Teachers’ Adaptions of the Percentage Bar Model for Creating Different Learning Opportunities

Christian Büscher

doi:10.29333/iejme/10942

Full Text (PDF)

Christian Büscher ¹ ^*

More Detail

¹ TU Dortmund University, GERMANY^* Corresponding Author

Abstract

Teachers do not directly implement new teaching materials, but rather adapt them. For changing teaching practice, research requires more insights into these adaptions. This study draws on the Theory of Instrumental Genesis to describe the ways teachers adopt the percentage bar model to create different learning opportunities. The results of the exploratory case study show two fundamentally different utilization schemes of the percentage bar model employed by teachers in the classroom. The utilization scheme of Partitioning and Counting creates learning opportunities for the conceptual core of percentages and proportional reasoning, whereas the utilization scheme of Mirror Movement only addresses scaling. Implications include that researchers need to pay close attention to the utilizations of new teaching materials, and teacher educators need to provide new routines along with new materials.

Keywords

case study
instrumental genesis
percentages
teacher practices
teaching materials

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, 2021, Volume 16, Issue 3, Article No: em0643

https://doi.org/10.29333/iejme/10942

Publication date: 28 May 2021

Article Views: 2262

Article Downloads: 1385

Open Access Disclosures References How to cite this article

Disclosure

Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

References

Ball, D. L., & Cohen, D. K. (1996). Reform by the book: What is: Or might be: The role of curriculum materials in teacher learning and instructional reform?. Educational Researcher, 25(9), 6-8. https://doi.org/10.2307/1177151
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. https://doi.org/10.1177/0022487108324554
Baratta, W., Price, B., Stacey, K., Steinle, V., & Gvozdenko, E. (2010). Percentages: The effect of problem structure, number complexity and calculation format. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education (pp. 61-68). Mathematics Education Research Group of Australasia.
Bass, H., & Ball, D. L. (2004). A practice-based theory on mathematical knowledge for teaching: the case of mathematical reasoning. In J. Wang (Ed.), Trends and challenges in mathematics education (pp. 295-313). East China Normal University Press.
Blömeke, S., Gustafsson, J.-E., & Shavelson, R. J. (2015). Beyond dichotomies. Zeitschrift für Psychologie, 223(1), 3-13. https://doi.org/10.1027/2151-2604/a000194
Brown, M. W. (2011). The teacher-tool relationship: Theorizing the design and use of curriculum materials. In J. T. Remillard, B. Herbel-Eisenmann, & G. M. Lloyd (Eds.), Mathematics Teachers at Work (pp. 17-36). Routledge.
Brown, R. E., Weiland, T., & Orrill, C. H. (2020). Mathematics teachers’ use of knowledge resources when identifying proportional reasoning situations. International Journal of Science and Mathematics Education, 18(6), 1085-1104. https://doi.org/10.1007/s10763-019-10006-3
Century, J., & Cassata, A. (2016). Implementation research. Review of Research in Education, 40(1), 169-215. https://doi.org/10.3102/0091732X16665332
Dreher, A., & Kuntze, (2015). Teachers facing the dilemma of multiple representations being aid and obstacle for learning: Evaluations of tasks and theme-specific noticing. Journal für Mathematik-Didaktik, 36(1), 23-44. https://doi.org/10.1007/s13138-014-0068-3
Drijvers, P., Godino, J. D., Font, V., & Trouche, L. (2013). One episode, two lenses - A reflective analysis of student learning with computer algebra from instrumental and onto-semiotic perspectives. Educational Studies in Mathematics, 82(1), 23-49. https://doi.org/10.1007/s10649-012-9416-8
Forzani, F. M. (2014). Understanding “core practices” and “practice-based” teacher education. Journal of Teacher Education, 65(4), 357-368. https://doi.org/10.1177/0022487114533800
Gravemeijer, K., Bruin-Muurling, G., Kraemer, J.-K., & van Stiphout, Irene (2016). Shortcomings of mathematics education reform in the Netherlands: A paradigm case?. Mathematical Thinking and Learning, 18(1), 25-44. https://10.1080/10986065.2016.1107821
Hafner, T. (2012). Proportionalität und prozentrechnung in der sekundarstufe I: Empirische untersuchung und didaktische analysen [Proportionality and percentage calculation in secondary level I: empirical research and didactic analyzes]. Springer. https://doi.org/10.1007/978-3-8348-8668-2
Hlas, A. C., & Hlas, C. S. (2012). A review of high-leverage teaching practices: Making connections between mathematics and foreign languages. Foreign Language Annals, 45(1), 76-97. https://doi.org/10.1111/j.1944-9720.2012.01180.x
Hußmann, S., & Prediger, S. (2016). Specifying and structuring mathematical topics – a four-level approach for combining formal, semantic, concrete, and empirical levels exemplified for exponential growth. Journal für Mathematik-Didaktik, 37(1), 33-67.
