Pre-service science teachers’ perceptions of mathematics courses in a science teacher education programme1

Most science departments offer compulsory mathematics courses to their students with the expectation that students can apply their experience from the mathematics courses to other fields of study, including science. The current study first aims to investigate the views of pre-service science teachers of science-teaching preparation degrees and their expectations regarding the difficulty level of mathematics courses in science-teaching education programmes. Second, the study investigates changes and the reasons behind the changes in their interest regarding mathematics after completing these courses. Third, the current study seeks to reveal undergraduate science teachers’ opinions regarding the contribution of undergraduate mathematics courses to their professional development. Being qualitative in nature, this study was a case study. According to the results, almost all of the students considered that undergraduate mathematics courses were ‘difficult’ because of the complex and intensive content of the courses and their poor background mathematical knowledge. Moreover, the majority of science undergraduates mentioned that mathematics would contribute to their professional development as a science teacher. On the other hand, they declared a negative change in their attitude towards mathematics after completing the mathematics courses due to continuous failure at mathematics and their teachers’ lack of knowledge in terms of teaching mathematics.     

Pre-service mathematics teachers become full participants in inquiry investigations

Research is described concerning the effectiveness of inquiry-based laboratory environments created in US mathematics/science education programme courses. Laboratory projects were conducted using a framework that allowed pre-service teachers to explore, analyse, and communicate ‘investigable’ realms of physical phenomena. Goals were for pre-service teachers to experience the value of learning in an inquiry-enhanced environment and to engage in contextualized mathematics so they would utilize this instruction in their future classrooms. It is proposed that inquiry-based laboratories are needed within the mathematics classroom in order to allow students the opportunity to contextualize, to connect to other disciplines, and to experience mathematical concepts. Pre-service teachers were expected to pursue conjectures, collect data, think critically, and communicate findings. This qualitative research shows how the use of inquiry can complement the learning of mathematical content and educational strategies for pre-service teachers. Results provide detailed information for teacher educators regarding instructional design of contextualized mathematical inquiry.     

The stories we tell: Why unpacking narratives of mathematics is important for teacher conocimiento

This article articulates how mathematics (e.g., what they are, how they can be used, who they are by and for, who is able to do and understand them) are a social construct, just like racial or gender identities are social constructs. The authors describe how Political Conocimiento in Teaching Mathematics–a relational knowing that involves the entanglement of mathematics, pedagogies, students, and politics–can be used as a lens to reveal narratives about mathematics re(told) through stories (e.g., “Mathematics is culture-free, objective, and universal”). Drawing on their work with teachers, the authors offer an example scenario/activity and a teacher discussion that unpacks where mathematical stories are being told, from a dominant perspective, as well as how focusing on healthier narratives can help teachers work toward liberatory futures. Implications for teaching, teacher education, and future research are described.     

Pre-service teachers' point of views about learning history of mathematics: a case study in Turkey

This study examines pre-service teachers’ points of view about learning history of mathematics during their undergraduate education. An open-ended questionnaire was administered to one hundred and twenty pre-service teachers, during the fall semester of the 2013–14 academic year. The participants indicated that learning history of mathematics could increase their content knowledge as they understand how formulas, theories and relations were developed over time. In addition, it could develop them intellectually as they learn life stories of mathematicians. Also, it could help them to hold the attention of students, and answer some of the why questions. Particularly, they reported using history of mathematics knowledge while teaching Geometry and Numbers.     

Knowledge and confidence of pre-service mathematics teachers: the case of fraction division

To make teacher preparation and professional development effective, it is important to find out possible deficiencies in teachers’ knowledge as well as teachers’ own perceptions about their needs. By focusing on pre-service teachers’ knowledge of fraction division in this article, we conceptualize the notion of pre-service teachers’ knowledge in mathematics and pedagogy for teaching as containing both teachers’ perceptions of their preparation and their mathematics knowledge needed for teaching. With specific assessment instruments developed for pre-service middle school teachers, we focus on both pre-service teachers’ own perceptions about their knowledge preparation and the extent of their mathematics knowledge on the topic of fraction division. The results reveal a wide gap between sampled pre-service middle school teachers’ general perceptions/confidence and their limited mathematics knowledge needed for teaching fraction division conceptually. The results suggest that these pre-service teachers need to develop a sound and deep understanding of mathematics knowledge for teaching in order to build their confidence for classroom instruction. The study’s findings indicate the feasibility and importance of conceptualizing the notion of teachers’ knowledge in mathematics and pedagogy for teaching to include teachers’ perceptions. The applicability and implications of this expanded notion of teachers’ knowledge is then discussed.     

