The book, the result of six years of activism and research into school and urban reform in Chicago, begins with a brief overview of neoliberalism. Following this, the first chapter presents Lipman’s central argument: neoliberal urban and education policies, supported and informed by White supremacist ideologies, displace African American and Latino/a working class communities as part of a project to attract urban investment. The second chapter expands upon this claim, linking post-Fordist global capitalism and White supremacy to school reform and urban policies in Chicago. The third chapter presents an analysis of the Chicago Public School Board’s Renaissance 2010 policy document and exposition of how policy actors use it together with federal education policies to further the marketization and disinvestment of public education in Chicago. In the fourth chapter, Lipman critiques mixed income housing and schooling policies and the discourses that underpin both while building further support for her claim that urban reform and school reform are part of the same neoliberal urban initiative. She finds that while framed in egalitarian rhetoric, mixed-income urban development and education policies are implicitly supported by racist discourses that disavow the structural problems facing African American and Latino/a working class communities. Moreover, the recodification of poverty as a cultural problem devalues these communities as spaces of intellectual and cultural production

https://journalhosting.ucalgary.ca/index.php/ajer/article/download/55682/42593

The New Political Economy of Urban Education: Neoliberalism, Race and the Right to the City

Stereotype management is introduced to explain high achievement and resilience among 23 Black mathematics and engineering college students. Characterized as a tactical response to ubiquitous forms of racism and racialized experiences across school and non-school contexts, stereotype management emerged along overlapping paths of racial, gender, and mathematics identity development. Interviews revealed that although stereotype management facilitated success in these domains, the students maintained an intense and perpetual state of awareness that their racial identities and Blackness are undervalued and constantly under assault within mathematics and engineering contexts. With age development and maturity, the students progressed from being preoccupied with attempts to prove stereotypes wrong to adopting more self-defined reasons to achieve. The results suggest that stereotype threat is not deterministic.

“You Would Not Believe What I Have to Go Through to Prove My Intellectual Value!” Stereotype Management Among Academically Successful Black Mathematics and Engineering Students

The National Council of Teachers of Mathematics

The topic of this paper is mathematical modelling or—as it is often, more broadly, called—applications and modelling. This has been an important topic in mathematics education during the last few decades, beginning with Pollak’s survey lecture (New Trends in Mathematics Teaching IV, Paris, pp. 232–248, 1979) at ICME-3, Karlsruhe 1976. By using the term “applications and modelling”, both the products and the processes in the interplay between the real world and mathematics are addressed. In this paper, I will try to summarize some important aspects, in particular, concerning the teaching of applications and modelling.

/pdf/quality-teaching-of-mathematical-modelling-what-do-we-know-215dvamef9.pdf

Quality Teaching of Mathematical Modelling: What Do We Know, What Can We Do?

Word problems are among the most difficult kinds of problems that mathematics learners encounter. Perhaps as a result, they have been the object of a tremendous amount research over the past 50 years. This opening article gives an overview of the research literature on word problem solving, by pointing to a number of major topics, questions, and debates that have dominated the field. After a short introduction, we begin with research that has conceived word problems primarily as problems of comprehension, and we describe the various ways in which this complex comprehension process has been conceived theoretically as well as the empirical evidence supporting different theoretical models. Next we review research that has focused on strategies for actually solving the word problem. Strengths and weaknesses of informal and formal solution strategies—at various levels of learners’ mathematical development (i.e., arithmetic, algebra)—are discussed. Fourth, we address research that thinks of word problems as exercises in complex problem solving, requiring the use of cognitive strategies (heuristics) as well as metacognitive (or self-regulatory) strategies. The fifth section concerns the role of graphical representations in word problem solving. The complex and sometimes surprising results of research on representations—both self-made and externally provided ones—are summarized and discussed. As in many other domains of mathematics learning, word problem solving performance has been shown to be significantly associated with a number of general cognitive resources such as working memory capacity and inhibitory skills. Research focusing on the role of these general cognitive resources is reviewed afterwards. The seventh section discusses research that analyzes the complex relationship between (traditional) word problems and (genuine) mathematical modeling tasks. Generally, this research points to the gap between the artificial word problems learners encounter in their mathematics lessons, on the one hand, and the authentic mathematical modeling situations with which they are confronted in real life, on the other hand. Finally, we review research on the impact of three important elements of the teaching/learning environment on the development of learners’ word problem solving competence: textbooks, software, and teachers. It is shown how each of these three environmental elements may support or hinder the development of learners’ word problem solving competence. With this general overview of international research on the various perspectives on this complex and fascinating kind of mathematical problem, we set the scene for the empirical contributions on word problems that appear in this special issue.

