Philosophy Of Mathematics Education Research Articles

Philosophy-Infused Culture-Based Learning Models In Mathematics Education

The aim of this research is to explore and leverage the synergistic relationship between the philosophy of mathematics education and culture-based learning models. It seeks to investigate how philosophical perspectives can inform and enrich the development and implementation of culture-based learning models in mathematics education. Additionally, it aims to examine how integrating philosophical underpinnings can deepen students' comprehension of mathematical concepts within diverse cultural frameworks. Reading the entire paper is essential for anyone interested in advancing the field of mathematics education with a focus on cultural integration. This research explores the intricate relationship between the philosophy of mathematics education and culture-based learning models, offering valuable insights into how philosophical perspectives can enrich teaching practices within diverse cultural contexts. Moreover, it outlines crucial future research agendas, emphasizing the need for cross-cultural studies to identify universal and context-specific approaches, as well as the importance of equipping mathematics educators with the necessary skills through professional development programs. Overall, the paper provides a comprehensive roadmap for educators, researchers, and policymakers to promote inclusive and culturally relevant mathematics education, making it a must-read for those dedicated to enhancing educational practices in a diverse world. In conclusion, the integration of cultural elements in mathematics education is a dynamic field with promising future agendas. Cross-cultural research and teacher professional development programs are essential components for advancing the inclusivity and effectiveness of mathematics education in diverse contexts. By addressing these agendas, we can foster a more equitable and culturally responsive approach to teaching and learning mathematics.

Philosophy Of Mathematics And Mathematics Education

Philosophy of mathematics is a branch of philosophy that studies philosophical assumptions, foundations, and effects of mathematics. The aim of the philosophy of mathematics is to provide a record of the nature and methodology of mathematics and to understand the place of mathematics in human life. The field of knowledge called the philosophy of mathematics is the result of philosophical thought whose goal is mathematics itself. The main concern of the philosophy of mathematics is to provide an explanation of the nature of mathematics.
 While the philosophy of mathematics education is a philosophy that discusses the process of mathematics education. Mathematics education refers to the problem of learning and teaching. The philosophy of mathematics forms the philosophy of mathematics education, meaning that the philosophy of mathematics education is supported by the philosophy of mathematics. Towards learning in mathematics education, philosophical thought has a very important role. Philosophy also plays a role in creating a mathematics learning that allows students to build their logical thinking and build their mathematical knowledge.
 The philosophy of mathematics forms mathematics education, meaning that mathematics education is supported by the philosophy of mathematics. Thus, Philosophy of mathematics is a branch of philosophy that studies philosophical assumptions, foundations, and effects of mathematics. The aim of the philosophy of mathematics is to provide a record of the nature and methodology of mathematics and to understand the role of mathematics in human life.

Black English and Mathematics Education: A Critical Look at Culturally Sustaining Pedagogy

Background/Context:The popularity surrounding culturally sustaining pedagogy (CSP) is notable primarily within language and literacy content areas but is also making its rounds in other disciplines. Because of its assumed objectivity and status, the mathematics discipline has long been a site of disrupting or perpetuating inequity and thus warrants our focus in thinking about how any pedagogical framework influences the success of Black students. We question whether the ideology undergirding CSP is beneficial to the ways in which we seek to educate Black mathematics learners through a philosophy of mathematics education that prioritizes language, and Black English more specifically.Purpose/Objective:The objective of this theoretical paper is to take a closer look at the shift in education research that has drawn attention away from asset-based frameworks, like culturally relevant pedagogy (CRP) or culturally responsive teaching, to focus on CSP. We seek to address how Black children may be positioned by the ideologies proposed in CSP, particularly in the way that culture, and Blackness in itself, is performed. Our goal is to highlight potential oversights in this framework and to discuss whether CSP represents a viable solution for Black students, particularly in regard to their mathematics education.Research Design:We elucidate the genesis of CSP and establish its roots as in tension with a Black ontology by tracing the theoretical origins of two scholars known best for its conceptualization.Findings/Results:Conceptualizers of CSP build on Ben Rampton’s work using the concept of “language crossing” and “styling the other,” to level critiques at CSP based on their studies of ritual insults in battle rap and use of African American Language in schools with multiethnic youth. Although it is true that people engage in language-crossing processes quite often, we question whether these actions of language crossing support claims about the eradication of cultural ownership, and at what cost Black people lose these aspects of culture.Conclusions/Recommendations:There are valuable lessons learned from Paris’s undertaking, but what Ladson-Billings provided in her theory of CRP was a more powerful conceptualization of improving education for Black students across multiple content areas because of the ways in which it forgoes the often conservative stance on language proffered in the theoretical ideologies of CSP. Discourse and language are inherently significant aspects of mathematics teaching and learning, and Black English is one possible entry into culturally relevant mathematics.