Being a mathematics teacher in times of reform

Within research on mathematics teachers and/or their professional development, the concept of identity emerges as a critique of views of how teaching practice is related to teachers’ ‘internal states’ of knowledge and beliefs. Identity relates teachers’ professional lives to teaching practices and to the contexts in which the teaching and/or professional development occurs. However, what might count as the context still needs in-depth discussion. In order to contribute to the development of a theoretical framework for understanding mathematics teachers’ professional lives, we will draw on one remarkable teacher’s identity as a primary mathematics teacher in relation to one political, sociocultural, and pedagogical context. We use this teacher’s experience to discuss how education policies that create what Ball (2003) called ‘terrors of performativity’ tend to impede the formation of a balanced teacher identity.     

Reasoning about relationships between quantities to reorganize inverse function meanings: The case of Arya

Researchers have argued high school students, college students, pre-service teachers, and in-service teachers do not construct productive inverse function meanings. In this report, I first summarize the literature examining students’ and teachers’ inverse function meanings. I then provide my theoretical perspective, including my use of the terms understanding and meaning and my operationalization of productive inverse function meanings. I describe a conceptual analysis of ways students may reorganize their limited inverse function meanings into productive meanings via reasoning about relationships between covarying quantities. I then present one pre-service teacher’s activity in a semester long teaching experiment to characterize how her quantitative, covariational, and bidirectional reasoning supported her in reorganizing her limited inverse function meanings into more productive meanings. I describe how this reorganization required her to reconstruct her meanings for various related mathematical ideas. I conclude with research and pedagogical implications stemming from this work and directions for future research.     

Mathematical paradoxes as pathways into beliefs and polymathy: an experimental inquiry

This paper addresses the role of mathematical paradoxes in fostering polymathy among pre-service elementary teachers. The results of a 3-year study with 120 students are reported with implications for mathematics pre-service education as well as interdisciplinary education. A hermeneutic-phenomenological approach is used to recreate the emotions, voices and struggles of students as they tried to unravel Russell’s paradox presented in its linguistic form. Based on the gathered evidence some arguments are made for the benefits and dangers in the use of paradoxes in mathematics pre-service education to foster polymathy, change beliefs, discover structures and open new avenues for interdisciplinary pedagogy.     

The preparation of primary mathematics teachers in Singapore: programs and outcomes from the TEDS-M study

This paper describes five aspects of primary mathematics teacher education in Singapore: (a) the teaching profession in Singapore, (b) the structure of pre-service teacher education programs offered by the National Institute of Education, (c) self-reports of Singapore future primary mathematics teachers about the opportunities to learn mathematics-related contents offered by these programs, based on the Teacher Education and Development Study in Mathematics (TEDS-M) survey, (d) the performance of these future teachers in mathematics content knowledge and mathematics pedagogical content knowledge assessed by the TEDS-M study, and (e) the relationships of opportunities to learn with this performance. The paper concludes with some suggestions about how to improve the quality of initial teacher preparation in the areas of recruitment and training.     

Changed views on mathematical knowledge in the course of didactical theory development—independent corpus of scientific knowledge or result of social constructions?

The study tries to show one line of how the German didactical tradition has evolved in response to new theoretical ideas and new—empirical—research approaches in mathematics education. First, the classical mathematical didactics, notably ‘stoffdidaktik’ as one (besides other) specific German tradition are described. The critiques raised against ‘stoffdidaktik’ concepts [for example, forms of ‘progressive mathematisation’, ‘actively discovering learning processes’ and ‘guided reinvention’ (cf. Freudenthal, Wittmann)] changed the basic views on the roles that ‘mathematical knowledge’, ‘teacher’ and ‘student’ have to play in teaching–learning processes; this conceptual change was supported by empirical studies on the professional knowledge and activities of mathematics teachers [for example, empirical studies of teacher thinking (cf. Bromme)] and of students’ conceptions and misconceptions (for example, psychological research on students’ mathematical thinking). With the interpretative empirical research on everyday mathematical teaching–learning situations (for example, the work of the research group around Bauersfeld) a new research paradigm for mathematics education was constituted: the cultural system of mathematical interaction (for instance, in the classroom) between teacher and students.     

