The International Baccalaureate (IB) commissioned the authors to write a report to provide insigh... more The International Baccalaureate (IB) commissioned the authors to write a report to provide insights into the use and integration of technology into curriculum, classroom practice and impact on learning in secondary mathematics courses and will inform possible direction and focus for the coming curriculum review of IBDP mathematics
The study aims are:
Aim 1. Explore types of technology used in mathematics curricula for students aged 16- 19 years old in different educational systems (within a country and internationally);
Aim 2. Examine approaches and strategies to technology integration in curriculum design, pedagogy and assessment;
Aim 3. Indicate issues involved in the use of technology in mathematics courses; Aim 4. Identify factors increasing the effectiveness of technology implementation in
classroom practice;
Aim 5. Analyse the effects of using and integrating different types of technology on the
development of mathematical skills and academic achievement in mathematics.
The use of digital technology has the potential to support students’ understanding in the mathema... more The use of digital technology has the potential to support students’ understanding in the mathematics classroom with the teacher playing a vital role. However, teaching with digital technology is not trivial, especially for teachers who are new to this. In this paper, we present an analysis of the enactment of a function lesson of a Sri Lankan mathematics teacher who used digital technology for the first time in her teaching. We combined the instrumental orchestration and ROG (resources, orientations and goals) frameworks into a conceptual framework to analyse her teaching. In particular, we used instrumental orchestration to identify how the teacher orchestrated the resources in her technology-rich classroom. This was combined with ROG theory to understand the reasons underpinning the decisions involved in moving from one orchestration to another. We demonstrate that this teacher showed diverse orchestrations and use the ROG framework to present these in the sequences in which they...
A crucial step in improving the use of digital technology (DT) for learning mathematical concepts... more A crucial step in improving the use of digital technology (DT) for learning mathematical concepts in the classroom appears to be increasing teacher involvement in task development. Hence, this research considered the effect of a professional development (PD) programme designed to assist teachers with DT task production for implementation in their classrooms. Four groups of three Sri Lankan teachers were observed and guided as they designed and implemented DT tasks. We examine the effectiveness of the PD programme in terms of the richness of the tasks produced by the groups before and after the PD. The results suggest the intervention led to richer, more student-centred tasks. The reasons behind this improvement are analysed, along with factors that might have influenced the DT task development. The findings have implications for the design of secondary school PD programmes and may help educators to facilitate the training of mathematics teachers in the use of DT.
We introduce the notion of a virtual space, which is a mathematical and cognitive space that is c... more We introduce the notion of a virtual space, which is a mathematical and cognitive space that is created through gestures. The notion of a virtual space is illustrated in a case study of two teachers who create a virtual space while constructing the graphical antiderivative of a function. We discuss some features of a virtual space, including the way it is physically constrained by elements of a person's gesture space, and its relationship to various types of gestures - namely deictic, iconic, and metaphoric gestures. We also discuss potential advantages and disadvantages of virtual spaces in mathematical thinking and learning.
This paper reports on some findings from the project 'Analysing the Transition from Secondary... more This paper reports on some findings from the project 'Analysing the Transition from Secondary to Tertiary Education in Mathematics'. A key variable in the school to university transition is the teacher/lecturer, and here we deal with data analysing secondary teachers' responses to four mathematics questions. Elsewhere we consider a comparison of teacher and lecturer knowledge, preparedness and teaching style etc, but this paper tracks the ability to use mathematical knowledge. We hypothesise that this is a function of what we pay attention to, as described in Mason's discipline of noticing. The results reveal that many teachers fail to notice the necessary conditions for problems that imply that procedures are not always applicable. Possible reasons for this along with implications for student learning are discussed.
This paper describes part of an international project considering graphical construction of antid... more This paper describes part of an international project considering graphical construction of antiderivative functions in the secondary mathematics classroom. We use Schoenfeld's Resources, Orientations and Goals (ROG) framework to analyse the decisions made in part of a lesson of a teacher, Adam. In this he discusses with his students constructs arising from the relationship between a function and its graphical antiderivative. We present details of Adam's ROG and see how this is related to resolution of the conflict between his competing goals and the decisions he makes. The results suggest that a beneficial professional development strategy might be to assist teachers to become more aware of their ROG and its influence on in-the-moment classroom decisions.
The International Baccalaureate (IB) commissioned the authors to write a report to provide insigh... more The International Baccalaureate (IB) commissioned the authors to write a report to provide insights into the use and integration of technology into curriculum, classroom practice and impact on learning in secondary mathematics courses and will inform possible direction and focus for the coming curriculum review of IBDP mathematics
The study aims are:
Aim 1. Explore types of technology used in mathematics curricula for students aged 16- 19 years old in different educational systems (within a country and internationally);
Aim 2. Examine approaches and strategies to technology integration in curriculum design, pedagogy and assessment;
Aim 3. Indicate issues involved in the use of technology in mathematics courses; Aim 4. Identify factors increasing the effectiveness of technology implementation in
classroom practice;
Aim 5. Analyse the effects of using and integrating different types of technology on the
development of mathematical skills and academic achievement in mathematics.