Word problems in mathematics education: a survey

Foreword, Ubiratan D'Ambrosio Acknowledgments Introduction, Brian Greer, Swapna Mukhopadhyay, Sharon Nelson-Barber, and Arthur B. Powell Part I: Foundations and Backgrounds 1. Culture and the Development of Mathematics: An Historical Perspective, Frank J. Swetz 2. New Philosophy of Mathematics: Implications for Mathematics Education, Paul Ernest 3. An Ethnomathematical Perspective on Culturally Responsive Mathematics Education, Swapna Mukhopadhyay, Arthur B. Powell and Marilyn Frankenstein 4. Seeing With Many Eyes: Connections Between Anthropology and Mathematics, Jim Barta and Mary E. Brenner 5. What Mathematics Teachers Need to Know about Culture and Language, Judit Moschkovich and Sharon Nelson-Barber 6. The Politics of Mathematics Education in the United States: Dominant and Counter Agendas, Eric Gutstein 7. Conceptions of Assessment of Mathematical Proficiency and their Implications for Cultural Diversity, Dalton Miller-Jones and Brian Greer Part II: Teaching and Learning 8. Preparing Culturally Responsive Mathematics Teachers, Geneva Gay 9. Mathematics Literacy and Liberation: Reframing Mathematics Education for African American Children, Danny Bernard Martin and Ebony O. McGee 10. Culturally Responsive Mathematics Education in the Algebra Project, Robert Moses, Mary Maxwell West and Frank E. Davis 11. A Two-Way Process for Developing Effective Culturally Based Math: Examples from Math in a Cultural Context, Jerry Lipka, Evelyn Yanez, Dora Andrew-Ihrke and Shehenaz Adam 12. Native-American Analogues to the Cartesian Coordinate System, Ron Eglash 13. Privileging Mathematics and Equity in Teacher Education: Framework, Counter-Resistance Strategies and Reflections from a Latina Mathematics Educator, Julia M. Aguirre 14. Latina Mothers' Perceptions about the Teaching and Learning of Mathematics: Implications for Parental Participation, Marta Civil and Beatriz Quintos 15. Culturally Responsive College Level Mathematics, Mark K. Davis, Shandy Hauk and M. Paul Latiolais Index

Culturally Responsive Mathematics Education

We make the case for introducing fundamental ideas about modelling early, in particular through reconceptualizing word problems that describe real-world situations as exercises in modelling. Further, we argue for modelling as a means of giving children a sense of agency through recognizing the potential of mathematics as a critical tool for analysis of issues important in their lives.

Modelling for Life: Mathematics and Children’s Experience

During the last 20 years, many scholars have argued in various ways that the (traditional) practice of word problems in school mathematics does not foster in students, indeed inhibits, a genuine disposition towards mathematical modelling and applied problem solving. In this article we give a brief review and discussion of this research, including a summary of earlier work culminating in the book by Verschaffel et al. (2000) and with special attention to the more recent empirical work. We begin with presenting the ascertaining studies documenting and illuminating the phenomenon of “suspension of sense-making” when doing school arithmetic word problems. Then we move to studies that have contributed to the explanation of the observed effects. This explanation is followed by a review of some recent design experiments wherein the modelling perspective has been implemented and tested. Afterwards we discuss some recent studies on the difficulties encountered by teachers who try to implement this new perspective into their daily classroom practices. Finally, we discuss a number of educational implications of the research done so far and some challenges for the future of teaching mathematical modelling.

Reconceptualising Word Problems as Exercises in Mathematical Modelling

Introduction A major argument for including verbal problems in the school curriculum has always been their potential role for the development in students of skills in knowing when and how to use their mathematical knowledge for approaching and solving problems in practical situations. The application of mathematics to solve problem situations in the real world, otherwise termed mathematical modeling, can be usefully thought of as a complex process involving a number of phases: understanding the situation described; constructing a mathematical model that describes the essence of those elements and relations embedded in the situation that are relevant; working through the mathematical model to identify what follows from it; interpreting the outcome of the computational work to arrive at a solution to the practical situation that gave rise to the mathematical model; evaluating that interpreted outcome in relation to the original situation; and communicating the interpreted results. As several authors have stressed, this process of solving mathematical application problems has to be considered as cyclic, rather than as a linear progression from givens to goals (Burkhardt, 1994; Greer, 1997; Lesh & Lamon, 1992). For several years, it has been argued by many mathematics educators that – in contrast to the intention mentioned above the current practice of word problems in school mathematics does not at all foster in students a genuine disposition towards mathematical modeling, i.e. treating the text as a description of some real-world situation to be modeled mathematically. According to these authors, by the end of the elementary school many pupils have constructed a set of beliefs and assumptions about doing mathematical application problems, whereby this activity is reduced to the selection and execution of one or a combination of the four arithmetic operations with the numbers given in the problem, without any serious consideration of possible constraints of the realities of the problem context that may jeopardize the appropriateness of their standard models and solutions (Davis, 1989; Greer, 1997; Freudenthal, 1991; Kilpatrick, 1987; Nesher, 1980; Reusser, 1988; Schoenfeld, 1991; Verschaffel & De Corte, 1997a). However, evidence supporting this claim was, until recently, rather scarce, except for some oft-cited examples of striking evidence of "suspension of sensemaking" by students when confronted with the well-known problem "How old is the captain?" (IREM de Grenoble, 1980) or the buses item from the NAEP in the U.S. (Carpenter, Lindquist, Matthews, & Silver, 1983). This chapter first reviews briefly a series of recent studies that provide robust empirical evidence showing the omnipresence and the strenght of the phenomenon of disconnecting word problem solving from the real world. Next it is argued that major features of the current mathematics classroom practice and culture are largely responsible for this phenomenon. Finally, a radically different approach to the teaching of mathematical problem solving, based on the so-called “modeling perspective”, is proposed, and exemplarily illustrated by a brief review of a design experiment. A much more detailed review and discussion of the theoretical and empirical work summarized in this paper, is given in Verschaffel, Greer, and De Corte (2000).

http://dipmat.math.unipa.it/~grim/Jdecorte.PDF

Connecting mathematics problem solving to the real world

(2000). Statistical Thinking and Learning. Mathematical Thinking and Learning: Vol. 2, No. 1-2, pp. 1-9.

Statistical Thinking and Learning

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