Work In Mathematics Education Research Articles

In the Shadow of the Palms: The Selected Works of David Eugene Smith

In the Shadow of the Palms: The Selected Works of David Eugene Smith

Mathematical knowledge for teaching as a didactic praxeology

It is widely acknowledged that teachers' work has both practical and theoretical dimensions, both praxis and logos, and that teacher education should address both dimensions. However, as argued in this article, existing discourses for describing the mathematical knowledge of teachers and what it takes to become competent in it are not always clear to what extent these discourses address knowledge about the practices of mathematics teaching or theories that provide arguments for the practices. Specifically, I argue for the coordination of the framework of mathematical knowledge for teaching (MKT) with the analytical distinction of logos and praxis combined in teaching practices. Moreover, I have backed this argument with examples of the proposed categories of the adjusted framework from the existing body of work in mathematics education. Each category of the proposed framework, whether concerning a teaching method or a theoretical consideration, was indeed exemplified by some concept, approach, or perspective from the field of mathematics education. The framework, I believe, would prove useful in engaging mathematics teacher education discursively, for instance, in analyzing teacher education materials to determine the extent to which they offer mere methods, theoretical arguments, or a combination of both.

Exploring undergraduate thesis manuscript assessment feedback

AbstractThe present case study explores the assessment practice of two examiners from different academic backgrounds on an undergraduate thesis work in mathematics education. Reflection notes and feedback from two instances of a thesis‐writing process are interrogated using a framework based on a semiotics perspective to meaning‐making. It is shown that the examiners utilize aspects that are ‘immediate and non‐contested’ to successively make accessible that which is ‘withdrawn yet to be revealed.’ In this process, varied interventional approaches are observed to support desirable aspects of teacher professional knowledge including critical‐analytical disposition. The study also highlights knowledge integration for teaching, scientific disposition, collaboration, and knowledge transformation as some of the desirable aspects of teacher professional knowledge. The findings indicate that knowledge integration and transformation remain an issue of concern for pre‐service teachers. This raises the question of how desirable traits for a teacher‐as‐a researcher can be promoted within the context of thesis work.

Author Correction: Does a flipped classroom model work in mathematics education? A meta-analysis

Author Correction: Does a flipped classroom model work in mathematics education? A meta-analysis

Does a flipped classroom model work in mathematics education? A meta-analysis

Does a flipped classroom model work in mathematics education? A meta-analysis

Academic Motherhood in Mathematics Education during COVID-19: Breaking the Silence and Shifting the Discourse

Despite decades of social change and institutional reform, the academic gender gap continues to exist in many countries around the world and disproportionately affects women with children. Early indicators suggest that COVID-19 will widen this gap and exacerbate issues academic mothers face. In this essay we seek to raise awareness to the challenges and tensions academic mothers in mathematics education face both outside of and during a pandemic. We use existing literature on academic motherhood to make sense of our lived experiences, working to reframe pieces that are so often viewed as deficits to assets for our work in mathematics education. We hope that this will bring visibility to the invisible ways our identities as mothers inform our work as mathematics teacher educators and researchers. We conclude this essay with a call for the university-based mathematics education community to break the silence around the inequities associated with academic motherhood in our field and to shift the discourse from deficits of academic mothers to asset orientated views.

Thoughts on the Orientation of Mathematics Education in Colleges and Universities

Mathematics is a science of structure, order, and relationship. It evolved from the basic practices of counting, measuring, and describing the shape of objects. It involves logical reasoning and quantity calculation. Since the 17th century, mathematics has been an indispensable aid to physical science and technology, and is considered to be the basic language of science. In the mathematics education work of colleges and universities, accurately positioning the education direction and improving the classroom teaching mode can effectively shape the students’ mathematical thinking, stimulate students’ innovative consciousness, and strengthen students’ ability to solve problems. This article will focus on the classroom teaching mode for the university mathematics education orientation, in order to provide theoretical reference for relevant teaching and research personnel.

