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Investigation of a Middle School Preservice Teacher’s Knowledge of Content and Students

Year 2021, Volume: 8 Issue: 4, 818 - 841, 04.12.2021
https://doi.org/10.21449/ijate.946573

Abstract

The purpose of this study was to explicate one preservice middle grades mathematics teacher’s Knowledge of Content and Students (KCS) in the context of multiple solution strategies. This study’s purpose is to underline the importance of preservice teachers’ KCS and provide possible investigative methods for evaluating preservice teachers’ KCS. Specifically, the research inquiry guiding this study focused on how a middle school preservice mathematics teacher displays KCS when engaging with tasks about pattern recognition and linear functions in the context of multiple solution strategies. The data consisted of three videotaped semi-structured interviews with the preservice mathematics teacher as well as the written work she produced during the interviews. This study explicated one preservice mathematic teacher’s performance regarding two important themes of KCS: generating multiple possible solution strategies of middle school students and explaining multiple student solution strategies. In terms of generating multiple solution strategies of middle school students, the study found that the preservice mathematics teacher provided the same solution strategies that she employed when she solved the problems by herself. Regarding explaining multiple student solution strategies, this study revealed that the preservice teacher did not explicate how typical middle school students reason. The preservice teacher had limitations when explaining the possible procedures that students might have used to solve problems when given the final student solutions. With regard to the teacher’s abilities to recognise and understand students’ typical understandings and misunderstandings, the study demonstrated that the preservice teacher was capable of explaining some solution strategies but not all of them.

