Learning from the Eastern and the Western debate: the case of mathematics teacher education

Comparative studies have gained significant influence in the last decades, and school systems of many countries have been revised referring to better results of other countries in international large-scale assessments. Authors of such studies commonly link their interpretations of the results to distinctions between “Eastern” and “Western” cultures, in particular with respect to the consistent and continuing outstanding performance of East Asian learners compared with their Western counterparts. One question is whether the same achievement pattern holds for future teachers and whether similar cultural differences may cause it. International Association for the Evaluation of Educational Achievement’s “Teacher Education and Development Study in Mathematics” (TEDS-M) was the first comparative study that focused on the outcomes of teacher education with standardised testing. In this paper—based on the TEDS-M results—commonalities and differences in the achievement of future teachers from Eastern and Western countries are explored and related to a cultural perspective. Cultural differences between Eastern and Western approaches concerning mathematics, mathematics education and mathematics teachers are analysed with respect to the achievement pattern. The paper closes with reflections on possible consequences concerning the development of teachers’ knowledge and teachers’ expertise in mathematics education.     

Reports: Vanderbilt's New Change School

Abstract

In my experience, students of all races are hungering to be heard, to listen to others, and to have honest conversations about race and racism. I recently taught one course that brought out particularly clearly the challenges of teaching racially volatile material, of integrating personal experience and academic learning, and of negotiating the minefields of identity politics. It taught me the satisfactions of helping students cross racial barriers and of learning from one another.

The class—“Race and Racism”— met once a week. A master's-level course with a few doctoral students, it raised pedagogical issues similar to those I'd found teaching undergraduates. The class consisted of nine black students, of whom one was African (from Ethiopia), one Jamaican (but had spent most of her life in the United States), the rest African American; in addition, it included one Cuban American, one Filipino American, one Russian Jewish immigrant (seven years in this country), and one Japanese student who had only recently arrived in the United States. The remaining 13 students were white and non-Hispanic.     

The New Stony Brook

Abstract

Except for modest sections of a few professional journals, the disciplines of most college faculty offer the world little evidence that most of us spend most of our time teaching. Political scientists not only are representative of college faculty in this regard, but are perhaps a “worst case.” Because higher education has the role of preparing citizens to think critically and act democratically, one would expect that political scientists would provide the world extensive evidence that they teach and that they teach for and about democratic society. The contents of political science, social science, and other disciplinary journals, however, give little hint of either role. They suggest instead that those of us in academe make our living grappling with each other—in print and, increasingly, electronically—over age-old dilemmas of human prospects, current conundrums, and new math models to explain the actions of nations and people.

Truth be told, this is how we gain professional reputations even though most of us gain our bread and butter by teaching. The dichotomy of our ordinary work and our system of professional recognition is only one irony in the professional life of faculty. We also face preparing citizens to think critically and act democratically while we work in bureaucratic, hierarchical, and/or elitist institutions with a contrary contextual curriculum.     

Logic of agreement: Foundations,semantic system and proof theory

In this paper a multi-valued propositional logic — logic of agreement — in terms of its model theory and inference system is presented. This formal system is the natural consequence of a new way to approach concepts as commonsense knowledge, uncertainty and approximate reasoning — the point of view of agreement. Particularly, it is discussed a possible extension of the Classical Theory of Sets based on the idea that, instead of trying to conceptualize sets as “fuzzy” or “vague” entities, it is more adequate to define membership as the result of a partial agreement among a group of individual agents. Furthermore, it is shown that the concept of agreement provides a framework for the development of a formal and sound explanation for concepts (e.g. fuzzy sets) which lack formal semantics. According to the definition of agreement, an individual agent agrees or not with the fact that an object possesses a certain property. A clear distinction is then established, between an individual agent — to whom deciding whether an element belongs to a set is just a yes or no matter — and a commonsensical agent — the one who interprets the knowledge shared by a certain group of people. Finally, the logic of agreement is presented and discussed. As it is assumed the existence of several individual agents, the semantic system is based on the perspective that each individual agent defines her/his own conceptualization of reality. So the semantics of the logic of agreement can be seen as being similar to a semantics of possible worlds, one for each individual agent. The proof theory is an extension of a natural deduction system, using supported formulas and incorporating only inference rules. Moreover, the soundness and completeness of the logic of agreement are also presented.     

