In this paper we unpack some possibilities around the importance of language within mathematical ... more In this paper we unpack some possibilities around the importance of language within mathematical inquiry communities in mainstream settings. Recognising that multiple forms of discourse and language can be used as a resource for facilitating mathematical communication within collaborative group work experiences, we explore the impact of a schoolbased intervention that incorporates visual features of New Zealand Sign Language (NZSL). Drawing on the experiences of introducing a range of vocabulary within mathematics lessons across Years One to Four in a mainstream school, we demonstrate some of the ways sign-supported communication can be used by teachers and students as part of everyday communication in the mainstream mathematics classroom. Using data from surveys and interviews, the community of learners report many positivesregarding communication practices. These include increased access to communication by previously hesitant students, increased teacher awareness of students’ thi...
Mathematics Education Research Group of Australasia, 2014
In early childhood settings narratives that capture children’s learning as they go about their da... more In early childhood settings narratives that capture children’s learning as they go about their day-to-day activities are promoted as a powerful assessment tool. However, in the New Zealand context there is increasing concern that learning stories currently downplay domain knowledge. Data from teacher interviews and samples of learning stories suggest that many teachers prefer to document and analyse mathematics learning that occurs within explicit mathematics activities rather than within play that involves mathematics.
The lack of full evaluations of curriculum change in NZ has prompted a project to establish a bas... more The lack of full evaluations of curriculum change in NZ has prompted a project to establish a basis for future evaluations. A longitudinal study of the curriculum is being done so that the interrelationships between parts of the curriculum can be identified., and the effect of change in any part can be monitored and/or predicted. Methodological problems of undertaking the project with limited resources is discussed. A new technique of 'icon development' using video material of students is described.
Mathematics Teacher Education and Development, 2019
Recently, calls have been made to improve student learning outcomes through focusing on teacher q... more Recently, calls have been made to improve student learning outcomes through focusing on teacher quality. Initial teacher education is considered to be one of the most important factors to enhance teacher quality and is closely linked with feelings of teaching efficacy in beginner teachers. Based on a study examining female Saudi preservice teachers’ (PSTs) sense of preparedness to teach mathematics at secondary or intermediate school level, this paper explores how well Saudi PSTs feel prepared to teach mathematics and their related teacher efficacy by examining interviews with a sample of PSTs, who were in the final year of their 4-year teacher education program. The findings show that these PSTs felt prepared regarding teaching methods and strategies but felt less prepared about other aspects of teaching, such as classroom management, lesson preparation, and integration of technology. The findings from this study contribute to the current efforts towards improving teacher quality w...
Practice-based initial teacher education reforms are typically organised around a set of core tea... more Practice-based initial teacher education reforms are typically organised around a set of core teaching practices, a set of normative principles to guide teachers’ judgement, and the knowledge needed to teach mathematics. Developing more than understandings, practices, and visions, practice-based pedagogies also need to support prospective teachers’ emergent dispositions for teaching. Based on the premise that an inquiry stance is a key attribute of adaptive expertise and teacher professionalism this paper examines the function and value of inquiry within practice-based learning. Findings from the Learning the Work of Ambitious Mathematics Teaching project are used to illustrate how opportunities to engage in critical and collaborative reflective practices can contribute to prospective teachers’ development of an inquiry-oriented stance. Exemplars of prospective teachers’ inquiry processes in action—both within rehearsal activities and a classroom inquiry—highlight the potential valu...
Qualitative data from lecturers and students were used to identify factors which were perceived a... more Qualitative data from lecturers and students were used to identify factors which were perceived as making the most important contributions to students' academic success or failure in fIrst-year mathematics courses. A questionnaire based on this information highlighted similarities and differences in the perceptions of lecturers and students about influences on students' success and failure. The results confIrm the importance of motivation and suggest further research is needed in the areas of active learning and student effort and workload. Introduction Most universities offer a range of first-year mathematics courses which cater for students of varying background knowledge and career aspirations. While in the past the assumption was that students entering a standard fIrst-year mathematics course had recently completed a complementary mathematics course at secondary school, it is increasingly evident that students in calculus and algebra courses come from a wider spectrum. O...
In New Zealand our newly qualified graduates for secondary teaching is increasingly dominated by ... more In New Zealand our newly qualified graduates for secondary teaching is increasingly dominated by of career change people. At a time when the media is continually questioning the status and capability of the teaching profession, we explore what or who motivates people to change their career paths and enter the teaching profession. Our sample of 70 change of career teachers reported multiple factors related to their decisions to pursue teaching. Factors included lifestyle concerns, increased job satisfaction, altruistic motives, interest in curriculum, and the influence of others. For some, the move to teaching was a return to an earlier decision; their intervening career viewed as a stop-off along the way. Whatever the matrix of motivations, it was notable that their career, family and personal interest experiences explicitly intersected with their decision to become a secondary teacher.
