0000000000064557
AUTHOR
Simon Goodchild
Critical alignment in inquiry-based practice in developing mathematics teaching
Published version of an article in the journal: Educational Studies in Mathematics. Also available from the publisher at: http://dx.doi.org/10.1007/s10649-013-9489-z This paper reports a case study from a mathematics teaching developmental research project. The theoretical foundation for the research comprises communities of inquiry and critical alignment, with which the developmental methodology has a particular synergy. This synergy is the main focus of the paper. The paper elaborates theoretical and methodological antecedents of the project and traces these through a case study of developments in the practices of one upper secondary school team and a group of university didacticians (mat…
University students’ learning approaches : An adaptation of the revised two-factor study process questionnaire to Norwegian
This paper reports a Norwegian validation study of a widely used instrument to measure students’ approaches to learning, namely, Bigg’s revised two-factor study process questionnaire (R-SPQ-2F). Its cultural sensitivity and psychometry evaluations have provoked rigorous discussion among educators in different languages. A survey design was adopted involving 253 undergraduate engineering students across two universities. Confirmatory factor analyses were used to test six models hypothesized to reflect the factor structures of R-SPQ-2F and unidimensionality of its subscales. The results showed appropriate fits of a two-factor first-order model with 10 items measuring deep approach and 9 items…
Critical stance within a community of inquiry in an advanced mathematics course for pre-service teachers
AbstractThis paper reports a study of university students’ experiences of learning mathematics in an introductory differential equations course that takes an inquiry approach to learning and teaching. The students are on a trajectory leading toward a bachelor’s degree in mathematics to be followed by a year-long teacher education credential program. The analysis of students’ end of course presentations and written portfolios is framed with community of practice theory, complemented with analytic categories from community of inquiry, including notions of inquiry stance and critical alignment. Our social theorization of university mathematics education adds a complementary perspective to the …
Mathematics teaching development: Learning from developmental research in Norway
Published version of an article in the journal: ZDM - International Journal on Mathematics Education. Also available from the publisher at: http://dx.doi.org/10.1007/s11858-013-0567-6 This paper is a product of mathematics teaching developmental research projects based on establishing communities of inquiry comprising schoolteachers working at all grades and university-based teacher educator/researchers (didacticians). The projects are established on the principle that teachers taking an inquiry stance in their practice can assert their agency to develop their teaching to enable improved learning experiences for their students. The educational context and the societal pressure to develop ma…
Theorising community of practice and community of inquiry in the context of teaching-learning mathematics at university
Biza, Jaworski, and Hemmi (2014) make a valuable contribution to theorising university mathematics teaching through the lens of community of practice theory (CPT) and by juxtaposing community of pr...
Revisiting the didactic triangle: from the particular to the general
Published version of an article in the journal: ZDM. Also available from the publisher at: http://www.springerlink.com/content/61p78l089tnx8rn5/ The basic notion of a didactic triangle is explained with historical annotations on its origins and subsequent theorization in the literature. Instances of its application to classroom environments to demonstrate its representational capabilities are presented. Generalizations of the triangle are proposed that integrate the role of technology, the researcher in mathematics teaching developmental research, and mediating complexes in the student–teacher–content interfaces. Further, the use of the didactic triangle as a heuristic device is also discus…
Switching to Fully Online Teaching and Learning of Mathematics: The Case of Norwegian Mathematics Lecturers and University Students During the Covid-19 Pandemic
AbstractTowards the end of 2019, a novel coronavirus, known as COVID-19, was detected and quickly spread worldwide. The resulting pandemic led many countries to lockdown and teaching and learning switched to fully online provision. This study explores how Norwegian higher education lecturers and students of mathematics experienced online provision following this switch in March 2020 when the national lockdown was imposed. Data are generated and analysed using an exploratory sequential mixed methods approach that first entailed interviews with ten mathematics lecturers and six undergraduate students as the foundation for developing a survey instrument. The instrument was designed to explore …
Mediating Mathematics Teaching Development and Pupils’ Mathematics Learning: The Life Cycle of a Task
A developmental research project in Norway, Learning Communities in Mathematics (LCM), a collaboration between university and schools, uses mathematical tasks as a basis for developing community in project workshops and for teachers’ design of tasks for classrooms. An aim in the project is that teachers and didacticians, through inquiry into design and use of tasks and reflection on and analysis of their use, will learn more about creating effective learning situations for pupils in mathematics. The processes involved are exemplified through an account of the design and use of the Mirror Task. An activity theory analysis traces the elements of learning of participants, teachers and didactic…
Online mathematics teaching and learning during the COVID-19 pandemic: The perspective of lecturers and students
The global spread of the novel coronavirus, Covid-19, reached Norway at the end of February 2020. MatRIC, Centre for Research, Innovation and Coordination of Mathematics Teaching conducted a national survey in Norwegian higher education institutions (HEIs) during June-July 2020 to explore lecturers’ and students’ experiences of online mathematics teaching and learning and to enable sharing of solutions to the challenges encountered. One hundred and twenty-seven students and eighteen lecturers participated in this survey. In this presentation, we will share some of the findings of the survey in relation to the following two themes: challenges of learning and teaching mathematics online, and …
Assessing first-year engineering students' pre-university mathematics knowledge: preliminary validity results based on an item response theory model
The importance of students’ prior knowledge to their current learning outcomes cannot be overemphasised. Students with adequate prior knowledge are better prepared for the current learning materials than those without the knowledge. However, assessment of engineering students' prior mathematics knowledge has been beset with a lack of uniformity in measuring instruments and inadequate validity studies. This study attempts to provide evidence of validity and reliability of a Norwegian national test of prior mathematics knowledge using an explanatory sequential mixed-methods approach. This approach involves use of an item response theory model followed by cognitive interviews of some students …
Commentary 1 on Reflections on Theories of Learning by Paul Ernest
Paul Ernest is an internationally recognised authority on the philosophy of social-constructivism particularly in the context of mathematics education. He has published widely on the issue, perhaps his two best known and widely cited works are ‘The Philosophy of Mathematics Education’ (Ernest 1991), and ‘Social Constructivism as a Philosophy of Mathematics’ (Ernest 1998). As one engages with this short paper it is evident that one is in the company of a ‘master’ of the topic. It is quite remarkable how within the space of about 4000 words he manages to produce an erudite and informative account of 4 related theories of learning, and outline some of their implications for teaching.
