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1.
Martin A. Simon 《Educational Studies in Mathematics》2017,94(2):117-137
Mathematical understanding continues to be one of the major goals of mathematics education. However, what is meant by “mathematical understanding” is underspecified. How can we operationalize the idea of mathematical understanding in research? In this article, I propose particular specifications of the terms mathematical concept and mathematical conception so that they may serve as useful constructs for mathematics education research. I discuss the theoretical basis of the constructs, and I examine the usefulness of these constructs in research and instruction, challenges involved in their use, and ideas derived from our experience using them in research projects. Finally, I provide several examples of articulated mathematical concepts. 相似文献
2.
Alan J. Bishop 《Educational Studies in Mathematics》1980,11(3):257-269
This paper examines the interface between two sets of psychological constructs. One set concerns the visual/spatial field and the other, mathematics education. But rather than do a conceptual analysis or report an empirical investigation, I have chosen to review the different research emphases which have contributed to knowledge in this area, and to describe what they can, or cannot, offer the mathematics educator. I show that this literature does contain many potentially fruitful ideas and approaches which we in mathematics education can use either in the classroom, or to guide our own research efforts. Also it will be seen that the goals of research psychologists may lead them in a direction which is away from our concerns, and that therefore we must exercise caution and keen judgement in selecting those ideas and approaches which will enable us to develop our own field. 相似文献
3.
Dionne I. Cross 《Journal of Mathematics Teacher Education》2009,12(5):325-346
This collective case study reports on an investigation into the relationship between mathematics teachers’ beliefs and their
classroom practices, namely, how they organized their classroom activities, interacted with their students, and assessed their
students’ learning. Additionally, the study examined the pervasiveness of their beliefs in the face of efforts to incorporate
reform-oriented classroom materials and instructional strategies. The participants were five high school teachers of ninth-grade
algebra at different stages in their teaching career. The qualitative analysis of the data revealed that in general beliefs
were very influential on the teachers’ daily pedagogical decisions and that their beliefs about the nature of mathematics
served as a primary source of their beliefs about pedagogy and student learning. Findings from the analysis concur with previous
studies in this area that reveal a clear relationship between these constructs. In addition, the results provide useful insights
for the mathematics education community as it shows the diversity among the inservice teachers’ beliefs (presented as hypothesized
belief models), the role and influence of beliefs about the nature of mathematics on the belief structure and how the teachers
designed their instructional practices to reflect these beliefs. The article concludes with a discussion of implications of
teacher education. 相似文献
4.
Candia Morgan 《Educational Studies in Mathematics》2007,64(2):239-242
What is the relationship between research into multilingualism and research concerned more generally with language and communication in mathematics education? Diversity in linguistic practices is universal in modern society and poses problems for teaching and learning even in apparently monolingual contexts. Research in multilingualism and mathematics education offers constructs and insights that can inform research and pedagogy more widely. 相似文献
5.
Mathematical biography and key rhetoric 总被引：1，自引：0，他引：1
Raimo Kaasila 《Educational Studies in Mathematics》2007,66(3):373-384
The intention of this article is to consider the use of narrative and rhetorical inquiry as research methods. I construct
a mathematical biography of one elementary teacher trainee, Sirpa, who had performed well in her advanced mathematics course
in upper secondary school. I describe her development as a mathematics teacher during teacher education from her second-year
methods course and teaching practice to fourth-year teaching practice. Narrative inquiry is more than a case study: Sirpa’s
mathematical biography is a story that describes how she constructs her mathematical identity. I also analysed the key rhetoric
that Sirpa used in her talk, key rhetoric here referring to the strategy by which she constructed continuity and coherence. 相似文献
6.
