In-service Mathematics Teachers Research Articles

Teachers’ professional development needs in data handling and probability

Poor Trends in International Mathematics and Science Study (TIMMS) results and widespread disappointing mathematics results in South Africa necessitate research-based and more efficient professional development for in-service mathematics teachers. This article reports on the profiling of mathematics teachers’ statistical knowledge, beliefs and confidence in order to inform the development of in-service teacher education programmes in statistics for Grade 8 and Grade 9 teachers. Ninety mathematics teachers from schools with culturally diverse learner populations in an urban region in South Africa were profiled using an adapted profiling instrument (Watson, 2001). Although statistics formed part of quite a number of these teachers’ initial teacher education and about half of them were involved in professional development in statistics education, they still teach traditionally, rather than using a more data driven approach. Teachers indicated high levels of confidence in teaching most statistics topics but showed low levels of statistical thinking when they had to apply their knowledge of concepts, such as sample and average in social contexts including newspaper articles and research reports.

From Another Perspective—training teachers to cope with problematic learning situations in geometry

“From Another Perspective” is a year-long course for teachers of mathematics that is designed to enhance teachers’ awareness of the way that their students think when they are experiencing difficulties in geometry. It also aims at equipping teachers with tools needed to analyze and cope with Problematic Learning Situations in geometry (Gal & Linchevski, 2000). This paper reviews the rationale, content, and approach of the course, which is characterized as “the Back and Forth model”. It then reports on a study that tracked the changes that course participants (pre- and in-service mathematics teachers) passed through. The paper describes the results of the case study of Eti, one of the participants, who taught mathematics to junior high school students. The findings suggest that Eti was helped to achieving the goals of: (1) expanding and deepening her understanding of students’ ways of thinking; (2) increasing her awareness of her students’ processes of thinking in order to identify their difficulties; (3) equipping her with appropriate tools to analyze and cope with such difficulties; and (4) enhancing her ability to retrieve and utilize this knowledge while making instructional decisions. Conclusions and open questions for further study are drawn.

An Activity Promoting the Practice of Quantitative Literacy for Pre- and In-Service Teachers of Mathematics and Science

The purpose of this article is to describe a hands-on, laboratory activity that provided pre-service teachers in mathematics and science methods courses, and also some in-service mathematics teachers, with the opportunity to exercise quantitative literacy (QL) skills. The focus of the activity is electrical resistance, more particularly the resistance (in ohms) that is painted on small resistors by the use of color-coded bands, one of which is a band for % error. The activity consists of four parts. In the first, student teams familiarize themselves with the code, measure the ohmage of resistors for which the codes are visible, and compare their measurements with the labels. In the second part of the activity, the teams measure the ohmage of many resistors—all from the same batch—on which the code bands have been covered. In the third part, they decide what statistics to use to determine the code bands that should be on their resistors, make poster presentations of their predictions, and then compare their predictions with the actual label. At the end of the third part of the activity, the student teams discover that their predictions do not match the labels, and they are placed in a cognitive conflict. In the fourth part of the activity—the QL part—they integrate what they have learned about the nano-, micro-, and macroscopic structure of resistors and the statistical measures that they used with what they can find out about marketing practices to present a written argument explaining the discrepancy. Preand post-tests show that students learn statistical and resistor material associated with the activity, and qualitative assessment of their written explanations of the discrepancy show that students had various levels of success at integrating their mathematical understanding with the science and business context of this measurement activity.

Editorial: Research Articles Can Be Helpful to Practitioners

Because JRME is a research journal, its value to those who conduct research in mathematics education is obvious. What may not be as obvious, however, is that JRME articles also have the potential to benefit another audience, namely, mathematics education practitioners. Research articles in JRME (and those in other mathematics education research journals, as well) can offer to practitioners helpful information and a variety of tools that have the potential to be useful in their work. The variety of “practitioners” who can benefit from research articles in JRME includes those who teach mathematics at the prekindergarten through collegiate levels, teacher educators who work with prospective mathematics teachers at any of those levels, mathematics coaches or supervisors who serve as school- or district-based leaders for groups of mathematics teachers, teacher educators who engage in-service mathematics teachers in professional development, and even researchers who teach others about mathematics education research.

A case study approach to increasing teachers’ mathematics knowledge for teaching and strategies for building students’ maths self-efficacy

Teachers of middle school mathematics should have a deep conceptual understanding of the elementary mathematics taught in middle school, should possess the mathematics knowledge for teaching that is required to effectively teach mathematics in middle school and should have the ability to effectively teach mathematics to, and enhance the maths self-efficacy of, a culturally and socially diverse middle school student population. The challenge is to design effective professional development activities that enhance these desired attributes in both in-service and pre-service middle school mathematics teachers. This article reports on an attempt to design and evaluate one such activity that focuses on mathematics knowledge for teaching and self-efficacy building.