Self-efficacy and approaches to learning mathematics among engineering students : empirical evidence for potential causal relations
Theories of self-efficacy and approaches to learning are well-established in the psychology of learning. However, studies on relationships between the primary constructs on which these theories are...
Gruppebasert prosjektoppgave i matematikk: Veiledernes erfaringer
I denne presentasjonen vil vi rapportere veilederes erfaringer med å bidra i et matematisk modelleringsprosjekt. Prosjektet ble introdusert i begynnelsen av første semester matematikkurs for ingeniørstudenter. Målet med prosjektet er å knytte matematikken til realistiske ingeniørgfag problemstillinger og at studentene skal få en nærmere tilknytning til faglærerne i sitt felt. Vi ønsker også å lære studentene flere matematiske kompetanser, som det er vanskelig å trene i forelesninger og øvingstimer. I prosjektet ble 483 studenter delt i 70 grupper som ble veiledet av 20 faglig ansatte fra alle seksjoner av ingeniøravdelingene. Veilederne rapporterer om at de opplever prosjektoppgaven som et …
A transition to online teaching and learning of mathematics in Norwegian higher education institutions: the perspectives of lecturers and students
Abstract This paper reports a study of university lecturers’ and students’ experiences of teaching and learning mathematics following the abrupt requirement to switch to online teaching in 2020. A goal of the study is to share experiences that could be useful to improve the teaching and learning of mathematics in online settings. The qualitative research described is a phenomenological study and draws on interviews with ten mathematics lecturers and six undergraduate students who were enrolled in at least one university mathematical course during the lockdown in 2020. The interview data were analysed using a thematic approach. This paper reports findings regarding perceptions of lecturers a…
Stimulating and facilitating Norwegian RUME
International audience; MatRIC – Centre for Research, Innovation and Coordination of Mathematics Teaching is a Norwegian centre of excellence in higher education. The centre focuses on innovation in university level mathematics teaching. We foster research in teaching and learning mathematics, especially but not exclusively in the context of innovative practice. MatRIC also seeks to facilitate the networking of university level mathematics teachers within Norway and with the international community. This poster focuses on MatRIC's activity aimed at the development of research in university mathematics education. The poster sets out strands of activity within MatRIC's research programme, typ…
Mediated action in teachers’ discussions about mathematics tasks
Published version of an article in the journal: ZDM. Also available from the publisher at: http://dx.doi.org/10.1007/s11858-012-0423-0 This paper presents analyses of teachers’ discussions within mathematics teaching developmental research projects, taking mediation as the central construct. The relations in the so-called ‘didactic triangle’ form the basic framework for the analysis of two episodes in which upper secondary school teachers discuss and prepare tasks for classroom use. The analysis leads to the suggestion that the focus on tasks places an emphasis on the task as object and its resolution as goal; mathematics has the role of a mediating artefact. Subject content in the didactic…
Educating to inspire active learning approaches in mathematics in Norwegian universities
This is a report of an analysis of some of the data generated by a national survey of teaching approaches used in higher education mathematics courses. The overall purpose of the survey was to explore how widespread is the use of teaching approaches that might promote students’ active learning of mathematics. The paper includes a brief presentation of the authors meaning of the expression “teaching actions that have the potential to promote active learning”. The analysis focuses on the responses of 95 lecturers working in 13 Norwegian HE institutions. The goal is to expose underlying patterns in lecturers’ responses to questions about the teaching actions they may incorporate in their pract…
Calculus Self-Efficacy Inventory : Its Development and Relationship with Approaches to Learning
This study was framed within a quantitative research methodology to develop a concise measure of calculus self-efficacy with high psychometric properties. A survey research design was adopted in which 234 engineering and economics students rated their confidence in solving year-one calculus tasks on a 15-item inventory. The results of a series of exploratory factor analyses using minimum rank factor analysis for factor extraction, oblique promin rotation, and parallel analysis for retaining extracted factors revealed a one-factor solution of the model. The final 13-item inventory was unidimensional with all eigenvalues greater than 0.42, an average communality of 0.74, and a 62.55% variance…