Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings

The goal of this article is to present a sketch of what, following the German social theorist Arnold Gehlen, may be termed “sensuous cognition.” The starting point of this alternative approach to classical mental-oriented views of cognition is a multimodal “material” conception of thinking. The very texture of thinking, it is suggested, cannot be reduced to that of impalpable ideas; it is instead made up of speech, gestures, and our actual actions with cultural artifacts (signs, objects, etc.). As illustrated through an example from a Grade 10 mathematics lesson, thinking does not occur solely in the head but also in and through a sophisticated semiotic coordination of speech, body, gestures, symbols and tools.

Deep intuition as a level in the development of the concept image

To explicate certain phenomena, e.g., the possibility of deduction without definition, we hypothesize that an individual is able to understand and appreciate reasoning with a due feeling of its necessity when the concept image of each concept involved in the reasoning has reached a certain level of development; we then speak of deep intuition. This conception is presented (with a variety of examples) in the framework of D. Tall’s theory of three worlds of mathematics (‘conceptual-embodied’, ‘proceptual-symbolic’, and ‘formal-axiomatic’).

Making Sense of Place: Sarah’s Story

Written from the vantage point of both a mother and teacher educator, the author recounts the journey taken by Sarah, her 4-year old daughter, as she is introduced to and explores map making as a means of representing and making sense of familiar and unfamiliar places. Offering Sarah’s experience as context, the author offers both a practical and theoretical discussion of children’s emerging geographic literacy, its relationship to identity development and the importance of understanding children’s experience and socio-emotional development to inform pedagogy.

Towards new documentation systems for mathematics teachers?

We study in this article mathematics teachers’ documentation work: looking for resources, selecting/designing mathematical tasks, planning their succession, managing available artifacts, etc. We consider that this documentation work is at the core of teachers’ professional activity and professional development. We introduce a distinction between available resources and documents developed by teachers through a documentational genesis process, in a perspective inspired by the instrumental approach. Throughout their documentation work, teachers develop documentation systems, and the digitizing of resources entails evolutions of these systems. The approach we propose aims at seizing these evolutions, and more generally at studying teachers’ professional change.

Knowing Who Your Friends Are: Aspects of the Politics of Logical Empiricism

This paper comments on Reisch’s book How the Cold War Transformed Philosophy of Science. Overall supportive of Reisch’s project and perspective, it raises certain points where the data appear inconclusive and either provides additional support or briefly explores some interpretative alternatives.

---

A Role for Experiment in Using the Law of Inertia to Explain the Nature of Science: A Comment on Lopes Celho

The whole mode of Galileo’s discovery of the Law of Inertia is an excellent exemplar of the Nature of Science. The law can, moreover be shown to be a direct consequence of the hypothesis that space is homogeneous and isotropic and time is homogeneous

---

Embodied design: constructing means for constructing meaning

Design-based research studies are conducted as iterative implementation-analysis-modification cycles, in which emerging theoretical models and pedagogically plausible activities are reciprocally tuned toward each other as a means of investigating conjectures pertaining to mechanisms underlying content teaching and learning. Yet this approach, even when resulting in empirically effective educational products, remains under-conceptualized as long as researchers cannot be explicit about their craft and specifically how data analyses inform design decisions. Consequentially, design decisions may appear arbitrary, design methodology is insufficiently documented for broad dissemination, and design practice is inadequately conversant with learning-sciences perspectives. One reason for this apparent under-theorizing, I propose, is that designers do not have appropriate constructs to formulate and reflect on their own intuitive responses to students’ observed interactions with the media under development. Recent socio-cultural explication of epistemic artifacts as semiotic means for mathematical learners to objectify presymbolic notions (e.g., Radford, Mathematical Thinking and Learning 5(1): 37–70, 2003) may offer design-based researchers intellectual perspectives and analytic tools for theorizing design improvements as responses to participants’ compromised attempts to build and communicate meaning with available media. By explaining these media as potential semiotic means for students to objectify their emerging understandings of mathematical ideas, designers, reciprocally, create semiotic means to objectify their own intuitive design decisions, as they build and improve these media. Examining three case studies of undergraduate students reasoning about a simple probability situation (binomial), I demonstrate how the semiotic approach illuminates the process and content of student reasoning and, so doing, explicates and possibly enhances design-based research methodology.

A review of Wolff-Michael Roth’s “In search of meaning and coherence: A life in research”

Wolff-Michael Roth’s In Search of Meaning and Coherence: A Life in Research, presents a selection of his previously published key works layered with current commentary and analysis. In this book review, we explore themes that emerge through the text to trace Roth’s development as a theoretician and as a researcher. We recommend this book for all those who are interested in Wolff-Michael Roth and the trajectory of his career, in particular those who are just beginning their journey towards academic scholarship.

Authentic science experiences as a vehicle for assessing orientation towards science and science careers relative to identity and agency: a response to “learning from the path followed by Brad”

This response draws from the literature on adaptive learning, traditional ecological knowledge, and social–ecological systems to show that Brad’s choice is not a simple decision between traditional ecological knowledge and authentic science. This perspective recognizes knowledge systems as dynamic, cultural and historical activities characterized by diverse worldviews and ways of constructing and legitimizing knowledge. Brad’s decision is seen as an example of adaptive learning, identity development and personal/collective agency oriented to increasing tribal influence in resource management decisions and policies. I will conclude that science literacy for all is not served by a transcendent, universal, Western modern view of science.

Beyond Borders: Reading “Other” Places in Children’s Literature

The author analyzes two texts, Gloria Whelan’s Homeless Bird and Deborah Ellis’s Parvana’s Journey, in an attempt to explain some of the problems and difficulties associated with those texts. The author examines Whelan’s representations of India and finds troubling binaries associated with that text. In comparison, the author finds Ellis’s depictions of Afghanistan more nuanced and complex. The author also discusses student reception of both texts and offers ways to problematize some of their reactions.

