Mathematics and Statistics Teaching (MAST) is a staff facing service set up by the University of ... more Mathematics and Statistics Teaching (MAST) is a staff facing service set up by the University of Bath Mathematics Resource Centre in September 2021. The service was created to collaborate with academics involved in mathematics and statistics teaching in their academic departments. In September 2023, MAST ended its pilot phase and entered a new growth phase fine-tuning existing structures and practices. During the pilot phase, MAST worked with academics consulting on enriching their programme of study and/or teaching practices. Specifically, the key principle that guides MAST is engaging in long-term sustainable collaborations with academic departments. As a means to address the key principle, we explore the potential of building communities of practice and supporting a wider network across the range of disciplines who encounter similar objectives. Facilitating a wider community of practice could be challenging, especially considering the tight schedule of the academics involved. We discuss our plans to cultivate communities of practice within departments and how we are working towards meeting our goal of establishing best practice and collecting evidence to support a wider community.
Le Centre pour la Communication Scientifique Directe - HAL - Université de Nantes, Feb 2, 2022
In this paper, we showcase a method of identifying opportunities during the lesson where the comm... more In this paper, we showcase a method of identifying opportunities during the lesson where the communicational patterns go beyond the mathematics of the moment, namely beyond the boundaries of the curriculum. Drawing on the literature around Horizon Content Knowledge and building on the Theory of Commognition, we look at a lesson from one teacher and study instances where her communication with the students goes beyond the mathematics of the moment. Our analysis identifies three types of opportunities (manifested, potentials of the discussion and potentials of the task). Further analysis of manifested opportunities indicates that intersubjectivity is a characteristic of the discourse of the teacher at the mathematical horizon.
Commognitive studies offer a nuanced lens on datasets that evidence micro-level accounts of mathe... more Commognitive studies offer a nuanced lens on datasets that evidence micro-level accounts of mathematical experience – and are now starting to explore the theory’s capacity to support the design, tracing and dissecting of discursive shifts in medium/long term interventions. Here, we focus on two university mathematics education (UME) examples of such interventions. The Norway-based study engaged biology students with biology-themed Mathematical Modelling activities to challenge deficit narratives about the role of mathematics in their discipline and about their mathematical competence and confidence. The Brazil-based study engaged teachers with activities which feature mathematical practices from the past and in today’s mathematics classrooms to trigger changes in teachers’ narratives about how mathematics comes to be and how its emergence can be negotiated in the mathematics classroom. We show how the discursive shifts orchestrated by these interventions generate new narratives abou...
INDRUM2018: Second conference of the International Network for Didactic Research in University Mathematics, Oct 27, 2018
The concept of linear span is one of the first abstract notions that students encounter in a cour... more The concept of linear span is one of the first abstract notions that students encounter in a course on Linear Algebra. Using the theoretical construct of concept image and concept definition (Tall & Vinner, 1981) along with observations about teaching and learning Linear Algebra, we present two tasks designed to enrich students' concept image regarding linear span. These tasks could be included in a problem workshop of an introductory university course on Linear Algebra. Each task is carefully created and/or selected so as to foster the ground for potential conflict factors to arise and be confronted. A preliminary evaluation shows that the tasks are well received by students and succeed in addressing certain conflicting factors.
British Society for Research into Learning Mathematics, 2021
Commognitive studies offer a nuanced lens on datasets that evidence microlevel accounts of mathem... more Commognitive studies offer a nuanced lens on datasets that evidence microlevel accounts of mathematical experience-and are now starting to explore the theory's capacity to support the design, tracing and dissecting of discursive shifts in medium/long term interventions. Here, we focus on two university mathematics education (UME) examples of such interventions. The Norway-based study engaged biology students with biology-themed Mathematical Modelling activities to challenge deficit narratives about the role of mathematics in their discipline and about their mathematical competence and confidence. The Brazil-based study engaged teachers with activities which feature mathematical practices from the past and in today's mathematics classrooms to trigger changes in teachers' narratives about how mathematics comes to be and how its emergence can be negotiated in the mathematics classroom. We show how the discursive shifts orchestrated by these interventions generate new narratives about mathematics and its pedagogy, de-ritualised participation in mathematical routines and, ultimately, meta-level learning.
Knowledge at the mathematical horizon' refers to a particular domain of teachers' knowledge relat... more Knowledge at the mathematical horizon' refers to a particular domain of teachers' knowledge related to connections across mathematics. This construct has been used and elaborated in research. Nonetheless, 'knowledge at the mathematical horizon' is still considered a 'grey area' with different interpretations and meanings. In this paper, I report a preliminary commognitive analysis of a sample of papers about knowledge at the mathematical horizon attending to the use of the term in the related research. The aim of this paper is to investigate different narratives in relation to the construct and how these narratives might be linked to how knowledge at the mathematical horizon is conceptualised and operationalised into research. To conclude, I argue that a discursive approach might provide better insight about the nature and use of mathematical horizon in research and set the scene for further development of these ideas as part of mathematics teachers' discourses.
This report introduces part of a larger study on secondary teachers’ mathematical and pedagogical... more This report introduces part of a larger study on secondary teachers’ mathematical and pedagogical discourses that are significant to the coherence of mathematical ideas and practices across educational levels. The study draws on the literature related to what is mostly called Horizon Content Knowledge and specifically on the theoretical construct of the Discourse at the Mathematical Horizon. The aim of this report is to propose and exemplify an analytical approach that conceptualises and identifies the characteristics of this discourse in a lesson observation and an interview with one newly qualified mathematics teacher. The proposed analytical approach illustrates the teacher’s actions of interpreting and giving meaning to students’ unexpected ideas and how these actions can lead in the identification of discursive patterns of how the teacher goes beyond the content of a specific teaching situation.
