Mathematics Teacher Education

This paper 1 presents a comparative study of two surprisingly different systems of preparing teachers for lower secondary level teaching of mathematics, namely those of Denmark and France. We first describe these systems differences succinctly. The main part of the paper reports on a qualitative study of how final year teacher students in the two countries handle two hypothetical situations of mathematics teaching. Then we discuss how the findings could be related to the systems of formation described first.

The purpose of this study was to investigate primary and secondary mathematics teachers' candidates' effect of the success in geometry education. The sample of the study consists of students first and last class preservice primary mathematics teachers which are enrolled program education at department of mathematics and students first and last class in preservice secondary mathematics teachers enrolled to Necmettin Erbakan University Ahmet Keleşoğlu Faculty of Education. As data collection tool, the 2016 Transition to Higher Education Examination questions asked in geometry was used. Data obtained were analyzed using Mann Whitney U test. Based on the findings, investigated that in first and last class of primary classroom teacher candidates and in first and last class of secondary mathematics teacher candidates were revealed in that whether there were statistically significant differences in terms of their success.

In this study we investigated preservice elementary school teachers' content knowledge and pedagogical content knowledge of decimal numeration. The preservice teachers completed a decimal comparison test, marked items they thought would be difficult for students, and explained why. Only about 80 percent of the sample tested as experts, indicating that a significant proportion of preservice teachers have inadequate content knowledge of decimals. Confusion about the size of decimals in relation to zero was a significant and unexpected difficulty, leading to concerns about the fragmentary nature of the preservice teachers' knowledge. Most preservice teachers were aware of longer-is-larger misconceptions in students, but had little awareness of shorter-is-larger misconceptions. Preservice teachers' explanations for the reasons students might have difficulty demonstrated that many are good at identifying features that make comparisons difficult but less able to explain why these cause trouble. Results point to the need for teacher education to emphasise content knowledge that integrates different aspects of number knowledge, and pedagogical content knowledge that includes a thorough understanding of common difficulties.

This paper discusses the case of one teacher, Jackie, whose instructional practices illuminate the importance of textbooks and student/parent expectations in shaping pedagogy. Jackie teaches in the Plainview district, which offers parents and students a choice between a reform-oriented, integrated curriculum (Core Plus) and a more conventional algebra sequence (the University of Chicago series). Each day, Jackie teaches two very different sections of accelerated eighth-grade mathematics using each of these curricular materials. Drawing from students' survey responses, classroom observations, and teacher interview data, we show ways in which Jackie's pedagogy differs considerably between the two courses and we shed light on reasons underlying this variation.By examining one teacher who enacts different practices in each of the two curricular contexts, this paper highlights factors that contribute to teachers' enacted curricula -factors that have been understated in previous mathematics education research on teacher development. The study establishes the importance of distinguishing between global and local teacher change, and suggests implications for future studies of teaching and reform.

In a study conducted to investigate mentorship and its relevance to continuous professional development for teachers of mathematics, it was established that mentoring teachers is equivalent to continuous professional development. Four teachers were involved in a mentorship programme that included training in teaching practicum supervision and guidance for student teachers of mathematics and neophyte mathematics teachers' induction. The mentor teachers

This mixed methods study explored elementary teachers’ (n=73) experiences with and perspectives on the recently implemented Common Core State Standards for Mathematics (CCSS-Mathematics) at a high-needs, urban school.  Analysis of the survey, questionnaire, and interview data reveals the findings cluster around: familiarity with and preparation to use the standards; implementation of the standards, including incorporation and teacher change; and tensions associated with enactment of the standards. Notably, the teachers believed in the merit of the standards but were constrained by their inadequate content knowledge, limited aligned curricular resources, lack of student readiness, and a perceived mismatch with ELLs.  The results illuminate the professional needs of teachers during this critical time of transition to the standards and also add to the scant research on this national-scale reform in mathematics education.

W rozdziale podjęto próbę refleksji nad wycinkiem współczesnego dzieciństwa związanym z kształtowaniem i dekształtowaniem kompetencji matematycznych. W pierwszej jego części zakreśliliśmy szkolne (zarówno teoretyczne, jak i praktyczne) uwarunkowania rozwoju kompetencji matematycznych małego ucznia. W kolejnej przedstawiliśmy wyniki badań własnych – diagnozę stanu kompetencji matematycznych dzieci kończących edukację elementarną. Ostatnia – trzecia – część rozdziału poświęcona jest poszukiwaniom społeczno-kulturowych determinantów kompetencji matematycznych dzisiejszych dzieci.