References

  • Alqahtani, M. M., & Powell, A. B. (2017). Mediational activities in a dynamic geometry environment and teachers’ specialized content knowledge. The Journal of Mathematical Behavior, 48, 77-94.
  • An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school, mathematics teachers in China and the US. Journal of Mathematics Teacher Education, 7(2), 145-172.
  • Asquith, P., Stephens, A. C., Knuth, E. J., & Alibali, M. W. (2007). Middle school mathematics teachers' knowledge of students' understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249-272.
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching. Journal of Teacher Education, 59(5), 389-407.
  • Baki, A. (2020). Matematiği öğretme bilgisi (3rd ed.). PegemAkademi
  • Bansilal, S., Mkhwanazi, T., & Brijlall, D. (2014). An exploration of the common content knowledge of high school mathematics teachers. Perspectives in Education, 32(1), 34-50.
  • Boerst, T. A., Sleep, L., Ball, D. L., & Bass, H. (2011). Preparing teachers to lead mathematics discussions. Teachers College Record, 113(12), 2844-2877.
  • Bryan, C. A., Wang, T., Perry, B., Wong, N., & Cai, J. (2007). Comparison and contrast: Similarities and differences of teachers’ views of effective mathematics teaching and learning from four regions. ZDM, 39(4), 329-340.
  • Charalambous, C. (2010). Mathematical knowledge for teaching and task unfolding: An exploratory study. The Elementary School Journal, 110(3), 247-278.
  • Diez, M. E. (2010). It is complicated: Unpacking the flow of teacher education’s impact on student learning. Journal of Teacher Education, 61(5), 441-450.
  • Dyer, E. B., & Sherin, M. G. (2016). Instructional reasoning about interpretations of student thinking that supports responsive teaching in secondary mathematics. ZDM, 48(1-2), 69-82.
  • Edelman, J. (2017). How preservice teachers use children’s literature to teach mathematical concepts: focus on mathematical knowledge for teaching. International Electronic Journal of Elementary Education, 9(4), 741-752.
  • Guberman, R., & Leikin, R. (2013). Interesting and difficult mathematical problems: changing teachers’ views by employing multiple-solution tasks. Journal of Mathematics Teacher Education, 16(1), 33-56.
  • Gvozdic, K., & Sander, E. (2018). When intuitive conceptions overshadow pedagogical content knowledge: Teachers’ conceptions of students’ arithmetic word problem solving strategies. Educational Studies in Mathematics, 98(2), 157-175.
  • Hiebert, J., & Berk, D. (2020). Foreword: Building a profession of mathematics teacher education. The Mathematics Enthusiast, 17(2), 325-336.
  • Hiebert, J., Berk, D., Miller, E., Gallivan, H., & Meikle, E. (2019). Relationships between opportunity to learn mathematics in teacher preparation and graduates' knowledge for teaching mathematics. Journal for Research in Mathematics Education, 50(1), 23-50.
  • Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Lawrence Erlbaum Associates.
  • Hill, H. C. (2010). The nature and predictors of elementary teachers' mathematical knowledge for teaching. Journal for Research in Mathematics Education, 41(5), 513-545.
  • Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400.
  • Jacob, R., Hill, H., & Corey, D. (2017). The impact of a professional development program on teachers' mathematical knowledge for teaching, instruction, and student achievement. Journal of Research on Educational Effectiveness, 10(2), 379-407.
  • Jacobs, V. R., & Empson, S. B. (2016). Responding to children’s mathematical thinking in the moment: An emerging framework of teaching moves. ZDM Mathematics Education, 48(1-2), 185-197.
  • Johnson, E., & Larsen, S. P. (2012). Teacher listening: The role of knowledge of content and students. The Journal of Mathematical Behavior, 31(1), 117-129.
  • Lannin, J. K., Barker, D. D., & Townsend, B. E. (2007). How students view the general nature of their errors. Educational Studies in Mathematics, 66(1), 43-59.
  • Lee, M. Y. (2021). Using a technology tool to help pre-service teachers notice students’ reasoning and errors on a mathematics problem. ZDM, 53(1), 135-149.
  • Lee, Y., Capraro, R. M., & Capraro, M. M. (2018). Mathematics teachers’ subject matter knowledge and pedagogical content knowledge in problem posing. International Electronic Journal of Mathematics Education, 13(2), 75-90.
  • Leikin, R., & Levav-Waynberg, A. (2007). Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks. Educational Studies in Mathematics, 66(3), 349-371.
  • Leikin, R., & Levav-Waynberg, A. (2008). Solution spaces of multiple-solution connecting tasks as a mirror of the development of mathematics teachers’ knowledge. Canadian Journal of Science, Mathematics and Technology Education, 8(3), 233-251.
  • Maxwell, J. A. (1996) Qualitative research design: An interactive approach. Sage Publications.
  • Nagle, C., Moore-Russo, D., & Styers, J. (2017) Teachers’ interpretations of student statements about slope. In E. Galindo, & J. Newton (Eds.), Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, (pp. 589-596).
  • Nathan, M. J., & Petrosino, A. (2003). Expert blind spot among preservice teachers. American Educational Research Journal, 40(4), 905-928.
  • National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. NCTM.
  • National Council of Teachers of Mathematics Principles to Actions Professional Learning Toolkit. https://www.nctm.org/PtAToolkit/
  • Ni Shuilleabhain, A. (2016). Developing mathematics teachers’ pedagogical content knowledge in lesson study. International Journal for Lesson and Learning Studies, 5(3), 212-226.
  • Norton, A., McCloskey, A., & Hudson, R. A. (2011). Prediction assessments: Using video-based predictions to assess prospective teachers’ knowledge of students’ mathematical thinking. Journal of Mathematics Teacher Education, 14(4), 305-325.
  • Patton, M. Q. (2002). Qualitative research and evaluation methods. (3rd ed.). SAGE.
  • Peterson, R., & Treagust, D. (1995). Developing preservice teachers' pedagogical reasoning ability. Research in Science Education, 25(3), 291-305.
  • Rittle-Johnson, B., Schneider, M., & Star, J. R. (2015). Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27(4), 587-597.
  • Schukajlow, S., & Krug, A. (2014). Do multiple solutions matter? Prompting multiple solutions, interest, competence, and autonomy. Journal for Research in Mathematics Education, 45(4), 497-533.
  • Shin, D. (2020). Preservice Mathematics Teachers’ Selective Attention and Professional Knowledge-Based Reasoning About Students’ Statistical Thinking. International Journal of Science and Mathematics Education, https://doi.org/10.1007/s10763-020-10101-w
  • 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. Harvard Educational Review, 57(1), 1-22.
  • Silver, E. A., Ghousseini, H., Gosen, D., Charalambous, C., & Strawhun, B. T. (2005). Moving from rhetoric to praxis: Issues faced by teachers in having students consider multiple solutions for problems in the mathematics classroom. The Journal of Mathematical Behavior, 24(3-4), 287-301.
  • Sitrava, R. T., (2020). Middle School Mathematics Teachers’ Reasoning about Students’ Nonstandard Strategies: Division of Fractions. International Journal for Mathematics Teaching and Learning, 21(1), 77-93.
  • Spalding, E., Klecka, C. L., Lin, E., Wang, J., & Odell, S. J. (2011). Learning to teach: It’s complicated but it’s not magic. Journal of Teacher Education, 62(1), 3-7.
  • Star, J. R., & Stylianides, G. J. (2013). Procedural and conceptual knowledge: Exploring the gap between knowledge type and knowledge quality. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 169-181.
  • Steele, M. D., & Rogers, K. C. (2012). Relationships between mathematical knowledge for teaching and teaching practice: The case of proof. Journal of Mathematics Teacher Education, 15(2), 159-180.
  • Styers, J. L., Nagle, C. R., & Moore-Russo, D. (2020). Teachers’ noticing of students’ slope statements: attending and interpreting. Canadian Journal of Science, Mathematics and Technology Education, 20(3), 504-520.
  • Taşdan, B. T., & Çelik, A. (2016). A Conceptual Framework for Examining Mathematics Teachers' Pedagogical Content Knowledge in the Context of Supporting Mathematical Thinking. European Journal of Education Studies, 2(5), 90-120.
  • Thomas, J., Jong, C., Fisher, M. H., & Schack, E. O. (2017). Noticing and knowledge: Exploring theoretical connections between professional noticing and mathematical knowledge for teaching. The Mathematics Educator, 26(2), 3-25.
  • Van Dooren, W., Verschaffel, L., & Onghena, P. (2002). The impact of preservice teachers' content knowledge on their evaluation of students' strategies for solving arithmetic and algebra word problems. Journal for Research in Mathematics Education, 33(5), 319-351.
  • Wuttke, E., & Seifried, J. (Eds.). (2017). Professional error competence of preservice teachers: Evaluation and support. Springer.

