On semiotics and subjectivity: a response to Tony Brown’s “signifying ‘students’, ‘teachers’, and ‘mathematics’: a reading of a special issue”

In this response we address some of the significant issues that Tony Brown raised in his analysis and critique of the Special Issue of Educational Studies in Mathematics on “Semiotic perspectives in mathematics education” (Sáenz-Ludlow & Presmeg, Educational Studies in Mathematics 61(1–2), 2006). Among these issues are conceptualizations of subjectivity and the notion that particular readings of Peircean and Vygotskian semiotics may limit the ways that authors define key actors or elements in mathematics education, namely students, teachers and the nature of mathematics. To deepen the conversation, we comment on Brown’s approach and explore the theoretical apparatus of Jacques Lacan that informs Brown’s discourse. We show some of the intrinsic limitations of the Lacanian idea of subjectivity that permeates Brown’s insightful analysis and conclude with a suggestion about some possible lines of research in mathematics education.

The relationship between performance on mathematical word problems and language proficiency for students learning through the medium of Irish

Ireland has two official languages—Gaeilge (Irish) and English. Similarly, primary- and second-level education can be mediated through the medium of Gaeilge or through the medium of English. This research is primarily focused on students (Gaeilgeoirí) in the transition from Gaeilge-medium mathematics education to English-medium mathematics education. Language is an essential element of learning, of thinking, of understanding and of communicating and is essential for mathematics learning. The content of mathematics is not taught without language and educational objectives advocate the development of fluency in the mathematics register. The theoretical framework underpinning the research design is Cummins’ (1976). Thresholds Hypothesis. This hypothesis infers that there might be a threshold level of language proficiency that bilingual students must achieve both in order to avoid cognitive deficits and to allow the potential benefits of being bilingual to come to the fore. The findings emerging from this study provide strong support for Cummins’ Thresholds Hypothesis at the key transitions—primary- to second-level and second-level to third-level mathematics education—in Ireland. Some implications and applications for mathematics teaching and learning are presented.

Toward a framework for the development of mathematical knowledge for teaching

Shulman (1986, 1987) coined the term pedagogical content knowledge (PCK) to address what at that time had become increasingly evident—that content knowledge itself was not sufficient for teachers to be successful. Throughout the past two decades, researchers within the field of mathematics teacher education have been expanding the notion of PCK and developing more fine-grained conceptualizations of this knowledge for teaching mathematics. One such conceptualization that shows promise is mathematical knowledge for teaching—mathematical knowledge that is specifically useful in teaching mathematics. While mathematical knowledge for teaching has started to gain attention as an important concept in the mathematics teacher education research community, there is limited understanding of what it is, how one might recognize it, and how it might develop in the minds of teachers. In this article, we propose a framework for studying the development of mathematical knowledge for teaching that is grounded in research in both mathematics education and the learning sciences.

Battle on the Gender Homefront: Depictions of the American Civil War in Contemporary Young-Adult Literature

The American Civil War has been a popular topic for young-adult writers for years, with new books now being written from young women’s perspectives. In this paper, I will examine the gender ideologies that infiltrate contemporary Civil War books for young adults. I will examine four recent young-adult Civil-War novels: G. Clifton Wisler’s Mr. Lincoln’s Drummer (1995); Maureen Stack Sappéy’s Letters from Vinnie (1999); Jim Murphy’s The Journal of James Edmond Pease: A Civil War Union Soldier (1998); and Karen Hesse’s A Light in the Storm: The Civil War Diary of Amelia Martin (1999). I will argue that in these books young women are often shown to be disengaged and apolitical, while their male counterparts use language in powerful and political ways, even despite the historical record.

Surviving Rescue: A Feminist Reading of Scott O’Dell’s <Emphasis Type="Italic">Island of the Blue Dolphins</Emphasis>

Scott O’Dell’s Island of the Blue Dolphins tells the archetypal story of the young, virgin, orphan girl who is vulnerable to either debauchery or rescue. That such a girl must succumb to either one or the other is a necessary element of the archetype. In O’Dell’s work—one intended, after all, for children—the heroine is rescued by a paternalistic figure and re-inscribed into the patriarchal world. Yet, in the hands of young readers, Island—part fairytale, part rescue narrative, part feminist parable—becomes a story of independence and survival, despite the heroine’s “rescue” at the end.

Re-mythologizing mathematics through attention to classroom positioning

With our conceptualization of Harré and van Langenhove’s (1999) positioning theory, we draw attention to immanent experience and read transcendent discursive practices through the moment of interaction. We use a series of spatial images as metaphors to analyze the way positioning is conceptualized in current mathematics education literature and the way it may be alternatively conceptualized. This leads us to claim that changing the way mathematics is talked about and changing the stories (or myths) told about mathematics is necessary for efforts to change the way mathematics is done and the way it is taught.

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.

Power Relationships in Rumpelstiltskin: A Textual Comparison of a Traditional and a Reconstructed Fairy Tale

Reconstructed fairy tales provide a different point of view and challenge the assumptions of a common set of values; for that reason, these stories provide a medium in which to examine power relationships in texts by applying a critical multicultural analysis (Botelho & Rudman, forthcoming, 2008, A critical multicultural analysis of children’s literature: Mirrors, windows and doors. New York: Lawrence Erlbaum) to identify and analyze power relations of Rumpelstiltskin (Grimm & Grimm, 1812/1987, New York: Bantam) and Rumpelstiltskin’s Daughter (Stanley, 1997, New York: Morrow Junior Books). Specifically, this study examines how power is exercised on a continuum: domination, collusion, resistance, and agency. Findings indicate that by identifying and questioning text ideologies, critical readers can consider how texts maintain, counteract, or promote alternative systemic power structures.