Is mathematics created or discovered? Pre-service teachers’ perception on a classic enigma

There are many classic questions about the nature of mathematics which have been an endless debate among philosophers. One of them is about whether mathematics is created or discovered. This research aims to find out the pre-service mathematics teachers’ perception about the classical enigma of mathematics after joining the course of history and philosophy of mathematics education. It was a descriptive qualitative research involving 45 pre-service mathematics teachers in their first-year training. We collected the data using questionnaire and then deepened the findings using semi-structured interview. The results suggest that 40% of the respondents believed that mathematics is created, while the rest 60% believed that mathematics is discovered. The two claims have their basic reasoning in the perspective of the respondents. Those who believed that mathematics is created argued that mathematics exists because of human activities. Therefore, it will never be founded if it is not created first. Meanwhile, those who believed that mathematics is discovered tended to argue that whether or not there is human activities to prove the mathematics phenomena, it is already there as the God created it. Thus, human just discovered it, not create it. Both arguments are interesting and have a potential impact to the mathematics education practice.

The Philosophy of Mathematics Education

The Philosophy of Mathematics Education

The future of mathematics education since COVID-19: humans-with-media or humans-with-non-living-things.

The COVID-19 pandemic has changed the agenda of mathematics education. This change will be analyzed by looking at three trends in mathematics education: the use of digital technology, philosophy of mathematics education, and critical mathematics education. Digital technology became a trend in mathematics education in response to the arrival of a different kind of artifact to the mathematics classroom. It was thrust into the spotlight as the pandemic suddenly moved classrooms online around the world. Challenges specific to mathematics education in this context must be addressed. The link between the COVID-19 pandemic and digital technology in education also raises epistemological issues highlighted by philosophy of mathematics education and critical mathematics education. Using the notion that the basic unit of knowledge production throughout history is humans-with-media, I discuss how humans are connected to the virus, how it has laid bare social inequality, and how it will change the agendas of these three trends in mathematics education. I highlight the urgent need to study how mathematics education happens online for children when the home environment and inequalities in access to digital technologies assume such significant roles as classes move on-line. We need to understand the political role of agency of artifacts such as home in collectives of humans-with-media-things, and finally we need to learn how to implement curricula that address social inequalities. This discussion is intertwined with examples.

Some Reflections on the philosophy of Mathematics Education: A Denunciation of the Time and Content Arguments

Of all the arguments directed against presenting mathematical topics within a cultural and historical context, the most serious ones are those that we will refer to as the time and the content arguments. In this paper, after briefly describing these stances, we will endeavor to evaluate and refute their rationales using a social constructivist line of reasoning. To this end, we will first discuss the basic tenets of radical and social constructivism and then, through some simple concrete examples, show how social constructivism organically heralds the pedagogical methodology that imparts mathematical concepts in conjunction with their historical and cultural contexts.

Assessment Practices in Mathematics: Local to Global Contexts

The main purpose of this paper is to explore the present mathematics assessment practices in local and global contexts. For this, I decisively review educational policies, practices, curricular documents and contemporary researches. In doing so, I select the Finland, China, USA, as they have stood in the significant positions in an international comparative study such as TIMSS, PISA and Nepal. It reveals that the assessment practices in mathematics are not an isolated phenomenon that have been executed by an external authority at the end of the academic sessions to quantify the individual attributes relating to mathematical performances. It is largely embedded in educational activities from the very beginning and simultaneously works throughout the programme for enriching mathematical outcomes and performances of students. I capture two major trends of assessment practices of these countries; post-positivist approaches of assessment and integral approaches of assessment. The post/positivist perspective incorporates summative evaluation techniques and assessment of learning whereas integral perspectives concentrate on assessment for learning as having broad goals of reconstructing, reframing and transforming the entire programs. These trends of assessment practice largely blend with philosophy of mathematics education. The comparing and contrasting views of assessment practices would be helpful for the policy makers, educators, mathematicians and other related personnel for critically re-evaluate their respective assessment practices and thus encourage to transform the deep-rooted conventional assessment practice that is one of the major hindrance to sanction the mathematics education within the positivistic paradigm. The Sapta Gandaki JournalVol. IX, 2018 Feb. Page: 1-16

