Approaches to teaching in thematic work: early childhood teachers’ integration of mathematics and art

Thematic work that integrates different knowledge areas is considered suitable for developing young children’s knowledge and skills in early childhood education. This paper reports evidence from a survey of early childhood teachers’ work with mathematics and art integrated in thematic work. In this study, we aim to explore how teachers perceive mathematics learning and teaching integrated with art. Data for analysis were collected from a questionnaire answered by 27 early childhood teachers from Finland and Sweden. Influenced by a sociocultural theoretical framework, the analysis concerns the teachers’ expressed goals for learning and their strategies for achieving these goals. The analysis reveals qualitatively different approaches to the learning goals addressed by the teachers – process-oriented, product-oriented, development-oriented and providing awareness – which, respectively, seem to generate different meanings of mathematical learning integrated with art. This study offers an overview of teachers’ approaches to teaching mathematics and art in thematic work, and of how different approaches may influence what mathematical meaning is offered to children to explore.     

Understanding and supporting Chinese middle Schoolers’ monitoring accuracy in mathematics

Metacognition and Learning - While many studies of monitoring accuracy have been conducted with college students, less is known about middle school students’ monitoring accuracy, especially...     

Routines and collective orientations in mathematics teachers’ professional development

There is an increasing awareness of the social dimension in mathematics teacher education. Collaboration and co-operation are regarded as key factors in professional development. In this paper I will analyse some tensions that might arise when the professional development of mathematics teachers is considered a collective enterprise. I will present phenomenological group interview as a method that is designed to reveal the collective character of teacher development. Some primary teachers’ collective reflections on an ongoing professional development process will be interpreted by focusing on the concepts of routine and collective orientation. The discussion is centred on the ambivalence of routines, as facilitators of practice, and collective orientations, as socially-agreed-upon knowledge base, for mathematics teachers’ professional development.

Prospective teachers’ analysis of a mathematics lesson: examining their claims and supporting evidence

Journal of Mathematics Teacher Education - This study examined elementary and secondary prospective teachers’ (PTs’) abilities to analyze a classroom lesson in order to make claims...     

EFL teachers’ challenges and dilemmas in transferring theories and practices cross-culturally

This paper explores the performance and shared learning experiences of a group of English as a foreign language (EFL) teachers studying in a U.S.-based graduate program. In order to assimilate the knowledge, a voluntary group was naturally formed outside a graduate course. The group meetings lasted from 4 to 5 hours on a weekly basis during a 13-week semester. The focus of this paper is to report and discuss the challenges and dilemmas facing EFL teachers when transferring new theories and knowledge to participants’ home contexts.     

Unpacking foreshadowing in mathematics teachers’ planned practices

This paper provides an empirical exploration of mathematics teachers’ planned practices. Specifically, it explores the practice of foreshadowing, which was one of Wasserman’s (2015) four mathematical teaching practices. The study analyzed n?=?16 lessons that were planned by pairs of highly qualified and experienced secondary mathematics teachers, as well as the dialogue that transpired, to identify the considerations the teachers made during this planning process. The paper provides empirical evidence that teachers engage in foreshadowing as they plan lessons, and it exemplifies four ways teachers engaged in this practice: foreshadowing concepts, foreshadowing techniques, foregrounding concepts, and foregrounding techniques. Implications for mathematics teacher education are discussed.

     

Provision of in-service training of mathematics and science teachers in Botswana: teachers’ perspectives

Teaching is a field that is dynamic, with innovations necessitating upgrading of skills and education of teachers for the successful implementation of reforms. The behaviour and attitudes of teachers towards teaching and learning and their knowledge banks are the result of the impact of in-service training. This study investigated the perceptions of mathematics and science teachers in Botswana towards in-service provision by the Department of Mathematics and Science Education In-service Training unit (DMSE-INSET), whose mandate is to improve the quality of teaching by supporting teachers through training programmes that enable them to take ownership of their professional development. Data were collected from a sample of 42 senior Mathematics and Science secondary school teachers, using structured interviews with open-ended questions, which were analyzed qualitatively. The findings show that teachers’ concerns included the lack of impact of current in-service training programmes on the education system, no regular follow-up activities to support the one-off workshops and insufficient skills acquired to sustain the implementation of the strategies solicited by the workshops.     

Supporting primary-level mathematics teachers’ collaboration in designing and using technology-based scenarios

In this article, we address how the design of educational scenarios can support teachers’ adoption of both technology and open-ended projects indorsing creativity and innovation. We do that by describing how groups of teachers develop digital learning environments supporting using a combination of GeoGebra and Google sites. Both teachers and pupils work with the concept of “game” as something they design, and furthermore, the pupils immerse themselves into the scenarios that the teachers create in a way similar to “playing a game.” We investigate teachers participation in collaborative development and testing through qualitative means, aiming to describe the teachers’ appropriation of (1) GeoGebra as a tool for doing and teaching mathematics, and (2) game as a metaphor supporting open-ended projects addressing creativity and innovation in the classroom. The data from the project suggest that the notion of “game” can support collaborative scenario design is a viable way of introducing technology and open-ended projects to primary school teachers.     