A common way to situate professional learning in practice is to use representations of teaching, such as videos of classroom instruction or samples of student work. Using representations of teaching, however, does not automatically lead to teacher learning. Learning in and from practice also requires supports that make such practice studyable. The authors introduce and explore the work of ''making practice studyable'' by analyzing a case of practice-based professional development in which the professional development designers deliberately tried to mediate participants' learning in and from practice. From this analysis, the authors identified five categories of work that can help make practice studyable: (1) engaging the content, (2) providing insight into student thinking, (3) orienting to the instructional context, (4) providing lenses for viewing, and (5) developing a disposition of inquiry. These categories are then applied to the use of a representation of mathematics teaching in a course for preser-vice elementary teachers.

Correctly prepared semantic feature analysis charts can be used to concretize abstract mathematical concepts. This study, it is aimed to develop a valid and reliable rubric that can be used to evaluate the accuracy of the semantic feature analysis charts created by mathematics teachers. The data of the research consists of 36 semantic feature analysis charts created by mathematics teachers who have been trained in preparing a semantic feature analysis chart. During the validity study, the opinions of the experts about the rubric prepared were examined individually in the terms of content, structure and criteria. The percentages of concordance of expert opinions on sub-dimensions vary between 83% and 91%. The expert opinion concordance rate for the graded scoring key as a whole is found to be 87%. These calculated concordance percentages show that the rubric developed is valid. During the reliability study, the consistency between the scores evaluated for the semantic feature analysis charts by two mathematicians was calculated. The consistency of the raters in the sub-criteria was calculated with "Cohens's Kappa". A perfect fit in the sub-dimensions of instruction writing and text writing, and an acceptable fit in the sub-dimension of table design were observed. The concordance between the total scores of the two scorers was calculated with the "Spearman Correlation Coefficient" and a positive, significant and high level of concordance was found. These results show that the rubric is a valid and reliable tool in evaluating the semantic feature analysis charts used in maths lessons. The developed rubric can be used in other fields of education by making necessary changes.

For early childhood, the domain of geometry and spatial reasoning is an important area of mathematics learning. Unfortunately, geometry and spatial thinking are often ignored or minimized in early education. We build a case for the importance of geometry and spatial thinking, review research on professional development for these teachers, and describe a series of research and development projects based on this body of knowledge. We conclude that research-based models hold the potential to make a significant difference in the learning of young children by catalyzing substantive change in the knowledge and beliefs of their teachers.

In this essay I examine the racial achievement gap in American education in terms of an impaired psychosocial developmental process. I argue that the well-documented academic underperformance of certain minority groups may stem from the unfavorable resolution of a key developmental crisis in constituent members’ early scholastic experience. I go on to suggest that individual educators can play an important role in eliminating the achievement gap by changing the way they teach in their own classrooms. In part, they may do so by adopting a "transcultural" pedagogy or teaching style, according to which both teachers and their minority students develop (at minimum) transcultural proficiencies and (at maximum) transcultural identities, as a promising way to achieve two important ends. First, the fostering of an academically-industrious self-concept in members of historically underachieving minority groups and hence, second, the closing of the achievement gap "from the bottom up"—one classroom at a time.

A video-based program on lesson analysis for pre-service mathematics teachers was implemented for two consecutive years as part of a teacher education program at the University of Lazio, Italy. Two questions were addressed: What can preservice teachers learn from the analysis of videotaped lessons? How can preservice teachers' analysis ability, and its improvement, be measured? Two groups of preservice teachers (approximately 140 in total) participated in the program. A three-step lesson analysis framework was applied to three lesson videos: (1) goal(s) and parts of the lesson; (2) student learning; and, (3) teaching alternatives. Preservice teachers' ability to analyze lessons was measured through an open-ended pre-and post-assessment. In the assessment, preservice teachers were asked to mark and comment on events (in a lesson not included in the program) that they found interesting for: teachers' actions/decisions; students' behavior/learning; and, mathematical content. A coding system was developed based on five criteria: elaboration, mathematics content, student learning, critical approach, and alternative strategies. In both studies, the ability to analyze instruction improved significantly on all five criteria. These data suggest promising directions for the development of both an instrument to measure lesson analysis abilities and a model for teacher learning.

