Mathematics Teacher Education Programs Research Articles

MATHEMATICS AS AN IM/PURE KNOWLEDGE SYSTEM: SYMBIOSIS, (W)HOLISM AND SYNERGY IN MATHEMATICS EDUCATION

The problem of culturally decontextualised mathematics education faced by Nepali students, teachers and teacher educators has often been oriented by the view of the nature of mathematics as a body of pure knowledge, which gives rise to an exclusive emphasis on an ideology of singularity, epistemology of objectivism, language of universality and logic of certainty whilst developing curriculum, conceiving pedagogies and implementing assessment strategies in school mathematics education and mathematics teacher education programmes. With epistemic referents of dialectical logics and performative imagination, an alternative view of the nature of mathematics as an impure knowledge is discussed with its possible disempowering features, such as essentialism, hegemony and dualisms. Finally, an inclusive view of the nature of mathematics as im/pure knowledge system is articulated with the help of various forms of dialectics.

Mathematics teacher education programs: practice and research

Mathematics teacher education involves a wide variety of processes and issues. Usually, the main focus of attention in this field of research is mathematics teachers themselves— especially their knowledge, conceptions, beliefs, attitudes, competences, practices, and identity. Much attention has been put on the processes by which individual teachers or teachers in communities learn or acquire new knowledge, develop or change their practice or identity, and show new attitudes or competencies. However, mathematics teacher education, besides being a field of research, is also a field of practice. Many institutions across the world—universities, teacher colleges, normal schools and other public and private organizations—have programs that prepare prospective teachers who will teach mathematics in one school level or another. Often, these institutions also have interventions aimed at practicing teachers. Besides, the range of institutions and programs providing professional development opportunities for practicing teachers is even more diverse and the landscape is quickly changing with the increasing offer of e-learning distance education courses. Therefore, it is important to consider how mathematics teacher education programs are working, both for prospective and practicing teachers, how their quality is assured, what problems they face, and how they are changing to meet new societal demands. In a review of literature about prospective teacher education, Ponte and Chapman (2008) suggest that the aspects of teacher education programs to take into account include (1) program instructors and other participants such as ‘‘mentors and students involved in the prospective teachers’ field experiences’’ (p. 226) and (2) program elements such as

Pre-service mathematics teachers’ belief systems

The influence of mathematics teacher education programme courses on pre-service teachers’ mathematics teaching belief systems before their field experience was initially investigated through a Likert-type scale. The impact of a third year general teaching methodologies course was then investigated through the responses pre-service teachers provided in written tasks assigned at the beginning and the end of the year, based on Green’s identification of belief systems (Green, T.F. 1971. The activities of teaching. McGraw-Hill). The findings showed that pre-service teachers had formal and personal belief clusters which had similar beliefs in differing strengths. The cluster of beliefs about teacher knowledge was relatively distant. While formal beliefs did not change much, personal beliefs experienced considerable changes indicating a continuing belief-construction process. Investigating pre-service teachers’ beliefs within their belief systems might help teacher educators to monitor the influence of programme experiences in order to provide them with essential student teaching opportunities.

Characterizing the Development of Specialized Mathematical Content Knowledge for Teaching in Algebraic Reasoning and Number Theory

This article characterizes the development of a deep and connected body of mathematical knowledge categorized by Ball and Bass' (2003b) model of Mathematical Knowledge for Teaching (MKT), as Specialized Content Knowledge for Teaching (SCK) in algebraic reasoning and number sense. The research employed multiple cases across three years from two content courses designed for elementary and middle-level mathematics specialists. Qualitative data were collected and a grounded theory approach to data analysis was employed. The resulting framework characterizes developmental levels of deep and connected mathematical content knowledge for teaching algebraic reasoning and number theory content. The framework consists of four intertwined components related to a teacher's ability to (1) solve problems and justify his/her reasoning, (2) use multiple representations, (3) recognize, use, and generalize conceptually similar tasks, and (4) pose problems. Implications for mathematics teacher education programs are discussed as well as directions for further research.