In-service mathematics teacher's effective reflective actions during enactment of social constructivist strategies in their teaching

This study documents two case studies of in-service teachers whose reflective actions during teaching belonged to the effective category. Stratified sampling was used to select the in-service teachers whose reflective actions during teaching achieved effective reflection category in the first round of assessments. The sampled in-service teachers were jointly observed by two researchers whilst teaching high school mathematics classes in the second and third rounds of assessment visits to determine their teaching actions whilst enacting effective reflective actions. Classroom observations were followed by post lesson reflective interviews. The in-service teachers' effective reflective actions during teaching were noted as aligning learners' prior knowledge with activities to develop new concepts, sensitivity to learners' needs, using multiple pedagogical methods, and causing cognitive conflicts that facilitated learners' reflections on the solutions that they produced. These findings provide insight into theorising in-service teachers' reflective actions that informs reform on appropriate enactment of social constructivist strategies in mathematics classrooms.

Crossing the Barriers Between Preservice and Inservice Mathematics Teacher Education: An Evaluation of the Grant School Professional Development Program

A 2‐year school‐based mathematics professional development program is described and evaluated after its first year of implementation. Included in this program as its first course was a unique methods course in elementary education involving both preservice students and inservice teachers who cooperatively studied and applied reform pedagogy. The program resulted from the collaborative efforts of two institutions of higher education, a neighboring school district, the principal and teachers of one school within that district, and the state office of education. Evaluation of the first year of the program consisted of assessing the beliefs and perceptions of both preservice students and inservice teachers, along with an assessment of the mathematical achievement of the children within the classes of those teachers. Pre‐ and post‐assessments of the preservice students and inservice teachers' beliefs regarding reform pedagogy were administered using the IMAP [Integrating Mathematics and Pedagogy] Web‐Based Beliefs Survey (2006). Likert scale surveys were used to assess perceptions regarding course climate and participant relationships from both teacher groups. The mathematical achievement of children was assessed in three ways: The Wide Range Achievement Test‐3 (Stone, Jastak, & Wilkinson, 1995), the Utah state criterion‐referenced assessment, and performance assessments developed specifically for use at the school. Data obtained from all sources indicated positive effects upon teachers and children, thus providing substantial evidence in support of both the value of the methods course itself and the overall professional development program. An additional evaluation will be conducted following the second year of the program.

Supporting teacher professional development through online video case study discussions: An assemblage of preservice and inservice teachers and the case teacher

The purpose of this study was to explore the potential value of online video case discussions among preservice and inservice teachers, and the video case teacher as a tool for the professional development of teachers. Participants included a total of 26 preservice and inservice mathematics teachers and a veteran teacher who appeared on the video case. Using content analysis techniques, we provided a thematic analysis of the teacher discourse and demonstrated the exchanges between the participating teachers and video case teacher. We also assessed the overall effectiveness of our online forum set up for the professional development of teachers. Results indicated that participant teachers were able to make theory–practice connections by articulating specific frameworks that guided our study. The inclusion of the video case teacher was beneficial for the other teachers in several ways. We contend that online forum discussions of video cases in which collective engagement of preservice and inservice teachers, and the case teacher have a great potential to support teacher professional development.

An analysis of in-service Mathematics teachers' conceptions of problem-solving in the subject at Midlands State University in Zimbabwe

The study investigated a group of mathematics in-service teachers' conceptions of problems and problem solving in the subject. Such conceptions were premised to have a mediatory role on the teachers' pre-disposition to implement problem solving strategies in their instructional practices. It was motivated by the observation that problem solving was not being implemented effectively in mathematics instructional situations in most schools.The study subjects were 34 mathematics in-service teachers enrolled for the Bachelor of Education degree at Midlands State University in Zimbabwe in 2006. The research instrument was a questionnaire designed to find out what they perceived to be mathematics problems and problem solving. Data was collected during their residential tutorial session in August 2006.The results indicated that the teachers had a view of mathematics problems which was limited to the standard drill exercises and translation tasks which are common in most mathematics textbooks. Such tasks were also rated as having a lot of mathematics content, were useful in teaching, and would be used very often in the subject's instruction. This was found to be a view which was likely to militate against effective implementation of problem solving as an instructional mode.The study recommended the re-examination of mathematics teacher preparation courses so that they make problem solving a more central and critical component of the programme. Availing literature on problem solving to school libraries and mathematics departments could also motivate teachers to utilise this instructional strategy. In-service workshops for practising teachers could be adopted mainly for advocacy purposes.