Exploring early childhood preservice teachers’ mathematics anxiety and mathematics efficacy beliefs

Early childhood preservice teachers participated in a qualitative multiple case study to explore and examine the effectiveness of reform-based constructivist methods used in a mathematics methods course to change their mathematics anxiety, mathematics self-efficacy, and mathematics teachers’ efficacy beliefs. Findings indicated that instructor’s use of a variety of reform-based strategies to teach and model concepts were effective in reducing their mathematics anxiety and improving their mathematics self-efficacy and mathematics teaching efficacy beliefs. Based on these findings, it is recommended that mathematics methods course instructors use reform-based constructivist methods in their courses as outlined by the NCTM’s (2014) principles. Teacher educators must also consider carefully their attitudes and disposition toward mathematics along with the type of classroom and learning environment they establish in mathematics methods courses. They must emphasize conceptual understanding during mathematics methods courses, understand the connection between preservice teachers’ mathematics anxiety and mathematics efficacy beliefs, and integrate field experiences as well as peer teaching opportunities into mathematics methods courses.     

Primary mathematics teachers’ goal orientations and student achievement

Primary mathematics teachers’ (N = 521) personal goal orientation and instructional practices were examined based on questionnaire responses. The teachers (grades 2 and 3) were oriented towards mastery goals and mastery approaches to instruction, and reported high teaching efficacy. Strong positive relation between performance orientation and performance instructional practices was established, and correspondingly between mastery orientation and mastery instructional practices. Positive relations between students’ (N = 9,980) basic mathematics performance (measured by paper and pencil tests) and both teacher mastery orientation and teaching efficacy were also found. Results indicate that mastery oriented teaching strategies are crucial for fostering basic mathematical competencies in primary students.     

Pre-service primary teachers’ conceptions of creativity in mathematics

Teachers in the UK and elsewhere are now expected to foster creativity in young children (NACCCE, 1999; Ofsted, 2003; DfES, 2003; DfES/DCMS, 2006). Creativity, however, is more often associated with the arts than with mathematics. The aim of the study was to explore and document pre-service (in the UK, pre-service teachers are referred to as ‘trainee’ teachers) primary teachers’ conceptions of creativity in mathematics teaching in the UK. A questionnaire probed their conceptions early in their course, and these were supplemented with data from semi-structured interviews. Analysis of the responses indicated that pre-service teachers’ conceptions were narrow, predominantly associated with the use of resources and technology and bound up with the idea of ‘teaching creatively’ rather than ‘teaching for creativity’. Conceptions became less narrow as pre-service teachers were preparing to enter schools as newly qualified, but they still had difficulty in identifying ways of encouraging and assessing creativity in the classroom. This difficulty suggests that conceptions of creativity need to be addressed and developed directly during pre-service education if teachers are to meet the expectations of government as set out in the above documents.     

Investigating teachers’ images of mathematics

Research suggests that understanding new images of mathematics is very challenging and can contribute to teacher resistance. An explicit exploration of personal views of mathematics may be necessary for pedagogical change. One possible way for exploring these images is through mathematical metaphors. As metaphors focus on similarities, they can be used to express already-held perceptions about the nature of mathematics. In addition to providing a way of talking about current views of mathematics, the analogous dimensions of metaphors can prompt new ways of thinking about these images. In this article, I consider the use of metaphors as a strategy for explicating elementary teachers’ views of mathematics. I claim that the investigation of metaphors of mathematics helped create a shared communicative space and enhanced the quality of the discussion with the teachers. In particular, our exploration of the metaphor mathematics is a language encouraged a consideration of the humanistic dimensions of mathematics and contributed to a varied re-imaging of mathematics.     

Pre-service versus in-service mathematics teachers’ opinions of mathematics reform in post-primary schools in Ireland

A new approach to the teaching and learning of mathematics has been introduced on a phased basis in post-primary education in Ireland. As part of the OECD PISA 2012, a survey was undertaken of in-service mathematics teachers in Ireland, with the aim of gathering data on the opinions of teachers about this reform. Here, a modified version of the survey was distributed to pre-service teachers immediately before and after a four-month teaching placement to ascertain if there were differences in the views expressed by pre-service and in-service teachers in relation to the teaching and learning of mathematics, and also if there were differences expressed by the pre-service teachers before and after their placement in post-primary schools. Analysis of the results showed considerable levels of agreement between all groups, with some exceptions in relation to confidence in teaching the reformed curriculum, emphasis on various teaching and learning activities, and usage of ICT in the classroom.     