People of my side ≈ people of the other side

In this philosophical inquiry into the foundations of Xavante mathematical thought, numbers emerge as categories structured by social praxis in central Brazil. Clans, moieties, age-sets, and specific kin relations can be viewed as conventional symbols, or numerals, representing essential constituencies of the Xavante socionumerical system. As in other Gé-speaking societies of the Brazilian Amazon, Xavante numbers catalyze a set of presuppositions about dialectical mathematical systems whose rationality is informed by the pervasive dualism that governs social interaction for an estimated 8,000 Xavante today. The binary nature of this numerical system is a product of an omnipresent dialectical view of the world, always oscillating between an “us” and a “them”—or people of my side ≈ people of the other side. Accordingly, a unit is defined as the union of 2 fundamental parts, and numerical place value assumes the significance of reciprocal social relationships. The dialectical association of beings, human or not, material or symbolic, within the dynamism of Xavante dualism synthesizes these and other key ideas about the philosophy of Gě mathematical thought.     

Competing Goods: Ethical Issues in the Scholarship of Teaching and Learning

Throughout the industrialized world, governments are attempting to provide greater social equality through the expansion of access to edcation. In so doing, they have nurtured attitudes of “entitlement” to good jobs among those of high educational qualifications. Unhappily, no economic system appears capable of fully keeping pace with this new inflation in employment expetations of younger workers. Simply put, there are not enough good jobs for everyone who wants one and whose educational credentials say he or she deserves one. Perversity, then, the well-intentioned social and educational policies of the developed nations are engendering more and more frustration and low morale among underemployed workers. Underemployment—the chronic under-utilization of education, skills, and other human resources—thus becomes a chronic societal contradiction in advanced nations.

There is growing evidence that this disjunction between educational opportunity and upper-grade jobs it beginning to create a series of potentially grave social, political, and economic problems. In last month's issue, I examined some of these new phenomena, such as increasing class conflict, Job dissatisfaction and credentialism, decreasing economic productivity, and dwindilng public support of education and its institutions. These problems have led to recognition in many nations that something must be done to bridge the gap between expectations and realities in industrial society In particular, it is frequently argued that ways must be found to provide greater complementarity between the learning and work aspects of life in order to realize such potentially conflictiong goals as extended opportunities for individual growth; increased social and economic productivity; and the provision of greater social justice, liberty, and equality. But how does society begin to develop policies for such a delicate tightrope act?     

How to Choose the Right Dean for Your University: Remembering the Five P's of Deanship

Abstract

In this column, as in many other print and electronic forums, information technology (IT) is discussed at length in terms of applications for students, faculty, staff, and administrators; in terms of hardware, software, and infrastructure; and in terms of strategic planning, budgeting, and fund-raising. There is only one person on every campus who must constantly assess and balance all these factors and constituencies: the president. However, a presidential perspective—the view from 30,000 feet—does not appear often in discussions about IT in higher education. This column shares my recent conversation on the subject with Carol A. Cartwright, president of Kent State University, a CEO to whom I am privileged to have unique access.     

Student Service Expenditures Matter

“Most of the people here are not wild experimenters—they are just tired of traditional education and its limitations”.     

The articulation of symbol and mediation in mathematics education

In this paper we include topics which we consider are relevant building blocks to design a theory of mathematics education. In doing so, we introduce a pretheory consisting of a set of interdisciplinary ideas which lead to an understanding of what occurs in the “central nervous system”—our metaphor for the classroom and eventually in more global settings. In particular we highlight the crucial role of representations, symbols viewed from an evolutionary perspective and mathematics as symbolic technology in which representations are embedded and executable.     