The use of digital technology has the potential to support students’ understanding in the mathema... more The use of digital technology has the potential to support students’ understanding in the mathematics classroom with the teacher playing a vital role. However, teaching with digital technology is not trivial, especially for teachers who are new to this. In this paper, we present an analysis of the enactment of a function lesson of a Sri Lankan mathematics teacher who used digital technology for the first time in her teaching. We combined the instrumental orchestration and ROG (resources, orientations and goals) frameworks into a conceptual framework to analyse her teaching. In particular, we used instrumental orchestration to identify how the teacher orchestrated the resources in her technology-rich classroom. This was combined with ROG theory to understand the reasons underpinning the decisions involved in moving from one orchestration to another. We demonstrate that this teacher showed diverse orchestrations and use the ROG framework to present these in the sequences in which they...
A crucial step in improving the use of digital technology (DT) for learning mathematical concepts... more A crucial step in improving the use of digital technology (DT) for learning mathematical concepts in the classroom appears to be increasing teacher involvement in task development. Hence, this research considered the effect of a professional development (PD) programme designed to assist teachers with DT task production for implementation in their classrooms. Four groups of three Sri Lankan teachers were observed and guided as they designed and implemented DT tasks. We examine the effectiveness of the PD programme in terms of the richness of the tasks produced by the groups before and after the PD. The results suggest the intervention led to richer, more student-centred tasks. The reasons behind this improvement are analysed, along with factors that might have influenced the DT task development. The findings have implications for the design of secondary school PD programmes and may help educators to facilitate the training of mathematics teachers in the use of DT.
We introduce the notion of a virtual space, which is a mathematical and cognitive space that is c... more We introduce the notion of a virtual space, which is a mathematical and cognitive space that is created through gestures. The notion of a virtual space is illustrated in a case study of two teachers who create a virtual space while constructing the graphical antiderivative of a function. We discuss some features of a virtual space, including the way it is physically constrained by elements of a person's gesture space, and its relationship to various types of gestures - namely deictic, iconic, and metaphoric gestures. We also discuss potential advantages and disadvantages of virtual spaces in mathematical thinking and learning.
This paper reports on some findings from the project 'Analysing the Transition from Secondary... more This paper reports on some findings from the project 'Analysing the Transition from Secondary to Tertiary Education in Mathematics'. A key variable in the school to university transition is the teacher/lecturer, and here we deal with data analysing secondary teachers' responses to four mathematics questions. Elsewhere we consider a comparison of teacher and lecturer knowledge, preparedness and teaching style etc, but this paper tracks the ability to use mathematical knowledge. We hypothesise that this is a function of what we pay attention to, as described in Mason's discipline of noticing. The results reveal that many teachers fail to notice the necessary conditions for problems that imply that procedures are not always applicable. Possible reasons for this along with implications for student learning are discussed.
This paper describes part of an international project considering graphical construction of antid... more This paper describes part of an international project considering graphical construction of antiderivative functions in the secondary mathematics classroom. We use Schoenfeld's Resources, Orientations and Goals (ROG) framework to analyse the decisions made in part of a lesson of a teacher, Adam. In this he discusses with his students constructs arising from the relationship between a function and its graphical antiderivative. We present details of Adam's ROG and see how this is related to resolution of the conflict between his competing goals and the decisions he makes. The results suggest that a beneficial professional development strategy might be to assist teachers to become more aware of their ROG and its influence on in-the-moment classroom decisions.
In this paper we describe the design and implementation of a technology-active introductory first... more In this paper we describe the design and implementation of a technology-active introductory first year university mathematics course. The design principles underpinning the course are presented. The results of the implementation show some areas where the technology-active approach has proven of value, as well as improvements that can be made for the next cycle. Some implications for the integration of technology in large lecture undergraduate teaching are presented.
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Research reports
The study aims are:
Aim 1. Explore types of technology used in mathematics curricula for students aged 16- 19 years old in different educational systems (within a country and internationally);
Aim 2. Examine approaches and strategies to technology integration in curriculum design, pedagogy and assessment;
Aim 3. Indicate issues involved in the use of technology in mathematics courses; Aim 4. Identify factors increasing the effectiveness of technology implementation in
classroom practice;
Aim 5. Analyse the effects of using and integrating different types of technology on the
development of mathematical skills and academic achievement in mathematics.
Papers
The study aims are:
Aim 1. Explore types of technology used in mathematics curricula for students aged 16- 19 years old in different educational systems (within a country and internationally);
Aim 2. Examine approaches and strategies to technology integration in curriculum design, pedagogy and assessment;
Aim 3. Indicate issues involved in the use of technology in mathematics courses; Aim 4. Identify factors increasing the effectiveness of technology implementation in
classroom practice;
Aim 5. Analyse the effects of using and integrating different types of technology on the
development of mathematical skills and academic achievement in mathematics.