Year 2020,
Volume 7,
Issue 2,
156 - 164,
30.12.2020
Pinar YILDIZ
Azime ATAY
S. Koza ÇİFTÇİ
References
- Agarwal, S. (2006). The nature of pre-service secondary mathematics teachers’ knowledge of mathematics for teaching of functions (Unpublished doctoral dissertation). State University of New York, Buffalo, United States.
- Akkan, Y., Baki, A. & Çakıroğlu, Ü. (2012). 5-8. sınıf öğrencilerinin aritmetikten cebire geçiş süreçlerinin problem çözme bağlamında incelenmesi [ Examination of the 5th – 8th grade students’ transition process from arithmetic to algebra with regard problem solving]. Hacettepe University Journal of Education, 43, 1-13.
- Attorps, I. (2003). Teachers’ images of the ‘equation’ concept. European Research in Mathematics Education, 3, 1-8.
- Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. Elementary School Journal, 90(4), 449-446.
- 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 (pp. 433-456). New York: Macmillan.
- Ball, D. B., Thames, M. H. & Phelps, G. (2008). Content knowledge for teaching: What makes it special?. Journal of Teacher Education, 59(5), 389-407.
- Black, D. J. W. (2007). The relationship of teachers’ content knowledge and pedagogical content knowledge in algebra, and changes in both types of knowledge as a professional development (Unpublished doctoral dissertation). Auburn University, Auburn.
- Brizuela, B. M. (2016). Variables in elementary mathematics education. The Elementary School Journal, 117(1), 46-71.
- Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2013). Bilimsel araştırma yöntemleri (15. Baskı) [Scientific research methods (15th ed.)]. Ankara: Pegem Akademi.
- Charalambous, C. Y., Hill, H. C., Chin, M. J. & McGinn, D. (2019). Mathematical content knowledge and knowledge for teaching: exploring their distinguishability and contribution to student learning. Journal of Mathematics Teacher Education, 1-35.
- Christou, K. P. & Vosniadou, S. (2012). What kinds of numbers do students assign to literal symbols? Aspects of the transition from arithmetic to algebra. Mathematical Thinking and Learning, 14(1), 1-27.
- Copur-Gencturk, Y. (2015). The effects of changes in mathematical knowledge on teaching: A longitudinal study of teachers' knowledge and instruction. Journal for Research in Mathematics Education, 46(3), 280-330.
- Chalouh, L. & Herscovics, N. (1988). Teaching algebraic expressions in a meaningful way. In A. F. Coxford (Eds.), The ideas of algebra, K-12. (pp. 33-42). Reston, VA: National Council of Teachers of Mathematics.
- Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). London: Sage.
- Dede, Y. & Argün, Z. (2003). Cebir, öğrencilere niçin zor gelmektedir? [Why do students have difficulty with algebra?]. Hacettepe University Journal of Education, 24, 180-185.
- Dreher, A., Lindmeier, A., Heinze, A. & Niemand, C. (2018). What kind of content knowledge do secondary mathematics teachers need?. Journal für Mathematik-Didaktik, 39(2), 319-341.
- Edwards, B. S. & Ward, M. B. (2004). Surprises from mathematics education research: Student (mis) use of mathematical definitions. The American Mathematical Monthly, 111(5), 411-424.
- Fennema, E., Sowder, J. & Carpenter, T. P. (1999). Creating classrooms that promote understanding. In E. Fennema, and T. A. Romberg (Eds.). Mathematics classrooms that promote understanding (pp. 185-199). Hilsdale, NJ: Lawrence Erlbaum Associates.
- Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2013). How to design and evaluate research in education (8th ed.). New York: McGraw-Hill.
- Hill, H. C. & 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.
- 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.
- Hohensee, C. (2017). Preparing elementary prospective teachers to teach early algebra. Journal of Mathematics Teacher Education, 20(3), 231-257.
- Kieran, C., Pang, J., Schifter, D. & Ng, S. F. (2016). Early Algebra. Research into its nature, its learning, its teaching. Hamburg: Springer Open.
- Ma, L. (2010). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Routledge.