Mathematics Teacher Education and Development, 2018
In looking to further understanding of how teacher-educators enhance their professional knowledge... more In looking to further understanding of how teacher-educators enhance their professional knowledge and expertise, this paper explores how involvement in a design-based study focused on implementing pedagogies of practice occasioned learning. Driven by our desire to prepare beginning teachers to do the work of ambitious mathematics teaching we explore the affordance and constraints when learning to enact cycles of enactment and investigation of public rehearsals within methods and school-based settings. The opening of practice-based spaces, involving rehearsals of practice-based mathematical activities, supported learning from and with our colleagues and prospective teachers. Collectively, collaboration and inquiry within practice-based setting occasioned new possibilities of being a teacher-educator; possibilities that are more inclusive and responsive to the diversity of our prospective teachers’ learning and to that of the students they will teach.
The practicum experience is a critical component of any initial teacher education (ITE) course. A... more The practicum experience is a critical component of any initial teacher education (ITE) course. As well as providing a near authentic setting for pre-service teachers (PSTs) to practice in, it also plays a key role in shaping their perceptions and sense of preparedness. Nevertheless, merely including a practicum period as a compulsory part of ITE may not in itself be enough to induce feelings of preparedness and efficacy; the quality of the classroom experience must also be considered. Drawing on findings of a larger study of secondary and intermediate level mathematics PSTs' sense of preparedness to teach, this paper examines the influence of the practicum experience in particular. The study sample comprised female mathematics PSTs who had almost completed their teaching methods course in their fourth year of ITE across 16 teacher education programs in Saudi Arabia. The impact of the practicum experience on PSTs' sense of preparedness was investigated via a mixed-methods ap...
Mathematics Teacher Education and Development, 2015
Inrecent years there have been calls for ambitious mathematics teaching whichplaces student think... more Inrecent years there have been calls for ambitious mathematics teaching whichplaces student thinking and reasoning at the centre of instruction. This studyfocuses on how mathematics teacher educators (MTE) cansupport prospective teachers (PT) to learn the work of ambitious teachingthrough rehearsal activities. We analyse a series of rehearsals during amathematics methods course to illustrate how the rehearsal process can affordopportunities for PTs to learn to professionally notice students’ mathematicalthinking. The findings highlight three areas of importance related toprofessional noticing: making students’ thinking visible; eliciting andresponding to student thinking; and encountering dilemmas. Our analysis links the PTs development ofprofessional noticing to the role of community, the challenging of priorexperiences and the trajectory of learning, and our role as coach.
Mathematics Education Research Group of Australasia, 2018
This study investigates how well Saudi pre-service teachers feel prepared to teach mathematics at... more This study investigates how well Saudi pre-service teachers feel prepared to teach mathematics at secondary or middle schools through an interview-based exploration. The participants, a sample of 16 female mathematics pre-service teachers, were near the end of the final year of their 4-year education degree. Key findings show that these graduate teachers felt prepared in teaching methods and strategies, but less prepared about some aspects, namely classroom management, lesson preparation, and integration of technology. Findings from this study will contribute to the current drive to improve teacher and teaching quality, including initial teacher education in Saudi Arabia.
Mathematics Education Research Group of Australasia, 2012
How prospective teachers can best be prepared to teach effectively in mathematics classrooms is a... more How prospective teachers can best be prepared to teach effectively in mathematics classrooms is a topic of current concern. In this paper, we describe our exploration of ways in which prospective teachers were supported to translate what they learnt in mathematics methods classes into pedagogical practice. We illustrate how the use of discourse routines, enacted in iterative cycles of guided rehearsals, disrupted previous beliefs about teaching and learning mathematics and led to them more confidently respond in pedagogically appropriate ways.
In recent years, there have been ongoing calls from educational reformers that advocate the use o... more In recent years, there have been ongoing calls from educational reformers that advocate the use of ‘responsible’ or ‘ambitious’ pedagogies (Janssen, Grossman, & Westbroek, 2015). Such pedagogies engage students actively in inquiring and justifying their reasoning within learning communities. In this frame, teaching is viewed as both an interactional and improvisational work centred on students’ mathematical thinking and reasoning. Managing the contingent nature of ambitious teaching requires that both novices and experienced teachers learn a range of core high-leverage practices including eliciting and interpreting student thinking, leading class discussions, and facilitating small group work, to name some examples (Kazemi, Franke, Lampert, 2009). To master these core practices, prospective teachers must not only learn about the practices but also have opportunities to become skilled in these practices in a safe environment with support and guidance. This requires different forms of...
