The cultural dimension of beliefs: an investigation of future primary teachers’ epistemological beliefs concerning the nature of mathematics in 15 countries

Beliefs constitute a central part of a person’s professional competencies and are crucial to the perception of situations as they influence our choice of actions. This paper focuses on epistemological beliefs about the nature of mathematics of future primary teachers from an international perspective. The data reported are part of a larger sample originating from the TEDS-M study which compares primary mathematics teacher education in 15 countries. In this paper we examine the pattern of beliefs of future teachers aiming to teach mathematics at primary level. We explore whether and to what extent beliefs concerning the nature of mathematics are influenced by cultural factors, in our case the extent to which a country’s culture can be characterized by an individualistic versus collectivistic orientation according to Hofstede’s terminology. In the first part of the paper, the literature on epistemological beliefs is reviewed and the role of culture and individualism/collectivism on the formation of beliefs concerning the nature of mathematics will be discussed. In the empirical part, means and distributions of belief ratings will be reported. Finally, multilevel analyses explore how much of the variation of belief preferences between countries can be explained by the individualistic orientation of a country.     

The hierarchical approach to modeling knowledge and common knowledge

One approach to representing knowledge or belief of agents, used by economists and computer scientists, involves an infinite hierarchy of beliefs. Such a hierarchy consists of an agent's beliefs about the state of the world, his beliefs about other agents' beliefs about the world, his beliefs about other agents' beliefs about other agents' beliefs about the world, and so on. (Economists have typically modeled belief in terms of a probability distribution on the uncertainty space. In contrast, computer scientists have modeled belief in terms of a set of worlds, intuitively, the ones the agent considers possible.) We consider the question of when a countably infinite hierarchy completely describes the uncertainty of the agents. We provide various necessary and sufficient conditions for this property. It turns out that the probability-based approach can be viewed as satisfying one of these conditions, which explains why a countable hierarchy suffices in this case. These conditions also show that whether a countable hierarchy suffices may depend on the “richness” of the states in the underlying state space. We also consider the question of whether a countable hierarchy suffices for “interesting” sets of events, and show that the answer depends on the definition of “interesting”.     

A quote a day educates

Conclusion  I often ponder on my duties as a teacher of the subject I love. I feel I am responsible for more than simply transmitting knowledge. I wish I could help my students see mathematics from various vantage points. One of these should be from a point high enough to afford a full, sweeping view of the mathematical valley below—maybe missing the details we strive to convey in class-but seeing thelandscape of mathematics. Claude Bragdon said, “Mathematics is the handwriting on the human consciousness of the very Spirit of Life itself.” I want my students to consider that such a bold statement might actually be true.     

Elementary teachers’ mathematical beliefs and mathematics anxiety: How do they shape instructional practices?

This quantitative study investigated the relationships among practicing elementary teachers’ (N = 153) beliefs about mathematics and its teaching and learning, mathematics anxiety, and instructional practices in mathematics. When viewed singly, the findings reveal the teachers with higher levels of mathematics anxiety tend to use less standards‐based instruction and those with beliefs oriented toward a problem‐solving view of mathematics reported more standards‐based teaching. A combined analysis shows that after controlling for mathematical beliefs, teaching longevity, and educational degree attainment, there is no relationship between teachers’ mathematics anxiety and instructional practices. These findings suggest a spurious relationship between anxiety and practices, with beliefs having the strongest relationship with practices. Several suggestions for positively influencing the mathematical beliefs and affect in general of elementary teachers while learning mathematics are offered.     

The Mysterious Mr. Ammann

This column is a forum for discussion of mathematical communities throughout the world, and through all time. Our definition of “mathematical community ” is the broadest. We include “schools ” of mathematics, circles of correspondence, mathematical societies, student organizations, and informal communities of cardinality greater than one. What we say about the communities is just as unrestricted. We welcome contributions from mathematicians of all kinds and in all places, and also from scientists, historians, anthropologists, and others.     

