Despite international interest on research into the preparation of pre-service mathematics teache... more Despite international interest on research into the preparation of pre-service mathematics teachers, the role of school-based subject mentors remains an under-explored area in the mathematics teacher education and professional development in general. In this paper, an exploratory study based on a multiple case approach that sought three experienced school-based mathematics mentors' views of their own roles in developing the pre-service teachers' knowledge for teaching mathematics is presented. With a particular focus on the specialised content knowledge (SCK) category from Ball et al.'s (2008) conceptualisation of mathematics knowledge for teaching, thematic analysis of the interview data indicates that development of pre-service teachers' such knowledge is influenced by and depends on mentors' own personal construct of subject specific mentoring. For pre-service teachers to fully benefit from their teaching practice, an explicit model of subject-specific mentoring is needed.
HAL (Le Centre pour la Communication Scientifique Directe), Feb 2, 2022
This paper presents a graduate student's reflections on the design of learning opportunities usin... more This paper presents a graduate student's reflections on the design of learning opportunities using the Desmos tool for carrying out mathematical activities and the online Zoom platform for facilitating mathematical learning. Using the theory of instrumental orchestration as our interpretative framework, we discuss the different types of orchestrations when a digital tool is used to support mathematical learning not in the familiar face-to-face classroom-based environment, but online instead. The contribution of this paper lies in the discussion of the design considerations and orchestrations to overcome the challenges of online learning and at the same time to capitalise on the opportunities it offers for mathematical learning.
The shortage of mathematics teachers in the UK has led to a number of government initiatives aimi... more The shortage of mathematics teachers in the UK has led to a number of government initiatives aiming to increase the supply of teachers of mathematics (e.g., DfE 2014). One set of initiatives concerns up-skilling teachers who are already employed at a school or college and who are teaching some mathematics, but who initially trained to teach in a subject other than mathematics. These non-specialist teachers of mathematics have come for in-service training at the university where they learn more mathematics relevant to the school curriculum. The participants in such courses expect to transfer their pedagogical knowledge from their initial specialism into the context of mathematics teaching as a result of developing their mathematical subject knowledge. We have run such courses for four years and this report draws on some of the data collected over this period. The particular finding that we report on here concerns participant aspiration and resistance. For instance, gaining certificat...
In this paper I will report on a project aimed at raising awareness of the undergraduates at Univ... more In this paper I will report on a project aimed at raising awareness of the undergraduates at University College London (UCL) about the research wealth and research culture of the math-ematics department. The project trialled the ‘Meet your researcher’ strategy for engaging undergraduates (UGs) and postgraduates (PGRs) in a partnership intended to develop UGs’ understanding from early on in their studies about what research is and what researchers do.
This paper reports on a research project based on designing and teaching in-service courses for N... more This paper reports on a research project based on designing and teaching in-service courses for Non-Specialist Teachers of Mathematics (NSTM). An NSTM is a school teacher who qualified to teach in a subject other than mathematics, yet teaches mathematics in secondary school (11-16 year old students). While the overall aim of our research was to describe what constitutes a trajectory towards a mathematics teacher identity for a NSTM, in this paper we explain how we sought indicators of a mathematics teacher identity. We do so by first describing how we adapted Wenger’s notion of identity and advanced our ‘Modes of Belonging’ Mathematics Teacher Identity framework. After that we exemplify how we used our framework to locate indicators of mathematics teacher identity in the data from a narrative of NSTMs working on a particular piece of mathematics.
use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you g... more use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this book are included in the book's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the book's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
In this paper we present the model behind our on-line master level module Digital Technologies fo... more In this paper we present the model behind our on-line master level module Digital Technologies for Mathematical Learning, which focuses on the teaching and learning supported by digital technologies. In our evaluation of the delivery of this module over two years, we reflect here on the emergence of two pedagogies: the online pedagogy of the tutors, ensuring that online teaching and learning is effective and the participants’ developing RiTPACK (Research Informed Technological Pedagogical Content Knowledge - our own acronym for this concept) as they start experimenting with using the digital technology in their classroom practice and linking it with the research knowledge base of the module.