In this paper we unpack some possibilities around the importance of language within mathematical ... more In this paper we unpack some possibilities around the importance of language within mathematical inquiry communities in mainstream settings. Recognising that multiple forms of discourse and language can be used as a resource for facilitating mathematical communication within collaborative group work experiences, we explore the impact of a schoolbased intervention that incorporates visual features of New Zealand Sign Language (NZSL). Drawing on the experiences of introducing a range of vocabulary within mathematics lessons across Years One to Four in a mainstream school, we demonstrate some of the ways sign-supported communication can be used by teachers and students as part of everyday communication in the mainstream mathematics classroom. Using data from surveys and interviews, the community of learners report many positivesregarding communication practices. These include increased access to communication by previously hesitant students, increased teacher awareness of students’ thi...
Mathematics Education Research Group of Australasia, 2014
In early childhood settings narratives that capture children’s learning as they go about their da... more In early childhood settings narratives that capture children’s learning as they go about their day-to-day activities are promoted as a powerful assessment tool. However, in the New Zealand context there is increasing concern that learning stories currently downplay domain knowledge. Data from teacher interviews and samples of learning stories suggest that many teachers prefer to document and analyse mathematics learning that occurs within explicit mathematics activities rather than within play that involves mathematics.
The lack of full evaluations of curriculum change in NZ has prompted a project to establish a bas... more The lack of full evaluations of curriculum change in NZ has prompted a project to establish a basis for future evaluations. A longitudinal study of the curriculum is being done so that the interrelationships between parts of the curriculum can be identified., and the effect of change in any part can be monitored and/or predicted. Methodological problems of undertaking the project with limited resources is discussed. A new technique of 'icon development' using video material of students is described.
Mathematics Teacher Education and Development, 2019
Recently, calls have been made to improve student learning outcomes through focusing on teacher q... more Recently, calls have been made to improve student learning outcomes through focusing on teacher quality. Initial teacher education is considered to be one of the most important factors to enhance teacher quality and is closely linked with feelings of teaching efficacy in beginner teachers. Based on a study examining female Saudi preservice teachers’ (PSTs) sense of preparedness to teach mathematics at secondary or intermediate school level, this paper explores how well Saudi PSTs feel prepared to teach mathematics and their related teacher efficacy by examining interviews with a sample of PSTs, who were in the final year of their 4-year teacher education program. The findings show that these PSTs felt prepared regarding teaching methods and strategies but felt less prepared about other aspects of teaching, such as classroom management, lesson preparation, and integration of technology. The findings from this study contribute to the current efforts towards improving teacher quality w...
Practice-based initial teacher education reforms are typically organised around a set of core tea... more Practice-based initial teacher education reforms are typically organised around a set of core teaching practices, a set of normative principles to guide teachers’ judgement, and the knowledge needed to teach mathematics. Developing more than understandings, practices, and visions, practice-based pedagogies also need to support prospective teachers’ emergent dispositions for teaching. Based on the premise that an inquiry stance is a key attribute of adaptive expertise and teacher professionalism this paper examines the function and value of inquiry within practice-based learning. Findings from the Learning the Work of Ambitious Mathematics Teaching project are used to illustrate how opportunities to engage in critical and collaborative reflective practices can contribute to prospective teachers’ development of an inquiry-oriented stance. Exemplars of prospective teachers’ inquiry processes in action—both within rehearsal activities and a classroom inquiry—highlight the potential valu...
Qualitative data from lecturers and students were used to identify factors which were perceived a... more Qualitative data from lecturers and students were used to identify factors which were perceived as making the most important contributions to students' academic success or failure in fIrst-year mathematics courses. A questionnaire based on this information highlighted similarities and differences in the perceptions of lecturers and students about influences on students' success and failure. The results confIrm the importance of motivation and suggest further research is needed in the areas of active learning and student effort and workload. Introduction Most universities offer a range of first-year mathematics courses which cater for students of varying background knowledge and career aspirations. While in the past the assumption was that students entering a standard fIrst-year mathematics course had recently completed a complementary mathematics course at secondary school, it is increasingly evident that students in calculus and algebra courses come from a wider spectrum. O...
In New Zealand our newly qualified graduates for secondary teaching is increasingly dominated by ... more In New Zealand our newly qualified graduates for secondary teaching is increasingly dominated by of career change people. At a time when the media is continually questioning the status and capability of the teaching profession, we explore what or who motivates people to change their career paths and enter the teaching profession. Our sample of 70 change of career teachers reported multiple factors related to their decisions to pursue teaching. Factors included lifestyle concerns, increased job satisfaction, altruistic motives, interest in curriculum, and the influence of others. For some, the move to teaching was a return to an earlier decision; their intervening career viewed as a stop-off along the way. Whatever the matrix of motivations, it was notable that their career, family and personal interest experiences explicitly intersected with their decision to become a secondary teacher.
