Influence of teachers’ pedagogical knowledge on their classroom practice when solving arithmetic word problems with their studentsAn exploratory study
-
1
Universidad de Salamanca
info
ISSN: 0210-3702, 1578-4126
Datum der Publikation: 2024
Ausgabe: 47
Nummer: 2
Seiten: 321-345
Art: Artikel
Andere Publikationen in: Journal for the Study of Education and Development, Infancia y Aprendizaje
Zusammenfassung
When primary school teachers solve arithmetic word problems with their students, they usually do so in a superficial manner, even when their semantic-mathematical structures are challenging and contain problem-solving aids. This could be due to the pedagogical knowledge that teachers have about teaching how to solve this type of problem. The aim of this study was to explore whether teachers with different levels of this knowledge solved standard problems (nonchallenging and without aids) and rewritten problems (challenging and with aids to reasoning) in different ways. A sample of eight teachers (four with high knowledge, four with low knowledge) were recorded and analysed solving two standard and two rewritten problems. The results showed that the teachers with high knowledge used more interaction cycles (mainly dedicated to reasoning) to solve the standard problems and especially the rewritten ones. This study is an initial approach to understanding teachers’ problem-solving behaviour and highlights the importance of developing their knowledge in how to teach problem-solving.
Bibliographische Referenzen
- Ball D. L., Thames M. H., Phelps G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389–407.
- Baumert J., Kunter M., Blum W., Brunner M., Voss T., Jordan A., Klusmann U., Krauss S., Neubrand M., Tsai Y. M. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133–180.
- Carpenter T. P., Fennema E., Peterson P., Carey D. (1988). Teachers’ pedagogical content knowledge of students’ problem solving in elementary arithmetic. Journal for Research in Mathematics Education, 19(5), 385–401. http://www.jstor.org/stable/749173
- Carpenter T. P., Moser J. M. (1984). The acquisition of addition and subtraction concepts. In Lesh R., Landau M. (Eds.), The acquisition of mathematical concepts and processes (pp. 7–44). Academic Press.
- Chapman O. (2006). Classroom practices for context of mathematics word problems. Educational Studies in Mathematics, 62, 211–230.
- Chapman O. (2015). Mathematics teachers’ knowledge for teaching problem solving. LUMAT, 3, 19–36.
- Charalambous C. Y., Hill H. C., Chin M. J., McGinn D. (2020). Mathematical content knowledge and knowledge for teaching: Exploring their distinguishability and contribution to student learning. Journal of Mathematics Teacher Education, 23, 579–613.
- Charalambous C. Y., Hill H. C., Mitchell R. N. (2012). Two negatives do not always make a positive: Exploring how limitations in teacher knowledge and the curriculum contribute to instructional quality. Journal of Curriculum Studies, 44(4), 489–513.
- Chico J., Martín-Díaz J. P., Montes M. A., Badillo E. (2023). What didactic intentions do prospective teachers show when transforming problems? In Jiménez-Gestal C., Magreñán A. A., Badillo E., Ivars P. (Eds.), Investigación en Educación Matemática XXVI (pp. 203–210). SEIEM.
- Csíkos C., Szitányi J. (2020). Teachers’ pedagogical content knowledge in teaching word problem solving strategies. ZDM Mathematics Education, 52, 165–178.
- Daroczy G., Wolska M., Meurers W. D., Nuerk H. C. (2015). Word problems: A review of linguistic and numerical factors contributing to their difficulty. Frontiers in Psychology, 6, 348.
- Depaepe F., De Corte E., Verschaffel L. (2010). Teachers’ approaches toward word problem solving: Elaborating or restricting the problem context. Teaching and Teacher Education, 26, 151–160.
- Depaepe F., Verschaffel L., Kelchtermans G. (2013). Pedagogical content knowledge: A systematic review of the way in which the concept has pervaded mathematics educational research. Teaching and Teacher Education, 34, 12–25.
- Gegenfurtner A., Lewalter D., Lehtinen E., Schmidt M., Gruber H. (2020). Teacher expertise and professional vision: Examining knowledge-based reasoning of pre-service teachers, in-service teachers, and school principals. Frontiers in Education, 5, 59.
- Getenet S., Callingham R. (2021). Teaching interrelated concepts of fraction for understanding and teachers’ pedagogical content knowledge. Mathematics Education Research Journal, 33, 201–221.
- Greer B. (1992). Multiplication and division as models of situations. In Grouws D. A. (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 276–295). Macmillan Publishing Co, Inc.
- Hanna G. (2020). Mathematical proof, argumentation, and reasoning. In Lerman S. (Ed.), Encyclopedia of Mathematics Education (pp. 561–566). SpringerLink.
- Hatisaru V., Erbas A. K. (2017). Mathematical knowledge for teaching the function concept and student learning outcomes. International Journal of Science and Mathematics Education, 15(4), 703–722.
- Hegarty M., Mayer R. E., Monk C. A. (1995). Comprehension of arithmetic word problem: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87(1), 18–32.
- Herbert S., Williams G. (2023). Eliciting mathematical reasoning during early primary problem solving. Mathematics Education Research Journal, 35(1), 77–103.
- Hill H. C., Blunk M., Charalambous C., Lewis J., Phelps G., Sleep L., Ball D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430–511.
- Hill H. C., Charalambous C. Y. (2012a). Teacher knowledge, curriculum materials, and quality of instruction: Lessons learned and open issues. Journal of Curriculum Studies, 44(4), 559–576.