In this paper, we report on four university lecturers' first-time experiences with computer-aided... more In this paper, we report on four university lecturers' first-time experiences with computer-aided assessments. They were required to automate a significant proportion of the pre-existing weekly coursework for modules in first-or second-year undergraduate mathematics using STACK. We consider lecturers' perspectives on the role of computer-aided assessments in course design for undergraduate mathematics; the knowledge of technical aspects required to implement STACKbased assessments; and the perceived merits of automated assessment for different aspects of mathematical study. We conclude with a series of reflections upon our departmental practice and the process of enculturating mathematicians into the realm of automated assessment.
Since ‘advanced mathematics knowledge’ (AMK) was first conceptualized by Zaskis and Leikin (2009)... more Since ‘advanced mathematics knowledge’ (AMK) was first conceptualized by Zaskis and Leikin (2009), researchers have striven to determine whether teachers’ ability to identify explicit connections between AMK and the mathematics taught in school is a rare gift of only a few teachers or whether specific prompting is needed to develop this ability in teachers. In this paper we provide empirical evidence showing that those teachers who attended a CPD designed to support them to ‘see’ and make explicit such connections, have increased their awareness of the implications for the teaching and learning of school mathematics topics in ways that allow for creating a solid foundation for development of further, more advanced ideas in the school mathematics curriculum. We thus propose that any mathematics teacher, irrespective of their academic background, could benefit from professional development opportunities where explicit guidance is provided in terms of the relevant AMK and how it inform...
In this paper I report on a study of secondary school mathematics teachers' use of ICT. The study... more In this paper I report on a study of secondary school mathematics teachers' use of ICT. The study adds new dimensions to understanding teachers' use of ICT by treating the teaching of mathematics and ICT use as interwoven aspects of a teacher's practice. The analysis of the data collected using a case study research strategy yielded a number of salient factors, of both contextual and personal nature, which were identified as key to the integration of ICT into mathematics teaching. A framework which conceptualises teachers' learning about the potential and limitations of ICT and teachers' incorporation of ICT in their teaching of mathematics will be advanced with the aim of contributing to a better understanding of the pedagogy of teaching mathematics with ICT.
Learning from the pandemic: Capitalising on opportunities and overcoming challenges for mathemati... more Learning from the pandemic: Capitalising on opportunities and overcoming challenges for mathematics teaching and learning practices with and through technology Conference or Workshop Item How to cite: Clark-Wilson, Alison; Bretscher, Nicola; Crisan, Cosette; Geraniou, Eirini; Gono, Ebert; Neate, Andrew and Shore, Chris (2021). Learning from the pandemic: Capitalising on opportunities and overcoming challenges for mathematics teaching and learning practices with and through technology. In: Proceedings of the British Society for Research into Learning Mathematics (Marks, R ed.), 41(2).
In order to help the participating teachers on our online course engage critically with research ... more In order to help the participating teachers on our online course engage critically with research to reflect on whether and how digital technology supports students’ understanding and learning of mathematics, we propose to trial the use of online video cases in the next presentation of our newly designed online course. In this paper we will be reporting on trialling the use of video cases with the course participants and on the potential of using these videos with the aim of supporting the development of the participants’ Research informed Teachers' Pedagogical Content Knowledge with a particular focus on how the digital environment supports students’ mathematical work.
As part of the MA Mathematics Education programme at UCL Institute of Education, we offer an onli... more As part of the MA Mathematics Education programme at UCL Institute of Education, we offer an online module that focuses on the potential the digital technology could have in supporting the teaching and learning of school mathematics. In this short paper we will outline and reflect on the emergence of the online pedagogy of the tutors, as we embarked on the design, then teaching of this module.
