Research reports by Mike Thomas
Thinking like a mathematician: An example of discovery-based learning
International Journal of Mathematical Education in Science and Technology, 2021
Survey on Research in University Mathematics Education at ICME 14
European Mathematical Society Magazine, 2021
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.
Papers by Mike Thomas
Journal of Mathematics Teacher Education
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...
Professional development for digital technology task design by secondary mathematics teachers
ZDM
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.
Higher Education Research & Development, 2020
This study involved an intervention designed to examine whether employability prospects for STEM ... more This study involved an intervention designed to examine whether employability prospects for STEM students studying mathematics could be improved. It incorporated use of non-routine problem solving in second-year mathematics courses at two New Zealand universities. From a theoretical standpoint, we conceptualised a novel construct called lateral thinking self-efficacy, which is defined as a learner's confidence in their ability to solve non-routine problems. It relates to the creative thinking ability needed for solving innovative real-life problems in the work place, and hence is pertinent in transfer of mathematical learning to novel domains. The findings suggest that the attitude profiles of students with high and low lateral thinking self-efficacy differ significantly with respect to three dimensions spanning their affective domain. Further, a significant difference between genders with regard to lateral thinking self-efficacy was observed, with a significantly greater proportion of confident males than females, although there was no significant association between gender and nonroutine problem-solving performance. These results raise questions about equity with regard to employability prospects for females in STEM companies and have implications for the underrepresentation of women in STEM fields.
ZDM, 2019
Proof has a prominent place in the linear algebra curriculum, teaching and learning but in first-... more Proof has a prominent place in the linear algebra curriculum, teaching and learning but in first-year courses it continues to be challenging for both instructors and students. While an introduction to new concepts through definitions and theorems adds to the complexity of the course, proof remains the number one hurdle for many students. How do students view proof in linear algebra? Do they distinguish argumentation and proof, and if so how? are among many questions that are still unanswered. Although research on proof in mathematics education is increasing, systematic studies on proof in linear algebra are still scarce. In this study, we examined responses to a set of interview questions on proof by a group of 16 first-year undergraduate students shortly after their final examination. This paper opens the case for a pedagogy of proof in linear algebra and examines students' reactions to, and voices on, proof in a first-year course in linear algebra. In particular, it addresses areas such as student views on understanding of proof, the purpose of a proof, and when and how proofs communicate to them. We employed Tall's Three Worlds as well as Harel's intellectual need to analyse the data. Although, these models are often applied to what students construct, we argue they can also be applied to how students perceive proofs. The results revealed that understanding a proof in order to gain personal conviction was a major concern of students.
A Graphic Calculator Approach to Algebra
Computers in primary schools: strategies for overcoming barriers in mathematics
Review of Hi-Flyer Decimal Software
A graphic calculator approach to understanding algebraic variables
Educational Studies in Mathematics
Conceptual Understanding of the Newton-Raphson Method
ABSTRACT
What do they see when they look? A student
Integrating CAS Calculators in Teaching: An Inexperienced Teacher's Approach
Calculator use in the mathematics classroom: A longitudinal study
Teaching with technology: Developing versatile thinking and pedagogical technology knowledge
Calculators in the mathematics classroom
The Electronic Journal of Mathematics and Technology
Gestures and Virtual Space
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.
Teachers' Mathematical Knowledge: The Influence of Attention
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.
Resolving conflict between competing goals in mathematics teaching decisions
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.
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Research reports by Mike Thomas
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 by Mike Thomas