Lamon, S. J. (2007). Proportional numbers and proportional reasoning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629-688). Information Age Publishing.
Leong, Y. H., Tay, E. G., Toh, T. L., Quek, K. S., & Yap, R. A. S. (2019). Concretisations: A support for teachers to carry out instructional innovations in the mathematics classroom. International Journal of Science and Mathematics Education, 17(2), 365-384. https://doi.org/10.1007/s10763-017-9868-5
Mayring, P. (2000). Qualitative content analysis. Forum Qualitative Social Sciences, 1(2), Article 20. http://www.qualitative-research.net/index.php/fqs/issue/view/28
Mitchell, R., Charalambous, C. Y., & Hill, H. C. (2014). Examining the task and knowledge demands needed to teach with representations. Journal of Mathematics Teacher Education, 17(1), 37-60. https://doi.org/10.1007/s10857-013-9253-4
Ngu, B. H., Yeung, A. S., & Tobias, S. (2014). Cognitive load in percentage change problems: unitary, pictorial, and equation approaches to instruction. Instructional Science, 42(5), 685-713. https://doi.org/10.1007/s11251-014-9309-6
Orrill, C. H., & Brown, R. E. (2012). Making sense of double number lines in professional development: exploring teachers’ understandings of proportional relationships. Journal of Mathematics Teacher Education, 15(5), 381-403.
Parker, M., & Leinhardt, G. (1995). Percent: A privileged proportion. Review of Educational Research, 65(4), 421-481. https://doi.org/10.3102/00346543065004421
Peltenburg, M., van den Heuvel-Panhuizen, M., & Robitzsch, A. (2012). Special education students’ use of indirect addition in solving subtraction problems up to 100—A proof of the didactical potential of an ignored procedure. Educational Studies in Mathematics, 79(3), 351-369. https://doi.org/10.1007/s10649-011-9351-0
Peltenburg, M., van den Heuvel‐Panhuizen, M., & Robitzsch, A. (2010). ICT‐based dynamic assessment to reveal special education students’ potential in mathematics. Research Papers in Education, 25(3), 319-334. https://doi.org/10.1080/02671522.2010.498148
Pepin, B., Xu, B., Trouche, L., & Wang, C. (2017). Developing a deeper understanding of mathematics teaching expertise: an examination of three Chinese mathematics teachers’ resource systems as windows into their work and expertise. Educational Studies in Mathematics, 94(3), 257-274. https://doi.org/10.1007/s10649-016-9727-2
Pöhler, B., & Prediger, (2015). Intertwining lexical and conceptual learning trajectories - A design research study on dual macro-scaffolding towards percentages. Eurasia Journal of Mathematics, Science & Technology Education, 11(6), 1697-1722.
Pöhler, B., Prediger, S., & Strucksberg, J. (2018). Prozente verstehen – Inklusive unterrichtseinheit in basis- und regelfassung [Understanding percentages - including the basic and standard version of the teaching unit]. Open Educational Resource. Retrieved from mathe-sicher-koennen.dzlm.de/100
Prediger, S., & Buró, R. (submitted). 50 Ways to Work with Students’ Diverse Abilities? A Video Study on Inclusive Teaching Practices in Secondary Mathematics Classrooms.
Prediger, S., Fischer, C., Selter, C., & Schöber, C. (2018). Combining material- and community-based implementation strategies for scaling up: the case of supporting low-achieving middle school students. Educational Studies in Mathematics, 102(1), 361-378. https://doi.org/10.1007/s10649-018-9835-2
Prediger, S., Kuhl, J., Büscher, C., & Buró, S. (2020). Mathematik inklusiv lehren lernen: Entwicklung eines forschungsbasierten interdisziplinären Fortbildungskonzepts [Learning to teach mathematics inclusive: Development of a research-based interdisciplinary advanced training concept]. Journal für Psychologie, 28(2), 288-312. https://doi.org/10.30820/0942-2285-2019-2-288
Rabardel, P. (2002). People and technology. Université Paris.
Rosenthal, L., Ilany, B.-S., & Almog, N. (2009). Intuitive knowledge of percentages prior to learning. Research in Mathematical Education, 13(4), 297-307.
Sherin, M. G., & Drake, C. (2009). Curriculum strategy framework: investigating patterns in teachers’ use of a reform‐based elementary mathematics curriculum. Journal of Curriculum Studies, 41(4), 467-500. https://doi.org/10.1080/00220270802696115
Shreyar, S., Zolkower, B., & Pérez, (2010). Thinking aloud together: A teacher’s semiotic mediation of a whole-class conversation about percents. Educational Studies in Mathematics, 73(1), 21-53. https://doi.org/10.1007/s10649-009-9203-3
Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized learning environments: Guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9, Article 281.
van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54(1), 9-35.
van Galen, F., & van Eerde, D. (2013). Solving problems with the percentage bar model. Journal on Mathematics Education, 4(1), 1-8. https://doi.org/10.22342/jme.4.1.558.1-8
Wilkie, K. J. (2019). The challenge of changing teaching: investigating the interplay of external and internal influences during professional learning with secondary mathematics teachers. Journal of Mathematics Teacher Education 22(1), 95-124. https://doi.org/10.1007/s10857-017-9376-0
Yin, R. K. (2002). Case study research. SAGE.

