Mathematics Enrichment for All – Noticing and Enhancing Mathematical Potentials of Underprivileged Students as An Issue of Equity

Susanne Schnell; Susanne Prediger

doi:10.12973/eurasia.2017.00609a

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Susanne Schnell ¹ ^* , Susanne Prediger ²

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¹ University of Cologne, GERMANY² TU Dortmund University, GERMANY^* Corresponding Author

Abstract

Whereas equity issues are mainly discussed with respect to students at risk, this article focuses on mathematical potentials of under-privileged students and therefore elaborates a wide, dynamic and participatory conceptualization of (sometimes still hidden) mathematical potentials. An extended research review theoretically and empirically grounds the presented approach for uncovering and enhancing (possibly underprivileged) students in design principles for the instructional design and the ways in which teachers notice students’ and situations’ potentials. Dual design research methodology on students’ and teachers’ level is adopted to develop whole class enrichment settings with rich tasks and empirically study the initiated processes. The empirical investigation of the classroom processes show that the chosen design principles can enhance the intended enrichment processes on the student side, but need to be strongly supported by teachers’ expertise in noticing and fostering students. An important outcome is the perspective model for teachers’ necessary diagnostic perspectives for noticing and enhancing the potentials. Consequences are formulated for professional development programs.

Keywords

mathematical potentials
task design
teacher noticing

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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