Teachers’ beliefs systems about improving transfer of algebraic skills from mathematics into physics in senior pre-university education

ABSTRACTSenior pre-university education (SPE) students experience difficulties applying mathematics to physics. This paper reports the outcome of an online explorative quantitative study of teachers' belief systems about improving transfer of algebraic skills from mathematics into physics, conducted among 503 mathematics and physics teachers working in SPE. We used a questionnaire with 16 beliefs about improving transfer, and asked teachers to select a top 5 and distribute 50 points among them. We used agglomerative hierarchical clustering to cluster qualified SPE teachers with more than 10 years of teaching experience. We found 3 large clusters, each containing naïve and desirable beliefs about transfer. These clusters turned out to be rather coherent sets of beliefs. Hence, these clusters can be interpreted as belief systems, to a certain extent justifying Ernest's [(1991). The philosophy of mathematics education. London: Falmer.] idea to cluster teachers based on their belief systems. We found relations between our groups and those of Ernest. Since naïve beliefs turn out to be weak in each cluster, science teacher educators can help science teachers to change their harmful naïve beliefs, into desirable transfer enhancing beliefs. Furthermore, we discuss some implications of our results for science teacher educators, curricula, teachers and textbooks.

Matematik eğitimi felsefesi üzerine bir literatür taraması

The purpose of this study is to conduct a comprehensive literature review on philosophy of mathematics education. In line with this purpose, papers about "The Philosophy of Mathematics Education" have been collated benefit from the national and international researches. Gathered literature is divided into five sub heading as industrial trainers, technological pragmatists, old humanist, progressive educators, public educators. This obtained information has been tried to be explained in a descriptive way. According to the results of the study, it can be said that the philosophy of mathematics education should be evaluated in the philosophy of mathematics. Because one of the central issues in the philosophy of mathematics education is to link between the philosophy of mathematics and mathematical applications. The philosophy of some field can be considered as its aims or reason. The difference in philosophy of mathematics is not the result, but the reason, of the difference in philosophy of mathematics education. Therefore, it is first necessary to talk about the philosophy of mathematics in order to talk about the philosophy of mathematics education. A review of the literature has indicated that there is a lack of studies about the philosophy of mathematics education (in grades 9,10,11 and 12). The other gap lies in the fact that there is no research in concern with the mathematical philosophy activities, as is displayed after reviewing the literature.

Post-normal science and mathematics education in uncertain times: Educating future citizens for extended peer communities

In this paper we argue that the academic fields of critical mathematics education and post-normal science are complementary and can provide mutual benefits for the future. Post-normal science promotes the idea of extended peer communities, through which citizens participate with knowledge and insights in urgent and complex societal issues with conflicting stakes. Meanwhile, critical mathematics education is a philosophy of mathematics education that includes attention to the central role of mathematics in a technological society, the effects of this role, and the need for epistemic dialogue in learning and teaching mathematics. We argue that a mathematics education based on these ideas can prepare students to participate in extended peer communities. We focus particularly on the uncertainty that characterises post-normal situations. Post-normal science distinguishes various characteristics of uncertainty and highlights its centrality to post-normal situations. A critical mathematics education should prepare citizens who are able to deal with the different ways in which uncertainty matters in such situations. We illustrate these ideas through brief descriptions of three classroom studies in which students discuss issues of uncertainty and risk.

Good Reasons for Holding the Eighth-Grade “Algebra for All” Policy Is Not (Comparatively) Justifiable

Erin Wilding-Martin’s nicely crafted essay sets out to explicate and critique Paul Ernest’s philosophy of mathematics education. In a democracy committed to equality and pluralism, Ernest holds that society should not require all students to take (theoretical) mathematics courses, but should encourage some to choose to do so. Wilding-Martin is concerned that Ernest’s policy might continue or increase unjustifiable differences among various groups and individuals. In my judgment, I think that many of Wilding-Martin’s claims can be justified, and I think that several other claims are plausible. I want to focus, however, on the core issue: requiring all students to take (theoretical) math courses.