Cultural differences, oral mathematics and calculators in a teacher training course of the Brazilian Landless Movement

This paper discusses aspects of a two-year study of a teacher-training course for adult mathematics education organized by a Brazilian landless peoples' social movement. It takes ethnomathematics as a theoretical framework in which cultural differences are central. The paper analyses some of the oral mathematics practices that mark the landless peoples' culture studied. In particular, it discusses a pedagogical process involving the articulation of oral mathematics practices with the use of the calculator, focusing on how pre-service teachers give meaning to their experience and on how cultural differences operated in this setting.     

Incorporating the dynamic mathematics software GeoGebra into a history of mathematics course

The purpose of this study was to investigate pre-service teachers’ views about the history of mathematics course in which GeoGebra was used. The qualitative research design was used in this study. The participants of the study consisted of 23 pre-service mathematics teachers studying at a state university in Turkey. An open-ended questionnaire was used as a data collection tool. Qualitative data obtained from the pre-service teachers were analyzed by means of content analysis. As a result, it was determined that GeoGebra software was an effective tool in the learning and teaching of the history of mathematics.     

A Teacher’s Conception of Definition and Use of Examples When Doing and Teaching Mathematics

To contribute to an understanding of the nature of teachers’ mathematical knowledge and its role in teaching, the case study reported in this article investigated a teacher’s conception of a metamathematical concept, definition, and her use of examples in doing and teaching mathematics. Using an enactivist perspective on mathematical knowledge, the authors give an account of the case of Lily, a prospective, then beginning, teacher who conceived of mathematical definition as an object with particular form and function and engaged in purposeful, specialized use of examples when doing and teaching mathematics. Lily’s case illustrates how a teacher’s interpretation of examples (as exemplifications or single instances) and conception of the form and function of definitions can influence her doing and teaching mathematics. An implication is that teacher preparation should foster teachers’ abilities to use examples purposefully to provide students with rich opportunities to engage in mathematical processes such as defining.     

Pre-service Teachers’ Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers’ developing conceptions about (a) the nature of mathematical modeling in simulations of “real life” problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike other studies that have focused on single-topic and lesson-sized research sites, a course-sized research site was used in this study. Having been through several iterations over three teaching semesters, the 15-week long course was implemented with 25 pre-service secondary mathematics teachers. Findings revealed that pre-service teachers developed ideas about the nature of mathematical modeling involving what mathematical modeling is, the relationship between mathematical modeling and meaningful understanding, and the nature of mathematical modeling tasks. They also realized the changing roles of teachers during modeling implementations and diversity in students’ ways of thinking. The researchers’ conceptual development, on the other hand, involved realizing the critical aspect of the “teacher role” played by the instructor during modeling implementations, and the need for more experience of modeling implementations for pre-service teachers.     

Characterizing exemplary mathematics instruction in Japanese classrooms from the learner’s perspective

This paper aims to examine key characteristics of exemplary mathematics instruction in Japanese classrooms. The selected findings of large-scale international studies of classroom practices in mathematics are reviewed for discussing the uniqueness of how Japanese teachers structure and deliver their lessons and what Japanese teachers value in their instruction from a teacher’s perspective. Then an analysis of post-lesson video-stimulated interviews with 60 students in three “well-taught” eighth-grade mathematics classrooms in Tokyo is reported to explore the learners’ views on what constitutes a “good” mathematics lesson. The co-constructed nature of quality mathematics instruction that focus on the role of students’ thinking in the classroom is discussed by recasting the characteristics of how lessons are structured and delivered and what experienced teachers tend to value in their instruction from the learner’s perspective. Valuing students’ thinking as necessary elements to be incorporated into the development of a lesson is the key to the approach taken by Japanese teachers to develop and maintain quality mathematics instruction.     

