### ELPSA AS A LESSON DESIGN FRAMEWORK

#### Abstract

This paper offers a framework for mathematics lesson design that is consistent with the way we learn about, and discover, most things in life. In addition, the framework provides a structure for identifying how mathematical concepts and understanding are acquired and developed. This framework is called ELPSA and represents five learning components, namely: Experience, Language, Pictorial, Symbolic and Applications. This framework has been used in developing lessons and teacher professional programs in Indonesia since 2012 in cooperation with the World Bank. This paper describes the theory that underlines the framework in general and in relation to each inter-connected component. Two explicit learning sequences for classroom practice are described, associated with Pythagoras theorem and probability. This paper then concludes with recommendations for using ELPSA in various institutional contexts.

Keywords: ELPSA, lesson design framework, Pythagoras theorem, probability

Â

#### References

Adler, J. (1998). A Language of teaching dilemmas: Unlocking the complex multilingual secondary mathematics classroom. For the Learning of Mathematics, 18(1), 24-33.

Bishop, A. J. (1988a). The interactions of mathematics education with culture. Cultural Dynamics, 1(2), 145-157.

Bishop, A. J. (1988b). Mathematics education in its cultural context. In A. J. Bishop (Ed.), Mathematics Education and Culture (pp. 179-191): Springer.

Boaler, J. (1998). Open and closed mathematics: Student experiences and understandings. Journal for Research in Mathematics Education, 29(1), 41-62.

Chubb, I. (2014). Classroom maths irrelevant to workplace. Retrieved 3 June, 2015, from http://www.couriermail.com.au/news/queensland/classroom-maths-irrelevant-to-workplace-says-professor-ian-chubb/story-fnn8dlfs-1227164607227

Cobb, P. (1988). The tension between theories of learning and instruction in mathematics education. Educational Psychologist, 23(2), 87.

De Cruz, H., & De Smedt, J. (2013). Mathematical symbols as epistemic actions. Synthese, 190(1), 3-19. doi: 10.1007/s11229-010-9837-9

Dienes, Z. P. (1959). The teaching of mathematicsâ€â€III: The growth of mathematical concepts in children through experience. Educational Research, 2(1), 9-28.

Diezmann, C. M., & Lowrie, T. (2008). Assessing primary studentsâ€™ knowledge of maps.

Goldin, G., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. The roles of representation in school mathematics, 2001, 1-23.

Gravemeijer, K. (2010). Realistic mathematics education theory as a guideline for problem-centered, interactive mathematics education. A decade of PMRI in Indonesia. Bandung, Utrecht: APS International.

Hegarty, M., & Kozhevnikov, M. (1999). Types of visualâ€“spatial representations and mathematical problem solving. Journal of Educational Psychology, 91(4), 684.

Heuvel-Panhuizen, M. V. D. (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.

Kosslyn, S. (1983). Ghosts in the mindâ€™s machine. New York: Norton.

Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation: Cambridge university press.

Lerman, S. (2003). Cultural, Discursive Psychology: A Sociocultural Approach to Studying the Teaching and Learning of Mathematics Learning Discourse. In C. Kieran, E. Forman & A. Sfard (Eds.), (pp. 87-113): Springer Netherlands.

Liebeck, P. (1984). How children learn mathematics: A guide for parents and teachers: Penguin.

Lowrie, T. (2011). â€œIf this was realâ€: tensions between using genuine artefacts and collaborative learning in mathematics tasks. Research in Mathematics Education, 13(1), 1-16.

Lowrie, T., & Logan, T. (2007). Using Spatial Skills to Interpret Maps: Problem Solving in Realistic Contexts. Australian Primary Mathematics Classroom, 12(4), 14-19.

Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Street mathematics and school mathematics. United States of America: Cambridge University Press.

Pape, S. J., & Tchoshanov, M. A. (2001). The Role of Representation(s) in Developing Mathematical Understanding. Theory into Practice, 40(2), 118-127. doi: 10.1207/s15430421tip4002_6

Setati, M., & Moschkovich, J. N. (2010). Mathematics education and language diversity: A dialogue across settings. Journal for Research in Mathematics Education, 41, 1-28.

Thomson, S., De Bortoli, L., & Buckley, S. (2013). PISA 2012: How Australia measures up. Victoria, Australia: Australian Council for Educational Research.

Uttal, D. H., Scudder, K. V., & DeLoache, J. S. (1997). Manipulatives as symbols: A new perspective on the use of concrete objects to teach mathematics. Journal of Applied Developmental Psychology, 18(1), 37-54.

Vygotsky, L. S. (1978). Mind in society : the development of higher psychological processes. Cambridge: Harvard University Press.

Wenger, E. (1999). Communities of practice: Learning, meaning, and identity: Cambridge university press.

Widjaja, W., Fauzan, A., & Dolk, M. (2010). The role of contexts and teacher's questioning to enhance students' thinking. Journal of Science and Mathematics Education in Southeast Asia, 33(2), 168-186.

World Bank. (2010). Inside Indonesia's mathematics classrooms: A TIMSS video study of teaching practices and student achievement. Jakarta: The World Bank Office Jakarta.

DOI: https://doi.org/10.22342/jme.6.2.2166.77-92

### Refbacks

- There are currently no refbacks.

**Journal on Mathematics Education**

Kampus FKIP Bukit Besar

Jl. Srijaya Negara, Bukit Besar

Palembang - 30139

p-ISSN: 2087-8885 | e-ISSN: 2407-0610

Journal on Mathematics Education is licensed under a Creative Commons Attribution 4.0 International License

View My Stats