In the workplace mathematics does not announce itself: towards overcoming the hiatus between mathematics education and work

Preparing students for their lives beyond schooling appears to be a universal goal of formal education. Much has been done to make mathematics education more “realistic,” but such activities nevertheless generally remain within the institutional norms of education. In this article, we assume that pedagogic relations are also an integral part of working life and draw on Bernstein’s work to address their significant features in this context. However, unlike participation in formal mathematics education, where the discipline is central, workers are likely to be confronted by, and need to reconcile, a range of other valued workplace discourses, both epistemic and social/cultural in nature. How might mathematics education work towards overcoming the hiatus between these two very different institutional settings? This article will argue that the skills of recontextualisation, central to teachers’ work, should be integral to the mathematics education of all future workers. It will consider theoretical perspectives on pedagogic discourse and the consequences of diverse knowledge structures at work, with implications for general and vocational mathematics education.

Alienation in mathematics education: critique and development of neo-Vygotskian perspectives

This paper aims to critique and develop neo-Vygotskian work in mathematics education from (i) within the Vygotskian and activity theoretic tradition, and where necessary from (ii) a Bourdieusian perspective. First, I critique Roth and Radford’s (2011) version of Cultural-historical Activity Theory, suggesting that a classroom episode presented as developmental might be seen as a process of alienation. I trace this to the institutional structure of schooling, in which curriculum and pedagogy are alienated from the learner’s everyday sense. Next, I examine and critique the Vygotskian ‘Funds of Knowledge’ approach to critical mathematics education, which seeks to overcome alienation by subjecting the curriculum to the needs of the poor communities the school serves. Here, the critical point on alienation in the Vygotskian approach is better argued in Bourdieu’s perspective on educational institutions as reproductive of class domination. Finally, the paper discusses the extent to which these critiques pertain to Vygotskian activity theory in general or only to these versions in particular and draws implications for the development of a critical mathematics education perspective in a synthesis of perspectives from Vygotsky and Bourdieu.

Research Problems in Community College Mathematics Education: Testing the Boundaries of K-12 Research

The purpose of this commentary is to articulate the need to investigate problems of mathematics instruction at community colleges. We briefly describe some features of this often-ignored institution and the current status of research. We also make an argument for how investigations of instruction in this setting can both advance our understanding of this particular context and give practitioners tools to deal with pressures from policymakers to show short-term results. This work is the result of a collaborative effort between community college practitioners and researchers, responding to the needs of their work in mathematics education.

Teaching Mathematics with Women in Mind

W e both work at institutions that have been awarded NSF ADVANCE grants. ADVANCE is a program that aims to develop systematic approaches to supporting academic women in science, technology, engineering, and mathematics (STEM) disciplines. ADVANCE looks at universities and asks, “What support can universities provide to help women faculty members thrive in STEM?” We took that question to heart and asked ourselves, “What support can we provide in our undergraduate mathematics classrooms to help women students thrive in mathematics?” We decided to take a hard look in the mirror. This meant examining our own approaches to teaching and confronting the limits of our own education and preparation. Trained as mathematicians, we found our preparation for understanding how gender affects undergraduate mathematics classroom environments lacking. We turned to resources from psychology, sociology, and women’s and gender studies to better understand our own teaching. Our personal goal—it might not be yours—is to understand how gender bias influences our mathematics teaching and to explore concrete steps we can take to reduce the effects of that bias. We’ve asked ourselves why our classrooms should look different from the classrooms in which we were undergraduate students. After all, we are both women who were successful undergraduate mathematics majors and went on to earn Ph.D.’s in mathematics. Call it survivor’s guilt: we both know that we were able to “fit in” in mathematics when many other women could not. We could say, “Other women should do what we did and learn to fit in.” Instead, we are asking, “What should we do differently as mathematics instructors so that more women, who wouldn’t otherwise be successful, will be and will persist in the study of our subject?” We have to make a few stipulations. First, we believe teaching can be taught. Though trained as applied mathematicians, we both now do research in and teach mathematics education. Our work in mathematics education is guided by the belief that great teaching can be taught. This is contrary to what popular culture has us believe: often teachers are characterized as “born to teach.” Sometimes great teachers believe it too. There is something to that—in the absence of preparation for teaching, there are those who will become better because they experiment, reflect, and revise their own teaching. They do this on their own and end up keeping the best of their experiments and learning from the ineffective ones. We don’t mean to diminish the greatness of those who have figured out how to become great teachers on their own; we want to understand what they do in classrooms and teach others to do the same. As we explore changes to make in a classroom to be responsive to gender, we are thinking of explicit teaching choices. Second, we believe there is inherent good in giving more people access to undergraduate mathematics. This is a value we stipulate. You might not share that value, but if that’s the case, then you and we are aiming at different things. We’ve thought a lot about what kinds of good come from access to mathematics, and we believe that what might resonate most with our students is the access to fulfilling, higher-paying jobs that comes with advanced technological knowledge. Some may argue that this is not why we teach mathematics, but it Jessica M. Deshler is assistant professor of mathematics at West Virginia University. Her email address is deshler@ math.wvu.edu.

