, no significant difference was found. The results underline the importance of teachers’ trigonometry teaching efficacy for students’ trigonometry self-efficacy, as well as the importance of measuring self-efficacy in a task-specific way.## References

Akkoc, H. (2008). Pre-service mathematics teachers’ concept images of radian. International Journal of Mathematical Education in Science and Technology, 39(7), 857 – 878.

Ashton, P. T., Webb, R. B., & Doda, N. (1983). A study of teachers’ sense of efficacy. Washington, DC: National Institute of Education.

Bandura, A. (1982). Self-Efficacy mechanism in human agency. American Psychologist, 37(2), 122-147.

Bandura, A. (1997). Self-efficacy: The exercise of control. New York: W. H. Freeman.

Bandura, A., Barbaranelli C., Caprara G. V., & Pastorelli C. (1996). Multifaceted Impact of Self-Efficacy Beliefs on Academic Functioning. Child Development, 67(6), 1206-1222.

Betz, N. E. & Hackett G. (1981). The relationship of career-related self-efficacy expectations to perceived career options in college women and men. Journal of Counseling Psychology, 28 (5), 399-410.

Bong, M. (1997). Generality of academic self-efficacy judgments: Evidence of hierarchical relations. Journal of Educational Psychology, 89(4), 696-709.

Capa Y., Cakiroglu J. & Sarikaya H. (2005). Development and validation of Turkish version of teachers’ sense of efficacy scale. Egitim ve Bilim, 30, 74-81.

Charalambous, C. Y., Philippou G. N. & Kyriakides, L. (2008). Tracing the development of pre-service teachers’ efficacy beliefs in teaching mathematics during field work. Educational Studies in Mathematics, 67(2), 125-142.

Cousins, J. B. & Walker, C. A. (2000). Predictors of educators’ valuing of systemic inquiry in schools. Canadian Journal of Program Evaluation, (Special Issue), 25–53.

Dede Y. (2008). Matematik ogretmenlerinin ogretimlerine yonelik oz-yeterlilik inanclari. Turk Egitim Bilimleri Dergisi, 6, 741-757.

Dogan, A. (2001). Genel liselerde okutulan trigonometri konularinin ogretiminde ogrencilerin yanilgilari, yanlislari ve trigonometri konularina karsi ogrenci tutumlari uzerine bir arastirma. Unpublished doctoral dissertation, SelcukUniversity, Konya, Turkey.

Durmus, S. (2004). Matematikte ogrenme gucluklerinin saptanmasi uzerine bir calisma. Kastamonu Egitim Dergisi, 12(1), 125-128.

Erdogan, A., Baloglu M. & Kesici S. (2009). Geometri ve matematik ders basari duzeyleri ile geometri oz-yeterlilik inanclarinda cinsiyet farkliliklari. Paper presented at the XVIII. Ulusal Egitim Bilimleri Kurultayi, Izmir, Turkey.

Fi, C. D. (2003). Pre-service secondary school mathematics teachers’ knowledge of trigonometry: Subject matter content knowledge, pedagogical content knowledge and envisioned pedagogy. Unpublished doctoral dissertation, University of Iowa, USA.

Gay, L. R., Mills, G. E. & Airasian, P. (2009). Educational Research: Competencies for Analysis and Applications. Pearson Education, London.

Ghaith, G. Y. & Yaghi, H. (1997). Relationships among experience, teacher efficacy, and attitudes toward the implementation of instructional innovation. Teaching and Teacher Education, 13 (4), 451-458.

Gordon, L. (2001). High teacher efficacy as a marker of teacher effectiveness in the domain of classroom management. Paper presented at the California Council on Teacher Education, San Diego, CA.

Guskey, T. R. (1988). Teacher efficacy, self-concept, and attitudes toward the implementation of instructional innovation. Teaching and Teacher Education, 4(1), 63-69.

Leech N., Barret K. & Morgan G. A. (2005). SPSS for intermediate statistics. Vancouver: Routledge.

Lent, R. W., Brown S. D., & Larkin K. C. (1984). Relation of self-efficacy expectations to academic achievement and persistence. Journal of Counseling Psychology, 31(4), 356-362.

Lopez, F. G., Lent, R. W., Brown, S. D., & Gore, P. A., (1997). Role of social-cognitive expectations in high school students’ mathematics-related interest and performance. Journal of Counseling Psychology, 44(1), 44-52.

