Categorization of Physmatic Misconseptions:

Theoretical background:
"Math in science (and particularly math in physics) is not the same as doing math. It has a different purpose—representing meaning about physical systems rather than expressing abstract relationships. It even has distinct semiotics—the way meaning is put into symbols—from pure mathematics." (Redish, Edward & Kuo, 2015).
“Physmatics” is the interplay between mathematics and physics in the context of physics education. This "Phys-Math" interplay is regarded as a complex two ways track by which the knowledge and understanding of physics are constructed by learners (Lehavi et al, 2015).
We present a model that combines students' content knowledge with physics, teachers' content knowledge and teachers' pedagogical content knowledge.
Several models have been offered to analyze teachers’ actions in explaining physics while constructing a description of a phenomenon. Some of these actions involve mathematical aspects and require the interplay between physics and mathematics. Hence we call that “the physmatic process”.
One recent model (Uhden et al., 2012) refers to separating the technical and structural skills used in mathematics within physics, having non-separable parts of learning ("physical-mathematical intersection"), and introduce five components of the physmatic process: simplifying the phenomenon, mathematization, interpretation, technical mathematical operations, and validation in relation to the real world. The model describes the processes involving physmatics but did not characterize it in the classroom and did not find specific physmatic difficulties in this process.
Research questions:
What defines students' physmatic difficulties as unique difficulties? how such difficulties are reflected in physics lessons and physics teachers pedagogical content knowledge (PCK)?
A clear characterization of those difficulties will contribute to the Physmatic-PCK (Lehavi et al, 2015) of physics-educators.
Research method:
The Data was collected by videotaping physics lessons at the high school level. The videos were scrutinized, looking for occasions in which a Phys-Math interplay was manifested. The analysis was conducted by qualitative content analysis.
The purpose was to find which “physmatics misconceptions” can students and teachers have, in a variety of subjects from the physics class.
The difficulties were mapped into two types of categories:
Categories from Uhden's model (top-down) that focus on the observed physmatic component in the physmatic process and new categories (bottom-up) that define different types of physmatic misconceptions of the student or the teacher.
Preliminary results:
Eight new categories were identified through the analysis that describes physmatics misconceptions, in addition to the categories from the literature that were extended to sub-categories.
References:
Redish, Edward F. & Kuo, E (2015). Language of Physics, Language of Math: Disciplinary Culture and Dynamic Epistemology. Science & Education 24 (5-6):561-590.
Y. Lehavi, E. Bagno, B-S. Eylon, R. Mualem, G. Pospiech, U. Böhm, O. Krey and R. Karam (2017). Classroom Evidence of Teachers’ PCK of the Interplay of Physics and Mathematics. In: Greczyło T., Dębowska E. (eds) Key Competences in Physics Teaching and Learning. Springer Proceedings in Physics, vol 190. Springer, Cham
Uhden, O., Karam, R., Pietrocola, M. et al. Modelling Mathematical Reasoning in Physics Education. Sci & Educ 21, 485–506 (2012) doi:10.1007/s11191-011-9396-6