- Milli Eğitim Bakanlığı (2018). Matematik dersi (1-8. sınıflar) öğretim programı [Mathematics curriculum (1st -8th grade)]. Ankara: Milli Eğitim Bakanlığı.
- Morgan, C. (2005). Word, definitions and concepts in discourses of mathematics, teaching and learning. Language and Education, 19(2), 102-116.
- Mosvold, R. & Fauskanger, J. (2013). Teachers’ beliefs about mathematical knowledge for teaching definitions. International Electronic Journal of Mathematics Education, 8(2-3), 43-61.
- Odumosu, O. & Fisayi, A. (2018). Teachers’ content and pedagogical knowledge on students’ achievement in algebra. International Journal of Education and Research, 6(3), 83-94.
- Patton, M. Q. (2002). Qualitative research and evaluation methods. Thousand Oaks, CA: Sage Publications.
- Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
- Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harward Educational Review, 57(1), 1-21.
- Stephens, A. C. (2008). What “counts” as algebra in the eyes of preservice elementary teachers?. Journal of Mathematical Behavior, 27, 33-47.
- Stephens, A. C., Ellis, A. B., Blanton, M. & Brizuela, B. M. (2017). Algebraic thinking in the elementary and middle grades. Compendium for Research in Mathematics Education, 386-420.
- Stump, S. L. & Bishop, J. (2002). Preservice elementary and middle school teachers’ conceptions of algebra revealed through the use of exemplary curriculum materials. In D. S. Mewborn, P. Sztajn, D.Y. White, H. G. Wiegel, R. L. Bryant, and K. Nooney (Eds.). Proceedings of the twenty-fourth annual meeting of the international group for the psychology of mathematics education (pp. 1903–1914). Columbus, OH: ERIC.
- Tanisli, D. & Kose, N. Y. (2013). Preservice Mathematics Teachers' Knowledge of Students about the Algebraic Concepts. Australian Journal of Teacher Education, 38(2), 1-18.
- Tchoshanov, M., Cruz, M. D., Huereca, K., Shakirova, K., Shakirova, L. & Ibragimova, E. N. (2017). Examination of lower secondary mathematics teachers’ content knowledge and its connection to students’ performance. International Journal of Science and Mathematics Education, 15(4), 683-702.
- Tirosh, D., Even, R. & Robinson, N. (1998). Simplifying algebraic expressions: Teacher awareness and teaching approaches. Educational Studies in Mathematics, 35(1), 51-64.
- Van de Walle, J. A., Karp, K. S. & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). New Jersey: Pearson Education.
- Weinberg, A., Dresen, J. & Slater, T. (2016). Students’ understanding of algebraic notation: A semiotic systems perspective. The Journal of Mathematical Behavior, 43, 70-88.
- Wasserman, N. H. (2016). Abstract algebra for algebra teaching: Influencing school mathematics instruction. Canadian Journal of Science, Mathematics and Technology Education, 16(1), 28-47.
- Welder, R. M. (2007). Preservice elementary teachers’ pedagogical content knowledge of prerequisite algebra concepts (Unpublished doctoral dissertation). Montana State University, Montana.
- Welder, R. M. & Simonsen, L. M. (2011). Elementary teachers’ mathematical knowledge for teaching prerequisite algebra concepts. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1.
- Yıldız, P. (2016). Middle mathematics teachers’ knowledge for teaching algebra: A multiple case study (Unpublished doctoral dissertation). Hacettepe University, Ankara.
- Zuya, H. E. (2017). Prospective teachers’ conceptual and procedural knowledge in mathematics: The case of algebra. American Journal of Educational Research, 5(3), 310-315.
