# Ricardo Avelar Sotomaior Karam

Associate Professor

**ORCID:**0000-0003-2567-8179

#### Primary fields of research

Due to my academic/professional background, my main research interests can be resumed as follows:

**The educational implications of the relationship between Physics and Mathematics**

I have recently guest edited a thematic issue of the journal Science & Education on this topic (Volume 24, Issues 5-6). Click here to view it.

This research involves considering the following three dimensions:

1) Historical and Epistemological Studies

Physics and Mathematics have been deeply interrelated since the very beginning of scientific knowledge and this mutual influence has played an essential role on both their developments. Historical case studies show us not only physics problems motivating the creation of mathematical concepts but also “pure” mathematics being used to derive conclusions about the “real” world.

Some references:

*Bochner, S. (1981). The role of mathematics in the rise of science. Princeton, New Jersey: Princeton University Press.*

*Boniolo, G., Budinich, P., & Trobok, M. (Eds.) (2005). The role of mathematics in physical sciences. Dordrecht: Springer.*

*Gingras, Y. (2001). What did mathematics do to physics? History of Science, 39, 383–416.*

2) Learning/Cognitive Perspective

The main difficulties students face when using mathematics to solve physics problems and/or transferring their knowledge from a mathematical to a physical context need to be investigated. Moreover, it is important to understand how the ability of using mathematics as a reasoning instrument in physics – instead of using it as a mere calculation tool – is developed.

Some references:

*Bing, T. J., & Redish, E. F. (2009). Analyzing problem solving using math in physics: Epistemological framing via warrants. Phys. Rev. ST Phys. Educ. Res. 5, 020108.*

*Hudson, H. T., & McIntire, W. R. (1977). Correlation between mathematical skills and success in physics. Am. J. Phys., 45(5), 470–471*

*Sherin, B. L. (2001). How students understand physics equations. Cognition and Instruction, 19(4), 479-541.*

3) Teaching/Didactic Perspective

Teaching activities and materials have to be carefully designed in order to encourage students to structure their thought mathematically in physical contexts. Due to the crucial responsability of the teacher for the success of this challenge, such didactical aspects have to be sistematically approached in teacher training courses. Aditionally, criteria for evaluating the quality of instruction, regarding the focus on several aspects of the relationship of physics and mathematics, should be established.

Some references:

*Bagno, E., Berger, H., & Eylon, B. S. (2008). Meeting the challenge of students’ understanding of formulae in high-school physics: A learning tool. Physics Education, 43(1), 75-82.*

*Dunn, J. W., & Barnabel, J. (2000). One model for an integrated math/physics course focusing on electricity and magnetism and related calculus topics. Am. J. Phys., 68(8), 749–757.*

*Tzanakis, C., & Thomaidis, Y. (2000). Integrating the close historical development of Mathematics and Physics in Mathematics education: some methodological and epistemological remarks. For the Learning of Mathematics, 20 (1), 44-55.*

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