Lynn Liao Hodge 《The Urban Review》2006,38(5):373-385
In this paper, I reflect on equity research in order to describe a perspective on the mathematics classroom as a non-neutral place where issues of power and identity play out in teaching and learning processes. This view of the mathematics classroom takes seriously issues of equity in the form of power and what becomes constituted as legitimate mathematics while attending to the out-of-school practices in which students engage. This orientation and its related issues are significant in that they provide an alternative perspective on investigating equity in mathematics classrooms that is in contrast to efforts that focus specifically on comparing standardized test scores of specific groups based solely upon racial classifications.Lynn Liao Hodge is an assistant professor in mathematics education. Her research interests include issues of equity and identity in mathematics education and how classroom practices create opportunities for students to develop both an appreciation and a deep understanding of mathematics. Additionally, she is interested in investigating experiences that support the increased participation of women and minorities in mathematics, science, and engineering related professions. Address correspondence to Lynn Liao Hodge, Department of Theory and Practice in Teacher Education, The University of Tennessee, Knoxville, TN 37996-3442, USA; e-mail: lhodge4@utk.edu 相似文献
7.
What is the place of social theory in mathematics education research, and what is it for? This special issue of Educational Studies in Mathematics offers insights on what could be the role of some sociological theories in a field that has historically privileged learning theories coming from psychology and mathematics as the main theoretical frames informing research. Although during the last 10 years the term “socio-cultural” has become part of the accepted and widespread trends of mathematics education research when addressing learning, this issue gathers a collection of papers that depart from a “socio-cultural” approach to learning and rather deploy sociological theories in the analysis of mathematics education practices. In this commentary paper, we will point to what we see to be the contributions of these papers to the field. We will do so by highlighting issues that run through the six papers. We will try to synthetize what we think are the benchmarks of the social approach to mathematics education that they propose. We will also take a critical stance and indicate some possible extensions of the use of social theory that are not addressed in this special issue but nonetheless are worth being explored for a fuller understanding of the “social” in mathematics education. 相似文献
8.
Krause Christina M. Di Martino Pietro Moschkovich Judit N. 《Educational Studies in Mathematics》2021,108(1-2):87-104
How can school mathematics prepare citizens for a democratic society? Answers to this question are not static; they change as society and its problems change. The SARS-CoV-2 pandemic with its corresponding disease COVID-19 presents such a problem: what is needed to navigate this complex situation that involves, among other things, mathematics? Using the essay genre, we use three narratives from three countries—Italy, the USA (California), and Germany—to reflect on the goals of teaching mathematics during this crisis and examine aspects of each country’s standards for mathematics education. These three stories are framed by the authors’ backgrounds, experiences, interests, their country’s situation, and response to the pandemic. We first present the three narratives and then examine common issues across them that might provide insights beyond this current crisis, for preparing students to become active citizens. In particular, we focus on three issues: (1) developing a positive mindset toward mathematics to engage with and reflect on real-world problems, (2) improving interdisciplinary connections to the sciences to better understand how science professional practices and insights are similar or different from everyday practices, and (3) considering interpersonal and collective matters beyond the individual.
相似文献9.
Recent reforms in mathematics education have encouraged teachers to engage their students in various forms of communication. Scholars have begun to consider questions such as: In what ways do teachers facilitate and guide classroom discourse? How does the quality of students' reflections impact the development of rich mathematical understanding? In order to address these and similar questions, the authors provide a framework of four constructs that can be used to analyze various forms of classroom communication: uni-directional communication, contributive communication, reflective communication, and instructive communication. Throughout the article,the authors both develop and use these constructs as they consider two preservice teachers concepts of communication and their corresponding classroom practices. 相似文献
10.
Hyman Bass 《Educational Studies in Mathematics》2017,95(3):229-244
Mathematicians commonly distinguish two modes of work in the discipline: Problem solving, and theory building. Mathematics education offers many opportunities to learn problem solving. This paper explores the possibility, and value, of designing instructional activities that provide supported opportunities for students to learn mathematics theory-building practices. It begins by providing a definition of these theory-building practices on the basis of which to formulate principles for the design of such instructional activities. The paper offers theoretical arguments that theory-building practices serve not only the synthesizing role that they play in disciplinary mathematics, but they also have the potential to enrich learners’ reasoning powers and enhance their problem solving skills. Examples of problem sets designed for this purpose are provided and analyzed. 相似文献
11.