Establishing Mathematics Education as an Academic Field: A Constructive Odyssey

Through my work in mathematics education, I have come to the realization that constituting mathematics education as an academic field entails constructing models of mathematical minds that are constructed by students in the context of mathematics teaching beginning in early childhood and proceeding onward throughout the years of schooling. In this article, I recount events that have led me to this realization.

(Developing) Teacher Discourse Moves: A Framework for Professional Development

We describe our ongoing efforts to design materials for supporting secondary mathematics teachers in using a set of Teacher Discourse Moves purposefully in order to develop classroom discourse that is both productive and powerful for students' learning. We focus on secondary mathematics classroom discourse because mathematical language and meanings get increasingly complex beginning in middle school, and most discourse-related work in mathematics education has focused on elementary school classrooms. We make explicit both the concepts we use and the translation of these theoretical concepts into ideas useful for practice. This article contributes to ongoing discussions about making visible the work of developing research-based professional development materials.

Analyzing effective communication in mathematics group work: The role of visual mediators and technical terms

Analyzing and designing productive group work and effective communication constitute ongoing research interests in mathematics education. In this article we contribute to this research by using and developing a newly introduced analytical approach for examining effective communication within group work in mathematics education. By using data from 12 to 13-year old students playing a dice game as well as from a group of university students working with a proof by induction, the article shows how the link between visual mediators and technical terms is crucial in students’ attempts to communicate effectively. The critical evaluation of visual mediators and technical terms, and of links between them, is useful for researchers interested in analyzing effective communication and designing environments providing opportunities for students to learn mathematics.

A Conversation With Uri Treisman

Dr. Uri Treisman, professor of mathematics and public affairs at The University of Texas at Austin and the director of the Charles A. Dana Center, has deep and active roots in mathematics and mathematics education. Dr. Treisman is well known for his early work at the University of California at Berkeley, where he developed the Calculus Workshop Model in response to differential outcomes in Calculus among African American, white, and Asian students. His continuing work in mathematics education, particularly his impact on equity in the field and his current work focusing on mathematics teaching and learning in community colleges was reflected in his remarks on September 29, 2012, during the annual Program in Mathematics Colloquium Series. Dr. Treisman had initially planned to give a talk on the technical aspects of scaling educational innovations, but seeing that the audience was composed largely of young teachers and teachers-to-be, he instead gave an impromptu talk on teaching mathematics. This is an edited version of those remarks. —Ed.

A Critical Examination of Learning Disabilities in Mathematics: Applying the Lens of Ableism