Mulholland, J. & Wallace J. (2001). Teacher induction and elementary science teaching: Enhancing self-efficacy. Teaching and Teacher Education, 17, 243-261.

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

Ghaith, G. Y. & Yaghi H. (1997). “Relationships among Experience, Teacher Efficacy, and Attitudes toward the Implementation of Instructional Innovation.” Teaching and Teacher Education 13 (4):451-458.

Nelson, S. (2007). Teacher efficacy and student motivation: A link to achievement in elementary mathematics. Unpublished doctoral dissertation, University of South Dakota, South Dakota, United States.

O’Brien, V., Martinez-Pons, M., & Kopala, M. (1999). Mathematics self-efficacy, ethnic identity, gender, and career interests related to mathematics and science. Journal of Educational Research, 92(4), 231.

Pajares, F. & Kranzler, J. (1995). Competence and confidence in mathematics: The role of self-efficacy, self-concept, anxiety, and ability. Paper presented at the American Educational Research Association, San Francisco.

Pajares, F. & Miller M. (1994). The role of self-efficacy and self-concept beliefs in mathematical problem-solving: A path analysis. Journal of Educational Psychology, 86(2), 193-203.

Pajares, F. (1996). Self-efficacy beliefs in academic settings. Review of Educational Research, 66(4), 543-578.

Philippou, G. N. & Christou, C. (1998). “The Effects of a Preparatory Mathematics Program in Changing Prospective Teachers’ Attitudes toward Mathematics”, Educational Studies in Mathematics, Vol. 35, No. 2, pp. 189-206.

Philippou, G. & Charalambos C. Y. (2005). Disentangling mentors’ role in the development of prospective teachers’ efficacy beliefs in teaching mathematic. Paper presented at the International Group for the Psychology of Mathematics Education, 28th Conference, Melbourne, Australia.

Pietsch J., Walker R., &Chapman, E. (2003). The relationship among self-concept, self-efficacy, and performance in mathematics during secondary school. Journal of Educational Psychology, 95( 3), 589–603.

Pintrich, P. R. & De Groot E. V. (1990). Motivational and self-regulated learning components of classroom academic performance. Journal of Educational Psychology, 82(5), 337-400.

Pintrich, P. R. & Schunk, D. H. (2002). Motivation in Education: Theory, Research and Applications, Merrill, Upper Saddle River, N.J.

Poulou, M. (2007). Personal teaching efficacy and its sources: Student teachers’ perceptions. Educational Psychology, 27(2), 191-218.

Riggs, I. (1995). The characteristics of high and low efficacy elementary teachers. Paper presented at the Annual Meeting of the National Association of Research in Science Teaching, San Francisco, CA.

Riggs, I. M., & Enochs, L. G. (1990). Toward the development of an elementary teacher’s science teaching efficacy belief instrument. Science Education, 74(3), 625-637.

Rose, J. S. & Medway F. J. (1981). Measurement of teachers’ beliefs in their control over student outcome. Journal of Educational Research, 74, 185-190.

Ross, J. A. (1992). Teacher efficacy and the effect of coaching on student achievement. Canadian Journal of Education, 17, 51−65.

Saglam, Z., Sevim M., Yurtseven T., Oguz T., Yildirim Y. & Saglam A. (2007). Matematik 10. Sinif Ders Kitabi. Istanbul: Rotamat Basim.

Sarac A. & Aslan-Tutak F. (2013). “Investigating Teachers’ Trigonometry Teaching Efficacy”. Proceedings of the Eight Congress of the European Society for Research in Mathematics Education, 1419-1429. Ankara: METU.

Siegle, D. & McCoach, D. B. (2007). Increasing students’ mathematics self-efficacy through teacher training. Journal of Advanced Academics, 18(2), 278-312.

Steckroth, J.J. (2007). Technology-enhanced mathematics instruction: Effects of visualization on student understanding of trigonometry. Unpublished doctoral dissertation, University of Virginia, USA.

Swars, S. L. (2005). Examining perceptions of mathematics teaching effectiveness among elementary pre-service teachers with differing levels of mathematics teacher efficacy. Journal of Instructional Psychology, 32(2), 139-147.

