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.     

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.

     

Prospective Turkish primary teachers’ views about the use of computers in mathematics education

The use of computers and technology in mathematics education affects students’ learning, achievements, and affective dimensions. This study explores prospective Turkish primary mathematics teachers’ views about the use of computers in mathematics education. The sample comprised of 129 fourth-year prospective primary mathematics teachers from two different universities in Turkey. Data consisting of participants’ written responses were qualitatively analyzed and categorized according to TPACK. Results show that the prospective teachers’ views about computers and their use in mathematics are usually positive. They enjoy working with computers, even though they are only able to perform relatively minor calculations with computers. They stated that improved use of computers can help them to learn and teach mathematics more effectively. However, they did not feel confident about their ability to teach mathematics using computers.     

Teachers’ assessment practices in mathematics: classrooms in the context of reform

This article responds to calls that have been made for research into how teachers incorporate new assessment ideas into their practice. We draw on a large‐scale study that examined the implementation of reform in mathematics in grades 7–10 in Ontario, Canada. We present teacher questionnaire data, and focus on data gathered from case studies for details of what new assessment practices look like in classrooms. We show teachers using a variety of forms of assessment and using assessment to improve student learning. Observed assessment practices went beyond tests to include the use of journals, observation, questioning, self‐assessment and unique forms of ‘quizzes’. These practices allowed teachers to examine students’ mathematical thinking and provided feedback to students and teachers to improve student learning. We also observed the important role of collaboration, coherence, and the teachers’ beliefs in supporting new assessment practices.     

Kyouzaikenkyuu: an exploration of Japanese mathematics teachers’ daily planning practices

Journal of Mathematics Teacher Education - Kyouzaikenkyuu (translated as instructional materials research) is said to be a crucial part of successful Japanese lesson study. Kyouzaikenkyuu is...     

Primary teachers’ epistemological beliefs: some perceived barriers to investigative teaching in primary mathematics

A recent investigation of primary teachers’ epistemological beliefs concerning the teaching and learning of mathematics discovered that teachers’ beliefs cannot be said to form neat world views. Teachers’ hybrid world views often included epistemological beliefs that supported teaching approaches which evidence suggests leads to greater conceptual understanding of mathematics. Classroom observations and semi‐structured interviews with primary teachers suggested that although there is a desire to adopt an investigative approach, this is perceived to be largely incompatible with some of the requirements of the UK National Curriculum. Common potential barriers identified by teachers included: the volume of curriculum content they are required to cover, the limited time available to cover it, some working practices perceived to be associated with the current emphasis on teacher accountability and the current method of assessment by Standard Assessment Task tests (SATs). The findings are discussed in relation to challenges facing UK policy‐makers if an approach to teaching primary mathematics, which is known to support conceptual understanding, is to flourish.     

Explanations of attitudes to change: Colombian mathematics teachers’ conceptions of the crucial determinants of their teaching practices of beginning algebra

This article arises from a study whose overall purpose was to investigate the relationship between Colombian mathematics teachers’ conceptions of beginning algebra and their conceptions of their own teaching practices. The teachers’ understandings of their teaching practices were explored with a view to unravelling their conceptions of change in their teaching. Focusing on the perspectives of teachers afforded opportunities that exposed the powerful role that the teachers’ conceptions of social/institutional factors of teaching played in their conceptions of their practices. The degree to which the teachers attributed these (external) factors as crucial reasons for what they do in their teaching was the basis of a categorisation of their conceptions of the crucial determinants of their teaching practices into three types. The findings are particularly relevant to our understanding of the stability of mathematics teaching approaches in the Colombian context but have likely implications for a range of international education contexts. Specific implications for the development of the research into teachers’ conceptions of mathematics and its teaching, and for teacher education programmes are presented.

The primary school’s invasion of the privacy of the child: unmasking the potential of some current practices

Privacy has been defined as “the protective buffer within which people can avoid another party’s taking something from them, keeping watch over them, or entering into their lives in a way that is both unwelcome and undesirable”. It is a premise of this paper that such a position needs to be taken very seriously in contemporary society, and particularly in the case of schools, as school personnel have the capacity to engage in practices which show great disregard for individual and family privacy. This is illustrated in the case of primary school education in the Republic of Ireland. Particular attention is paid to assessment, pedagogical and curricular practices that derive from patterns of systematic and mandatory disclosure that are confessional, performative and public.     