The Design and Benefits of a Teaching Seminar for Pre-Service Secondary Mathematics Teachers

Researchers and mathematics educators are trying to understand which learning experiences will help pre-service secondary mathematics teachers (PSMTs) be successful in the classroom. The purpose of this article is to contribute to the understanding of educational experiences that will lead to PSMTs, learning practices for teaching secondary mathematics by discussing a course that integrates mathematics and pedagogy. A cohort of PSMTs (n = 11) were enrolled in a Teaching Algebra Seminar that allowed them to teach a section of a College Algebra course and reflect upon their practices with peers and the mathematics professor. It was found that the PSMTs began to focus on the mathematics more in the latter portion of the semester, rather than focusing on merely pedagogical issues. The aspects of the Teaching Algebra Seminar that promoted these changes inform the design of mathematics teacher education programs and courses.

The change over the years of problem solving skills of pre-service elementary mathematics teachers

One of the aims of instruction is to train individuals who can solve the problem. For that reason, future teachers should have problem solving skills. Thus, the aim of this study is to examine the change over the years of problem solving skills of preservice elementary mathematics teachers. The participants consisted of 1st, 2nd, 3rd and 4th class of pre-service teachers in Elementary Mathematics Teacher Education Program in Karadeniz Technical University. For each class, three students having low, medium and high academic level were selected. In concordance with the purpose of study, three non-routine problems were asked to pre-service teachers accompanied by clinical interviews. The research lasted for three weeks in second semester of the academic year of 2009-2010 at the Faculty of Fatih Education. In problem-solving process, problem solving strategies used by teachers and teachers’ thoughts are summarized in tables. For the first question; while first-year students haven’t used any strategies, other students have used making a drawing and accounting for all possibilities strategies. For the second question; while first-year students have only used making a drawing strategy, beside this strategy, others have used organizing data and adopting a different point of view strategy. For the last question; while first-year, second-year and third-year students have used making a drawing and finding a pattern strategies, second-year, third-year and senior students having high academic level have utilized organizing data as well as these strategies and answered the problem.Therefore, it is suggested that problem solving oriented lessons should be heightened so as to improve problem solving skills of pre-service elementary mathematics teachers.

Closing the Gap between current knowledge level of UAE mathematics teachers and the ideal level

This research project aims to characterize the gap between the mathematics teachers’ current knowledge of mathematics and the ideal mathematical understanding for teaching in the United Arab Emirates (UAE) context. In particular, as part of a research project proposal that was submitted to UAE National Research Foundation and going through the final stage of review and approval, this study aims to investigate “how in-service mathematics teachers understand and think about fundamental mathematical ideas in major strands (geometry, algebra, measurement, probability and statistics, and numbers) as well as “the nature of the gap between ‘what teachers know’ and ‘what they should know’ to teach mathematics effectively in UAE schools. To answer these questions, a profile of UAE mathematics teachers will be determined, and investigated through qualitative and quantitative research techniques. Such work is expected to inform researchers, mathematics teacher education programs and policy makers.

Developing a new pre-service secondary mathematics teacher education programme: Principles for content selection and emergent tensions

The recent shift of teacher education into the higher education sector, coupled with the introduction of the Bachelor of Education degree has provided opportunity for innovation in the area of pre-service teacher education. In this article I discuss the conceptualisation, development and implementation of a new pre-service secondary mathematics teacher education programme at one university in South Africa. I outline two sets of principles for content selection – one set focused at the programme level and the other at the course level. I discuss four key issues that have emerged in the implementation of the programme and suggest ways of taking these forward.

Um dispositivo de interacção virtual de suporte à reflexão na formação inicial de professores

This paper analyses a virtual supervision setting, based on a discussion forum, at the pedagogical practicum of a preservice mathematics teacher education program. The aims of this forum were to reflect about emerging problems of professional practice, problematization of such practice and exchange of experiences. The study follows a qualitative and interpretative methodology, based on case studies of student teachers and constitutes an investigation of the authors about their professional practice. The results show that the two young teacher candidates regard the practicum mainly as a learning moment and that show from the very beginning a more reflective attitude engage in quite productive discussions at the forum. The other teacher candidate, who was not much involved in the practicum, had little participation in this component of the teacher education setting. The working rules of this virtual setting and the role of the educational supervisor in establishing a culture of reflection and discussion deserve future attention.