Mathematics Teacher Education and Development, 2018
In looking to further understanding of how teacher-educators enhance their professional knowledge... more In looking to further understanding of how teacher-educators enhance their professional knowledge and expertise, this paper explores how involvement in a design-based study focused on implementing pedagogies of practice occasioned learning. Driven by our desire to prepare beginning teachers to do the work of ambitious mathematics teaching we explore the affordance and constraints when learning to enact cycles of enactment and investigation of public rehearsals within methods and school-based settings. The opening of practice-based spaces, involving rehearsals of practice-based mathematical activities, supported learning from and with our colleagues and prospective teachers. Collectively, collaboration and inquiry within practice-based setting occasioned new possibilities of being a teacher-educator; possibilities that are more inclusive and responsive to the diversity of our prospective teachers’ learning and to that of the students they will teach.
The practicum experience is a critical component of any initial teacher education (ITE) course. A... more The practicum experience is a critical component of any initial teacher education (ITE) course. As well as providing a near authentic setting for pre-service teachers (PSTs) to practice in, it also plays a key role in shaping their perceptions and sense of preparedness. Nevertheless, merely including a practicum period as a compulsory part of ITE may not in itself be enough to induce feelings of preparedness and efficacy; the quality of the classroom experience must also be considered. Drawing on findings of a larger study of secondary and intermediate level mathematics PSTs' sense of preparedness to teach, this paper examines the influence of the practicum experience in particular. The study sample comprised female mathematics PSTs who had almost completed their teaching methods course in their fourth year of ITE across 16 teacher education programs in Saudi Arabia. The impact of the practicum experience on PSTs' sense of preparedness was investigated via a mixed-methods ap...
Mathematics Teacher Education and Development, 2015
Inrecent years there have been calls for ambitious mathematics teaching whichplaces student think... more Inrecent years there have been calls for ambitious mathematics teaching whichplaces student thinking and reasoning at the centre of instruction. This studyfocuses on how mathematics teacher educators (MTE) cansupport prospective teachers (PT) to learn the work of ambitious teachingthrough rehearsal activities. We analyse a series of rehearsals during amathematics methods course to illustrate how the rehearsal process can affordopportunities for PTs to learn to professionally notice students’ mathematicalthinking. The findings highlight three areas of importance related toprofessional noticing: making students’ thinking visible; eliciting andresponding to student thinking; and encountering dilemmas. Our analysis links the PTs development ofprofessional noticing to the role of community, the challenging of priorexperiences and the trajectory of learning, and our role as coach.
Mathematics Education Research Group of Australasia, 2018
This study investigates how well Saudi pre-service teachers feel prepared to teach mathematics at... more This study investigates how well Saudi pre-service teachers feel prepared to teach mathematics at secondary or middle schools through an interview-based exploration. The participants, a sample of 16 female mathematics pre-service teachers, were near the end of the final year of their 4-year education degree. Key findings show that these graduate teachers felt prepared in teaching methods and strategies, but less prepared about some aspects, namely classroom management, lesson preparation, and integration of technology. Findings from this study will contribute to the current drive to improve teacher and teaching quality, including initial teacher education in Saudi Arabia.
Mathematics Education Research Group of Australasia, 2012
How prospective teachers can best be prepared to teach effectively in mathematics classrooms is a... more How prospective teachers can best be prepared to teach effectively in mathematics classrooms is a topic of current concern. In this paper, we describe our exploration of ways in which prospective teachers were supported to translate what they learnt in mathematics methods classes into pedagogical practice. We illustrate how the use of discourse routines, enacted in iterative cycles of guided rehearsals, disrupted previous beliefs about teaching and learning mathematics and led to them more confidently respond in pedagogically appropriate ways.
In recent years, there have been ongoing calls from educational reformers that advocate the use o... more In recent years, there have been ongoing calls from educational reformers that advocate the use of ‘responsible’ or ‘ambitious’ pedagogies (Janssen, Grossman, & Westbroek, 2015). Such pedagogies engage students actively in inquiring and justifying their reasoning within learning communities. In this frame, teaching is viewed as both an interactional and improvisational work centred on students’ mathematical thinking and reasoning. Managing the contingent nature of ambitious teaching requires that both novices and experienced teachers learn a range of core high-leverage practices including eliciting and interpreting student thinking, leading class discussions, and facilitating small group work, to name some examples (Kazemi, Franke, Lampert, 2009). To master these core practices, prospective teachers must not only learn about the practices but also have opportunities to become skilled in these practices in a safe environment with support and guidance. This requires different forms of...
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