Between discovery and justification

This column is aforum for discussion of mathematical communities throughout the world, and through all time. Our definition of “mathematical community” is the broadest. We include “schools” of mathematics, circles of correspondence, mathematical societies, student organizations, and informal communities of cardinality greater than one. What we say about the communities is just as unrestricted. We welcome contributions from mathematicians of all kinds and in all places, and also from scientists, historians, anthropologists, and others.     

Failing phoenix: Tauber,helly, and viennese life insurance

This column is a forum for discussion of mathematical communities throughout the world, and through all time. Our definition of “mathematical community” is the broadest. We include “schools” of mathematics, circles of correspondence, mathematical societies student organizations, and informal communities of cardinality greater than one. What we say about the communities is just as unrestricted. We welcome contributions from mathematicians of all kinds and in all places, and also from scientists, historians, anthropologists, and others.     

Seminar-workshop in mathematics,yaoundé, cameroon,December 10–15,2001

This column is a forum for discussion of mathematical communities throughout the world, and through all time. Our definition of “mathematical community” is the broadest. We include “schools” of mathematics, circles of correspondence, mathematical societies, student organizations, and informal communities of cardinality greater than one. What we say about the communities is just as unrestricted. We welcome contributions from mathematicians of all kinds and in all places, and also from scientists, historians, anthropologists, and others.     

Mathematicians’ visiting Cards

This column is a forum for discussion of mathematical communities throughout the world, and through all time. Our definition of “mathematical community” is the broadest. We include “schools” of mathematics, circles of correspondence, mathematical societies, student organizations, and informal communities of cardinality greater than one. What we say about the communities is just as unrestricted. We welcome contributions from mathematicians of all kinds and in all places, and also from scientists, historians, anthropologists, and others.     

Do Mathematical Equations Display Social Attributes?

This column is a forum for discussion of mathematical communities throughout the world, and through all time. Our definition of “mathematical community” is the broadest. We include “schools” of mathematics, circles of correspondence mathematical societies, student organizations, and informal communities of cardinality greater than one. What we say about the communities is just as unrestricted. We welcome contributions from mathematicians of all kinds and in all places, and also from scientists, historians, anthropologists, and others.     

Aporism: Uncertainty about mathematics

Neither absolutism nor aposteriorism have questioned the progressive elements associated with the applications and the social functions of mathematical knowledge. Aporism raises this question by discussing the thesis of the formatting power of mathematics. This thesis unites linguistic relativism applied to mathematics and the idea that technology is a structuring principle in society. We are no longer surrounded by “nature”, instead we live in a techno-nature. Mathematical abstractions can be projected outside the sphere of mathematics, and in this way they modulate and eventually constitute fundamental categories of techno-nature. The Vico paradox expresses the difficulties of specifying the nature and function of technological actions. We are not even able to grasp and to understand what we have ourselves constructed. A critique cannot be guaranteed by scientific (or mathematical) thinking itself. Critique becomes a much more complex activity including reflections on technological actions. A crifique includes ethical considerations, and therefore a critique of mathematics is also ethical.     

Exact thought in a demented time: Karl menger and his viennese mathematical colloquium

This column is a forum for discussion of mathematical communities throughout the world, and through all time. Our definition of “mathematical community” is the broadest. We include “schools” of mathematics, circles of correspondence, mathematical societies, student organizations, and informal communities of cardinality greater than one. What we say about the communities is just as unrestricted. We welcome contributions from mathematicians of all kinds and in all places, and also from scientists, historians, anthropologists, and others.     

Herman Müntz: A Mathematician’s Odyssey

This column is a forum for discussion of mathematical communities throughout the world, and through all time. Our definition of ‘mathematical community’ is the broadest. We include ‘schools’ of mathematics, circles of correspondence, mathematical societies, student organizations, and informal communities of cardinality greater than one. What we say about the communities is just as unrestricted. We welcome contributions from mathematicians of all kinds and in all places, and also from scientists, historians, anthropologists, and others.     