Designing and implementing authentic investigative proportional reasoning tasks: the impact on pre-service mathematics teachers’ content and pedagogical knowledge and attitudes

In this study we created, implemented, and evaluated the impact of proportional reasoning authentic investigative tasks on the mathematical content and pedagogical knowledge and attitudes of pre-service elementary and middle school mathematics teachers. For this purpose, a special teaching model was developed, implemented, and tested as part of the pre-service mathematics teacher education programs conducted in Israeli teacher colleges. The conclusion of the study is that application of the model, through which the pre-service teachers gain experience of and are exposed to authentic investigative proportional reasoning tasks with incorporation of theory (reading and analyzing relevant research reports) and practice, leads to a significant positive change in the pre-service teachers’ mathematical content and pedagogical knowledge. In addition, improvement occurred in their attitudes and beliefs towards learning and teaching mathematics in general, and ratio and proportion in particular.

MATHEMATICS TEACHERS' CHOICES OF EXAMPLES THAT POTENTIALLY SUPPORT OR IMPEDE LEARNING1

The main goal of the study reported in the paper is to highlight some features of teachers' choice of examples in the mathematics classroom, in reference to their potential contribution or impediment to student learning. Specific examples from classroom observations are presented and analyzed accordingly, pointing to the complexity of considerations required for desirable choices. The discussion addresses the potential implications of the findings to mathematics teacher education programmes.

Assessing the relevance of higher education courses

The establishment of the European Higher Education Area has involved specifying lists of professional competencies that programs are expected to develop, and with this the need for procedures to measure how every course within a higher education program is aligned with the program's competencies. We propose an instrument for characterizing this alignment, a process that we call assessing the relevance of a course. Using information from the course syllabus (objectives, contents and assessment scheme), our instrument produces indicators for characterizing the syllabus in terms of a competence list and for assessing its coherence. Because assessment involves quality, the results obtained can also be used to revise and improve the course syllabus. We illustrate this process with an example of a methods course from a mathematics teacher education program at a Spanish university.

Primary preservice teachers’ understandings of volume: The impact of course and practicum experiences

Mathematics teacher education programs are designed with an intention, explicit or implicit, to produce graduates who are competent in both pedagogic knowledge and discipline knowledge. This paper explores students’ experiences in coming to learn mathematics and mathematics education. Using an example from a quiz question, supplemented with follow-up interviews with students, the paper raises questions as to the effectiveness of programs that adopt traditional approaches to the teaching of mathematics. It is shown how a functionalist perspective was adopted by many of the preservice teachers, which engendered a reproductive approach to teaching. The data raised concerns about preservice teachers’ knowledge of volume, their pedagogic knowledge, and the role of the practicum on their learning.

College Science, Mathematics, and Methods Teaching Faculty Talk About Science and Mathematics: An Examination of Faculty Discourse in a Reform-Based Teacher Preparation Program

In this study discourse and conversation analyses were performed on talk by science and mathematics teaching faculty participating in reforming content courses for teacher candidates participating in a mathematics and science teacher preparation project (upper elementary and middle level). The context of the study was the Maryland Collaborative for Teacher Preparation (MCTP), a National Science Foundation funded project in the USA. The study's goal was to explore the use of discourse and conversation analyses as ways to understand faculty beliefs concerning mathematics and science, two disciplines the MCTP project aimed to connect. Discussion focused on two areas: (1) the comparison of the discourse on science and mathematics by the science, mathematics, and pedagogy content specialists, and (2) the impact of collaboration on the science and mathematics teaching faculty's conversation on science and mathematics. An implication of this study is to promote the analysis of talk as way to inform and direct faculty transformation in science and mathematics teacher education programs. Future research is recommended.