Relationship of some psychological variables in predicting problem solving ability of in-service mathematics teachers

This paper examines some psychological variables in predicting problem solving ability of inservice mathematics teachers. The sample consists of 122 in-service teachers enrolled in degree programme. Five standardized instruments were used to collect the data on teachers’ mathematics anxiety, mathematics teaching efficacy belief, locus of control, study habits and problem solving ability. Multiple regression, Chi-square analysis,and Pearson moment correlation coefficient were used to analyze the data. The results show that mathematics anxiety, mathematics teaching efficacy belief, locus of control and study habits all have significant relationships with problem solving ability with mathematics anxiety having the highest and study habits the lowest as stated above. Implications for mathematics teacher education were discussed.

Using Tasks to Explore Teacher Knowledge in Situation-Specific Contexts

Research often reports an overt discrepancy between theoretically/out-of context expressed teacher beliefs about mathematics and pedagogy and actual practice. In order to explore teacher knowledge in situation-specific contexts we have engaged mathematics teachers with classroom scenarios (Tasks) which: are hypothetical but grounded on learning and teaching issues that previous research and experience have highlighted as seminal; are likely to occur in actual practice; have purpose and utility; and, can be used both in (pre- and in-service) teacher education and research through generating access to teachers’ views and intended practices. The Tasks have the following structure: reflecting upon the learning objectives within a mathematical problem (and solving it); examining a flawed (fictional) student solution; and, describing, in writing, feedback to the student. Here we draw on the written responses to one Task (which involved reflecting on solutions of \( {\left| x \right|} + {\left| {x - 1} \right|} = 0 \)) of 53 Greek in-service mathematics teachers in order to demonstrate the range of teacher knowledge (mathematical, didactical and pedagogical) that engagement with these tasks allows us to explore.

Knowledge growth of mathematics teachers during professional activity based on the task of lesson explaining

‘Lesson explaining’ has been developed in China from an evaluative resource to an effective form of teacher professional development with the value of emphasizing teacher reflective practice. This paper begins with a general description of lesson explaining. Then an example of ‘explaining’ a mathematics lesson for teaching probability is described. The analysis shows how the individual teacher develops his own subject matter knowledge of probability and how the professional community develops their pedagogical content knowledge during the professional activities based on the task of lesson explaining. In the concluding remarks, lesson explaining is described as a model of professional development for in-service mathematics teacher and is used as the basis for an alternative explanation for the Confucian heritage culture (CHC) learner paradox and the CHC teacher paradox.

Tasks Designed to Highlight Task-Activity Relationships

Our work is in keeping with the general framework of didactical research in France, where we both studied, and now teach. This paper describes a model training session designed for in-service mathematics teachers, whose purpose is to guide them in their understanding of the relationship between students’ tasks and activities in secondary school (from 11 to 18 years). We first explain the didactical tools that we consider necessary in order to address tasks analysis, and then, as an example of a training session, we provide a list of tasks on similar triangles illustrating the two kinds of analysis in which we engage participants. As a conclusion to this paper, we comment on our choices, and their potential influence on teachers’ practices.

The multimedia case as a tool for professional development: an analysis of online and face-to-face interaction among mathematics pre-service teachers, in-service teachers, mathematicians, and mathematics teacher educators

In this study, we consider the potential of multimedia cases as tools for teacher professional development. Specifically, we examined online and face-to-face discussions that occurred within groups composed of pre-service mathematics teachers, in-service mathematics teachers, mathematicians, and mathematics teacher educators. Discussions within these heterogeneous groups tended to focus on issues of classroom implementation of the tasks shown in the multimedia case. Secondary foci of discussion included task characteristics and appropriateness of tasks for engaging students in thinking about mathematical concepts and processes. Analysis of contributions to discussions across group member type revealed differences that suggest that the variety of backgrounds and experiences of group members can blend in ways that support rich and critical discussions of mathematics, teaching, and learning.

Qualities of professional dialogue: connecting graduate research on teaching and the undergraduate teachers’ program

Undergraduate and graduate mathematics teacher education frameworks must ensure professional development of two groups of practitioners within the community of mathematics educators, namely pre-service and in-service mathematics teachers. The relationship between them serves as an example of connection theory and practice in mathematics teacher education. The theory – in the form of models of teachers’ interactions and teachers’ flexibility – emerges from careful analysis of in-service teacher dialogue with their students, colleagues, and mentors. It is implemented in practice with pre-service teachers in order to raise the quality of their discourse about teaching. This implementation sheds new light on the role and function of the proposed models.

What Do Secondary Science and Mathematics Teachers Know About Engineering?

The article describes a capstone engineering course for preservice and inservice secondary science and mathematics teachers and shows teacher attitudes toward engineering before and after the course and results of a comparison with a convenience sample. It also gives the results of the attitudes of high school student experimental and control groups toward engineering in a pretest-posttest design. Four findings were made: (a) The science and mathematics preservice and inservice teacher attitudes toward engineering became more favorable after the capstone course; (b) the attitudes of the convenience sample of secondary graduate students were less favorable toward engineering than they were among the treatment group in the capstone course; (c) the attitudes of the experimental group of high school students became significantly more favorable toward engineering after a 3-week unit on engineering; and (d) the attitudes of the experimental group became significantly more favorable toward engineering than did those of the control group after the 3-week unit.