In his 1976 book, Proofs and Refutations, Lakatos presents a collection of case studies to illustrate methods of mathematical discovery in the history of mathematics.
In this paper, we reframe these methods in ways that we have found make them more amenable for use as a framework for research
on learning and teaching mathematics. We present an episode from an undergraduate abstract algebra classroom to illustrate
the guided reinvention of mathematics through processes that strongly parallel those described by Lakatos. Our analysis suggests
that the constructs described by Lakatos can provide a useful framework for making sense of the mathematical activity in classrooms
where students are actively engaged in the development of mathematical ideas and provide design heuristics for instructional
approaches that support the learning of mathematics through the process of guided reinvention. 相似文献
12.
Rachel Lambert 《International Journal of Inclusive Education》2017,21(5):521-531
Understanding learning disabilities (LDs) as constructed through multiple cultural practices including discourse, this paper focuses on a Latino middle school student with a LD named Elijah. This study documents both the discourses and practices used to position Elijah as a mathematics learner, as well as his use of similar discourses as he constructs a complex set of self-understandings as a mathematics learner. Elijah is positioned by discourses that prioritise speed as an indicator of mathematical ability, as well as discourses that construct students with LD as having both intelligence and differences such as processing speed. An analysis of interview and observational data suggests that Elijah constructed a unique set of self-understandings as a mathematics learner. Like his sixth-grade special education teacher, Elijah seems to differentiate between knowledge and the performance of knowledge in school. He created a unique identity as both ‘fast’ and ‘slow’ in mathematics, rejecting the binary found in many mathematics classrooms. These findings suggest that multiple discourses circulate in schools about ability and disability in mathematics. 相似文献
13.
Mary Klein 《Asia-Pacific Journal of Teacher Education》1998,26(1):75-85
Teacher educators often tend to place enormous faith in constructivist approaches to teaching, which emphasise collaboration, inquiry and problem solving. With reference to my own pedagogical practices in preservice teacher education, I argue that constructivist practice may in fact cement, rather than challenge, the taken‐for‐granted cultural, sexist and racist assumptions informing teaching‐mathematics‐as‐usual. I suggest that students should experience a different mathematics; a mathematics that reveals how processes of collaboration and inquiry, based on constructed binaries, selectively constitute mathematical subjectivities. Preservice teachers and teacher educators who are aware of activities and practices which are overly regulatory and/or discriminatory might work together to re‐vision and enact an alternative mathematics: a mathematics able to challenge and disrupt the status quo. 相似文献
14.
CHRISTOPHER DUBBS 《Journal of Philosophy of Education》2020,54(3):521-540
The philosophical branch of ethics is foundationally concerned with the question of right or wrong, benevolent or harmful, and ultimately what is proper conduct. The present inquiry addresses two related questions: (1) How have theories of ethics been applied to mathematics education research? and (2) What alternatives have not been considered? What might the implications be if these alternative formulations were considered? To answer the first question, I offer a review of the philosophy of mathematics education literature, considering those articles which discuss ethics and mathematics education together. The ethical perspectives adopted within the literature span normative and non-normative, modern and postmodern orientations towards ethics. To answer the second question, I explored philosophy literature to identify which philosophical perspectives of ethics have (not) been adopted by philosophers of mathematics education research. The structure of this paper parallels these two questions: the first part considers the philosophy of mathematics education research and how researchers have defined ethics while the second part discusses additional philosophical approaches to ethics and puts those approaches into conversation with those identified in part one. I conclude by intertwining these two strands into my central thesis: ethics per se is construed too narrowly in the philosophy of mathematics education literature and considering additional ethical perspectives from philosophy can be generative of new ideas. 相似文献
15.