Despite international interest on research into the preparation of pre-service mathematics teache... more Despite international interest on research into the preparation of pre-service mathematics teachers, the role of school-based subject mentors remains an under-explored area in the mathematics teacher education and professional development in general. In this paper, an exploratory study based on a multiple case approach that sought three experienced school-based mathematics mentors' views of their own roles in developing the pre-service teachers' knowledge for teaching mathematics is presented. With a particular focus on the specialised content knowledge (SCK) category from Ball et al.'s (2008) conceptualisation of mathematics knowledge for teaching, thematic analysis of the interview data indicates that development of pre-service teachers' such knowledge is influenced by and depends on mentors' own personal construct of subject specific mentoring. For pre-service teachers to fully benefit from their teaching practice, an explicit model of subject-specific mentoring is needed.
HAL (Le Centre pour la Communication Scientifique Directe), Feb 2, 2022
This paper presents a graduate student's reflections on the design of learning opportunities usin... more This paper presents a graduate student's reflections on the design of learning opportunities using the Desmos tool for carrying out mathematical activities and the online Zoom platform for facilitating mathematical learning. Using the theory of instrumental orchestration as our interpretative framework, we discuss the different types of orchestrations when a digital tool is used to support mathematical learning not in the familiar face-to-face classroom-based environment, but online instead. The contribution of this paper lies in the discussion of the design considerations and orchestrations to overcome the challenges of online learning and at the same time to capitalise on the opportunities it offers for mathematical learning.
The shortage of mathematics teachers in the UK has led to a number of government initiatives aimi... more The shortage of mathematics teachers in the UK has led to a number of government initiatives aiming to increase the supply of teachers of mathematics (e.g., DfE 2014). One set of initiatives concerns up-skilling teachers who are already employed at a school or college and who are teaching some mathematics, but who initially trained to teach in a subject other than mathematics. These non-specialist teachers of mathematics have come for in-service training at the university where they learn more mathematics relevant to the school curriculum. The participants in such courses expect to transfer their pedagogical knowledge from their initial specialism into the context of mathematics teaching as a result of developing their mathematical subject knowledge. We have run such courses for four years and this report draws on some of the data collected over this period. The particular finding that we report on here concerns participant aspiration and resistance. For instance, gaining certificat...
In this paper I will report on a project aimed at raising awareness of the undergraduates at Univ... more In this paper I will report on a project aimed at raising awareness of the undergraduates at University College London (UCL) about the research wealth and research culture of the math-ematics department. The project trialled the ‘Meet your researcher’ strategy for engaging undergraduates (UGs) and postgraduates (PGRs) in a partnership intended to develop UGs’ understanding from early on in their studies about what research is and what researchers do.
This paper reports on a research project based on designing and teaching in-service courses for N... more This paper reports on a research project based on designing and teaching in-service courses for Non-Specialist Teachers of Mathematics (NSTM). An NSTM is a school teacher who qualified to teach in a subject other than mathematics, yet teaches mathematics in secondary school (11-16 year old students). While the overall aim of our research was to describe what constitutes a trajectory towards a mathematics teacher identity for a NSTM, in this paper we explain how we sought indicators of a mathematics teacher identity. We do so by first describing how we adapted Wenger’s notion of identity and advanced our ‘Modes of Belonging’ Mathematics Teacher Identity framework. After that we exemplify how we used our framework to locate indicators of mathematics teacher identity in the data from a narrative of NSTMs working on a particular piece of mathematics.
use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you g... more use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this book are included in the book's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the book's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
In this paper we present the model behind our on-line master level module Digital Technologies fo... more In this paper we present the model behind our on-line master level module Digital Technologies for Mathematical Learning, which focuses on the teaching and learning supported by digital technologies. In our evaluation of the delivery of this module over two years, we reflect here on the emergence of two pedagogies: the online pedagogy of the tutors, ensuring that online teaching and learning is effective and the participants’ developing RiTPACK (Research Informed Technological Pedagogical Content Knowledge - our own acronym for this concept) as they start experimenting with using the digital technology in their classroom practice and linking it with the research knowledge base of the module.
