According to the ableist world-view, the able-bodied are the norm in society and disability is an... more According to the ableist world-view, the able-bodied are the norm in society and disability is an unfortunate failing, a disadvantage that must be overcome. Within education, ableism results in institutional and personal prejudice against learners with disabilities, and has a drastic effect on approaches to teaching. Our project investigates how ableist perspectives impact on the teaching of mathematics, a quintessential part of the curriculum, and a discipline where public perceptions of ability as innate often shape pedagogical perspectives and practice. Our focus is on mathematical faculties typically associated with visual and auditory perception. In this one-year project we are establishing a partnership which combines Nardi & Biza’s Task design approaches to investigatingand transforming teachers' beliefs about mathematics and about teaching in the UK and Healy’s research with mathematics learners with disabilities. We are developing and trialling tasks that invite teacher...
International Journal of Research in Undergraduate Mathematics Education
introduce the Special Issue. Calculus courses are widely considered an important gateway, or gate... more introduce the Special Issue. Calculus courses are widely considered an important gateway, or gate keeper, in many academic and professional paths (Bressoud et al., 2016; Thompson & Harel, 2021). Calculus is also widely recognized as a critical stage in various transition processes, such as the transition from secondary mathematics to tertiary mathematics, the transition within and across university courses, or the transition from university to the workplace (Hochmuth et al., 2021). There is ample evidence that students around the world struggle in their calculus courses, that rates of failure in these courses are comparably high, and that students' experiences in calculus courses are strongly linked to student dropout in STEM programs (Artigue et al., 2007; Faulkner et al., 2019). Considering the critical role and varied goals of calculus in different contexts, it may seem contradictory that calculus is very often taught de-facto as one and uniform
In this paper, we present examples of activities and their assessment frame for mathematics under... more In this paper, we present examples of activities and their assessment frame for mathematics undergraduate students' introduction to mathematics education research. The activities are inspired by studies that have identified and addressed differences between discursive practices in mathematics and in mathematics education. The proposed set of activities uses task design principles that contextualise mathematical content and the use of mathematics education theory to specific learning situations. Students' responses to these activities are assessed in relation to: clarity; coherence; consistency; specificity; use of terms and constructs from mathematics education theory; and, use of terms and processes from mathematical theory. We exemplify the application of these activities through responses from one student.
In this paper I present a collaborative research and development programme, in which we design si... more In this paper I present a collaborative research and development programme, in which we design situation specific tasks and use them to explore, challenge and change knowledge and beliefs of in- and pre-service secondary mathematics teachers. In this work we use practice-based and research-informed tasks in which we invite teachers to consider a mathematical problem and typical student responses (and teacher reactions) to this problem. So far the programme develops in four stands: (1) mathematical knowledge for teaching; (2) classroom management and mathematics learning; (3) disability and inclusion in the mathematics classroom; and, (4) meta-use of tasks and task development. Examples of tasks from these strands will be discussed in the session.
This paper draws on the Knowledge Quartet (Rowland, Huckstep, & Thwaites, 2005) to analyse an int... more This paper draws on the Knowledge Quartet (Rowland, Huckstep, & Thwaites, 2005) to analyse an introductory to the Iterative Numerical Method Year 13 lesson of a secondary mathematics teacher who uses a range of paper based and electronic resources including Autograph, a mathematics-education software. Data were collected during one lesson observation and a follow up interview with the teacher. Analysis identifies the different aspects of the Knowledge Quartet dimensions: foundation, transformation, connection and contingency, in relation to the introduction to the Iterative method and to the teaching of Year 13 students. Findings demonstrate how the teacher used students’ contributions as resource for his teaching; how he balanced his use of resources; and how he created connections between these resources while he remained attentive to exam requirements.
This paper reports on a study that investigates the difficulties encountered by first year underg... more This paper reports on a study that investigates the difficulties encountered by first year undergraduate mathematics students during their transition from school to university mathematics. The research is a case study of five students who were followed regularly from the beginning until the end of the semester through questionnaires and interviews while they were attending a Calculus course. The results of the research revealed difficulties faced by undergraduate students regarding the content of the module and the social and academic context. In addition, the research suggests a categorization according to the approaches that students adopted in order to tackle these problems.