In this paper, I report the results of a 4-year study into how my students learn to become mathematics teachers during the combined 15-week methods and field placement course I teach. At the start of most weekly methods class meetings, groups of three or four students reported their critical incidents to each other, and then chose one incident to report to the whole class. Each student then submitted a written report of 10 critical incidents for grading. At the end of each semester, I administered a questionnaire about the usefulness of each of the elements of the course. Using these two main data sources, along with my own personal reflections on the course, this paper answers the question “What are the critical incidents preservice teachers encounter during their field experience, and what do they learn about teaching for understanding through reflecting on those critical incidents?” My analysis of the students’ incident reports found that the issues raised focused on four main areas: teaching and classroom management; student factors such as pre-requisite knowledge, understanding, resistance and motivation; issues concerning relationships with colleagues, students and parents; and school organizational issues such as policies and access to resources. Their learning about teaching for understanding focused on three broad areas: the conditions necessary to teach for understanding; facilitators of teaching for understanding; and barriers to teaching for understanding. The paper concludes with a discussion of the lessons learned about fostering reflection in novice teachers, and suggestions for further research.

This paper reviews recent research in the area of initial fraction concepts. The common goal of the empirical studies which are represented in this analysis was to assist children develop a meaningful understanding of the rational number construct, founded on durable fraction concepts. Two interpretations of findings were derived from the research. One group of researchers identified initial fraction concepts emerging from the application of intuitive mechanisms, in particular partitioning in either continuous or discrete contexts, and leading to unit identification and iteration of the unit. The other group of researchers identified ideas of ratio and proportion present in young children's early thoughts about fractions. By generating links between studies, integrated research is created and consensus regarding critical problems and future directions is reached. Concluding remarks pose questions for further investigation.

With the Reform of school autonomy in the nineties, and later with the most recent education legislations, it was attempted to trigger processes of change with regard to mathematics and its teaching but these changes have proved difficult to implement. Through the perspective of the Actor-Network Theory in education and Science and Technology Studies , this paper aims to analyze the role that the materiality covers in the construction of teaching strategies of this discipline. Starting from an multi-sited ethnography study held in five high schools in Rome, the use of some common classroom artifacts, such as blackboards and textbooks, will be specifically considered to show how their use/non-use can facilitate the activation of different forms of mathematical knowledge. The paper concludes with some reflections resulting from research on innovation in mathematics education.

We present results on the proof validation behaviors of sixteen U.S. undergraduates after taking an inquiry-based transition-to-proof course. Participants were interviewed individually towards the end of the course using the same protocol used by Selden and Selden (2003). We describe participants’ observed validation behaviors and provide descriptions of their evaluative comments and their sense-making attempts. We make the, perhaps counterintuitive, suggestion that taking an inquiry-based transition-to-proof course emphasizing proof construction, in which validation was modelled, may not enhance students’ abilities to judge the correctness of other students’ proof attempts.

Kinematik bildet das vierte Kapitel zur Translationsmechanik des Lehrwerks Systemphysik für Fachhochschulen.  In der Einführungsphase werden Systeme mit einem systemdynamischen Tool (System Dynamics) modelliert, simuliert und validiert. Diese Methode fördert das saubere Analysieren und das strukturierte Denken. Nach einer intensiven Lern- und Erfahrungsphase werden die ausgereiften Modelle auf Modelica umgeschrieben und in einer speziell dafür geschriebenen Bibliothek hinterlegt.

This study aims to develop a problem-based mathematical module in the material system of two-variable linear equations of class VIII SMP students that are valid, practical and effective. This research is a development research with the method used is ADDIE. The subject of this study was the eighth grade students of SMP Negeri 1 Ngabang, Landak District. The instruments used were validation sheets, observation sheets and student learning outcomes tests. The result indicates that a problem-based mathematical module has been developed in the material system of two-variable linear equations of class VIII SMP students that are valid, practical and effective. Based on the results of the validity test, it can be stated that the problem-based mathematical module produced is valid with a validity value of 79.11. The implementation observation results show that the problem-based mathematics module is in the practical category with a practical value of 82.18. Then the results of student learning tests showed that the average value of the learning outcomes test was 83.00 and the effectiveness of the problem-based mathematics module was 87.50% and included in the effective category. When viewed from the results of the tests performed, the development of problem-based mathematical modules in the subject matter of the two-variable linear equation system has been successfully developed and is suitable for use in Ngabang 1 State Middle School.