Psychometric Re‐evaluation of the Image of Science and Scientists Scale (ISSS)

An enduring concern among science education researchers is the “swing away from science” ( Osborne. 2003 ). One of their central dilemmas is to identify—or construct—a valid outcome measure that could assess curricular effectiveness, and predict students' choices of science courses, university majors, or careers in science. Many instruments have been created and variably evaluated. The primary purpose of this paper was to re‐evaluate the psychometric properties of the Image of Science and Scientists Scale (ISSS) ( Krajkovich 1978 ). In the current study, confirmatory factor analysis (CFA) was used to examine the dimensionality of the 29‐item ISSS, which was administered to 531 middle school students in three San Antonio. Texas school districts at the beginning of the 2004–2005 school year. The results failed to confirm the presumed 1‐factor structure of the ISSS. but instead showed a 3‐factor structure with only marginal fit with the data, even after removal of 12 inadequate items. The three dimensions were “Positive Images of Scientists” (5 items). “Negative Images of Scientists” (9 items), and “Science Avocation” (3 items). The results do not support use of the original form of the ISSS for measuring “attitudes toward science,”“images of scientists. “or “scientific attitudes. “Shortening the scale from 29 to 17 items makes it more feasible to use in a classroom setting. Determining whether the three dimensions identified in our analysis. “Positive Images of Scientists. ““Negative Images of Scientists. “and “Science Avocation “contain useful assessments of middle school student impressions and attitudes will require independent investigation in other samples.     

The decorative impulse: ethnomathematics and Tlingit basketry

Pattern is a key element in both the esthetics of design and mathematics, one definition of which is “the study of all possible patterns”. Thus, the geometric patterns that adorn cultural artifacts manifest mathematical thinking in the artisans who create them, albeit their lack of “formal” mathematics learning. In describing human constructions, Franz Boas affirmed that people, regardless of their economic conditions, always have been engaged in activities that reveal their deeply held esthetic sense. The Tlingit Indians from Sitka, Alaska, are known for their artistic endeavors. Art aficionados and museum collectors revere their baskets and other artifacts. Taking the approach of ethnomathematics, I report my analysis of the complex geometrical patterns in Tlingit basketry.     

Computational Literacy and “The Big Picture” Concerning Computers in Mathematics Education

This article develops some ideas concerning the “big picture” of how using computers might fundamentally change learning, with an emphasis on mathematics (and, more generally, STEM education). I develop the big-picture model of computation as a new literacy in some detail and with concrete examples of sixth grade students learning the mathematics of motion. The principles that define computational literacy also serve as an analytical framework to examine competitive big pictures, and I use them to consider the plausibility, power, and limitations of other important contemporary trends in computationally centered education, notably computational thinking and coding as a social movement. While both of these trends have much to recommend them, my analysis uncovers some implausible assumptions and counterproductive elements of those trends. I close my essay with some more practical and action-oriented advice to mathematics educators on how best to orient to the long-term trajectory (big picture) of improving mathematics education with computation.     

Correspondence and canonical analysis of relational data

Correspondence analysis, a data analytic technique used to study two‐way cross‐classifications, is applied to social relational data. Such data are frequently termed “sociometric” or “network” data. The method allows one to model forms of relational data and types of empirical relationships not easily analyzed using either standard social network methods or common scaling or clustering techniques. In particular, correspondence analysis allows one to model:

—two‐mode networks (rows and columns of a sociomatrix refer to different objects)

—valued relations (e.g. counts, ratings, or frequencies).