The study we report builds on previous research conducted by Nardi, Biza and colleagues, which ex... more The study we report builds on previous research conducted by Nardi, Biza and colleagues, which examined mathematics teachers’ considerations of what makes a claim an acceptable mathematical argument in the secondary classroom. We identify teachers’ considerations in their written responses to tasks and then in semi-structured interviews that probe these written responses. Here we present data from six teachers and one such task, a (GCSE-level) Algebra Task. The tasks we invite the teachers to engage with, of which the Algebra Task is one, are structured as follows: a mathematical problem that students are likely to encounter in typical secondary mathematics lessons; fictional student responses to the problem (grounded on student responses found by relevant research as typical); and, an invitation to teachers to solve the problem, consider the purposes of its use in the lesson, reflect on the student responses and describe the feedback they would provide to the students. So far, we h...
MathTASK é um programa de pesquisa e desenvolvimento que engaja professores de matemática em situ... more MathTASK é um programa de pesquisa e desenvolvimento que engaja professores de matemática em situações de sala de aula desafiadoras e altamente contextualizadas na forma de tarefas (chamadas de mathtasks). As respostas de professores às tarefas revelam seus discursos matemáticos e pedagógicos e abrem oportunidades para articular, considerar e reconstruir tais discursos. As tarefas foram usadas como instrumento de pesquisa e também de formação de professores e desenvolvimento profissional no Reino Unido, na Grécia e no Brasil. Neste artigo, apresentamos o programa MathTASK e um exemplo de mathtask. Em seguida, apresentamos um resumo dos construtos teóricos que emergiram na análise dos dados do programa MathTASK. Então, indicamos os princípios gerais do uso de mathtasks na pesquisa e formação de professores e damos quatro exemplos dos princípios, cada um dirigido a diferentes aspectos do ensino e da aprendizagem de matemática, e cada um desenvolvido tendo em mente níveis educacionais ...
According to the ableist world-view, the able-bodied are the norm in society and disability is an... more According to the ableist world-view, the able-bodied are the norm in society and disability is an unfortunate failing, a disadvantage that must be overcome. Within education, ableism results in institutional and personal prejudice against learners with disabilities, and has a drastic effect on approaches to teaching. Our project investigates how ableist perspectives impact on the teaching of mathematics, a quintessential part of the curriculum, and a discipline where public perceptions of ability as innate often shape pedagogical perspectives and practice. Our focus is on mathematical faculties typically associated with visual and auditory perception. In this one-year project we are establishing a partnership which combines Nardi & Biza’s Task design approaches to investigatingand transforming teachers' beliefs about mathematics and about teaching in the UK and Healy’s research with mathematics learners with disabilities. We are developing and trialling tasks that invite teacher...
International Journal of Research in Undergraduate Mathematics Education
introduce the Special Issue. Calculus courses are widely considered an important gateway, or gate... more introduce the Special Issue. Calculus courses are widely considered an important gateway, or gate keeper, in many academic and professional paths (Bressoud et al., 2016; Thompson & Harel, 2021). Calculus is also widely recognized as a critical stage in various transition processes, such as the transition from secondary mathematics to tertiary mathematics, the transition within and across university courses, or the transition from university to the workplace (Hochmuth et al., 2021). There is ample evidence that students around the world struggle in their calculus courses, that rates of failure in these courses are comparably high, and that students' experiences in calculus courses are strongly linked to student dropout in STEM programs (Artigue et al., 2007; Faulkner et al., 2019). Considering the critical role and varied goals of calculus in different contexts, it may seem contradictory that calculus is very often taught de-facto as one and uniform
In this paper, we present examples of activities and their assessment frame for mathematics under... more In this paper, we present examples of activities and their assessment frame for mathematics undergraduate students' introduction to mathematics education research. The activities are inspired by studies that have identified and addressed differences between discursive practices in mathematics and in mathematics education. The proposed set of activities uses task design principles that contextualise mathematical content and the use of mathematics education theory to specific learning situations. Students' responses to these activities are assessed in relation to: clarity; coherence; consistency; specificity; use of terms and constructs from mathematics education theory; and, use of terms and processes from mathematical theory. We exemplify the application of these activities through responses from one student.