- Hill H. C., Charalambous C. Y. (2012b). Teaching (un)connected mathematics: Two teachers’ enactment of the Pizza problem. Journal of Curriculum Studies, 44(4), 467–487.
- Kelcey B., Hill H. C., Chin M. J. (2019). Teacher mathematical knowledge, instructional quality, and student outcomes: A multilevel quantile mediation analysis. School Effectiveness and School Improvement, 30(4), 1–34.
- Koopman M., Thurlings M., den Brok P. (2019). Factors influencing students’ proficiency development in the fraction domain: The role of teacher cognitions and behavior. Research Papers in Education, 34(1), 14–37.
- Lester F. K., Cai J. (2016). Can mathematical problem solving be taught? Preliminary answers from 30 years of research. In Felmer P., Pehkonen E., Kilpatrick J. (Eds.), Posing and solving mathematical problems (pp. 117–135). Springer.
- Leung S. K. Y., Wu J., Li H. (2023). Explaining kindergarten teachers’ beliefs and practices regarding early visual arts education: A perspective from the theory of planned behavior. Journal for the Study of Education and Development, 46(1), 190–224.
- López F. (2002). Content analysis as a research method. Revista de Educación, 4, 167–179.
- Melhuish K., Thanheiser E., Guyot L. (2020). Elementary school teachers’ noticing of essential mathematical reasoning forms: Justification and generalization. Journal of Mathematics Teacher Education, 23, 35–67.
- Muñoz-Catalán M. C., Ramírez-García M., Joglar-Prieto N., Carrillo-Yáñez J. (2022). Early childhood teachers’ specialized knowledge to promote algebraic thinking as from a task of additive decomposition. Journal for the Study of Education and Development, 45(1), 37–80,
- Orrantia J., Tarín J., Vicente S. (2011). The use of situational information in arithmetic problem solving. Infancia y aprendizaje, 34(1), 81–94.
- Piñeiro J. L., Castro-Rodríguez E., Castro E. (2019). Teacher knowledge components for teaching problem solving in elementary education. PNA, 13(2), 104–129.
- Piñeiro J. L., Chapman O., Castro-Rodríguez E., Castro E. (2022). Prospective primary teachers’ initial mathematical problem-solving knowledge. International Journal of Mathematical Education in Science and Technology, 1–24.
- Ramos M., Rosales J., Vicente S. (2020). In-service and preservice teachers’ knowledge of arithmetic problem solving. Universitas Psychologica, 19, 1–15.
- Riley M. S., Greeno J. G. (1988). Developmental analysis of understanding language about quantities of solving problems. Cognition and Instruction, 5(1), 49–101.
- Rosales J., Vicente S., Chamoso J. M., Muñez D., Orrantia J. (2012). Teacher-student interaction in joint word problem solving. The role of situational and mathematical knowledge in mainstream classrooms. Teaching and Teacher Education, 28, 1185–1195.
- Sánchez M. R., Vicente S. (2015). Models and processes of arithmetic word problem solving proposed by Spanish mathematics textbooks. Culture and Education, 27(4), 695–725.
- Schneider R. M., Plasman K. (2011). Science teacher learning progressions: A review of science teachers’ pedagogical content knowledge development. Review of Educational Research, 81(4), 530–565.
- Shulman L. (1987). Knowledge and teaching: Foundations of new reform. Harvard Educational Review, 57(1), 1–22.
- Sie C. H., Agyei D. D. (2023). Relationship between preservice teachers’ mathematical knowledge for teaching fractions and their teaching practices: What is the role of teacher anxiety? Contemporary Mathematics and Science Education, 4(2), ep23017.
- Siswono T. Y. E., Kohar A. W., Rosyidi A. H., Hartono S. (2017). Primary school teachers’ beliefs and knowledge about mathematical problem-solving and their performance in a problem-solving task. World Transactions on Engineering and Technology Education, 15(2), 126–131.
- Stylianou D. A., Stroud R., Cassidy M., Knuth A., Stephens A., Gardiner A., Demers L. (2019). Putting early algebra in the hands of elementary school teachers: Examining fidelity of implementation and its relation to student performance. Childhood and Learning, 42(3), 523–569.
- Tárraga R., Tarín J., Lacruz I. (2021). Analysis of word problems in primary education mathematics textbooks in Spain. Mathematics, 9(17), 2123.
- Verschaffel L., Greer B., De Corte E. (2000). Making sense of word problems. Swerts and Zeitlinger Publishers.
- Verschaffel L., Schukajlow S., Star J., Van Dooren W. (2020). Word problems in mathematics education: A survey. ZDM Mathematics Education, 52(1), 1–16.
- Vicente S., Sánchez R., Verschaffel L. (2020). Word problem solving approaches in mathematics textbooks: A comparison between Singapore and Spain. European Journal of Psychology of Education, 35(3), 567–587.
- Vicente S., Verschaffel L., Sánchez R., Múñez D. (2022). Arithmetic word problem solving. Analysis of Singaporean and Spanish textbooks. Educational Studies in Mathematics, 111, 375–397.
- Wells G. (1999). Dialogic inquiry: Toward a sociocultural practice and theory of education. CUP.
- Xin Y. P. (2007). Word problem solving tasks in textbooks and their relation to student performance. The Journal of Educational Research, 6, 347–359.
- Zhang Q. (2022). Understanding Chinese mathematics teaching: How secondary Mathematics teachers’ beliefs and knowledge influence their teaching on the mainland China. ZDM Mathematics Education, 54, 693–707.