Preservice Middle School Mathematics Teachers’ Definitions of Algebraic Expression and Equation
Year 2020,
Volume 7,
Issue 2,
156 - 164,
30.12.2020
Pinar YILDIZ
Azime ATAY
S. Koza ÇİFTÇİ
Abstract
Using correct definitions of the mathematical concepts is crucial for learning and teaching of any mathematical content. Being able to make mathematically correct definition of the concepts is an indicator of teachers’ content knowledge. The purpose of this study is to determine how preservice middle school mathematics teachers define the concept of algebraic expression and equation. The participants of this case study were 35 preservice middle school mathematics teachers. The data were collected through written exam and semi-structured interviews. Written exam includes two questions asking preservice teachers to define equation and algebraic expression and write an example of each. Only 9 of participants correctly defined algebraic expression. Preservice teachers’ definitions of algebraic expression were classified under three themes which are expressions containing unknown, expressions containing equality, and mathematical expressions. Two themes arose from preservice teachers’ definition of equation: expressions with unknown, and expressions with equality.
References
- Agarwal, S. (2006). The nature of pre-service secondary mathematics teachers’ knowledge of mathematics for teaching of functions (Unpublished doctoral dissertation). State University of New York, Buffalo, United States.
- Akkan, Y., Baki, A. & Çakıroğlu, Ü. (2012). 5-8. sınıf öğrencilerinin aritmetikten cebire geçiş süreçlerinin problem çözme bağlamında incelenmesi [ Examination of the 5th – 8th grade students’ transition process from arithmetic to algebra with regard problem solving]. Hacettepe University Journal of Education, 43, 1-13.
- Attorps, I. (2003). Teachers’ images of the ‘equation’ concept. European Research in Mathematics Education, 3, 1-8.
- Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. Elementary School Journal, 90(4), 449-446.
- 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 (pp. 433-456). New York: Macmillan.
- Ball, D. B., Thames, M. H. & Phelps, G. (2008). Content knowledge for teaching: What makes it special?. Journal of Teacher Education, 59(5), 389-407.
- Black, D. J. W. (2007). The relationship of teachers’ content knowledge and pedagogical content knowledge in algebra, and changes in both types of knowledge as a professional development (Unpublished doctoral dissertation). Auburn University, Auburn.
- Brizuela, B. M. (2016). Variables in elementary mathematics education. The Elementary School Journal, 117(1), 46-71.
- Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2013). Bilimsel araştırma yöntemleri (15. Baskı) [Scientific research methods (15th ed.)]. Ankara: Pegem Akademi.
- Charalambous, C. Y., Hill, H. C., Chin, M. J. & McGinn, D. (2019). Mathematical content knowledge and knowledge for teaching: exploring their distinguishability and contribution to student learning. Journal of Mathematics Teacher Education, 1-35.
- Christou, K. P. & Vosniadou, S. (2012). What kinds of numbers do students assign to literal symbols? Aspects of the transition from arithmetic to algebra. Mathematical Thinking and Learning, 14(1), 1-27.
- Copur-Gencturk, Y. (2015). The effects of changes in mathematical knowledge on teaching: A longitudinal study of teachers' knowledge and instruction. Journal for Research in Mathematics Education, 46(3), 280-330.
- Chalouh, L. & Herscovics, N. (1988). Teaching algebraic expressions in a meaningful way. In A. F. Coxford (Eds.), The ideas of algebra, K-12. (pp. 33-42). Reston, VA: National Council of Teachers of Mathematics.
- Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). London: Sage.
- Dede, Y. & Argün, Z. (2003). Cebir, öğrencilere niçin zor gelmektedir? [Why do students have difficulty with algebra?]. Hacettepe University Journal of Education, 24, 180-185.
- Dreher, A., Lindmeier, A., Heinze, A. & Niemand, C. (2018). What kind of content knowledge do secondary mathematics teachers need?. Journal für Mathematik-Didaktik, 39(2), 319-341.
- Edwards, B. S. & Ward, M. B. (2004). Surprises from mathematics education research: Student (mis) use of mathematical definitions. The American Mathematical Monthly, 111(5), 411-424.
- Fennema, E., Sowder, J. & Carpenter, T. P. (1999). Creating classrooms that promote understanding. In E. Fennema, and T. A. Romberg (Eds.). Mathematics classrooms that promote understanding (pp. 185-199). Hilsdale, NJ: Lawrence Erlbaum Associates.
- Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2013). How to design and evaluate research in education (8th ed.). New York: McGraw-Hill.
