Research Forums & Plenary Panel: Information & Pre-Reading

Research Forum 1: Perceptuo-Motor Activity and Imagination in Mathematics Learning (Information)

Research Forum 2: Equity, mathematics learning and technology (Information)

 

Plenary Panel: Teachers Who Navigate Between Their Research And Their Practice (Information)

DG 8 See information at bottom of this page.

DG 7 A paper from Fulvia Furinghetti may be downloaded here.

WS 1 A bibliography on gesture and a paper may be downloaded here and here. Potential participants should contact Laurie Edwards (ledwards@stmarys-ca.edu) to join a list-serv being set up for the session.


RF2: Co-ordinators: Colleen Vale (Australia), Gilah Leder (Australia), and Helen Forgasz (Australia)

[Papers may be downloaded by clicking on underlined authors' names.]

In recent times there has been growing recognition of the complexity of the settings in which mathematics learning occurs. Concurrently, more careful attention is being paid to the definitions and dimensions of equity, and to the interactions of these dimensions. In response, mathematics education researchers have adopted a wider range of research designs to explore equity issues. The nature and extent of the use of technology in mathematics classrooms varies between and within nations. Thus equity concerns should take on a new focus.
The challenges presented by the combination of these effects are significant and will be addressed in this forum. Does access to the technology per se promote mathematical learning, as is often proclaimed and generally assumed? In this changing learning environment, what are the implications for mathematics teaching and learning of gender, culture/ethnicity/race, and socio-economic background/class? The advent of particular technologies in classrooms raises other vital questions related to equity. Do all students have equal access to the technology? Are all students advantaged by the use of technology as they learn mathematics? If not, are there new privileged and new disadvantaged groups?
In this forum, we will be exploring issues, identifying research questions that need to be asked, and examining the range of methodological approaches that may be useful in finding the answers.

Session One: Equity issues in mathematics when teaching with technology
In this session, presenters and forum participants will draw attention to particular equity issues and raise questions for further research. With a focus on gender, culture/race/ethnicity and/or socio-economic class, Helen Forgasz (Australia), Christine Keitel (Germany) and Mamokgethi Setati (South Africa) will situate their responses within particular socio-cultural educational contexts. Gilah Leder (Australia) will lead a discussion among forum participants for the remainder of this session.
The key questions to be addressed by speakers and participants include:
• What is meant by equity with respect to mathematics learning and the use of technology?
• What are the factors that contribute to inequitable learning outcomes when teaching mathematics with technology?
• Are these factors the same in all contexts, that is, across and within national boundaries?
• What research questions should be asked in order to advance equity when learning mathematics with technology?
• How does socio-cultural context play a role in framing research questions for advancing equity when technology is used for mathematics learning?

Session Two: Designing research about equity in mathematics learning when teaching with technology
The second session of the research forum will be devoted to examining theoretical frameworks and research methodologies that may inform studies of the research problems and questions raised in the first session. Gabriele Kaiser (Germany), Colleen Vale (Australia) and Walter Secada (USA) will discuss the strengths and weaknesses of research approaches relevant to researching equity. Gilah Leder (Australia) will lead discussion among participants.
The key questions to be addressed by speakers and participants include:
• What research and experiences from countries around the world can we draw on, or take as exemplars, when designing research for advancing equity in mathematics when teaching with technology?
• How may the various theoretical frameworks concerning equity in mathematics inform the design of further research involving teaching mathematics with technology?
• How may socio-cultural context inform the design of further research involving teaching mathematics with technology?
• How do we encourage research in teaching mathematics with technology to respond to questions concerning equity and socio-cultural context?

How can you participate?
We invite you to react to prior readings (listed below) or to the Research Forum papers published in the Proceedings [available for download above; click on presenters' names]. We would like to encourage you to draw attention to issues or research findings that may not otherwise be considered in the forum.
If you would like to speak during one of the sessions in the forum please submit a brief statement or commentary in writing (up to 250 words) before the forum to the convenor, Colleen Vale.
Email: colleen.vale@vu.edu.au
The facilitator, Gilah Leder, will respond to you prior to the forum to plan the discussion.
Time will also be set aside for questions and general discussion from the floor.