Investigation of a Middle School Preservice Teacher’s Knowledge of Content and Students

Year 2021, Volume: 8 Issue: 4, 818 - 841, 04.12.2021
https://doi.org/10.21449/ijate.946573

Abstract

The purpose of this study was to explicate one preservice middle grades mathematics teacher’s Knowledge of Content and Students (KCS) in the context of multiple solution strategies. This study’s purpose is to underline the importance of preservice teachers’ KCS and provide possible investigative methods for evaluating preservice teachers’ KCS. Specifically, the research inquiry guiding this study focused on how a middle school preservice mathematics teacher displays KCS when engaging with tasks about pattern recognition and linear functions in the context of multiple solution strategies. The data consisted of three videotaped semi-structured interviews with the preservice mathematics teacher as well as the written work she produced during the interviews. This study explicated one preservice mathematic teacher’s performance regarding two important themes of KCS: generating multiple possible solution strategies of middle school students and explaining multiple student solution strategies. In terms of generating multiple solution strategies of middle school students, the study found that the preservice mathematics teacher provided the same solution strategies that she employed when she solved the problems by herself. Regarding explaining multiple student solution strategies, this study revealed that the preservice teacher did not explicate how typical middle school students reason. The preservice teacher had limitations when explaining the possible procedures that students might have used to solve problems when given the final student solutions. With regard to the teacher’s abilities to recognise and understand students’ typical understandings and misunderstandings, the study demonstrated that the preservice teacher was capable of explaining some solution strategies but not all of them.