In this paper I present a collaborative research and development programme, in which we design si... more In this paper I present a collaborative research and development programme, in which we design situation specific tasks and use them to explore, challenge and change knowledge and beliefs of in- and pre-service secondary mathematics teachers. In this work we use practice-based and research-informed tasks in which we invite teachers to consider a mathematical problem and typical student responses (and teacher reactions) to this problem. So far the programme develops in four stands: (1) mathematical knowledge for teaching; (2) classroom management and mathematics learning; (3) disability and inclusion in the mathematics classroom; and, (4) meta-use of tasks and task development. Examples of tasks from these strands will be discussed in the session.
This paper draws on the Knowledge Quartet (Rowland, Huckstep, & Thwaites, 2005) to analyse an int... more This paper draws on the Knowledge Quartet (Rowland, Huckstep, & Thwaites, 2005) to analyse an introductory to the Iterative Numerical Method Year 13 lesson of a secondary mathematics teacher who uses a range of paper based and electronic resources including Autograph, a mathematics-education software. Data were collected during one lesson observation and a follow up interview with the teacher. Analysis identifies the different aspects of the Knowledge Quartet dimensions: foundation, transformation, connection and contingency, in relation to the introduction to the Iterative method and to the teaching of Year 13 students. Findings demonstrate how the teacher used students’ contributions as resource for his teaching; how he balanced his use of resources; and how he created connections between these resources while he remained attentive to exam requirements.
This paper reports on a study that investigates the difficulties encountered by first year underg... more This paper reports on a study that investigates the difficulties encountered by first year undergraduate mathematics students during their transition from school to university mathematics. The research is a case study of five students who were followed regularly from the beginning until the end of the semester through questionnaires and interviews while they were attending a Calculus course. The results of the research revealed difficulties faced by undergraduate students regarding the content of the module and the social and academic context. In addition, the research suggests a categorization according to the approaches that students adopted in order to tackle these problems.
The study we report builds on previous research conducted by Nardi, Biza and colleagues, which ex... more The study we report builds on previous research conducted by Nardi, Biza and colleagues, which examined mathematics teachers’ considerations of what makes a claim an acceptable mathematical argument in the secondary classroom. We identify teachers’ considerations in their written responses to tasks and then in semi-structured interviews that probe these written responses. Here we present data from six teachers and one such task, a (GCSE-level) Algebra Task. The tasks we invite the teachers to engage with, of which the Algebra Task is one, are structured as follows: a mathematical problem that students are likely to encounter in typical secondary mathematics lessons; fictional student responses to the problem (grounded on student responses found by relevant research as typical); and, an invitation to teachers to solve the problem, consider the purposes of its use in the lesson, reflect on the student responses and describe the feedback they would provide to the students. So far, we h...
MathTASK é um programa de pesquisa e desenvolvimento que engaja professores de matemática em situ... more MathTASK é um programa de pesquisa e desenvolvimento que engaja professores de matemática em situações de sala de aula desafiadoras e altamente contextualizadas na forma de tarefas (chamadas de mathtasks). As respostas de professores às tarefas revelam seus discursos matemáticos e pedagógicos e abrem oportunidades para articular, considerar e reconstruir tais discursos. As tarefas foram usadas como instrumento de pesquisa e também de formação de professores e desenvolvimento profissional no Reino Unido, na Grécia e no Brasil. Neste artigo, apresentamos o programa MathTASK e um exemplo de mathtask. Em seguida, apresentamos um resumo dos construtos teóricos que emergiram na análise dos dados do programa MathTASK. Então, indicamos os princípios gerais do uso de mathtasks na pesquisa e formação de professores e damos quatro exemplos dos princípios, cada um dirigido a diferentes aspectos do ensino e da aprendizagem de matemática, e cada um desenvolvido tendo em mente níveis educacionais ...
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Papers by Irene Biza