The Contribution of Trade Books to Early Science Literacy: In and Out of School

Lifelong science literacy begins with attitudes and interests established early in childhood. The use of trade books (i.e., a literary work intended for sale to the general public) in North American school classrooms to support the development of science literacy invites an examination of the quality of science content disseminated to students. A total of 116 trade books were examined to: (a) determine the degree to which science trade books complement expected science knowledge outcomes outlined in school curricula, and (b) compare trade book content to the goals of scientific literacy. Analysis across four science topics, Dinosaurs, Space, Inheritance, and Growth and Life Properties, revealed that this body of children’s literature is inconsistent in its coverage of curricular goals and elements of scientific literacy. Because trade books represent children’s first exposure to science, these shortcomings should be addressed if these books are to be maximally effective in promoting science literacy. Implications for using trade books in the classroom are discussed.

The Role of Doctoral Advisors: A Look at Advising from the Advisor’s Perspective

The doctoral advisor is said to be one of the most important persons—if not the single most critical person—with whom doctoral students will develop a relationship during their doctoral degree programs (Baird 1995). However, we have limited knowledge regarding how doctoral advisors see their roles and responsibilities as advisors. Therefore, through in-depth interviews, we explored the perceptions of 25 exemplary doctoral advisors, who have graduated a large number of doctoral students, about their roles and responsibilities as advisors. We conclude this article with implications for doctoral education.

Amartya Sen’s Capability Approach and the Brokering of Learning Provision for Young Adults

This paper argues that Amartya Sen’s (Development as freedom, New York: Random House, 1999) concept of “capabilities” provides a useful framework for interpreting the brokering of learning provisions that emerged as a key feature of reforms to education and training in Queensland (Australia) for young people. Sen’s capability approach is presented as a way of understanding the place of vocational learning in capability deprivation and enhancement. Methodologically, this account comes from a case study of the reforms’ birthing and trial phases (2000–2006) (Harreveld and Singh 2007, Queensland’s education and training reforms for the future: the journey so far in senior phase learning. Brisbane, Qld: Department of Education, Training and the Arts). Evidence about the brokering of learning provision for young people comes from Queensland’s youth support coordinators, community mentoring scheme, flexible learning services and a work readiness program.

Investigating imagination as a cognitive space for learning mathematics

Our work is inspired by the book Imagining Numbers (particularly the square root of minus fifteen), by Harvard University mathematics professor Barry Mazur (Imagining numbers (particularly the square root of minus fifteen), Farrar, Straus and Giroux, New York, 2003). The work of Mazur led us to question whether the features and steps of Mazur’s re-enactment of the imaginative work of mathematicians could be appropriated pedagogically in a middle-school setting. Our research objectives were to develop the framework of teaching mathematics as a way of imagining and to explore the pedagogical implications of the framework by engaging in an application of it in middle school setting. Findings from our application of the model suggest that the framework presents a novel and important approach to developing mathematical understanding. The model demonstrates in particular the importance of shared visualizations and problem-posing in learning mathematics, as well as imagination as a cognitive space for learning.

National Identity in a Multicultural Society: Malaysian Children’s Literature in English

This article explores the question of how children’s literature reflects national identity in a diverse society. Drawing parallels with Ellison’s Invisible Man, it speculates on how literary omissions and misrepresentations of diverse groups may influence the minds of young readers in their attitudes toward themselves, their nation, and others. In a sampling of the current children’s picture book literature of Malaysia in English, it relates current thinking in multiculturalist and post-colonial theory to the forms of multiculturalism found in these works. It examines this literature’s representations of history, diversity, class, gender, and values to determine who is represented, how they are portrayed, who is excluded, and what values are promoted, exploring what image of national identity this literature projects.

Characteristics of teachers’ choice of examples in and for the mathematics classroom

The main goal of the study reported in our paper is to characterize teachers’ choice of examples in and for the mathematics classroom. Our data is based on 54 lesson observations of five different teachers. Altogether 15 groups of students were observed, three seventh grade, six eighth grade, and six ninth grade classes. The classes varied according to their level—seven classes of top level students and six classes of mixed—average and low level students. In addition, pre and post lesson interviews with the teachers were conducted, and their lesson plans were examined. Data analysis was done in an iterative way, and the categories we explored emerged accordingly. We distinguish between pre-planned and spontaneous examples, and examine their manifestations, as well as the different kinds of underlying considerations teachers employ in making their choices, and the kinds of knowledge they need to draw on. We conclude with a dynamic framework accounting for teachers’ choices and generation of examples in the course of teaching mathematics.

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.

Preschool Teachers’ Shared Beliefs About Appropriate Pedagogy for 4-Year-Olds

The 18 preschool teachers in the study tended to agree that preschool education for 4-year-olds should foremost be fun and engaging, not stressful. Teachers should develop curricula based on children’s interests and everyday lives, and allow children to choose their activities and to direct their own play and exploration at their own pace. The goal of preschool education should be to promote children’s social, emotional, and physical well-being, and not focus so much on academic learning.

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’).