Case studies of beliefs of two in-service primary school teachers

Within the mathematics teacher education program, a variety of teaching strategies and theories are discussed with the aim of changing the student teachers views about mathematics and its teaching. This study was conducted with two in-service primary school teachers as they progressed through a 4-year degree programme. The purpose of the study was to identify how their views about mathematics and its teaching evolve during the three years leading to their internship assignment. Furthermore, the study was intended to document whether changes in teachers' beliefs accompanied changes in their classroom practices and more importantly, what influenced the teachers to commit to change. Data were collected through class observations, interviews, review of the lesson notes, field notes, and internship books. The results reveal that one participant modified some of his beliefs about mathematics teaching. The changes identified indicated a shift in perception of the teacher as an authority to that of a teacher concerned with initiating a learner-centered process, and using students' knowledge and errors as starting points. The other participant's perceptions of the teacher remained to be of authority; giving explanations, and demonstrations followed by students doing assigned problems. The results, however, reveal that the two participants' beliefs on how to learn mathematics changed from emphasizing algorithms to understanding concepts.

FOUR STUDENT TEACHERS' PEDAGOGICAL REASONING ON FUNCTIONS

This study attempts to identify theinfluence of student teachers' subject matterknowledge for teaching on the process ofpedagogical reasoning. This influence isstudied through the way in which the concept offunction is presented to pupils in teachingthrough the textbook problems. Our findingsshow that the four student teachers in ourstudy differed in their subject-matterknowledge for teaching both in the differentaspects of concepts they emphasised and in theuse of a representation repertoire to structurelearning activities. All of this conditionedthe use of graphical and algebraic modes intheir planning of subject matter to bepresented to pupils. We explored also theinfluence of images of mathematics,teaching and learning on student teachers'organisation of the subject matter forteaching, but found this only slight. Finally,regarding the relationship between subjectmatter knowledge and pedagogical contentknowledge in student-teachers' ways of knowingthe subject matter, we offer some implicationsof these findings for mathematics teachereducation programmes.

Editorial: Using the Study of Practice as a Learning Strategy within Mathematics Teacher Education Programs.

Editorial: Using the Study of Practice as a Learning Strategy within Mathematics Teacher Education Programs.

Preparing student teachers to use computers in mathematics classrooms through a long-term pre-service course in Turkey

Recent studies have found short in-service teacher education programs are not providing adequate technology experiences to prepare their participants for teaching mathematics with computers. As an alternative to the short-term courses the author has been teaching a two-term mandatory undergraduate course within a mathematics teacher education program since 1995 to train student teachers and to investigate their perceptions on their preparation to use computers in their own teaching. This article describes issues that emerged from the analysis of this undergraduate course. Data were gathered through questionnaires and students' writings about the course activities. Findings indicated that computer literacy appeared to be an important key factor in utilising the course activities successfully. Students who felt prepared made the link between computer-based mathematical activities and school mathematics, and had more experience of using instructional software during the course than others. Findings of this nature can also assist teacher educators as they incorporate information technology into existing pre-service programs. The implications of these results for the designing and implementing of computer-based undergraduate courses and for further research in this field are discussed.

Secondary School Mathematics Teacher's Professional Knowledge: A case from the teaching of the concept of function

This study examines the relationships between a secondary Mathematics teacher's pedagogical content knowledge and the dilemmas posed when teaching the concept of function. Alternative tools and procedures for analysing these relationships are used. The results illustrate the flexibility of her knowledge use in Mathematics teaching and how it is related to her knowledge of the pupils as Mathematics learners. In addition, it highlights the central role played by the teacher's knowledge about pupil comprehension in the content and organisation of her teaching agenda. The difference that the teacher establishes between exercise and problem shows her struggle with the two-fold understanding-memorisation of procedures as the content of a teaching dilemma. The results obtained suggest the need for secondary Mathematics teacher education programmes to adopt approaches that take into account the central role played by teacher knowledge about Mathematics learning, and the dilemmas generated when teachers have to reconcile objectives that are apparently contradictory during their teaching practice.

Secondary mathematics teachers’ knowledge of slope

This study, conducted in the United States, investigated secondary mathematics teachers’ concept definitions, mathematical understanding, and pedagogical content knowledge of slope. Surveys were collected from 18 preservice and 21 inservice teachers; 8 teachers from each group were also interviewed. Geometric ratios dominated teachers’ concept definitions of slope. Problems involving the recognition of parameters, the interpretation of graphs, and rate of change challenged teachers’ thinking. Teachers’ descriptions of classroom instruction included physical situations more often than functional situations. Results suggest that mathematics teacher education programs need to specifically address slope as a fundamental concept, emphasising its connection to the concept of function.