- Hill, H. C. & 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.
- 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.
- Hohensee, C. (2017). Preparing elementary prospective teachers to teach early algebra. Journal of Mathematics Teacher Education, 20(3), 231-257.
- Kieran, C., Pang, J., Schifter, D. & Ng, S. F. (2016). Early Algebra. Research into its nature, its learning, its teaching. Hamburg: Springer Open.
- Ma, L. (2010). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Routledge.
- Milli Eğitim Bakanlığı (2018). Matematik dersi (1-8. sınıflar) öğretim programı [Mathematics curriculum (1st -8th grade)]. Ankara: Milli Eğitim Bakanlığı.
- Morgan, C. (2005). Word, definitions and concepts in discourses of mathematics, teaching and learning. Language and Education, 19(2), 102-116.
- Mosvold, R. & Fauskanger, J. (2013). Teachers’ beliefs about mathematical knowledge for teaching definitions. International Electronic Journal of Mathematics Education, 8(2-3), 43-61.
- Odumosu, O. & Fisayi, A. (2018). Teachers’ content and pedagogical knowledge on students’ achievement in algebra. International Journal of Education and Research, 6(3), 83-94.
- Patton, M. Q. (2002). Qualitative research and evaluation methods. Thousand Oaks, CA: Sage Publications.
- Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
- Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harward Educational Review, 57(1), 1-21.
- Stephens, A. C. (2008). What “counts” as algebra in the eyes of preservice elementary teachers?. Journal of Mathematical Behavior, 27, 33-47.
- Stephens, A. C., Ellis, A. B., Blanton, M. & Brizuela, B. M. (2017). Algebraic thinking in the elementary and middle grades. Compendium for Research in Mathematics Education, 386-420.
- Stump, S. L. & Bishop, J. (2002). Preservice elementary and middle school teachers’ conceptions of algebra revealed through the use of exemplary curriculum materials. In D. S. Mewborn, P. Sztajn, D.Y. White, H. G. Wiegel, R. L. Bryant, and K. Nooney (Eds.). Proceedings of the twenty-fourth annual meeting of the international group for the psychology of mathematics education (pp. 1903–1914). Columbus, OH: ERIC.
- Tanisli, D. & Kose, N. Y. (2013). Preservice Mathematics Teachers' Knowledge of Students about the Algebraic Concepts. Australian Journal of Teacher Education, 38(2), 1-18.
- Tchoshanov, M., Cruz, M. D., Huereca, K., Shakirova, K., Shakirova, L. & Ibragimova, E. N. (2017). Examination of lower secondary mathematics teachers’ content knowledge and its connection to students’ performance. International Journal of Science and Mathematics Education, 15(4), 683-702.
- Tirosh, D., Even, R. & Robinson, N. (1998). Simplifying algebraic expressions: Teacher awareness and teaching approaches. Educational Studies in Mathematics, 35(1), 51-64.
- Van de Walle, J. A., Karp, K. S. & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). New Jersey: Pearson Education.
- Weinberg, A., Dresen, J. & Slater, T. (2016). Students’ understanding of algebraic notation: A semiotic systems perspective. The Journal of Mathematical Behavior, 43, 70-88.
- Wasserman, N. H. (2016). Abstract algebra for algebra teaching: Influencing school mathematics instruction. Canadian Journal of Science, Mathematics and Technology Education, 16(1), 28-47.
- Welder, R. M. (2007). Preservice elementary teachers’ pedagogical content knowledge of prerequisite algebra concepts (Unpublished doctoral dissertation). Montana State University, Montana.
- Welder, R. M. & Simonsen, L. M. (2011). Elementary teachers’ mathematical knowledge for teaching prerequisite algebra concepts. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1.
- Yıldız, P. (2016). Middle mathematics teachers’ knowledge for teaching algebra: A multiple case study (Unpublished doctoral dissertation). Hacettepe University, Ankara.
- Zuya, H. E. (2017). Prospective teachers’ conceptual and procedural knowledge in mathematics: The case of algebra. American Journal of Educational Research, 5(3), 310-315.