Students’ and teachers’ perceptions of classroom learning environment in Bhutanese eighth-grade mathematics classes

This paper reports a study of students’ and teachers’ perceptions of their classroom learning environment in Bhutanese eighth-grade mathematics classes. Research suggests that positive perceptions of the learning environment can have a positive influence on students’ learning outcomes, interest and engagement in classroom activities. The study was conducted in 2013, using the survey samples of 608 students and 98 teachers from 22 lower- and middle-secondary schools in western Bhutan. Students’ and teachers’ perceptions of the classroom environment were measured using the Mathematics Classroom Learning Environment Survey (MCLES). Students and teachers mostly perceived their classroom environments favourably on the MCLES scales irrespective of gender, school level and school location. The study is significant for understanding and evaluating the implementation of new mathematics curriculum in Bhutanese schools because it could guide the development of strategies for more-productive mathematics classroom learning. It is also significant from the perspective of Bhutan’s national goal of Gross National Happiness because perceptions and happiness always go hand-in-hand.     

Characteristics of teachers’ choice of examples in and for the mathematics classroom

The main goal of the study reported in our paper is to characterize teachers’ choice of examples in and for the mathematics classroom. Our data is based on 54 lesson observations of five different teachers. Altogether 15 groups of students were observed, three seventh grade, six eighth grade, and six ninth grade classes. The classes varied according to their level—seven classes of top level students and six classes of mixed—average and low level students. In addition, pre and post lesson interviews with the teachers were conducted, and their lesson plans were examined. Data analysis was done in an iterative way, and the categories we explored emerged accordingly. We distinguish between pre-planned and spontaneous examples, and examine their manifestations, as well as the different kinds of underlying considerations teachers employ in making their choices, and the kinds of knowledge they need to draw on. We conclude with a dynamic framework accounting for teachers’ choices and generation of examples in the course of teaching mathematics.

Characterizing pivotal teaching moments in beginning mathematics teachers’ practice

Although skilled mathematics teachers and teacher educators often “know” when interruptions in the flow of a lesson provide an opportunity to modify instruction to improve students’ mathematical understanding, others, particularly novice teachers, often fail to recognize or act on such moments. These pivotal teaching moments (PTMs), however, are key to instruction that builds on student thinking about mathematics. Video of beginning secondary school mathematics teachers’ instruction was analyzed to identify and characterize PTMs in mathematics lessons and to examine the relationships among the PTMs, the teachers’ decisions in response to them, and the likely impacts on student learning. These data were used to develop a preliminary framework for helping teachers learn to identify and respond to PTMs that occur during their instruction. The results of this exploratory study highlight the importance of teacher education preparing teachers to (a) understand the mathematical terrain their students are traversing, (b) notice high-leverage student mathematical thinking, and (c) productively act on that thinking. This preparation would improve beginning teachers’ abilities to act in ways that would increase their students’ mathematical understanding.     

Prospective elementary teachers’ aesthetic experience and relationships to mathematics

Previous research has adopted various approaches to examining teachers’ and students’ relationships to mathematics. The current study extended this line of research and investigated six prospective elementary school teachers’ experiences in mathematics and how they saw themselves as learners of mathematics. One-on-one interviews with the participants were conducted, and their written reflections were collected. A grounded-theory approach and a framework for analyzing mathematics identities were adopted in data analysis. The findings showed that the participants’ development of obligations-to-oneself was associated with not only their opportunity to exercise conceptual agency but also their aesthetic experience with mathematics. Their views on themselves as learners of mathematics had cognitive, affective, and aesthetic dimensions. The findings suggest that teachers and students can engage in a reflection on their aesthetic involvement in doing mathematics. There is a need for a local theory of aesthetics in K-12 mathematics.     

Preservice teachers’ use of contrasting cases in mathematics instruction

Drawing comparisons between students’ alternative solution strategies to a single mathematics problem is a powerful yet challenging instructional practice. We examined 80 preservice teachers’ when asked to design a short lesson when given a problem and two student solutions—one correct and one incorrect. These micro-teaching events were videotaped and coded, revealing that fewer than half of participants (43%) made any explicit comparison or contrasts between the two solution strategies. Those who did were still not likely to use additional support strategies to draw students’ attention to key elements of the comparison. Further, correlations suggest that participants’ mathematical content knowledge may be related to whether participants’ showed contrasting cases but not to whether they used specific pedagogical cues to support those comparisons. While these micro-teaching events differ from the interactive constraints of a classroom, they reveal that participants did not immediately orient toward differing student solutions as a discussion opportunity, and that future instruction on contrasting cases must highlight the utility of this practice.