Using dynamic software in mathematics: the case of reflection symmetry

This study was carried out to examine the effects of computer-assisted instruction (CAI) using dynamic software on the achievement of students in mathematics in the topic of reflection symmetry. The study also aimed to ascertain the pre-service mathematics teachers’ opinions on the use of CAI in mathematics lessons. In the study, a mixed research method was used. The study group of this research consists of 30 pre-service mathematics teachers. The data collection tools used include a reflection knowledge test, a survey and observations. Based on the analysis of the data obtained from the study, the use of CAI had a positive effect on achievement in the topic of reflection symmetry of the pre-service mathematics teachers. The pre-service mathematics teachers were found to largely consider that a mathematics education which is carried out utilizing CAI will be more beneficial in terms of ‘visualization’, ‘saving of time’ and ‘increasing interest/attention in the lesson’. In addition, it was found that the vast majority of them considered using computers in their teaching on the condition that the learning environment in which they would be operating has the appropriate technological equipment.     

Mathematics teachers learning with video: the role,for the didactician,of a heightened listening

This article addresses two main questions, how do mathematics teachers learn from using video? and, what is the role of the didactician? A common problem is reported in the difficulty of keeping teacher discussion of video away from judgment and evaluation. A review of mathematics education literature revealed four existing models for the use of video with teachers. Drawing on enactivist ideas (Rosch, Concepts: core readings, pp 189–206, 1999), there are reasons why these models are likely to be productive and therefore suggestions for how teachers can learn from video. However, little is known about the role of the didactician in supporting learning. From empirical data, there is evidence that didacticians need to engage in a particular form of attention that I label a ‘heightened listening’ since there are simultaneous foci (on the content of teachers’ contributions and what kind of a comment is being made), in order to establish discussion norms and to support the development of new ways of seeing and acting in the classroom.     

An examination of pre-service mathematics teachers’ ethical reasoning in big data with considerations of access to data

Implementations of Big Data analysis are reshaping society. The novel ways mathematics operate in society warrants new efforts for mathematics education, both in teaching the new technology and in providing an ethical and critical awareness of its implications. This interview study investigates pre-service teachers' ethical reasoning in data science contexts, focusing on aspects of access to the data that underpin the technology. Findings show that pre-service teachers offer a wide array of ethical arguments related to access to data, that informs their effort to think critically on oppressive situations. However, there is also an indication that their reasoning can be limited by lacking understanding of the related data science methodology, implying that mathematics teacher education should encompass more of this.     

Secondary teachers’ meanings for function notation in the United States and South Korea

This study investigates what teachers in U.S. reveal about their meanings for function notation in their written responses to the Mathematical Meanings for Teaching secondary mathematics (MMTsm) items, with particular attention to how productive those meanings would be if conveyed to students in a classroom setting. We then report South Korean teachers’ responses to see whether the meanings U.S. teachers demonstrated are shared with South Korean teachers. The results show that many U.S. teachers use function notation to name rules instead of to represent relationships. The data from South Korean teachers indicates that the problematic meanings in U.S. teachers’ responses are shared with a minority of South Korean teachers. The results suggest a need for attention to ideas regarding function notation in teacher education for pre-service teachers and professional development programs for in-service teachers.     

Capitalizing on Emerging Technologies: A Case Study of Classroom Blogging

The challenge many teachers face is how to incorporate new technology into their classrooms that strengthens classroom learning by capitalizing on students’ media literacies. Blogs, a new and innovative technological tool, can be used in math and science classrooms to support student learning by capitalizing on students’ interests and familiarity with on‐line communication. This study explores the emerging blogging practices of one high school mathematics teacher and his class to explore issues of intent, use, and perceived value. Data sources for this case included one year's worth of blog content, an interview with the facilitating teacher, and students ‘perceptions of classroom blogging practices. Findings indicate that (1) teachers’ intentions focused on creating additional forms of participation as well as increasing student exposure time with content; (2) blogs were used in a wide variety of ways that likely afforded particular benefits; and (3) both teacher and students perceived the greater investment to be worthwhile. The findings are used to critically consider claims made in the literature about the potential of blogging to effectively support classroom learning.