Introduction Background and Rationale Over half of the students who receive special education services are labeled as learning disabled (LD); they comprise approximately five to six percent of the entire K-12 student population (Hehir, 2005). Most students are labeled LD in reading; however, approximately twenty percent are either labeled as LD in mathematics or LD in both reading and mathematics (G. Williamson, personal communication on March 9, 2006). Therefore, it is likely that one in every one hundred students in American public schools carries the label of LD in mathematics. Many may perceive one percent to be a small and insignificant slice of the K-12 population and may wonder why I would choose to focus my on such a small group of students. My response is three-fold. First, federal legislation such as the No Child Left Behind Act (NCLB, 2001) and the Individuals with Disabilities in Education Act (IDEA, 2004) require us to pay attention to the quality of all students' education and (probably more so) their academic performance. Second, not much literature exists in mathematics education on this topic. As a field, we have published mathematics education work relating to race, gender, and socioeconomic status, but on the subgroup of special education, particularly students carrying the label of LD in mathematics, we remain largely silent. Lastly, the social, emotional, educational and political realities for those involved--the labeled student him/herself, his/her parents, the labeled student's general education mathematics teacher as well as his/her special education teacher, the administrators and in fact the labeled student's entire school--are extremely significant. I am deeply concerned with issues of equity and the power differentials inherent in our society, and I want our schools to seek ways to eradicate practices in mathematics education that privilege some at the expense of others. Theoretical Perspective In this article, I apply a critical pedagogy (Kincheloe & McLaren, 1994; Freire, 1997) perspective looking through the lens of ableism (Rauscher & McClintock, 1977; Hehir, 2005) to examine current educational policy, research and practice regarding the identification of and labeling of students as LD in mathematics. Kincheloe and McLaren (1994, p. 453) state, inquiry that aspires to the name critical must be connected to an to confront the injustice of a particular society or public sphere within the society. A critical pedagogy perspective, then, seeks to uncover hegemonic (power) relations, ideologies, and inequities in education, critique instrumental rationality, and inspire a movement for toward social justice. The following are assumptions from a critical pedagogy perspective that are pertinent to this article: 1. Acknowledging schooling as a form of cultural politics that endorses only particular forms of knowledge, thus creating a dominant group of successful knowers and others (Brantlinger, 1997, 2001); 2. Challenging the traditional view of education as a neutral and just process, and instead, recognizing it serves as an oppressive social structure (Freire, 1997) for some students; 3. Believing that self and social empowerment should precede mastery of technical skills tied to the marketplace and that educators should attempt to see and experience education from the perspective of those who are not dominant and work towards positive social change (Pasco, 2003, p. 5). Hehir (2005) discusses how the ideology of ableism negatively affects the education of children labeled with disabilities and urges educators and policymakers to focus on making just and equitable decisions about the policies and practices that support the educational, emotional and social progress of individual children. In his book on eliminating ableism, he utilizes (and in this paper I adopt) the following definition for ableism: Ableism is a pervasive system of discrimination and exclusion that oppresses people who are perceived to have cognitive, emotional, and/or physical disabilities. …

Unpacking Mathematics for Teaching: A Study of Preservice Elementary Teachers’ Evolving Mathematical Understandings and Beliefs

This study examined the mathematical understandings and beliefs held by preservice elementary teachers in a mathematics methods course taken as part of a one year teacher certification program, and re-examined these characteristics at the end of the course. The notion of ‘understanding mathematics for teaching’ was examined in a way that might begin to support the work of mathematics educators working with such preservice teacher candidates. Preservice teacher beliefs about what is important in mathematics learning and therefore the teaching of it are examined along with mathematics understanding at both procedural and conceptual levels. The goal is to shed some light on how initial understanding and beliefs about mathematics teaching co-exist, and how these might develop during a preservice teacher education program. A preliminary model designed to promote participant self-reflection is suggested.

Reflections on Math Reforms in the U.S.