Prior reading
Adler, J. (2001). Resourcing practice and equity: A dual challenge for mathematics education. In B. Atweh, H. Forgasz & B. Nebres (Eds.) Sociocultural research on mathematics education: An international perspective (pp. 185-200). Mahwah, NJ: Lawrence Erlbaum Associates.
Kaiser, G. & Rogers, P. (1995). Introduction: Equity in mathematics education. In P. Rogers & G. Kaiser (Eds.) Equity in mathematics education. Influences of feminism and culture (pp. 1-10). London: Falmer Press.
Secada, W. G. & Berman, P. W. (1999). Equity as a value-added dimension in teaching for understanding in school mathematics. In E. Fennema & T. A. Romberg (Eds.), Classrooms that promote student understanding in mathematics (pp. 33-42). Mahwah, NJ: Lawrence Erlbaum.
Tate, W. F. (1997). Race-ethnicity, SES, gender, and language proficiency trends in mathematics achievement: An update. Journal for Research in Mathematics Education, 28(6), 652-679.
Volman, M. & van Eck, E. (2001). Gender equity and information technology in education: The second decade. Review of Educational Research, 71(4), 613- 634.

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RF1: Co-ordinators: Ricardo Nemirovsky (USA) and Marcelo Borba (Brazil)

Introduction
The idea that perceptuo-motor experiences are important in mathematics learning is not new, of course; it is often associated with the use of manipulatives. The use of manipulatives in mathematics education is part of a long tradition enriched by noted educators such as Maria Montessori, Georges Cuisenaire, Caleb Gattegno, and Zoltan Dienes. Like many teachers, these educators have observed that numerous students will become engaged with materials that they can manipulate with their hands and move physically, with an intensity and insight that are not present when they simply observe a visual display on a blackboard, a screen, or a textbook. While researchers justly observe that students’ experimentation with manipulatives and devices does not automatically cause them to learn mathematics (1-5), there is something valuable that sustains the use of manipulatives even though it is straightforward to simulate most physical manipulatives on a computer. It is a very different experience to watch a movie displaying a geometrical object than it is to touch and walk around a plastic model of the same object. Clearly both experiences can be useful, but even if one would argue that they both reflect the same mathematical principle, they are not mere repetitions. One difference is that the use of appropriate materials and devices facilitates the inclusion of touch, proprioception (perception of our own bodies), and kinesthesia (self-initiated body motion) in mathematics learning.

An emerging body of work, sometimes called “Exploratory Vision,” describes vision as fully integrated with all the body senses and actions. Our eyes are constantly moving in irregular ways, momentarily fixing our gaze on a part of the environment and then jumping to another one. It is as if we are constantly posing questions to the visual environment and making bodily adjustments that might answer them. The bodily adjustments enacted in search of those answers constitute a critical aspect of what one calls seeing.

On this view, no end-product of perception, no inner picture or description is ever created. No thing in the brain is the percept or image. Rather, perceptual experience consists in the ongoing activity of schema-guided perceptual exploration of the environment. (6, p. 218, italics in the original)

A reason often drawn on to set aside touch, kinesthesia, etc. in mathematics learning is that mathematical entities cannot be “materialized”, one cannot touch, say, an infinite series or the set of even numbers. While true, the fact that these entities are imaginable with the symbols we use to work with them, is profoundly connected to perception and bodily action (7). In fact. it is increasingly evident that there is a major overlap between perception and imagination (8, 9). To imagine, for instance, a limit process, one extends perceivable aspects to physically impossible circumstances and conditions. In this regard, touch and kinesthesia can be instrumental to imagining. It is not unusual that to imagine inexistent objects and events one gestures shapes and motions or takes hold of an object, say a cardboard box, to help see them from different sides.

This research forum attempts to advance these themes by addressing the following research questions:
• What are the roles of perceptuo-motor activity, by which we mean bodily actions, gestures, manipulation of materials, acts of drawing, etc., in the learning of mathematics?
• How do classroom experiences, as constituted by the body in interaction with others, tools, technologies, and materials, open up spaces for mathematics learning?
• How does bodily activity become part of imagining the motion and shape of mathematical entities?
• How does language reflect and shape kinesthetic experiences?
The ensuing text [available for download here together with this introduction] encompasses five different papers. The first one outlines conjectures on the relationship between perceptuo motor activity and mathematical understanding. The ensuing four papers describe classroom-based cases, examine the research questions, and elaborate on the initial conjectures.

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Plenary Panel: Coordinator: Jarmila Novotná (Czech Republic) Panelists: Agatha Lebethe (South Africa), Gershon Rosen (Israel), Vicki Zack (Canada)

[To download the relevant paper, click here.]


DG 8 Stochastic Thinking--Here is a brief list of possible topics/people sent along by Mike Shaughnessy.

* Supporting Teachers’ Understandings of Statistical Data Analysis
--Kay McClain
* The natural frequency approach for teaching youngsters how to deal with risks.
--Laura Martigon
*A theoretical framework for the micro-evolution of probabilistic knowledge
--David Pratt
*The interaction of software with the way statistical concepts are framed
--Susan Friel
*Statistical Literacy: A research project
--Jane Watson
*Secondary Students' conceptions of variability: A research project
--Mike Shaughnessy

 

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