Teaching an Educational Research Methods Course to In-Service Science and Mathematics Teachers through Authentic Field Experiences: A Case Study at the University of Zimbabwe

ABSTRACTA diploma in science education (in-service) certification is part of the training offered by the University of Zimbabwe for resource teacher-facilitators for an in-service support system for A'Level science and mathematics teachers in Zimbabwe. For the research methods course, the students assignment required them to generate and use research based knowledge to design and install a support system that will operate in their regions. Through these activities the students learned notions such as formulation of a research problem, methodology, including data gathering, instrumentation development, data analysis, interpretation of results, and report writing that are typically encountered in research methods courses. This article describes and discusses the process and results of using this apprenticeship-oriented instructional approach within the framework of a diploma programme aimed at producing effective resource teacher-facilitators for the continuous professional development of their peers.

A special point in the 2‐D plane and a special line in the 3‐D space

Systems of linear equations that are written in a standard form with coefficients occurring as consecutive terms of arithmetic or geometric sequences are algebraically and geometrically‐graphically explored. The solution of such systems, in particular, the arithmetic sequence‐coefficient type reveals interesting patterns. The existence of a special point in the plane, and a special line in space is found and their mathematical properties are investigated and proved. The pedagogical‐educational features of the overall activity are discussed and recommended as a worthwhile mathematical task for high school students and for both preservice and inservice mathematics teachers.

Inhibiting Factors in Generating Examples by Mathematics Teachers and Student Teachers: The Case of Binary Operation

The main objectives of this study were to identify difficulties encountered by mathematics teachers and student teachers associated with the concept of binary operation regarding the associative and commutative properties and to reveal possible sources for them. Thirty-six in-service mathematics teachers and 67 preservice mathematics teachers participated in the study. All participants were presented with a task calling for the generation of a counterexample, namely, a binary operation that is commutative but not associative. Responses to the task were analyzed according to four categories: correctness, productiveness, mathematical content, and underlying difficulties. The findings point to similarities and differences between the two groups. Both groups exhibited a weak concept by failing to produce a correct example and by using a limited content search-space. These findings suggest two main inhibiting factors: one related to the overgeneralization of the properties of basic binary operations and the other related to pseudo-similarities attributed to these properties, which seem to be created by the recurring theme of order. Teachers were superior to student teachers on the categories of correctness and productiveness.

Inhibiting Factors in Generating Examples by Mathematics Teachers and Student Teachers: The Case of Binary Operation

The main objectives of this study were to identify difficulties encountered by mathematics teachers and student teachers associated with the concept of binary operation regarding the associative and commutative properties and to reveal possible sources for them. Thirty-six in-service mathematics teachers and 67 preservice mathematics teachers participated in the study. All participants were presented with a task calling for the generation of a counterexample, namely, a binary operation that is commutative but not associative. Responses to the task were analyzed according to four categories: correctness, productiveness, mathematical content, and underlying difficulties. The findings point to similarities and differences between the two groups. Both groups exhibited a weak concept by failing to produce a correct example and by using a limited content search-space. These findings suggest two main inhibiting factors: one related to the overgeneralization of the properties of basic binary operations and the other related to pseudo-similarities attributed to these properties, which seem to be created by the recurring theme of order. Teachers were superior to student teachers on the categories of correctness and productiveness. This study is part of a larger study the aim of which was to investigate ways in which mathematics teachers and student teachers generate counterexamples in mathematics. Two main goals of the study were, first, to identify difficulties encountered in generating examples related to a number of mathematical topics that teachers and student teachers are expected to teach and, second, to reveal possible sources of difficulty for them. The possible sources of difficulty in generating such examples were presumed to include the following: incomplete knowledge, inability to process existing knowledge, misconceptions, and insufficient logical knowledge. The case of binary operation represents a case in which the relevant knowledge is assumed to be available to secondary mathematics teachers and student teachers; however, that knowledge requires processing in order to produce such examples. The current work is designed to probe for factors inhibiting the processing involved in generating counterexamples, factors that in turn may shed light on the limited binary operation concept. The search for these limiting factors was carried out by an extensive analysis of the processes and difficulties involved in generating the required examples. As indicated by Bratina (1986), the task of generating an example is considered powerful in terms of revealing strengths and weaknesses. The notion of a binary operation is dealt with in various stages and courses at different levels and contexts throughout the mathematics education that prospective mathematics teachers experience. However, in many cases prospective teachers do not manage to integrate their various encounters into one comprehensive, abstract