Understanding how various aspects of mathematics education work together is necessary if reform efforts are to succeed, Ms. Newton argues. She compares U.S. and Chinese mathematics education to provide perspectives that might further such understanding. ********** IN TRADITIONAL Chinese medicine, a key maxim is Bing Yao Zhi Gen, which literally means, To cure a disease (you) must cure the underlying cause. am reminded of this principle whenever reflect on K-12 math education reform in the U.S. President Bush's 2006 State of the Union Address prompted yet another wave of debate on what actions the government should take in order to improve math and science education so that the U.S. can sustain its economic competitiveness internationally. What has not been brought to the forefront, however, is that cultural beliefs about mathematics and how it should be taught will profoundly influence how reform efforts, such as new curricula or teaching methods, will work themselves out in practice. As someone who was educated in mainland China and has subsequently studied math teaching and learning in the U.S., have been struck by the many differences in the beliefs surrounding math instruction between the two countries. hope my reflections on what have seen can help highlight some key issues identified in the mathematics reform literature and provide a lens for examining how mathematics instruction functions in the U.S. and China. CULTURAL BELIEFS AND ATTITUDES When it comes to attitudes about who can learn math, it is common in the U.S. to give more weight to ability than to effort. (1) It is widely acceptable for anyone in the U.S. to say, I just can't do math. Since ability is widely believed to be fixed and uncontrollable, attributing success or failure to high or low ability has an important impact on motivation. Presumably, inasmuch as ability is seen as fixed and not subject to individual control, ascribing failure to low ability leads students to give up. Effort, on the other hand, is clearly within an individual's control, and so ascribing success in learning mathematics to effort leads students to sustain their hope and increase their persistence. Unlike the U.S., some societies put greater emphasis on effort than on ability. (2) That is certainly the case with China, as can attest. Though English was the only school subject that was passionate about when growing up, was nonetheless pushed by my engineer father into being a math and science major in high school. He often said, If you aren't good at math, physics, and chemistry, how can you make a living? What are you going to do? My father's attitude toward the importance of math and science was typical of the value placed on such subjects by Chinese society in general. In my high school, only about 15% of the students were on the liberal arts and humanities track, while the rest of us pursued math and science. Persistent effort was highly regarded and encouraged. Our teachers liked to emphasize that, if you do not think you can grasp a concept as fast as others, then you must work harder or start earlier (e.g., preview the textbook before the class when a new concept will be taught). People's beliefs about what mathematics is also seem to differ. In Western thinking, mathematics is often described as the most certain branch of human knowledge. In mathematics, people in the West will say, it is easy to distinguish right from wrong. (3) Such a heavy emphasis on truth and correctness in mathematics contrasts sharply with how mathematics is treated in some high-achieving Asian countries. For instance, the Third International Mathematics and Science Study (TIMSS) revealed that Japanese math teachers emphasize developing conceptual understanding rather than simply obtaining correct answers. (4) The Singapore math curriculum at both the elementary and secondary levels clearly specifies that the essence of school mathematics is problem solving. …

The Rationality Debate: Application of Cognitive Psychology to Mathematics Education

Research in mathematics education usually attempts to look into students’ learning and other mental processes. It could therefore be expected to build on knowledge acquired within the academic discipline of cognitive psychology. Our aim in this paper is to show how some recent developments in cognitive psychology can help interpret empirical results from mathematics education. In particular, we will be looking into the heuristics-and-biases research by Kahneman and Tversky, the alternative views by Gigerenzer et al., and the more recent dual-process theory that has come to play a central role in interpreting this research. We first introduce the relevant background from cognitive psychology and survey its connections to previous work in mathematics education; then we apply this theoretical framework for re-interpreting previously-published empirical data from mathematics education research. We conclude with a discussion of potential theoretical and practical benefits of such synthesis.

What Could be More Practical than Good Research?

These seem to be very special times for mathematics education. The public interest in the topic has never been greater. Probably the most prominent among the occurrences that occasioned this recent leap in popularity are international comparative studies such as TIMSS and PISA. The fact that, in spite of the ongoing efforts toward reform in mathematics education, many countries found the results of the international measurements of their students’ achievements rather disappointing led the ICME 10 Program Committee to create the Survey Team on Relations between Mathematics Education Research and Practice. The team, coordinated by the author of this talk, and including Aline Robert from France, Ole Skovsmose from Denmark, Yoshihiko Hashimoto from Japan, and Gelsa Knijnik from Brazil, was invited to reflect on the question of how research has been informing the practice of mathematics education over the last decade. Following the invitation, the Survey Team turned to the members of the mathematics education community asking them to answer three queries about their own work: (1) How would you describe the essence of your work in mathematics education over the last 5 years or so? (2) During this period, to what extent was your work stirred and influenced by the current state of mathematics education in your country and/or in the world? (3) Do you think that the work done by you and by your colleagues over the last five years or so had, or is going to have, an actual impact on the practice of mathematics education? Analysis of the 74 responses received from all over the world revealed several interesting trends. This article is the text of the ICME plenary address in which the author presented an “executive summary” of the findings.