EURASIA J Math Sci Tech Ed, 2017, Volume 13, Issue 1, 143-165

https://doi.org/10.12973/eurasia.2017.00609a

Publication date: 18 Jan 2017

Article Views: 2926

Article Downloads: 2616

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References

Bauersfeld, H. (1993). Mathematische Lehr-Lern-Prozesse bei Hochbegabten. Journal für Mathematikdidaktik, 14(3/4), 243–266.
Bauersfeld, H. (2002). Das Anderssein der Hochbegabten. Merkmale, frühe Förderung und geeignete Aufgaben. Mathematica didactica, 25(1), 5–16
Benölken, R. (2011). Mathematisch begabte Mädchen. Münster: WTM.
Benölken, R. (2015). The impact of mathematics interest and attitudes as determinants in order to identify girls’ mathematical talent. K. Krainer & N. Vondrova (Eds.), Proceedings of CERME 9 - Ninth congress of ERME (pp. 970–976). Prague: ERME. Retrieved from https://hal.archivesouvertes.fr/hal-01287295
Bikner-Ahsbahs, A. (2014). Turning disinterest into interest in class: An intervention study. In C. Nicol, P. Liljedahl, S. Oesterle, & D. Allan (Eds.), Proceedings of the joint meeting of PME 38 and PME-NA 36 (Vol. 2, pp. 145–152). Vancouver: PME.
Cheng, P.W. (1993). Metacognition and giftedness: The state of the relationship. Gifted Child Quarterly, 37, 105–112.
Deci, E.L. & Ryan, R. M. (Eds.) (2002). Handbook of self-determination research. Rochester: University of Rochester Press.
Diezmann, C. M. & Watters, J. J. (2001). The collaboration of mathematically gifted students on challenging tasks. Journal for the Education of the Gifted, 25(1), 7–31.
DIME - Diversity in Mathematics Education Center for Learning and Teaching (2007). Culture, race, power in mathematics education. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 405–433). Charlotte: Information Age.
Flewelling, G. & Higginson, W. (2003). Teaching with rich learning tasks: a handbook. Adelaide: AAMT Inc. Adelaide.
Foster, C. (2015). The Convergent–Divergent Model. Educational Designer, 2(8). Retrieved from http://www.educationaldesigner.org/ed/volume2/issue8/article28/.
Goldin, G. A. (2009). The affective domain and students’ mathematical inventiveness. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in Mathematics and the Education of Gifted Students (pp. 181–194). Rotterdam: Sense.
Gravemeijer, K.P.E. & van Eerde, H.A.A. (2009). Design research as a means for building a knowledge base for teachers and teaching in mathematics education. The Elementary School Journal, 109(5), 510–524.
Hengartner, E., Hirt, U., Wälti, B., & Primarschulteam Lupsingen (2006). Lernumgebungen für langsam Lernende bis Hochbegabte. Natürliche Differenzierung im Mathematikunterricht. Zug: Klett und Balmer.
Käpnick, F. (1998). Mathematisch begabte Kinder. Frankfurt: Peter Lang.
Kilpatrick, J., Swafford, J., & Findell, B. (Eds.) (2001). Adding it up: Helping children learn mathematics. Washington: National Academy Press.
Krapp, A. (2005). Basic needs and the development of interest and intrinsic motivational orientations. Learning and Instruction, 15(5), 381–395.
Krutetskii, V. A. (1976). The psychology of mathematical abilities in school children. Chicago: University of Chicago Press.
Leder, G. C. (1992). Mathematics and gender: Changing perspectives. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 597–622). New York: National Council of Teachers of Mathematics.
Leikin, R (2009a). Bridging research and theory in mathematics education with research and theory in creativity and giftedness. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 383–409). Rotterdam: Sense.
Leikin, R (2009b). Exploring mathematical creativity using multiple solution tasks. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 129– 145). Rotterdam: Sense.
Leikin, R. (2011). The education of mathematically gifted students: Some complexities and questions. The Montana Mathematics Enthusiast, 8(1 & 2), 167–188.
Leikin, R. & Lev, M. (2007). Multiple solution tasks as a magnifying glass for observation of mathematical creativity. In J.-H. Woo, H.-C. Lew, K.-S. Park, & D.-Y. Seo (Eds.), Proceedings of the 31st International Conference for the Psychology of Mathematics Education (Vol. 3, pp. 161–168). Korea: Korea Society of Educational Studies in Mathematics.
Leikin, R., Berman, A., & Koichu, B. (Eds.) (2009). Creativity in mathematics and the education of gifted students. Rotterdam: Sense.
Lesh, R. & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics: Teaching, learning, and problem solving. In R. A. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspective on mathematics problem solving, learning, and teaching (pp. 3–34). Mahwah, NJ: Lawrence Erlbaum Associates.
Lubinski, D. & Humphreys, L. G. (1990). A broadly based analysis of mathematical giftedness. Intelligence, 14(3), 327–355.
Pajares, F. (1996). Self-Efficacy Beliefs and Mathematical Problem-Solving of Gifted Students. Contemporary Educational Psychology, 21, 325–344.
Parker, M. & Leinhardt, G. (1995). Percent: A Privileged Proportion. Review of Educational Research, 65(4), 421–481.
Pateman, N. A. & Lim, C. S. (2013). The Politics of Equity and Access in Teaching and Learning Mathematics. In M. A. Clements, A. J. Bishop, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Third International Handbook of Mathematics Education (pp. 243–263). New York: Springer.
Piggott, J. (2004). Developing a Framework for Mathematics Enrichment. Paper presented at the symposium on Critical Thinking in Teaching and Learning. University of West Indies, Trinidad. Retrieved from http://nrich.maths.org/content/id/2719/a-framework-for-enrichment.doc
Prediger, S., Gravemeijer, K., & Confrey, J. (2015). Design research with a focus on learning processes – an overview on achievements and challenges. ZDM Mathematics Education, 47(6), 877–891. Doi: 10.1007/s11858-015-0722-3
Prediger, S., Schnell, S., & Rösike, K.-A. (2016, in press). Design Research with a focus on contentspecific professionalization processes: The case of noticing students’ potentials. Paper presented at ETC 3: ERME Topic Conference on Teacher Education, Berlin 2016.
Rinn, A. N., Plucker, J. A., & Stocking, V.B. (2010). Fostering Gifted Students’ Affective Development: A Look at the Impact of Academic Self-Concept. TEACHING Exceptional Children Plus, 6(4), no page numbers. Retrieved from http://escholarship.bc.edu/education/tecplus/vol6/iss4/art1
Schnell, S. (2016). Teachers noticing students’ potentials while analysing video clips. Paper presented at 13th International Congress on Mathematical Education, Hamburg, 24-31 July 2016.
Schoenfeld, A. H. (1992). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense-Making in Mathematics. In D. Grouws (Ed.), Handbook for Research on Mathematics Teaching and Learning (pp. 334–370). New York: MacMillan.
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.
Secada, W. G. (1992). Race, ethnicity, social class, language and achievement in mathematics. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 623–660). New York: MacMillan.
Shade, D.D. (1991). Developmentally appropriate software. Day Care and Early Education, 18(4), 34–36.
Sheffield, L. J. (1994). The development of gifted and talented mathematics students and the National Council of Teachers of Mathematics Standards (Report No. RBDM 9404). Storrs: National Research Center on the Gifted and Talented, University of Connecticut.
Sheffield, L. J. (2003). Extending the challenge in mathematics: Developing mathematical promise in K-8 students. Thousand Oaks: Corwin Press.
Sherin, M. G. (2007). The development of teachers’ professional vision in video clubs. In R. Goldman, R. Pea, B. Barron, & S. J. Derry (Eds.), Video Research in the Learning Sciences (pp. 383–395). Mahwah: Erlbaum.
Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28
Silver, E.A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing, ZDM, 29(3), 75–80.
Singer, F.A., Sheffield, L.J., Freiman, V., & Brandl, M. (2016). Research on and Activities for Mathematically Gifted Students. ICME-13 Topical Surveys. Cham: Springer.
Suh, J. & Fulginiti, K. (2011). Developing Mathematical Potential in Underrepresented Populations through Problem Solving, Mathematical Discourse and Algebraic Reasoning. In B. Sriraman & K. Lee (Eds.), The elements of creativity and giftedness in mathematics (Vol. 1, pp. 67–79). Rotterdam: Sense.
Swan, M. (2008). A Designer Speaks: Designing a multiple representation learning experience in secondary algebra. Educational Designer, 1(1), no page numbers. Retrieved from www.educationaldesigner.org/ed/volume1/issue1/article3
Taskinen, P. (2010). Naturwissenschaften als zukünftiges Berufsfeld für Schülerinnen und Schüler mit hoher naturwissenschaftlicher und mathematischer Kompetenz. PhD-Thesis, University of Kiel. Retrieved from macau.uni-kiel.de/receive/dissertation_ diss_00005685
Vygotsky, L. (1996). Thought and Language (translated by A. Kouzlin, 9th Ed.). Cambridge: Massachusetts Institute of Technology Press.
Vygotsky, L. (1930/1984). Imagination and creativity in adolescent. In D. B. Elkonin (Ed.), Child psychology. The collected works of L. S. Vygotsky (pp. 199–219). Moscow: Pedagogika.
Wittmann, E. Ch. (1995). Mathematics Education as a ‘Design Science’. Educational Studies in Mathematics, 29(4), 355–374.