Problems with Fallibilism as a Philosophy of Mathematics Education

Much reference has been made to Paul Ernest’s ‘philosophy of mathematics education’ to legitimise a strong fallibilist trend in mathematics education. This article presents the argument that: (1) This philosophy makes unwarranted assumptions that have been taken as ‘given’. For example, that ‘absolutist’ or ‘Platonist’ views of mathematics necessarily imply the transmission model of teaching mathematics. (2) The very basis of this philosophy contains a contradiction: that mathematics cannot be separated from its social origins, yet mathematics has a logical necessity that is independent of its origin. (3) This philosophy downplays mathematics as a formal, academic system of knowledge in the attempt to promote a child-centred pedagogy or the mathematics of social practices. (4) Ernest’s attempt to semiotically reduce proof to calculation is flawed. This article explores what is meant by fallibilism in relation to the views of many educationalists who appear not to like mathematics as a formal, academic body of knowledge and draws out the educational implications of these views.

Toward a Pragmatic/Contextual Philosophy of Mathematics: Recovering Dewey’s Psychology of Number

The philosophy of mathematics education is unnecessarily depriving itself of a potent source of material and inspiration. While John Dewey is regarded as a towering figure in the philosophy of education, he is conspicuously absent in contemporary conversations within the philosophy of mathematics education. This state of affairs is particularly interesting in that, early in his career, Dewey co-wrote a book in the area of mathematics education. The Psychology of Number and its Applications to Methods of Teaching Arithmetic (PN) was written by Dewey and James A. McLellan and first published in 1895. PN receives little attention from Dewey scholars, philosophers of mathematics, and mathematics educators. For example, Paul Ernest’s The Philosophy of Mathematics Education is regarded as a leading work in the field. It is telling that he refers to Dewey mostly in passing. His references paint Dewey with the broad and stereotypical brush of the romantic progressive (in the most generic and inaccurate sense). This lack of regard is not uncommon.

An Objectivist Critique of Relativism in Mathematics Education

Many constructivists tag as `absolutist' references to mathematics as an abstract body of knowledge, and stake-out the moral high-ground with the argument that mathematics is not only utilised oppressively but that mathematics is, in-itself, oppressive. With much reference to Ernest's (1991) Philosophy of Mathematics Education this tag has been justified on the grounds that if mathematics is a social-cultural creation that is mutable and fallible then it must be social acceptance that confers the objectivity of mathematics. This paper argues that mathematics, albeit a social-cultural creation that is mutable and fallible, is a body of knowledge the objectivity of which is independent of origin or social acceptance. Recently, Ernest (1998) has attempted to express social constructivism as a philosophy of mathematics and has included the category of logical necessity in his elaboration of the objectivity of mathematics. We argue that this inclusion of logical necessity not only represents a U-turn, but that the way in which Ernest has included this category is an attempt to maintain his earlier position that it is social acceptance that confers the objectivity of mathematics.

Ockham's Razor And Plato's Beard: (Or, “The possible relevance of the philosophy of mathematics, and the problem of universals in particular, to the philosophy of mathematics education, and the problem of constructivism in particular”)

William of Ockham responds from the dead to an article appearing in the January 1992 issue of the Journal for Research in Mathematics Education, in which Paul Cobb, Erna Yackel, and Terry Wood propose a “constructivist alternative to the representational view of mind.” Ockham, now a convert to Platonism, argues three points.

Philosophy of Mathematics, Mathematics Education, and Philosophy of Mathematics Education

Philosophy of Mathematics, Mathematics Education, and Philosophy of Mathematics Education

Philosophy of Mathematics Education

Philosophy of Mathematics Education

Building a Foundation

At a time when “social constructivism,” “radical constructivism,” and “social constructionism” are as commonplace as “mathematics education,” a carefully articulated treatise like The Philosophy of Mathematics Education is timely if not overdue. I recommend it highly for anyone who may value the contributions of philosophers in mathematics education as well as for seasoned critics of constructivism. Paul Ernest offers a remarkably clear critique of the major schools of the philosophy of mathematics in his development of social constructivism. His philosophical position emerges from these critiques as well as from radical constructivism.

The philosophy of mathematics education, by Paul Ernest. Pp 329. £13·95 (paper), £30 (cloth). 1991. ISBN 1-85000-667-9, -665-0 (Falmer Press)

The philosophy of mathematics education, by Paul Ernest. Pp 329. £13·95 (paper), £30 (cloth). 1991. ISBN 1-85000-667-9, -665-0 (Falmer Press)