References

  • Alqahtani, M. M., & Powell, A. B. (2017). Mediational activities in a dynamic geometry environment and teachers’ specialized content knowledge. The Journal of Mathematical Behavior, 48, 77-94.
  • An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school, mathematics teachers in China and the US. Journal of Mathematics Teacher Education, 7(2), 145-172.
  • Asquith, P., Stephens, A. C., Knuth, E. J., & Alibali, M. W. (2007). Middle school mathematics teachers' knowledge of students' understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249-272.
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching. Journal of Teacher Education, 59(5), 389-407.
  • Baki, A. (2020). Matematiği öğretme bilgisi (3rd ed.). PegemAkademi
  • Bansilal, S., Mkhwanazi, T., & Brijlall, D. (2014). An exploration of the common content knowledge of high school mathematics teachers. Perspectives in Education, 32(1), 34-50.
  • Boerst, T. A., Sleep, L., Ball, D. L., & Bass, H. (2011). Preparing teachers to lead mathematics discussions. Teachers College Record, 113(12), 2844-2877.
  • Bryan, C. A., Wang, T., Perry, B., Wong, N., & Cai, J. (2007). Comparison and contrast: Similarities and differences of teachers’ views of effective mathematics teaching and learning from four regions. ZDM, 39(4), 329-340.
  • Charalambous, C. (2010). Mathematical knowledge for teaching and task unfolding: An exploratory study. The Elementary School Journal, 110(3), 247-278.
  • Diez, M. E. (2010). It is complicated: Unpacking the flow of teacher education’s impact on student learning. Journal of Teacher Education, 61(5), 441-450.
  • Dyer, E. B., & Sherin, M. G. (2016). Instructional reasoning about interpretations of student thinking that supports responsive teaching in secondary mathematics. ZDM, 48(1-2), 69-82.
  • Edelman, J. (2017). How preservice teachers use children’s literature to teach mathematical concepts: focus on mathematical knowledge for teaching. International Electronic Journal of Elementary Education, 9(4), 741-752.
  • Guberman, R., & Leikin, R. (2013). Interesting and difficult mathematical problems: changing teachers’ views by employing multiple-solution tasks. Journal of Mathematics Teacher Education, 16(1), 33-56.
  • Gvozdic, K., & Sander, E. (2018). When intuitive conceptions overshadow pedagogical content knowledge: Teachers’ conceptions of students’ arithmetic word problem solving strategies. Educational Studies in Mathematics, 98(2), 157-175.
  • Hiebert, J., & Berk, D. (2020). Foreword: Building a profession of mathematics teacher education. The Mathematics Enthusiast, 17(2), 325-336.
  • Hiebert, J., Berk, D., Miller, E., Gallivan, H., & Meikle, E. (2019). Relationships between opportunity to learn mathematics in teacher preparation and graduates' knowledge for teaching mathematics. Journal for Research in Mathematics Education, 50(1), 23-50.
  • Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Lawrence Erlbaum Associates.
  • Hill, H. C. (2010). The nature and predictors of elementary teachers' mathematical knowledge for teaching. Journal for Research in Mathematics Education, 41(5), 513-545.
  • Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400.
  • Jacob, R., Hill, H., & Corey, D. (2017). The impact of a professional development program on teachers' mathematical knowledge for teaching, instruction, and student achievement. Journal of Research on Educational Effectiveness, 10(2), 379-407.
  • Jacobs, V. R., & Empson, S. B. (2016). Responding to children’s mathematical thinking in the moment: An emerging framework of teaching moves. ZDM Mathematics Education, 48(1-2), 185-197.
  • Johnson, E., & Larsen, S. P. (2012). Teacher listening: The role of knowledge of content and students. The Journal of Mathematical Behavior, 31(1), 117-129.
  • Lannin, J. K., Barker, D. D., & Townsend, B. E. (2007). How students view the general nature of their errors. Educational Studies in Mathematics, 66(1), 43-59.
  • Lee, M. Y. (2021). Using a technology tool to help pre-service teachers notice students’ reasoning and errors on a mathematics problem. ZDM, 53(1), 135-149.
  • Lee, Y., Capraro, R. M., & Capraro, M. M. (2018). Mathematics teachers’ subject matter knowledge and pedagogical content knowledge in problem posing. International Electronic Journal of Mathematics Education, 13(2), 75-90.
  • Leikin, R., & Levav-Waynberg, A. (2007). Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks. Educational Studies in Mathematics, 66(3), 349-371.
  • Leikin, R., & Levav-Waynberg, A. (2008). Solution spaces of multiple-solution connecting tasks as a mirror of the development of mathematics teachers’ knowledge. Canadian Journal of Science, Mathematics and Technology Education, 8(3), 233-251.