Tatar, E., Okur M., & Tuna A. (2008). Ortaogretim matematiginde ogrenme gucluklerinin saptanmasina yonelik bir calisma. Kastamonu Egitim Dergisi, 16(2), 507-516.

Taylor, K. M. & Betz, N. E. (1983). Applications of self-efficacy theory to the understanding and treatment of career indecision. Journal of Vocational Behaviour, 22(1), 63-81.

Topcu, T., Kertil, M., Akkoc, H., Yilmaz, K. & Onder, O. (2006). Preservice and in-service mathematics teachers’ concept images of radian. Paper presented at Psychology of Mathematics Education (PME30), Proceedings of the 30th International Conference, Prague, Czech Republic, 5, 281 - 288.

Tschannen-Moran, M. & Woolfolk-Hoy, A. (2001). Teacher efficacy: Capturing elusive construct. Teaching and Teacher Education, 17(4), 783-805.

Tschannen-Moran, M., Woolfolk-Hoy A., & Hoy W. K. (1998). Teacher efficacy: Its Meaning and Measure. Review of Educational Research, 68(2), 202-248.

Usher, E. L. (2009). Sources of middle school students’ self-efficacy in mathematics: A qualitative investigation. American Educational Research Journal, 46(1), 275-314.

Ustuner, M., Demirtas, H., Comert, M., & Ozer, N. (2009). Ortaogretim ogretmenlerinin oz-yeterlik algilari. Mehmet Akif Ersoy Universitesi Egitim Fakultesi Dergisi, 9 (17), 1-16.

Winters, J. M. (2000). A study of teacher efficacy and student achievement. Unpublished doctoral dissertation, Auburn University, USA.

Witcher, L. A., Onwuegbuzie, A. J., Collings, K. M. T., Witcher, A. E., Minor L. C. & James, T. L. (2002). “Relationship between Teacher Efficacy and Beliefs about Education among Preservice Teachers”, In Mid-South Educational Research Association, Annual Meeting, Chattanooga, TN.

Woolfolk, A. E., Rosoff B. & Hoy, W. K. (1990). Teachers’ sense of efficacy and their beliefs about managing students. Teaching and Teacher Education, 6(2), 137-148.

Zimmerman, B. J. (2000). Self-efficacy: An essential motive to learn. Contemporary Educational Psychology, 25(1), 82–91.

Ashton, P. T., Webb, R. B., & Doda, N. (1983). A study of teachers’ sense of efficacy. Washington, DC: National Institute of Education.

Bandura, A. (1982). Self-Efficacy mechanism in human agency. American Psychologist, 37(2), 122-147.

Bandura, A. (1997). Self-efficacy: The exercise of control. New York: W. H. Freeman.

Bandura, A., Barbaranelli C., Caprara G. V., & Pastorelli C. (1996). Multifaceted Impact of Self-Efficacy Beliefs on Academic Functioning. Child Development, 67(6), 1206-1222.

Betz, N. E. & Hackett G. (1981). The relationship of career-related self-efficacy expectations to perceived career options in college women and men. Journal of Counseling Psychology, 28 (5), 399-410.

Bong, M. (1997). Generality of academic self-efficacy judgments: Evidence of hierarchical relations. Journal of Educational Psychology, 89(4), 696-709.

Capa Y., Cakiroglu J. & Sarikaya H. (2005). Development and validation of Turkish version of teachers’ sense of efficacy scale. Egitim ve Bilim, 30, 74-81.

Charalambous, C. Y., Philippou G. N. & Kyriakides, L. (2008). Tracing the development of pre-service teachers’ efficacy beliefs in teaching mathematics during field work. Educational Studies in Mathematics, 67(2), 125-142.

Cousins, J. B. & Walker, C. A. (2000). Predictors of educators’ valuing of systemic inquiry in schools. Canadian Journal of Program Evaluation, (Special Issue), 25–53.

Dede Y. (2008). Matematik ogretmenlerinin ogretimlerine yonelik oz-yeterlilik inanclari. Turk Egitim Bilimleri Dergisi, 6, 741-757.

Dogan, A. (2001). Genel liselerde okutulan trigonometri konularinin ogretiminde ogrencilerin yanilgilari, yanlislari ve trigonometri konularina karsi ogrenci tutumlari uzerine bir arastirma. Unpublished doctoral dissertation, SelcukUniversity, Konya, Turkey.