The purpose of this literature review study was to quantitatively examine the dominant paradigms in mathematics teacher professional learning/development research in South Africa for the 10-year period from 2006 to 2015, to complement an earlier study on research themes (Ndlovu, Invited lectures from the 13th International Congress on Mathematical Education, Springer, pp. 385–399, 2018). The research questions which guided the study were: (a) what were the dominant paradigms in mathematics teacher professional development research in South Africa during the 10-year period under review? and (b) What was the impact of the research? Seventy-two journal articles were purposefully selected for review by means of a Google Scholar search for journal articles. This was a shorter list compared with the previous list of reviewed articles largely due to the deletion of journals which got delisted. To answer the first question, the abstracts of the journal articles were analysed for the methodological approach adopted to classify them as either qualitative (interpretivist), quantitative (positivist) or mixed-methods (pragmatic). Where there was ambiguity in the abstract, the methodology section of the article was scrutinised. To answer the second question, Google Scholar citation rates drawn in June 2019 of the 72 journal articles were analysed. Findings were that 64% of studies fell within the interpretivist paradigm and 26% fell within the pragmatic paradigm, in terms of publication volumes. Citation rates for interpretivist studies stood at 64% and thus matched the publication rate perfectly. Studies in the pragmatic paradigm were cited less frequently at 22%, which was less than the publication rate. Studies in the positivist paradigm achieved the least number of citations collectively (136) but were the most cited per capita. An article-by-article citation rate showed the most frequently cited interpretivist themes to have been language in mathematics, professional learning communities as a sustainable vehicle for TP, mathematical knowledge for teaching and making connections in mathematics teaching and learning. The most frequently cited themes in the pragmatic paradigm were utilising learning environment assessment to improve teaching practices, school-based teacher professional learning (TPL) and mentoring as strategies for TPL. The most cited positivist themes were technology integration into the teaching and learning of mathematics and understanding of mathematical literacy.

Keywords
Interpretivist Positivist Pragmatic Mathematics teacher Professional learning Mathematical knowledge for teaching Practice-based professional learning Mentoring

Teachers are one of the key factors in students' learning; they shape the future of their students. TPACK is a framework designed by Mishra and Koehler (2006) to evaluate teachers' knowledge. Learning mathematics is an essential competency for students for their future lives. There are also many variables that influence the teaching of this discipline, such as human factors, social factors, and educational/ instructional factors.

new new This issue of The Progress of Education Reform reveals five surprising findings about the strong relationship between early math instruction and later student achievement. Researchers have found that early knowledge of math not only predicts later success in math, but also predicts later reading achievement even better than do early reading skills. The paper concludes with implications and recommendations for state policy that will support the development of early math competencies and young children. (Doug Clements and Julie Sarama, University of Denver, October 2013)

In this paper, I present and discuss findings from a research study the aim of which is to investigate the activity of proving as constituted in a Cypriot classroom for 12 year old students. Through Cultural-Historical Activity Theory (CHAT), the influence of research literature, curriculum prescriptions, the students and critically the teacher is documented. The evolution of objects, in particular the aims of the teacher, and other components in the activity systems is traced. Perceiving the mathematics classroom as a nested activity within educational context levels, this paper considers the role of the broader social context in which this classroom is situated. Theoretical framework. It is now acknowledged that proof and proving should become part of students' experiences throughout their schooling (Hanna, 2000; Stylianides, 2007; Yackel & Hanna, 2003). It is also argued that argumentation, explanation and justification provide a foundation for further work on developing deductive reasoning and the transition to a more formal mathematical study in which proof and proving are central (Yackel & Hanna, 2003). But what is meant by proof and proving? Mathematical argumentation is a discursive activity based on reasoning that supports or disproves an assertion and includes the exploration process, the formulation of hypotheses and conjectures, explaining and justifying the steps towards the outcome and the proof of the statement. Thus, proof is at the core of mathematical argumentation, as a justification, an explanation and a valid argument. Research has responded to the need to conceptualize proof and proving in such a way that it can be applied not only to older students but also to those in elementary school (Stylianides, 2007). The challenge remains however to understand how proof and proving is shaped by the practices in the mathematics classroom. This is in accordance with Herbst and Balacheff (2009), who argue that the focus should not only be on proof as the culminating stage of mathematical activity, but also on the proving process and how this is shaped by the classroom environment. Thus, in understanding how proving is constituted in the classroom, a wider network of ideas is required as these ideas no doubt have an impact on how proof in the narrow sense is constituted. To address this issue, I refer to pre-proving, that aspect of mathematical reasoning that might nurture proving. What are the roots of proving? The purpose of this study is to investigate proof and proving in the naturalistic setting of the classroom and the way the structuring resources of the classroom's setting shape this process. Instances of students proving statements have been identified in this classroom community but instances where the argument was not in the conceptual reach of the classroom have also been identified. However, this study also points to those aspects of reasoning that appear to have the qualities of proving, even though they may not be proving in themselves. That is, analyses of video-recorded whole class discussions show how processes of explaining and exploring are key subsystems within the central activity of proving as they provide a key pathway, which often includes defining. Thus, pre-proving refers to those elements that direct mathematical reasoning towards the ultimate goal of formal proving, namely exploring, explaining,