  • Maxwell, J. A. (1996) Qualitative research design: An interactive approach. Sage Publications.
  • Nagle, C., Moore-Russo, D., & Styers, J. (2017) Teachers’ interpretations of student statements about slope. In E. Galindo, & J. Newton (Eds.), Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, (pp. 589-596).
  • Nathan, M. J., & Petrosino, A. (2003). Expert blind spot among preservice teachers. American Educational Research Journal, 40(4), 905-928.
  • National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. NCTM.
  • National Council of Teachers of Mathematics Principles to Actions Professional Learning Toolkit. https://www.nctm.org/PtAToolkit/
  • Ni Shuilleabhain, A. (2016). Developing mathematics teachers’ pedagogical content knowledge in lesson study. International Journal for Lesson and Learning Studies, 5(3), 212-226.
  • Norton, A., McCloskey, A., & Hudson, R. A. (2011). Prediction assessments: Using video-based predictions to assess prospective teachers’ knowledge of students’ mathematical thinking. Journal of Mathematics Teacher Education, 14(4), 305-325.
  • Patton, M. Q. (2002). Qualitative research and evaluation methods. (3rd ed.). SAGE.
  • Peterson, R., & Treagust, D. (1995). Developing preservice teachers' pedagogical reasoning ability. Research in Science Education, 25(3), 291-305.
  • Rittle-Johnson, B., Schneider, M., & Star, J. R. (2015). Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27(4), 587-597.
  • Schukajlow, S., & Krug, A. (2014). Do multiple solutions matter? Prompting multiple solutions, interest, competence, and autonomy. Journal for Research in Mathematics Education, 45(4), 497-533.
  • Shin, D. (2020). Preservice Mathematics Teachers’ Selective Attention and Professional Knowledge-Based Reasoning About Students’ Statistical Thinking. International Journal of Science and Mathematics Education, https://doi.org/10.1007/s10763-020-10101-w
  • 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. Harvard Educational Review, 57(1), 1-22.
  • Silver, E. A., Ghousseini, H., Gosen, D., Charalambous, C., & Strawhun, B. T. (2005). Moving from rhetoric to praxis: Issues faced by teachers in having students consider multiple solutions for problems in the mathematics classroom. The Journal of Mathematical Behavior, 24(3-4), 287-301.
  • Sitrava, R. T., (2020). Middle School Mathematics Teachers’ Reasoning about Students’ Nonstandard Strategies: Division of Fractions. International Journal for Mathematics Teaching and Learning, 21(1), 77-93.
  • Spalding, E., Klecka, C. L., Lin, E., Wang, J., & Odell, S. J. (2011). Learning to teach: It’s complicated but it’s not magic. Journal of Teacher Education, 62(1), 3-7.
  • Star, J. R., & Stylianides, G. J. (2013). Procedural and conceptual knowledge: Exploring the gap between knowledge type and knowledge quality. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 169-181.
  • Steele, M. D., & Rogers, K. C. (2012). Relationships between mathematical knowledge for teaching and teaching practice: The case of proof. Journal of Mathematics Teacher Education, 15(2), 159-180.
  • Styers, J. L., Nagle, C. R., & Moore-Russo, D. (2020). Teachers’ noticing of students’ slope statements: attending and interpreting. Canadian Journal of Science, Mathematics and Technology Education, 20(3), 504-520.
  • Taşdan, B. T., & Çelik, A. (2016). A Conceptual Framework for Examining Mathematics Teachers' Pedagogical Content Knowledge in the Context of Supporting Mathematical Thinking. European Journal of Education Studies, 2(5), 90-120.
  • Thomas, J., Jong, C., Fisher, M. H., & Schack, E. O. (2017). Noticing and knowledge: Exploring theoretical connections between professional noticing and mathematical knowledge for teaching. The Mathematics Educator, 26(2), 3-25.
  • Van Dooren, W., Verschaffel, L., & Onghena, P. (2002). The impact of preservice teachers' content knowledge on their evaluation of students' strategies for solving arithmetic and algebra word problems. Journal for Research in Mathematics Education, 33(5), 319-351.
  • Wuttke, E., & Seifried, J. (Eds.). (2017). Professional error competence of preservice teachers: Evaluation and support. Springer.
There are 51 citations in total.

Details

Primary Language English
Subjects Studies on Education
Journal Section Articles
Authors

Ebru Ersarı 0000-0002-0324-3185

Publication Date December 4, 2021
Submission Date June 1, 2021
Published in Issue Year 2021 Volume: 8 Issue: 4

Cite

APA Ersarı, E. (2021). Investigation of a Middle School Preservice Teacher’s Knowledge of Content and Students. International Journal of Assessment Tools in Education, 8(4), 818-841. https://doi.org/10.21449/ijate.946573

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