In this paper, we report on four university lecturers' first-time experiences with computer-aided... more In this paper, we report on four university lecturers' first-time experiences with computer-aided assessments. They were required to automate a significant proportion of the pre-existing weekly coursework for modules in first-or second-year undergraduate mathematics using STACK. We consider lecturers' perspectives on the role of computer-aided assessments in course design for undergraduate mathematics; the knowledge of technical aspects required to implement STACKbased assessments; and the perceived merits of automated assessment for different aspects of mathematical study. We conclude with a series of reflections upon our departmental practice and the process of enculturating mathematicians into the realm of automated assessment.
Since ‘advanced mathematics knowledge’ (AMK) was first conceptualized by Zaskis and Leikin (2009)... more Since ‘advanced mathematics knowledge’ (AMK) was first conceptualized by Zaskis and Leikin (2009), researchers have striven to determine whether teachers’ ability to identify explicit connections between AMK and the mathematics taught in school is a rare gift of only a few teachers or whether specific prompting is needed to develop this ability in teachers. In this paper we provide empirical evidence showing that those teachers who attended a CPD designed to support them to ‘see’ and make explicit such connections, have increased their awareness of the implications for the teaching and learning of school mathematics topics in ways that allow for creating a solid foundation for development of further, more advanced ideas in the school mathematics curriculum. We thus propose that any mathematics teacher, irrespective of their academic background, could benefit from professional development opportunities where explicit guidance is provided in terms of the relevant AMK and how it inform...
In this paper I report on a study of secondary school mathematics teachers' use of ICT. The study... more In this paper I report on a study of secondary school mathematics teachers' use of ICT. The study adds new dimensions to understanding teachers' use of ICT by treating the teaching of mathematics and ICT use as interwoven aspects of a teacher's practice. The analysis of the data collected using a case study research strategy yielded a number of salient factors, of both contextual and personal nature, which were identified as key to the integration of ICT into mathematics teaching. A framework which conceptualises teachers' learning about the potential and limitations of ICT and teachers' incorporation of ICT in their teaching of mathematics will be advanced with the aim of contributing to a better understanding of the pedagogy of teaching mathematics with ICT.
Learning from the pandemic: Capitalising on opportunities and overcoming challenges for mathemati... more Learning from the pandemic: Capitalising on opportunities and overcoming challenges for mathematics teaching and learning practices with and through technology Conference or Workshop Item How to cite: Clark-Wilson, Alison; Bretscher, Nicola; Crisan, Cosette; Geraniou, Eirini; Gono, Ebert; Neate, Andrew and Shore, Chris (2021). Learning from the pandemic: Capitalising on opportunities and overcoming challenges for mathematics teaching and learning practices with and through technology. In: Proceedings of the British Society for Research into Learning Mathematics (Marks, R ed.), 41(2).
In order to help the participating teachers on our online course engage critically with research ... more In order to help the participating teachers on our online course engage critically with research to reflect on whether and how digital technology supports students’ understanding and learning of mathematics, we propose to trial the use of online video cases in the next presentation of our newly designed online course. In this paper we will be reporting on trialling the use of video cases with the course participants and on the potential of using these videos with the aim of supporting the development of the participants’ Research informed Teachers' Pedagogical Content Knowledge with a particular focus on how the digital environment supports students’ mathematical work.
As part of the MA Mathematics Education programme at UCL Institute of Education, we offer an onli... more As part of the MA Mathematics Education programme at UCL Institute of Education, we offer an online module that focuses on the potential the digital technology could have in supporting the teaching and learning of school mathematics. In this short paper we will outline and reflect on the emergence of the online pedagogy of the tutors, as we embarked on the design, then teaching of this module.
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