ArticlePDF Available

WHAT NONVERBAL INTERACTIONS WITH DIAGRAMS TEACHERS PERCEIVE AS MEANINGFUL ELEMENTS OF STUDENTS’ MATHEMATICAL WORK

Authors:

Abstract and Figures

NSF grant ESI-0353285 http://deepblue.lib.umich.edu/bitstream/2027.42/62487/1/PHetal-gesture-web.pdf
Content may be subject to copyright.
A preview of the PDF is not available
ResearchGate has not been able to resolve any citations for this publication.
Article
Full-text available
We report on the development of representations of teaching based on sequential-art sketches of classroom stories. We demonstrate with focus group data that these resources can help sketch compelling classroom stories and elicit the practical rationality of mathematics teaching. For quite some time policy makers have looked for levers for instructional improvement – whether increasing teacher knowledge, upgrading instructional resources, or raising standards for student achievement. But instruction, like many other human activities that take time and recur over time, is organized by a rationality, a way of doing the activity that makes sense to participants and that tends to keep the activity stable and viable. We posit therefore that in order to design and promote improvements that are feasible and sustainable reformers also need to know about the mathematical work that teachers and students customarily do as they interact in classrooms. We have borrowed from Bourdieu (1998) the notion that a practical rationality, tacit and shared, undergirds the decisions and actions of the mathematics teacher in specific instructional situations. In the present paper we describe and illustrate a novel technique that project ThEMaT (Thought Experiments in Mathematics Teaching) has developed in order to study this practical rationality empirically, in selected situations in secondary algebra and geometry. The project is based on the hypothesis that practitioners' instructional actions respond to obligations to the discipline, the students, and the school institution, but are neither determined by those obligations nor chosen at will through individual management of personal resources. Rather, courses of instructional action are constructed as viable, tactical plays of a game that pursues curricular and other stakes through the collective production of work over time. We conceive of the practical rationality invested in the teaching of algebra and geometry as composed of a system of dispositions that serves the purpose of warranting a range of possible tactical plays that a teacher of a given school subject might consider viable to do. We conceive of this system of dispositions as including the categories of perception and appreciation that actors of a practice can draw upon to relate to (possible or real) events and things in that practice. By categories of perception we mean the categories available in a practice with which a teacher can identify and describe events or things. By categories of appreciation we mean the categories available in a practice with which a teacher can have an attitude toward, or allocate value to, events or things. In this paper we report on our conceptualization of a novel resource for eliciting the practical rationality of mathematics teaching based on sequential-art sketches of classroom stories deployed in three media forms: animation, slide show, and comic book. These stories are designed to engage practitioners in thought experiments about instruction, thought experiments that, we argue, can elicit practitioners' practical rationality. We conceptualize the use of this media against the background of our prior use of video for similar purposes and illustrate the kind of data that we have been able to collect with it.
Article
Full-text available
Seeing is investigated as a socially situated, historically constituted body of practices through which the objects of knowledge that animate the discourse of a profession are constructed and shaped. Analysis of videotapes of archaeologists making maps and lawyers animating events visible on the Rodney King videotape focuses on practices that are articulated in a work-relevant way within sequences of human interaction, including coding schemes, highlighting, and graphic representations. Through the structure of talk in interaction, members of a profession hold each other accountable for, and contest the proper constitution and perception of, the objects that define their professional competence.
Conference Paper
Full-text available
This paper investigates the difference between seeing and perceiving in animation. It analyses character design in the light of experiments in face recognition, in particular how iconic a character can be in design. It discusses whether a universal theory can be applied and if caricatures are really 'super-portraits' that echo how brains recall faces. The psychophysical perception of motion in animation is analysed in the light of animation principles such as 'squash and stretch' and 'isolation'. Using made and found examples, the paper looks at how signature movement and animation principles are now being supplemented or even supplanted by motion capture and posits what this means for animation in the future. The paper maps popular animation characters within two specially designed triangular charts for image and for motion. It analyses the resulting images in terms of perceived and received information, looking particularly at the region of empathic connection coined by Dr Masahiro Mori as the 'Uncanny Valley'. [1] By examining the different empathic demands motion capture makes on an audience it reaches the conclusion that both image and motion must be treated symbiotically for full analysis to be achieved.
Article
Two questions are asked that concern the work of teaching high school geometry with problems and engaging students in building a reasoned conjecture: What kinds of negotiation are needed in order to engage students in such activity? How do those negotiations impact the mathematical activity in which students participate? A teacher's work is analyzed in two classes with an area problem designed to bring about and prove a conjecture about the relationship between the medians and area of a triangle. The article stresses that to understand the conditions of possibility to teach geometry with problems, questions of epistemological and instructional nature need to be asked not only whether and how certain ideas can be conceived by students as they work on a problem but also whether and how the kind of activity that will allow such conception can be summoned by customary ways of transacting work for knowledge.
Conference Paper
This paper highlights the role of gestures in communicating and particularly in thinking in mathematics. The research interest is on the relation between the use of gestures and the birth of new perceivable signs. This link is shown through the description of a concrete example, referring to a discussion among 8th grade students around a geometrical problem in 3D, to be solved without the use of devices and paper and pencil. It is interesting to observe the progression in the construction of the solution, obtained with the introduction of new signs from gestures, and at the end even of a common tool used by children, the plasticine.
Article
We report preliminary results of research on the underlying rationality of geometry teaching, especially as regards to the role of proof in teaching theorems. Building on prior work on the classroom division of labor in situations of "doing proofs," we propose that the division of labor is different in situations when learning a theorem is at stake. In particular, the responsibility for producing a proof stays with the teacher, who may opt to produce the proof in a less stringent form than when students are doing proofs and who may do so for reasons other than conferring truth to the statement. We ground this claim on reactions from experienced geometry teachers to an animated representation of the teaching of theorems about medians in a triangle.
Article
While every theorem has a proof in mathematics, in US geometry classrooms not every theorem is proved. How can one explain the practitioner’s perspective on which theorems deserve proof? Toward providing an account of the practical rationality with which practitioners handle the norm that every theorem has a proof we have designed a methodology that relies on representing classroom instruction using animations. We use those animations to trigger commentary from experienced practitioners. In this article we illustrate how we model instructional situations as systems of norms and how we create animated stories that represent a situation. We show how the study of those stories as prototypes of a basic model can help anticipate the response from practitioners as well as suggest issues to be considered in improving a model.
Generalizing in Interaction
  • A Jurow
Jurow, A. (2004). Generalizing in Interaction. Mind, Culture, and Activity, 11, 279-300.