Durmus, S. (2004). Matematikte ogrenme gucluklerinin saptanmasi uzerine bir calisma. Kastamonu Egitim Dergisi, 12(1), 125-128.

Erdogan, A., Baloglu M. & Kesici S. (2009). Geometri ve matematik ders basari duzeyleri ile geometri oz-yeterlilik inanclarinda cinsiyet farkliliklari. Paper presented at the XVIII. Ulusal Egitim Bilimleri Kurultayi, Izmir, Turkey.

Fi, C. D. (2003). Pre-service secondary school mathematics teachers’ knowledge of trigonometry: Subject matter content knowledge, pedagogical content knowledge and envisioned pedagogy. Unpublished doctoral dissertation, University of Iowa, USA.

Gay, L. R., Mills, G. E. & Airasian, P. (2009). Educational Research: Competencies for Analysis and Applications. Pearson Education, London.

Ghaith, G. Y. & Yaghi, H. (1997). Relationships among experience, teacher efficacy, and attitudes toward the implementation of instructional innovation. Teaching and Teacher Education, 13 (4), 451-458.

Gordon, L. (2001). High teacher efficacy as a marker of teacher effectiveness in the domain of classroom management. Paper presented at the California Council on Teacher Education, San Diego, CA.

Guskey, T. R. (1988). Teacher efficacy, self-concept, and attitudes toward the implementation of instructional innovation. Teaching and Teacher Education, 4(1), 63-69.

Leech N., Barret K. & Morgan G. A. (2005). SPSS for intermediate statistics. Vancouver: Routledge.

Lent, R. W., Brown S. D., & Larkin K. C. (1984). Relation of self-efficacy expectations to academic achievement and persistence. Journal of Counseling Psychology, 31(4), 356-362.

Lopez, F. G., Lent, R. W., Brown, S. D., & Gore, P. A., (1997). Role of social-cognitive expectations in high school students’ mathematics-related interest and performance. Journal of Counseling Psychology, 44(1), 44-52.

Mulholland, J. & Wallace J. (2001). Teacher induction and elementary science teaching: Enhancing self-efficacy. Teaching and Teacher Education, 17, 243-261.

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

Ghaith, G. Y. & Yaghi H. (1997). “Relationships among Experience, Teacher Efficacy, and Attitudes toward the Implementation of Instructional Innovation.” Teaching and Teacher Education 13 (4):451-458.

Nelson, S. (2007). Teacher efficacy and student motivation: A link to achievement in elementary mathematics. Unpublished doctoral dissertation, University of South Dakota, South Dakota, United States.

O’Brien, V., Martinez-Pons, M., & Kopala, M. (1999). Mathematics self-efficacy, ethnic identity, gender, and career interests related to mathematics and science. Journal of Educational Research, 92(4), 231.

Pajares, F. & Kranzler, J. (1995). Competence and confidence in mathematics: The role of self-efficacy, self-concept, anxiety, and ability. Paper presented at the American Educational Research Association, San Francisco.

Pajares, F. & Miller M. (1994). The role of self-efficacy and self-concept beliefs in mathematical problem-solving: A path analysis. Journal of Educational Psychology, 86(2), 193-203.

Pajares, F. (1996). Self-efficacy beliefs in academic settings. Review of Educational Research, 66(4), 543-578.

Philippou, G. N. & Christou, C. (1998). “The Effects of a Preparatory Mathematics Program in Changing Prospective Teachers’ Attitudes toward Mathematics”, Educational Studies in Mathematics, Vol. 35, No. 2, pp. 189-206.

Philippou, G. & Charalambos C. Y. (2005). Disentangling mentors’ role in the development of prospective teachers’ efficacy beliefs in teaching mathematic. Paper presented at the International Group for the Psychology of Mathematics Education, 28th Conference, Melbourne, Australia.

Pietsch J., Walker R., &Chapman, E. (2003). The relationship among self-concept, self-efficacy, and performance in mathematics during secondary school. Journal of Educational Psychology, 95( 3), 589–603.

Pintrich, P. R. & De Groot E. V. (1990). Motivational and self-regulated learning components of classroom academic performance. Journal of Educational Psychology, 82(5), 337-400.