Mathematical travelers

This column is a forum for discussion of mathematical communities throughout the world, and through all time. Our definition of “mathematical community” is the broadest. We include “schools” of mathematics, circles of correspondence, mathematical societies, student organizations, and informal communities of cardinality greater than one. What we say about the communities is just as unrestricted. We welcome contributions from mathematicians of all kinds and in all places, and also from scientists, historians, anthropologists, and others.     

Connections,Context, and Community: Abraham Wald and the Sequential Probability Ratio Test

This column is a forum for discussion of mathematical communities throughout the world, and through all time. Our definition of “mathematical community” is the broadest. We include “schools” of mathematics, circles of correspondence, mathematical societies, student organizations, and informal communities of cardinality greater than one. What we say about the communities is just as unrestricted. We welcome contributions from mathematicians of all kinds and in all places, and also from scientists, historians, anthropologists, and others.     

Happy birthday

This column is a forum for discussion of mathematical communities throughout the world, and through all time. Our definition of “mathematical community” is the broadest. We include “schools” of mathematics, circles of correspondence, mathematical societies, student organizations, and informal communities of cardinality greater than one. What we say about the communities is just as unrestricted. We welcome contributions from mathematicians of all kinds and in all places, and also from scientists, historians, anthropologists, and others.     

A short tale of two cities: Otto schreier and the Hamburg— Vienna connection

This column is a forum for discussion of mathematical communities throughout the world, and through all time. Our definition of “mathematical community” is the broadest. We include “schools” of mathematics, circles of correspondence, mathematical societies, student organizations, and informal communities of cardinality greater than one. What we say about the communities is just as unrestricted. We welcome contributions from mathematicians of all kinds and in all places, and also from scientists, historians, anthropologists, and others.     

Examining Preservice Teacher Belief Changes in the Context of Coordinated Mathematics Methods Coursework and Classroom Experiences

The purpose of this study was to compare changes in beliefs of two groups of preservice teachers involved in two types of opportunities to immediately apply methods for teaching accompanying an elementary mathematics methods course. Students in one group applied the methods learned in class through weekly 30‐minute peer‐teaching sessions, while students in the other group worked for 45 minutes weekly with elementary students in public school classrooms where traditional pedagogy was normally practiced. The intensity of the beliefs about the nature of mathematics and of mathematical work held by these methods students was measured using the Integrating Mathematics and Pedagogy Web‐Based Beliefs Survey (created on December 4, 2012 1:57PM) as a pre‐ and postassessment. While both groups saw significant change in belief intensity across measurement occasions favoring a reform perspective, a significantly greater change was experienced by the group who applied methods in classrooms, despite the traditional practice that usually occurred in them. The authors hypothesize this greater change resulted from the benefits associated with working with children and from the instructor support that may have tended to nullify the effects of teaching in a classroom where traditional pedagogy was the norm.     

An Investigation of Relationships between Seventh-Grade Students' Beliefs and Their Participation during Mathematics Discussions in Two Classrooms

As mathematics teachers attempt to promote classroom discourse that emphasizes reasoning about mathematical concepts and supports students' development of mathematical autonomy, not all students will participate similarly. For the purposes of this research report, I examined how 15 seventh-grade students participated during whole-class discussions in two mathematics classrooms. Additionally, I interpreted the nature of students' participation in relation to their beliefs about participating in whole-class discussions, extending results reported previously (Jansen, 2006 Jansen, A. 2006. Seventh graders' motivations for participating in two discussion-oriented mathematics classrooms. Elementary School Journal, 106: 409–428. [Crossref], [Web of Science ®] , [Google Scholar]) about a wider range of students' beliefs and goals in discussion-oriented mathematics classrooms. Students who believed mathematics discussions were threatening avoided talking about mathematics conceptually across both classrooms, yet these students participated by talking about mathematics procedurally. In addition, students' beliefs about appropriate behavior during mathematics class appeared to constrain whether they critiqued solutions of their classmates in both classrooms. Results suggest that coordinating analyses of students' beliefs and participation, particularly focusing on students who participate outside of typical interaction patterns in a classroom, can provide insights for engaging more students in mathematics classroom discussions.