Lodge-Scharff on mental models in mathematics and physics

Savannah E. Lodge-Scharff

Investigating Student Mental Models at the Intersection of Mathematics and Physical Reasoning in Physics

Thesis for the Master's of Science in Teaching (MST)

A significant challenge in learning science and mathematics is coordinating different types of mental models, such as mathematical and physical mental models, that represent different aspects of a given phenomenon. This challenge is illustrated in the present study, in which we observed a small number of college students reasoning about forces as both physical and mathematical quantities as they reasoned about a physical system. Using video analysis of the students’ gesture and as they reasoned qualitatively and mathematically about the system, we documented the construction and coordination of participants’ mental models. We found that participants constructed mathematical mental models as imagined lines uniquely to physical mental models as imagined pulls. Moreover, students rarely exhibited the coordination of these two mental models. These findings suggest that instructors that they cannot assume that students generate models, even circumstances designed to support them.

Recommended Citation
Lodge-Scharff, Savannah E., "Investigating Student Mental Models at the Intersection of Mathematics and Physical Reasoning in Physics" (2017). Electronic Theses and Dissertations. 2718.
http://digitalcommons.library.umaine.edu/etd/2718

Flood Harrar Wittmann and many others on embodied cognition in chemistry

Virginia J. Flood, François G. Amar, Ricardo Nemirovsky, Benedikt W. Harrer, Mitchell R. M. Bruce, and Michael C. Wittmann

Paying Attention to Gesture when Students Talk Chemistry: Interactional Resources for Responsive Teaching

Journal of Chemical Education
J. Chem. Educ., 2015, 92 (1), pp 11–22
DOI: 10.1021/ed400477b
Publication Date (Web): October 21, 2014

Abstract: When students share and explore chemistry ideas with others, they use gestures and their bodies to perform their understanding. As a publicly visible, spatio–dynamic medium of expression, gestures and the body provide productive resources for imagining the submicroscopic, three-dimensional, and dynamic phenomena of chemistry together. In this paper, we analyze the role of gestures and the body as interactional resources in interactive spaces for collaborative meaning-making in chemistry. With our moment-by-moment analysis of video-recorded interviews, we demonstrate how creating spaces for, attending to, and interacting with students’ gestures and bodily performances generate opportunities for learning. Implications for teaching and assessment that are responsive to students’ ideas in chemistry are discussed.

Evan Chase MST on gestures regarding accelerated motion

Evan Chase

Investigating Physics Students’ Simultaneous Use of Gestures and Speech to Describe Multiple Quantities of a Vertically-Tossed Ball

In physics education research, we are often concerned with understanding students’ ideas. For these purposes, teachers often assess student knowledge on the basis of summative assessment: exams, quizzes, and lab reports, etc. Teachers and researchers also attend to conversation, where people typically produce hand gestures that can communicate additional information to the listener. Due to this, it is important to be able to understand what gestures may mean, so that any information within them can be accessed. If there is valuable information about student knowledge available in a gesture, then this information can easily be missed if exclusively written methods of assessment and research are used. Teachers and researchers could benefit from the ability to decipher and utilize a student’s gestures to better understand the student’s level of comprehension.

To study how physics students use gestures in addition to their speech to explain a ball being tossed into the air, individual interviews were conducted with physics majors who had completed half of an eight-semester physics program at the University of Maine. These interviews conformed to the standards set by current qualitative education research. Students were asked to discuss kinematic quantities and forces associated with the motion of a ball thrown straight up, both with and without the force of air resistance. The video episodes selected for detailed analysis contained moments of students gesturing and speaking simultaneously, such that the referents of the speech and gesture did not appear to match. A more explicit methodology than that found in the current literature on gesture research in physics is defined. This methodology is used to show that these physics students were able to portray information about kinematics and force quantities simultaneously with gestures and speech, and in some cases were able to describe changes in one quantity with a hand and another quantity with the fingers on the same hand.

Wittmann, Flood, and Black on embodiment in separating variables

Algebraic manipulation as motion within a landscape
Michael C. Wittmann, Virginia J. Flood, Katrina E. Black
Educational Studies in Mathematics
February 2013, Volume 82, Issue 2, pp 169-181

We show that students rearranging the terms of a mathematical equation in order to separate variables prior to integration use gestures and speech to manipulate the mathematical terms on the page. They treat the terms of the equation as physical objects in a landscape, capable of being moved around. We analyze our results within the tradition of embodied cognition and use conceptual metaphors such as the path-source-goal schema and the idea of fictive motion. We find that students solving the problem correctly and efficiently do not use overt mathematical language like multiplication or division. Instead, their gestures and ambiguous speech of moving are the only algebra used at that moment.

Chase and Wittmann on Embodied Cognition

Evidence of embodied cognition via speech and gesture complementarity
 Evan A. Chase and Michael C. Wittmann
 AIP Conf. Proc. 1513, 94 (2013)

We are studying how students talk and gesture about physics problems involving directionality. Students discussing physics use more than words and equations; gestures are also a meaningful element of their thinking. Data come from one-on-one interviews in which students were asked to gesture about the sign and direction of velocity, acceleration, and other quantities. Specific contexts are a ball toss in the presence and absence of air resistance, including situations where the ball starts at greater than terminal velocity. Students show an aptitude for representing up to 6 characteristics of the ball with 2 hands. They switch quickly while talking about velocity, acceleration, and the different forces, frequently representing more than one quantity using a single hand. We believe that much of their thinking resides in their hands, and that their gestures complement their speech, as indicated by moments when speech and gesture represent different quantities.