Pintrich, P. R. & Schunk, D. H. (2002). Motivation in Education: Theory, Research and Applications, Merrill, Upper Saddle River, N.J.

Poulou, M. (2007). Personal teaching efficacy and its sources: Student teachers’ perceptions. Educational Psychology, 27(2), 191-218.

Riggs, I. (1995). The characteristics of high and low efficacy elementary teachers. Paper presented at the Annual Meeting of the National Association of Research in Science Teaching, San Francisco, CA.

Riggs, I. M., & Enochs, L. G. (1990). Toward the development of an elementary teacher’s science teaching efficacy belief instrument. Science Education, 74(3), 625-637.

Rose, J. S. & Medway F. J. (1981). Measurement of teachers’ beliefs in their control over student outcome. Journal of Educational Research, 74, 185-190.

Ross, J. A. (1992). Teacher efficacy and the effect of coaching on student achievement. Canadian Journal of Education, 17, 51−65.

Saglam, Z., Sevim M., Yurtseven T., Oguz T., Yildirim Y. & Saglam A. (2007). Matematik 10. Sinif Ders Kitabi. Istanbul: Rotamat Basim.

Sarac A. & Aslan-Tutak F. (2013). “Investigating Teachers’ Trigonometry Teaching Efficacy”. Proceedings of the Eight Congress of the European Society for Research in Mathematics Education, 1419-1429. Ankara: METU.

Siegle, D. & McCoach, D. B. (2007). Increasing students’ mathematics self-efficacy through teacher training. Journal of Advanced Academics, 18(2), 278-312.

Steckroth, J.J. (2007). Technology-enhanced mathematics instruction: Effects of visualization on student understanding of trigonometry. Unpublished doctoral dissertation, University of Virginia, USA.

Swars, S. L. (2005). Examining perceptions of mathematics teaching effectiveness among elementary pre-service teachers with differing levels of mathematics teacher efficacy. Journal of Instructional Psychology, 32(2), 139-147.

Tatar, E., Okur M., & Tuna A. (2008). Ortaogretim matematiginde ogrenme gucluklerinin saptanmasina yonelik bir calisma. Kastamonu Egitim Dergisi, 16(2), 507-516.

Taylor, K. M. & Betz, N. E. (1983). Applications of self-efficacy theory to the understanding and treatment of career indecision. Journal of Vocational Behaviour, 22(1), 63-81.

Topcu, T., Kertil, M., Akkoc, H., Yilmaz, K. & Onder, O. (2006). Preservice and in-service mathematics teachers’ concept images of radian. Paper presented at Psychology of Mathematics Education (PME30), Proceedings of the 30th International Conference, Prague, Czech Republic, 5, 281 - 288.

Tschannen-Moran, M. & Woolfolk-Hoy, A. (2001). Teacher efficacy: Capturing elusive construct. Teaching and Teacher Education, 17(4), 783-805.

Tschannen-Moran, M., Woolfolk-Hoy A., & Hoy W. K. (1998). Teacher efficacy: Its Meaning and Measure. Review of Educational Research, 68(2), 202-248.

Usher, E. L. (2009). Sources of middle school students’ self-efficacy in mathematics: A qualitative investigation. American Educational Research Journal, 46(1), 275-314.

Ustuner, M., Demirtas, H., Comert, M., & Ozer, N. (2009). Ortaogretim ogretmenlerinin oz-yeterlik algilari. Mehmet Akif Ersoy Universitesi Egitim Fakultesi Dergisi, 9 (17), 1-16.

Winters, J. M. (2000). A study of teacher efficacy and student achievement. Unpublished doctoral dissertation, Auburn University, USA.

Witcher, L. A., Onwuegbuzie, A. J., Collings, K. M. T., Witcher, A. E., Minor L. C. & James, T. L. (2002). “Relationship between Teacher Efficacy and Beliefs about Education among Preservice Teachers”, In Mid-South Educational Research Association, Annual Meeting, Chattanooga, TN.

Woolfolk, A. E., Rosoff B. & Hoy, W. K. (1990). Teachers’ sense of efficacy and their beliefs about managing students. Teaching and Teacher Education, 6(2), 137-148.

Zimmerman, B. J. (2000). Self-efficacy: An essential motive to learn. Contemporary Educational Psychology, 25(1), 82–91.

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2017-05-14

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Articles