Jordanian twelfth-grade science teachers’ self-reported usage of science and engineering practices in the next generation science standards

This study investigated the degree that Science and Engineering Practices (SEPs) criteria from the Next Generation Science Standards (NGSS) were included in self-reported teaching practices of twelfth-grade science teachers in Jordan. This study sampled (n?=?315) science teachers recruited from eight different public school directorates. The sample was surveyed using an instrument adapted from Kawasaki (2015). Results found that Jordanian science teachers incorporate (SEPs) in their classroom teaching at only a moderate level. SEPs applied most frequently included ‘using the diagram, table or graphic through instructions to clarify the subject of a new science,’ and to ‘discuss with the students how to interpret the quantitative data from the experiment or investigation’. The practice with the lowest frequency was ‘teach a lesson on interpreting statistics or quantitative data,’ which was moderately applied. No statistically significant differences at (α?=?0.05) were found among these Jordanian science teachers’ self-estimations of (SEP) application into their own teaching according to the study’s demographic variables (specialisation, educational qualification, teaching experience). However, a statistically significant difference at (α?=?0.05) was found among Jordanian high school science teachers’ practice means based on gender, with female teachers using SEPs at a higher rate than male teachers.     

Spoon-feeding to tongue-biting and beyond: factors that contributed to changes in Irish primary school teachers’ mathematics practice

Research that aimed to examine teachers’ experiences whilst implementing a reform approach to mathematics teaching in an Irish primary school forms the basis of this paper. In particular, factors that contributed to changing mathematics practice in this case study school are outlined. The school engaged in professional development (PD) that focused on using an instructional framework [Hiebert, J., T. P. Carpenter, E. Fennema, K. C. Fuson, D. Wearne, H. Murray, A. Olivier, and P. Human. 1997. Making Sense: Teaching and Learning Mathematics with Understanding. Portsmouth: Heinemann] in the school-identified strand units of length and weight. Four classes were tracked throughout the study and each class acted as a sub-case within the larger study. Data collected through lesson observations, teacher interviews, pupil work samples, and pupil focus group interviews were used to compare teachers’ experiences and to identify what supported and enabled them to change their practice, in addition to highlighting challenges that may have prevented such change. Findings were that shifts in practice were evident to different degrees in the four classes during the study. In relation to enabling factors, findings suggest that tailored PD, and the use and refinement of an instructional framework contributed to enabling teachers in changing their mathematics teaching. In particular, teachers reported that the 4Ts instructional framework was a very useful tool in supporting them to change mathematics teaching.     

The impact of instruction in enhancing teachers’ knowledge of teaching mathematics in some Lesotho primary schools

The quality of mathematics teaching in Lesotho primary education remains one of the vexing problems in the education system. The study investigated how teachers viewed the impact of instruction on enhancing their knowledge of teaching. Data for the study were elicited from the second-year students enrolled for a Bachelor of Education in the 2009/10 academic year at the National University of Lesotho. Questionnaires and interviews were used for data collection. The findings show that before instruction, the teachers operated with limited knowledge of teaching. At the end of the course the teachers’ knowledge of teaching was enhanced. Significant change was apportioned to engaging in reflection and teaching for relational understanding. Implications of the findings for the course, teacher education and professional development are also 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.     

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.

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.     

Implementing inclusion in disabling settings: the role of teachers’ attitudes and practices

Teachers’ attitudes towards disabled students seem to define the extent to which teaching practices are inclusive. Aiming to explore Cyprus secondary education teachers’ attitudes and practice, and the consequent implications for the future of disabled students and inclusive education, we conducted mixed methods research. Our research typology was sequential and integrated. First, we conducted a survey, during which we received 536 questionnaires from our randomly selected stratified sample of Cyprus secondary education teachers. The survey was followed by interviews with 21 Greek Philology teachers that enriched the findings from the quantitative phase. Data analysis revealed that even though Cyprus secondary education teachers have a rather positive attitude towards disabled students, they have low expectations from them and do not employ inclusive teaching practice. In addition, they tend to categorise students based on abstract notions about ability. Stereotypes and prejudice are more evident regarding students with cognitive disabilities. Despite the observed disabling practices, participants postulated that there is hope to implement inclusive education, if teachers are trained for inclusion and thereby begin to see the person and not the disability.     

Supporting school teachers: primary teachers’ conceptions of their responses to diverse sexualities

Teachers experience a range of situations in the primary school context where students talk about, share ideas and use words and actions that might be described as non-heteronormative in character. This article reports on teachers’ experiences of the ways in which they respond to actions and events they see as non-heteronormative. It identifies six different ways in which teachers conceptualise their pedagogical responses to the situations they encounter: (1) being nonchalant, (2) avoiding a response, (3) being uncertain, (4) maintaining home and school boundaries, (5) protecting students’ well-being and (6) embracing non-heteronormative sexualities. Teachers’ responses to these events are important in that their actions may affect how students interpret and understand the world. Primary school teachers will benefit from support in knowing how to respond appropriately when faced with a scenario or situation that is non-heteronormative in character.