Research Article
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INVESTIGATING TEACHING PRACTICES FOR ALGEBRAIC EXPRESSIONS WITHIN A MULTIPLE CASE STUDY

Year 2017, Volume: 6 , 31 - 37, 04.08.2017

Abstract

As
effective teaching practices support students’ learning; it is essential to
investigate teachers’ teaching practices. It can also
shed light on the causes of students’
difficulties
.
In this regard, proposing teaching practices might be important as the
practices can give insight about what is going on in teaching process. Thus,
the aim of this study is to extract the practices by focusing on the teachers’
actions during the teaching of operations with algebraic expressions.
Mathematical Knowledge for Teaching (MKT) model which is a practice-based
approach to the knowledge concept is used as a framework in this study. Thus,
this study focuses on teaching practices of operations with algebraic
expressions (addition, subtraction, and multiplication). Data were collected
from two middle school mathematics teachers’ instructions. The two teachers
were the cases in this qualitative research and the data were analyzed by
compare and contrast method. The practices that are found in the study are:
defining the concept of term, like term, constant term, and coefficient; using
equal sign; using analogies to explain addition and subtraction; using algebra
tiles; providing mathematical explanations for distributive property; and
noticing students’ misconceptions in simplification and equivalence of
algebraic expression. The results suggest that the conceptual teacher knowledge
influences teaching practices positively and teacher knowledge should be used
in appropriate pedagogical organization to develop teaching practices. 

References

  • Alibali, M. W., Knuth, E. J., Hattikudur, S., McNeil, N. M., & Stephens, A. C. (2007). A longitudinal examination of middle school students' understanding of the equal sign and equivalent equations. Mathematical Thinking and Learning, 9(3), 221-247. Anderson, J., White, P., & Sullivan, P. (2005). Using a schematic model to represent influences on, and relationships between, teachers’ problem-solving beliefs and practices. Mathematics Education Research Journal, 17(2), 9-38. 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. Banerjee, R., & Subramaniam, K. (2012). Evolution of a teaching approach for beginning algebra. Educational Studies in Mathematics, 80(3), 351-367. Baş, S., Çetinkaya, B., & Erbaş, A. K. (2011). Öğretmenlerin dokuzuncu sınıf öğrencilerinin cebirsel düşünme yapılarıyla ilgili Bilgileri. Eğitim ve Bilim, 36(159). Caglayan, G. (2013). Prospective mathematics teachers’ sense making of polynomial multiplication and factorization modeled with algebra tiles. Journal of Mathematics Teacher Education, 16(5), 349-378. Capraro, M. M. & Joffrion, H. (2006). Algebraic equations: Can middle-school students meaningfully translate from words to mathematical symbols? Reading Psychology, 27, 147–164. Charalambous, C. Y. (2016). Investigating the knowledge needed for teaching mathematics an exploratory validation study focusing on teaching practices. Journal of Teacher Education, 67(3), 220-237. Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five traditions (2nd ed.). Thousand Oaks, CA: Sage Publications. Depaepe, F., Torbeyns, J., Vermeersch, N., Janssens, D., Janssen, R., Kelchtermans, G., ... & Van Dooren, W. (2015). Teachers' content and pedagogical content knowledge on rational numbers: A comparison of prospective elementary and lower secondary school teachers. Teaching and Teacher Education, 47, 82-92. Doerr, H. M. (2004). Teachers’ knowledge and the teaching of algebra. In K. Stacey & H. Chick (Eds.), The Future of the Teaching and Learning of Algebra: The 12th ICMI Study (pp. 267-290). Dordrecht, The Netherlands: Kluwer. Fennema, E., & Franke, M. L. (1992). Teachers' knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). NewYork: Macmillan. Filloy, E. & Sutherland, R. (1996). Designing curricula for teaching and learning algebra. In A. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (vol. 1, pp. 139-160). Dordrecht: Kluwer Academic. Franke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice. In F. K. Lester (Ed.) Second handbook of research on mathematics teaching and learning (vol. 1, pp. 225-256). USA: Information Age Publishing. Hallagan, J. E. (2004). A teacher’s model of students’ algebraic thinking about equivalent expressions. In M. J. Hoines, & A. B. Fuglestad (Eds). Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (vol. 3, pp. 1-8). Bergen, Norway: International Group for the Psychology of Mathematics Education. Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202. Kieran, C. (1989). The early learning of algebra: A structural perspective. Research Issues in the Learning and Teaching of Algebra, 4, 33-56. Livneh, D., & Linchevski, L. (2007). Algebrification of arithmetic: Developing algebraic structure sense in the context of arithmetic. In J. W. Woo, H. C., Lew, K. S. Park, & D. Y. Seo (Eds). Proceedings of the 31st Conference of the Psychology of Mathematics Education (vol. 3, pp. 217-225). Seoul, Korea: International Group for the Psychology of Mathematics Education. MacGregor, M., & Stacey, K. (1997). Students’ understanding of algebraic notation: 11–15. Educational Studies in Mathematics, 33(1), 1–19. Ojose, B. (2015). Common Misconceptions in Mathematics: Strategies to Correct Them. America: University Press of America. Saxe, G. B.., Gearhart, M., & Seltzer, M. (1999). Relations between classroom practices and student learning in the domain of fractions. Cognition and Instruction, 17, 1–24. Seng, L. K. (2010). An error analysis of form 2 (grade 7) students in simplifying algebraic expressions: A descriptive study. Electronic Journal of Research in Educational Psychology, 8(1), 139-162. Tchoshanov, M. A. (2011). Relationship between teacher knowledge of concepts and connections, teaching practice, and student achievement in middle grades mathematics. Educational Studies in Mathematics, 76(2), 141-164. Tirosh, D., Even, R., & Robinson, N. (1998). Simplifying algebraic expressions: Teacher awareness and teaching approaches. Educational Studies in Mathematics, 35, 51-64. Wilkie, K. J. (2014). Upper primary school teachers’ mathematical knowledge for teaching functional thinking in algebra. Journal of Mathematics Teacher Education, 17(5), 397-428. Yin, R. K. (2003). Case study research: Design and methods (3rd ed.). Thousand Oaks, California: Sage Publications.
Year 2017, Volume: 6 , 31 - 37, 04.08.2017