Background: Statistical graphs are widely used in society and are important in presenting data related to different topics. Statistics education aims improve the teaching and learning of statistics, which include the approaches to statistics graphs. Objectives: This article analyses the construction of statistical graphs by in-service teachers and their reasons for choosing these graphs. Design: It was conducted an empirical study from a qualitative perspective which investigated teachers' choices and constructions of statistical graphs. Setting and Participants: The participants were 22 primary school teachers from public schools located in Recife Metropolitan Area, Brazil. They expressed their intention to be interviewed when they responded to a questionnaire applied among a larger number of teachers. Data collection and analysis: The interviews were composed of two tasks comprised of statistical data in which participants had to choose a type of graph, justify the choice, and construct a graph of a chosen type. It was carried out a content analysis of speech protocols. Results: The reasons for participants' choices seemed to be related to their familiarity with the type of graph, and they constructed graphs with high levels of complexity. Conclusions: The results of this study emphasised the importance of primary school teachers developing specific knowledge about graphs through pre-service and in-service elementary school teacher education. The results from this research study offer new questions concerning the construction and the choice for statistical graphs, which include the influence of new technologies and the use of textbooks.

This research aimed to analyse the induction experiences of preservice mathematics teachers during their school placements through the lens of communities of practice. The main research question was concerned with how preservice mathematics teachers perceive what constitutes the practice of a professional community of mathematics teachers. A qualitative cross-sectional study was designed. Data collection tools consisted of face-to-face interviews and journals written by participants. Data was analysed using three modes of belonging in communities of practice framework: engagement, imagination and alignment. Findings indicated that participants had valuable observations with regard to professional relationships among mathematics teachers such as openness to exchange of ideas and collaboration. Data also revealed how preservice teachers align themselves with norms and values of university and school cultures. In most cases, preservice teachers endorsed norms of teacher education programs; e.g., they were critical about the traditional methods and the way technology was used in the partnership school. Their beliefs about the importance of confidence, strong subject knowledge and formative assessment were reinforced as a result of their observations in the partnership school.

Reforms in education of Science, Technology, Engineering, and Mathematics (STEM) disciplines have been particularly critical for the economic competitiveness of Turkey. There has been some criticism of the reforms at the teacher education level, claiming that Turkish teachers were not prepared to address the needs of their profession. The authors of this article introduced the STEM education model, which was designed with a critical investigation of the previous research on curriculum integration, STEM education, teaching knowledge, and Turkish educational reforms. By focusing on the interaction of mathematics and science, the model emphasized the importance of integrated teaching knowledge to successfully transition from the departmentalized model of teaching to an integrated model that promotes innovation.

La investigación en Educación Matemática suele centrarse en compartir los resultados de la aplicación de instrumentos de obtención de información. Si bien dichos instrumentos suelen describirse en la sección de metodología, el proceso de su desarrollo no suele ser muy transparente para el lector. En esta investigación el objetivo es abordar dicha problemática y describir con todo detalle el proceso de generación de un cuestionario, basado en el modelo MTSK, para la exploración del conocimiento del profesor acerca de la parábola, entendida como cónica. Se presenta el diseño de un instrumento de carácter cualitativo que permite hacer una aproximación al conocimiento matemático del profesor acerca de la parábola, poniendo énfasis tanto en el uso de la teoría, como de la triangulación, interna y externa, como elementos clave en el diseño metodológico. El principal aporte fue determinar pautas para el diseño de cuestionarios basados en el modelo MTSK, las cuales pueden ser tomadas en cuenta al margen de los contenidos matemáticos.