In general, the technique provides scale values for row and column units, visual presentation of relationships among rows and columns, and criteria for assessing “dimensionality” or graphical complexity of the data and goodness‐of‐fit to particular models. Correspondence analysis has recently been the subject of research by Goodman, Haberman, and Gilula, who have termed their approach to the problem “canonical analysis” to reflect its similarity to canonical correlation analysis of continuous multivariate data. This generalization links the technique to more standard categorical data analysis models, and provides a much‐needed statistical justificatioa

We review both correspondence and canonical analysis, and present these ideas by analyzing relational data on the 1980 monetary donations from corporations to nonprofit organizations in the Minneapolis St. Paul metropolitan area. We also show how these techniques are related to dyadic independence models, first introduced by Holland, Leinhardt, Fienberg, and Wasserman in the early 1980's. The highlight of this paper is the relationship between correspondence and canonical analysis, and these dyadic independence models, which are designed specifically for relational data. The paper concludes with a discussion of this relationship, and some data analyses that illustrate the fart that correspondence analysis models can be used as approximate dyadic independence models.     

Trends in the evolution of models & modeling perspectives on mathematical learning and problem solving

In this paper we briefly outline the models and modelling (M&M) perspective of mathematical thinking and learning relevant for the 21st century. Models and modeling (M&M) research often investigates the nature of understandings and abilities that are needed in order for students to be able to use what they have (presumably) learned in the classroom in “real life” situations beyond school Nonetheless, M&M perspectives evolved out of research on concept development more than research on problem solving; and, rather than being preoccupied with the kind of word problems emphasized in textbooks and standardized tests, we focus on (simulations of) problem solving “in the wild.” Also, we give special attention to the fact that, in a technology-basedage of information, significant changes are occurring in the kinds of “mathematical thinking” that is coming to be needed in the everyday lives of ordinary people in the 21^st century—as well as in the lives of productive people in future-oriented fields that are heavy users of mathematics, science, and technology.     

The Anatomy of Academic Discontent

Abstract

“Take a few minutes to think about your personal journey as a graduate student, on your way toward your professional goals as a teaching scholar. How would you describe the process you've been going through? You may want to capture this visually or with words—whichever is helpful for you.”     

How We Live,How We Love: Double Fault by Judith Chemaik and Party Party; Girlfriends,by Ronni Sandroff

Abstract

As anyone who has read anything about American higher education in the last year or two must know, “political correctness” is one of the most hotly debated topics on campuses throughout the country and at the annual meetings of many of the various learned societies. In some circles, the battle lines are clearly drawn and the DMZ precariously narrow - if it exists at all. But because the smoke from bomb shells has clouded the field, it is difficult to tell whether things are as bad as recent reports in academic journals and the popular press suggest. Only time will tell.     

The ostensive dimension through the lenses of two didactic approaches

The paper presents how two different theories—the APC-space and the ATD—can frame in a complementary way the semiotic (or ostensive) dimension of mathematical activity in the way they approach teaching and learning phenomena. The two perspectives coincide in the same subject: the importance given to ostensive objects (gestures, discourses, written symbols, etc.) not only as signs but also as essential tools of mathematical practices. On the one hand, APC-space starts from a general semiotic analysis in terms of “semiotic bundles” that is to be integrated into a more specific epistemological analysis of mathematical activity. On the other hand, ATD proposes a general model of mathematical knowledge and practice in terms of “praxeologies” that has to include a more specific analysis of the role of ostensive objects in the development of mathematical activities in the classroom. The articulation of both theoretical perspectives is proposed as a contribution to the development of suitable frames for Networking Theories in mathematics education.     

Something out of nothing: a Bayesian learning computational model for the social construction of value

ABSTRACT

This article develops a formalism for the social construction of value. Using a model based on Bayesian agents, it demonstrates how “something” arises out of “nothing” via the emergence of durable value conventions and shows how the developed framework can be used to investigate socially constructed valuations under a variety of circumstances. The resulting analysis clarifies why assumptions that collectives will converge upon the “intrinsic” (i.e., non-socially originating) value of an object (e.g., market efficiency) may not hold for mixed social and non-social valuation regimes, explains the dependency of socially constructed valuations on early accidents, demonstrates the effects of confident actors on constructed values, and identifies the production of time-dependent ratcheting effects from the interaction of bubbles with value conventions.