Abstract

References

  • Alibali, M. W., Knuth, E. J., Hattikudur, S., McNeil, N. M., & Stephens, A. C. (2007). A longitudinal examination of middle school students' understanding of the equal sign and equivalent equations. Mathematical Thinking and Learning, 9(3), 221-247. Anderson, J., White, P., & Sullivan, P. (2005). Using a schematic model to represent influences on, and relationships between, teachers’ problem-solving beliefs and practices. Mathematics Education Research Journal, 17(2), 9-38. 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. Banerjee, R., & Subramaniam, K. (2012). Evolution of a teaching approach for beginning algebra. Educational Studies in Mathematics, 80(3), 351-367. Baş, S., Çetinkaya, B., & Erbaş, A. K. (2011). Öğretmenlerin dokuzuncu sınıf öğrencilerinin cebirsel düşünme yapılarıyla ilgili Bilgileri. Eğitim ve Bilim, 36(159). Caglayan, G. (2013). Prospective mathematics teachers’ sense making of polynomial multiplication and factorization modeled with algebra tiles. Journal of Mathematics Teacher Education, 16(5), 349-378. Capraro, M. M. & Joffrion, H. (2006). Algebraic equations: Can middle-school students meaningfully translate from words to mathematical symbols? Reading Psychology, 27, 147–164. Charalambous, C. Y. (2016). Investigating the knowledge needed for teaching mathematics an exploratory validation study focusing on teaching practices. Journal of Teacher Education, 67(3), 220-237. Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five traditions (2nd ed.). Thousand Oaks, CA: Sage Publications. Depaepe, F., Torbeyns, J., Vermeersch, N., Janssens, D., Janssen, R., Kelchtermans, G., ... & Van Dooren, W. (2015). Teachers' content and pedagogical content knowledge on rational numbers: A comparison of prospective elementary and lower secondary school teachers. Teaching and Teacher Education, 47, 82-92. Doerr, H. M. (2004). Teachers’ knowledge and the teaching of algebra. In K. Stacey & H. Chick (Eds.), The Future of the Teaching and Learning of Algebra: The 12th ICMI Study (pp. 267-290). Dordrecht, The Netherlands: Kluwer. Fennema, E., & Franke, M. L. (1992). Teachers' knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). NewYork: Macmillan. Filloy, E. & Sutherland, R. (1996). Designing curricula for teaching and learning algebra. In A. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (vol. 1, pp. 139-160). Dordrecht: Kluwer Academic. Franke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice. In F. K. Lester (Ed.) Second handbook of research on mathematics teaching and learning (vol. 1, pp. 225-256). USA: Information Age Publishing. Hallagan, J. E. (2004). A teacher’s model of students’ algebraic thinking about equivalent expressions. In M. J. Hoines, & A. B. Fuglestad (Eds). Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (vol. 3, pp. 1-8). Bergen, Norway: International Group for the Psychology of Mathematics Education. Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202. Kieran, C. (1989). The early learning of algebra: A structural perspective. Research Issues in the Learning and Teaching of Algebra, 4, 33-56. Livneh, D., & Linchevski, L. (2007). Algebrification of arithmetic: Developing algebraic structure sense in the context of arithmetic. In J. W. Woo, H. C., Lew, K. S. Park, & D. Y. Seo (Eds). Proceedings of the 31st Conference of the Psychology of Mathematics Education (vol. 3, pp. 217-225). Seoul, Korea: International Group for the Psychology of Mathematics Education. MacGregor, M., & Stacey, K. (1997). Students’ understanding of algebraic notation: 11–15. Educational Studies in Mathematics, 33(1), 1–19. Ojose, B. (2015). Common Misconceptions in Mathematics: Strategies to Correct Them. America: University Press of America. Saxe, G. B.., Gearhart, M., & Seltzer, M. (1999). Relations between classroom practices and student learning in the domain of fractions. Cognition and Instruction, 17, 1–24. Seng, L. K. (2010). An error analysis of form 2 (grade 7) students in simplifying algebraic expressions: A descriptive study. Electronic Journal of Research in Educational Psychology, 8(1), 139-162. Tchoshanov, M. A. (2011). Relationship between teacher knowledge of concepts and connections, teaching practice, and student achievement in middle grades mathematics. Educational Studies in Mathematics, 76(2), 141-164. Tirosh, D., Even, R., & Robinson, N. (1998). Simplifying algebraic expressions: Teacher awareness and teaching approaches. Educational Studies in Mathematics, 35, 51-64. Wilkie, K. J. (2014). Upper primary school teachers’ mathematical knowledge for teaching functional thinking in algebra. Journal of Mathematics Teacher Education, 17(5), 397-428. Yin, R. K. (2003). Case study research: Design and methods (3rd ed.). Thousand Oaks, California: Sage Publications.
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Details

Journal Section Articles
Authors

Dilek Girit

Didem Akyuz This is me

Publication Date August 4, 2017
Published in Issue Year 2017 Volume: 6

Cite

APA Girit, D., & Akyuz, D. (2017). INVESTIGATING TEACHING PRACTICES FOR ALGEBRAIC EXPRESSIONS WITHIN A MULTIPLE CASE STUDY. The Eurasia Proceedings of Educational and Social Sciences, 6, 31-37.