How to cite this article

APA

Schnell, S., & Prediger, S. (2017). Mathematics Enrichment for All – Noticing and Enhancing Mathematical Potentials of Underprivileged Students as An Issue of Equity. Eurasia Journal of Mathematics, Science and Technology Education, 13(1), 143-165. https://doi.org/10.12973/eurasia.2017.00609a

Vancouver

Schnell S, Prediger S. Mathematics Enrichment for All – Noticing and Enhancing Mathematical Potentials of Underprivileged Students as An Issue of Equity. EURASIA J Math Sci Tech Ed. 2017;13(1):143-65. https://doi.org/10.12973/eurasia.2017.00609a

AMA

Schnell S, Prediger S. Mathematics Enrichment for All – Noticing and Enhancing Mathematical Potentials of Underprivileged Students as An Issue of Equity. EURASIA J Math Sci Tech Ed. 2017;13(1), 143-165. https://doi.org/10.12973/eurasia.2017.00609a

Chicago

Schnell, Susanne, and Susanne Prediger. "Mathematics Enrichment for All – Noticing and Enhancing Mathematical Potentials of Underprivileged Students as An Issue of Equity". Eurasia Journal of Mathematics, Science and Technology Education 2017 13 no. 1 (2017): 143-165. https://doi.org/10.12973/eurasia.2017.00609a

Harvard

Schnell, S., and Prediger, S. (2017). Mathematics Enrichment for All – Noticing and Enhancing Mathematical Potentials of Underprivileged Students as An Issue of Equity. Eurasia Journal of Mathematics, Science and Technology Education, 13(1), pp. 143-165. https://doi.org/10.12973/eurasia.2017.00609a

MLA

Schnell, Susanne et al. "Mathematics Enrichment for All – Noticing and Enhancing Mathematical Potentials of Underprivileged Students as An Issue of Equity". Eurasia Journal of Mathematics, Science and Technology Education, vol. 13, no. 1, 2017, pp. 143-165. https://doi.org/10.12973/eurasia.2017.00609a