How to cite this article

APA

Büscher, C. (2021). Teachers’ Adaptions of the Percentage Bar Model for Creating Different Learning Opportunities. International Electronic Journal of Mathematics Education, 16(3), em0643. https://doi.org/10.29333/iejme/10942

Vancouver

Büscher C. Teachers’ Adaptions of the Percentage Bar Model for Creating Different Learning Opportunities. INT ELECT J MATH ED. 2021;16(3):em0643. https://doi.org/10.29333/iejme/10942

AMA

Büscher C. Teachers’ Adaptions of the Percentage Bar Model for Creating Different Learning Opportunities. INT ELECT J MATH ED. 2021;16(3), em0643. https://doi.org/10.29333/iejme/10942

Chicago

Büscher, Christian. "Teachers’ Adaptions of the Percentage Bar Model for Creating Different Learning Opportunities". International Electronic Journal of Mathematics Education 2021 16 no. 3 (2021): em0643. https://doi.org/10.29333/iejme/10942

Harvard

Büscher, C. (2021). Teachers’ Adaptions of the Percentage Bar Model for Creating Different Learning Opportunities. International Electronic Journal of Mathematics Education, 16(3), em0643. https://doi.org/10.29333/iejme/10942

MLA

Büscher, Christian "Teachers’ Adaptions of the Percentage Bar Model for Creating Different Learning Opportunities". International Electronic Journal of Mathematics Education, vol. 16, no. 3, 2021, em0643. https://doi.org/10.29333/iejme/10942