Mathematics and Statistics Teaching (MAST) is a staff facing service set up by the University of ... more Mathematics and Statistics Teaching (MAST) is a staff facing service set up by the University of Bath Mathematics Resource Centre in September 2021. The service was created to collaborate with academics involved in mathematics and statistics teaching in their academic departments. In September 2023, MAST ended its pilot phase and entered a new growth phase fine-tuning existing structures and practices. During the pilot phase, MAST worked with academics consulting on enriching their programme of study and/or teaching practices. Specifically, the key principle that guides MAST is engaging in long-term sustainable collaborations with academic departments. As a means to address the key principle, we explore the potential of building communities of practice and supporting a wider network across the range of disciplines who encounter similar objectives. Facilitating a wider community of practice could be challenging, especially considering the tight schedule of the academics involved. We discuss our plans to cultivate communities of practice within departments and how we are working towards meeting our goal of establishing best practice and collecting evidence to support a wider community.
Le Centre pour la Communication Scientifique Directe - HAL - Université de Nantes, Feb 2, 2022
In this paper, we showcase a method of identifying opportunities during the lesson where the comm... more In this paper, we showcase a method of identifying opportunities during the lesson where the communicational patterns go beyond the mathematics of the moment, namely beyond the boundaries of the curriculum. Drawing on the literature around Horizon Content Knowledge and building on the Theory of Commognition, we look at a lesson from one teacher and study instances where her communication with the students goes beyond the mathematics of the moment. Our analysis identifies three types of opportunities (manifested, potentials of the discussion and potentials of the task). Further analysis of manifested opportunities indicates that intersubjectivity is a characteristic of the discourse of the teacher at the mathematical horizon.
Commognitive studies offer a nuanced lens on datasets that evidence micro-level accounts of mathe... more Commognitive studies offer a nuanced lens on datasets that evidence micro-level accounts of mathematical experience – and are now starting to explore the theory’s capacity to support the design, tracing and dissecting of discursive shifts in medium/long term interventions. Here, we focus on two university mathematics education (UME) examples of such interventions. The Norway-based study engaged biology students with biology-themed Mathematical Modelling activities to challenge deficit narratives about the role of mathematics in their discipline and about their mathematical competence and confidence. The Brazil-based study engaged teachers with activities which feature mathematical practices from the past and in today’s mathematics classrooms to trigger changes in teachers’ narratives about how mathematics comes to be and how its emergence can be negotiated in the mathematics classroom. We show how the discursive shifts orchestrated by these interventions generate new narratives abou...
INDRUM2018: Second conference of the International Network for Didactic Research in University Mathematics, Oct 27, 2018
The concept of linear span is one of the first abstract notions that students encounter in a cour... more The concept of linear span is one of the first abstract notions that students encounter in a course on Linear Algebra. Using the theoretical construct of concept image and concept definition (Tall & Vinner, 1981) along with observations about teaching and learning Linear Algebra, we present two tasks designed to enrich students' concept image regarding linear span. These tasks could be included in a problem workshop of an introductory university course on Linear Algebra. Each task is carefully created and/or selected so as to foster the ground for potential conflict factors to arise and be confronted. A preliminary evaluation shows that the tasks are well received by students and succeed in addressing certain conflicting factors.
British Society for Research into Learning Mathematics, 2021
Commognitive studies offer a nuanced lens on datasets that evidence microlevel accounts of mathem... more Commognitive studies offer a nuanced lens on datasets that evidence microlevel accounts of mathematical experience-and are now starting to explore the theory's capacity to support the design, tracing and dissecting of discursive shifts in medium/long term interventions. Here, we focus on two university mathematics education (UME) examples of such interventions. The Norway-based study engaged biology students with biology-themed Mathematical Modelling activities to challenge deficit narratives about the role of mathematics in their discipline and about their mathematical competence and confidence. The Brazil-based study engaged teachers with activities which feature mathematical practices from the past and in today's mathematics classrooms to trigger changes in teachers' narratives about how mathematics comes to be and how its emergence can be negotiated in the mathematics classroom. We show how the discursive shifts orchestrated by these interventions generate new narratives about mathematics and its pedagogy, de-ritualised participation in mathematical routines and, ultimately, meta-level learning.
Knowledge at the mathematical horizon' refers to a particular domain of teachers' knowledge relat... more Knowledge at the mathematical horizon' refers to a particular domain of teachers' knowledge related to connections across mathematics. This construct has been used and elaborated in research. Nonetheless, 'knowledge at the mathematical horizon' is still considered a 'grey area' with different interpretations and meanings. In this paper, I report a preliminary commognitive analysis of a sample of papers about knowledge at the mathematical horizon attending to the use of the term in the related research. The aim of this paper is to investigate different narratives in relation to the construct and how these narratives might be linked to how knowledge at the mathematical horizon is conceptualised and operationalised into research. To conclude, I argue that a discursive approach might provide better insight about the nature and use of mathematical horizon in research and set the scene for further development of these ideas as part of mathematics teachers' discourses.
This report introduces part of a larger study on secondary teachers’ mathematical and pedagogical... more This report introduces part of a larger study on secondary teachers’ mathematical and pedagogical discourses that are significant to the coherence of mathematical ideas and practices across educational levels. The study draws on the literature related to what is mostly called Horizon Content Knowledge and specifically on the theoretical construct of the Discourse at the Mathematical Horizon. The aim of this report is to propose and exemplify an analytical approach that conceptualises and identifies the characteristics of this discourse in a lesson observation and an interview with one newly qualified mathematics teacher. The proposed analytical approach illustrates the teacher’s actions of interpreting and giving meaning to students’ unexpected ideas and how these actions can lead in the identification of discursive patterns of how the teacher goes beyond the content of a specific teaching situation.
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