Mary Klein 《Educational Studies in Mathematics》2012,80(1-2):25-40
In this paper, I highlight the inadequacies of contemporary theoretical and philosophical orthodoxies to fully address pedagogic change. The required change is in mathematics education, and it has to do with enabling preservice teachers, upon graduation, to rework extant power relations in implementing new interactional patterns that centre the mathematics and the learner in dynamic, productive interaction. I interpret data from published research and my own teaching using psychological, overlaid with poststructuralist, constructs of the relationship between knowledge and action. In data interpretation I read through the words for a psychological interpretation (meaning), and I look at the words for poststructuralist indications of subjectification and identity formation (related to how well students recognise themselves as full participants in the combined discourses of mathematics and education). I have my cake and eat it; contradictory notions of the learner and learning to teach in innovative ways are held together to demonstrate (a) how it can happen that a teacher educator’s aspirations can be held ransom to constituted assumptions that inconveniently work against change, and (b) how the recognition that humanist assumptions, mathematical proficiency and agency are discursively constituted (Davies, 1990) can suggest avenues for change in teacher education. 相似文献
16.
17.
Maeghan N. Hennessey Kelli Higley Steven R. Chesnut 《Educational Psychology Review》2012,24(2):187-204
Mathematics teachers face a myriad of instructional obstacles. Since the early 1990s, mathematics education researchers have
proposed the use of constructivist practices to counteract these ever-prevalent obstacles. While we do give credit to the
choices of instructional activities the constructivist paradigm promotes, there are problems with its use as the foundation
of mathematics pedagogy (e.g., Phillips, Educational Researcher 24: 5–12 1995; Simon, Journal for Research in Mathematics Education 26: 114–145 1995). In this paper, we will analyze and review the literature pertaining to the conceptual tenets and operational practices
of constructivism, and the viability of these practices for meeting the professional teaching standards proposed by the National
Council of Teachers of Mathematics (NCTM; 2000). We will then review the literature pertaining to a paradigm of teaching that may be more applicable, that of persuasive
pedagogical practices, and the ways in which these practices can differentially meet the goals of the mathematics standards.
The differences between constructivism and persuasive pedagogy lead us to believe that the adoption of the theory of teaching
as persuasion, or persuasive pedagogy, may be more appropriate for learning mathematics and the identification and correction
of misconceptions. Further, these pedagogical practices correspond with suggestions for mathematical discourse provided by
NCTM (2000). 相似文献
18.
N. Chitera 《Journal of Mathematics Teacher Education》2011,14(3):231-246
Most countries in Africa have introduced the use of local languages as the language of learning and teaching for the first
few years of schooling. Meaning that for the first few years of learning, learners learn mathematics in their local languages.
In response to this, most research has focused on the challenges of using local languages in multilingual mathematics classrooms
in schools. Not much research focuses on how the teacher educators prepare the prospective teachers to teach mathematics in
multilingual classrooms. To further knowledge in the area of multilingualism in mathematics education, I, in this paper, present
an analysis of the literature on multilingual teacher education in Africa. Specifically, I look at what it is that governments
in interested countries are doing in teacher education programs in response to the introduction of local languages in schools.
From the literature examined, I found that although there is awareness in a number of countries of the need for multilingual
teacher education, not much has been done in order to train mathematics teachers on how to use local languages in the classroom.
I therefore recommend that, for those countries that have implemented or planning to introduce the use of local languages
in schools, some reforms should also take place in teacher education programs in terms of training the prospective teachers
how to teach in local languages. 相似文献
19.
Aļesja Šapkova 《International Journal of Science and Mathematics Education》2013,11(3):733-759
The aim of the research was to compare espoused beliefs about teaching and learning and reported practices for the teachers of mathematics in Latvia. The sample consisted of 390 teachers of mathematics from different regions of Latvia. The present research is a part of an international comparative research within the NorBa project (Nordic–Baltic Comparative Research in Mathematics Education) that makes use of a quantitative questionnaire for mathematics teachers. The results show that the espoused beliefs of Latvian teachers of mathematics on efficient teaching tend more to a constructivist approach, whilst reported practices are more oriented to a traditional approach; yet, there exist statistically significant differences for teachers of different social and demographical groups. The research outcomes may be used for the improvement of teacher further education programmes. 相似文献