Nightmares,Idylls, Mystery,and Hope: <Emphasis Type="Italic">Walk Two Moons</Emphasis> and the Artifice of Realism in Children’s Fiction

Sharon Creech’s Walk Two Moons is a defining example of contemporary realistic fiction for children. This article argues that Walk Two Moons models storytelling as a tool which children need to understand their own relationship to reality and to literature. Rather than employing a grim verisimilitude, as some critics have charged, Creech has created a novel of realistic character development which also challenges any simplistic understanding of children’s realistic fiction through its complex and self-referential narrative structure and use of literary language. The result is a narrative which, in the face of painful and tragic circumstances, empowers readers toward a hopeful and optimistic view of life’s mysteries.

The importance of socio-cultural context for understanding students’ meaning making in the study of genetics

In this rejoinder to Ann Kindfield and Grady Venville’s comments on our article “Reconsidering conceptual change from a socio-cultural perspective: Analyzing students’ meaning making in genetics in collaborative learning activities,” we elaborate on some of the critical issues they raise. Their comments make apparent some of the crucial differences between a socio-cultural and a socio-cognitive approach towards conceptual change. We have selected some issues that are addressed, either implicitly or explicitly, in their comments. The main issues discussed are talk and interaction as data, the significance of context in interaction studies, the feasibility of generic claims in small-scale interaction studies, and the difference between studying students’ understanding of science concepts as opposed to studying the construction of meaning.

Exercise and Children’s Intelligence, Cognition, and Academic Achievement

Studies that examine the effects of exercise on children’s intelligence, cognition, or academic achievement were reviewed and results were discussed in light of (a) contemporary cognitive theory development directed toward exercise, (b) recent research demonstrating the salutary effects of exercise on adults’ cognitive functioning, and (c) studies conducted with animals that have linked physical activity to changes in neurological development and behavior. Similar to adults, exercise facilitates children’s executive function (i.e., processes required to select, organize, and properly initiate goal-directed actions). Exercise may prove to be a simple, yet important, method of enhancing those aspects of children’s mental functioning central to cognitive development.

In the Ellison Tradition: In/Visible Bodies of Adolescent and YA Fiction

When Ralph Ellison’s Invisible Man was published in 1952, he could not have known the impact his metaphor of invisibility would have on adolescent and YA literature. However, upon closer inspection, the importance and prevalence of his metaphor becomes evident. Authors of adolescent and YA literature routinely use the metaphor as an intertextual shortcut to discuss issues that shape adolescent subjectivity, which is demonstrated through an examination of Sapphire’s Push, Virginia Hamilton’s The Planet of Junior Brown, and Robert Cormier’s Fade.

Sanmao, the Vagrant: Homeless Children of Yesterday and Today

The intensifying globalization has made street survival more brutal and miserable for homeless children, especially in Third World countries. Sanmao, the Vagrant is a wordless picture book which tells of the adventures of a boy named Sanmao in streets of Shanghai during WWII. The essay analyzes how the artist’s ingenious visual narrative authentically anticipates the omnipresent impact of globalization on innocent children. Sanmao’s survival totally relies on his resilience and proactivity. He falls prey to unbridled exploitation and coercive and abusive treatment. Originally a comic intended for adults, the book is the artist’s furious protest against the indifferent attitude of the adult world.

Ocean to outback: Léonie Rennie’s contribution to science education in Australia

In this article I initially borrow a metaphor from an art exhibition, Ocean to Outback, as a way to express my perspective on the contribution that Léonie Rennie has made to science education in Australia. I then consider Léonie’s contributions as overlapping themes. In particular, Léonie’s well-known research on gender and issues of equity in science education is explored as well as her highly regarded work on learning science in out-of-school settings. Curriculum integration is a less well-known aspect of Léonie’s research that also is considered. Léonie’s important contributions to research training and policy in science education are briefly described and commented on. Finally, I return to the metaphor of Ocean to Outback that reflects the enormity of the contribution that Léonie has made but also gives insight into her personal journey and qualities.

Prospective teachers’ reasoning and response to a student’s non-traditional strategy when dividing fractions

Recognizing meaning in students’ mathematical ideas is challenging, especially when such ideas are different from standard mathematics. This study examined, through a teaching-scenario task, the reasoning and responses of prospective elementary and secondary teachers to a student’s non-traditional strategy for dividing fractions. Six categories of reasoning were constructed, making a distinction between deep and surface layers. The connections between the participants’ reasoning, their teaching response, and their beliefs about mathematics teaching were investigated. We found that there were not only differences but also similarities between the prospective elementary and secondary teachers’ reasoning and responses. We also found that those who unpacked the mathematical underpinning of the student’s non-traditional strategy tended to use what we call “teacher-focused” responses, whereas those doing less analysis work tended to construct “student-focused” responses. These results and their implications are discussed in relation to the influential factors the participants themselves identified to explain their approach to the given teaching-scenario task.

Prisoners of Childhood? Child Abuse and the Development of Heroes and Monsters in <Emphasis Type="Italic">Ender’s Game</Emphasis>

Alice Miller’s work provides a theoretical framework to assess the effects of child abuse and its relationship to the development of creativity, hatred, and violence in the novel Ender’s Game. Analysis focuses on the extent to which children are manipulated in order to meet the needs of adults, the presence of behaviors such as the repression of feelings and memories, the idealization of perpetrators, blind obedience to authority, and the expression of repressed feelings in destructive acts, and identification of a helping witness as predictors for the actions and outcomes in this story.