NOMAD artikelregister

  1. NOMAD 22(4), 2017

    Peer assessment of mathematical understanding using comparative judgement

    Ian Jones and David Sirl

    Abstract

    It is relatively straightforward to assess procedural knowledge and difficult to assess conceptual understanding in mathematics. One reason is that conceptual understanding is better assessed using open-ended test questions that invite an unpredictable variety of responses that are difficult to mark. Recently a technique, called comparative judgement, has been developed that enables the reliable and valid scoring of open-ended tests. We applied this technique to the peer assessment of calculus on a first-year mathematics module. We explored the reliability and criterion validity of the outcomes using psychometric methods and a survey of participants. We report evidence that the assessment activity was reliable and valid, and discuss the strengths and limitations, as well as the practical implications, of our findings.

    Ian Jones

    Ian Jones obtained a PhD in Mathematics Education from the University of Warwick and is a Senior Lecturer in the Mathematics Education Centre at Loughborough University, UK. Prior to this he was a Royal Society Shuttleworth Education Research Fellow and taught in primary and secondary schools for ten years. His research interests are in school children’s learning of algebra and the assessment of procedural and conceptual understanding of mathematics.

    David Sirl

    David Sirl is a Lecturer in the School of Mathematical Sciences at the University of Nottingham. He is enjoying spending some time working with education researchers to explore new ways of improving teaching and learning.

    Skapad: 2018-01-04 kl. 00:00

  2. NOMAD 22(4), 2017

    Developing practice through research into university mathematics education

    Simon Goodchild and Barbara Jaworski

    Abstract

    The paper provides a very brief outline review of research into some key issues that affect students’ performance in mathematics in higher education. Community of practice theory is used to frame and focus the discussion. Policies regarding the recruitment of students, institutional practices for grouping students and the cultures of teaching and learning mathematics are considered. The research reviewed provides a context for examining the contributions of the research reports included within this thematic issue of NOMAD. The reports address three themes: regular approaches adopted in teaching mathematics in higher education, innovative approaches to teaching and learning, with emphasis on student participation in the educational process, and the characteristics of mathematical knowledge students appropriate. The paper endorses calls for large scale studies, especially those which relate teaching approaches, both regular and innovative, to the qualities and characteristics of students’ learning. The absence of a single overarching theoretical framework that embraces all the studies is also perceived as an obstacle that interferes with scientific developments in the field of researching university mathematics education. However, the value of teachers researching their own practice and their students’ learning is argued to be crucial for developing knowledge ”in practice” and this underscores the value of the papers included in this issue of NOMAD, both for the authors and the inspiration of other higher education mathematics teachers who, it is hoped, will be inspired to engage in similar studies.

    Simon Goodchild

    Simon Goodchild is Professor of Mathematics Education at the University of Agder, he is also leader of MatRIC, Centre for Research Innovation and Coordination of Mathematics Teaching. MatRIC is one of eight Norwegian centres for excellence in higher education. He has over two decades of experience of school classroom research and school mathematics teaching development. In his role leading MatRIC he is using and extending his experience of mathematics teaching development in the context of university mathematics education.

    Barbara Jaworski

    Barbara Jaworski is Professor of Mathematics Education at Loughborough University and coordinates research, including a group of eight PhD research fellows, within MatRIC. She has held positions of Chair of the British Society for Research into Learning Mathematics; President of the Congress of European Researchers in Mathematics Education; and President of the International Group for the Psychology of Mathematics Education. She has been research mathematics teaching and teaching development for over three decades.

    Skapad: 2018-01-04 kl. 00:00

  3. NOMAD 22(4), 2017

    Characterising undergraduate mathematics teaching across settings and countries: an analytical framework

    Angeliki Mali and Georgia Petropoulou

    Abstract

    This paper explores the characteristics of teaching of a sample of university mathe-matics teachers in two countries, Greece and Great Britain, and in two settings, lectures and tutorials, seeking to identify a common ground for undergraduate mathe-matics teaching. Our observations of teaching and our sociocultural perspectives enabled us to develop a framework for a detailed description of the observed teaching. The description reveals categories of teaching actions, and the associated tools teachers use in selecting tasks for their students, providing comprehensive explanations, extending students’ mathematical thinking, or evaluating students’ mathematical meaning. The findings are across settings and countries in the direction of a profound understanding of undergraduate mathematics teaching.

    Angeliki Mali

    Angeliki Mali is a Postdoctoral Research Fellow in the School of Education at the University of Michigan. Prior to her fellowship, she was member of the Culture, Pedagogy and Identity group in the Mathematics Education Centre at Loughborough University, where she was awarded her PhD. She holds a BSc in Mathematics, and an MSc in Didactics and Methodology of Mathematics from the University of Athens in Greece. Her research focuses on university mathematics education. She has experience in teaching mathematics to students attending STEM programmes at university level.

    Georgia Petropoulou

    Georgia Petropoulou is finishing her PhD in the Mathematics Department at the University of Athens, Greece. Her PhD is in mathematics education, focusing on university mathematics teaching for students’ learning needs. She has an MSc in Didactics and Methodology of Mathe-matics and a BSc in Mathematics, both awarded by the University of Athens. Her research interests are in university mathematics teaching practice and its development to meet students’ learning needs.

    Skapad: 2018-01-04 kl. 00:00

  4. NOMAD 22(4), 2017

    Stimulating critical mathematical discussions in teacher education: use of indices such as the BMI as entry points

    Suela Kacerja, Toril Eskeland Rangnes, Rune Herheim, Meinrad Pohl, Inger Elin Lilland and Ragnhild Hansen

    Abstract

    The main purpose of our research project is to gain insight into, and develop teaching on indices and their applications in society. In this paper, the focus is to present insights into teachers’ reflections when discussing the Body Mass Index (BMI). Skovsmose´s concept of mathemacy, and source criticism, are chosen as conceptual framework. The data analysed were collected in a numeracy across the curriculum class with practising teachers. The findings show that the practising teachers engaged in meaning making of the index formula, and they critically discussed how BMI is used in society and the role the BMI index can have in our lives. We gain insight into the potential of such an index for developing teachers’ awareness of the application of mathematics­ to the real world and the issues it raises, both for the teachers and for ourselves.

    Suela Kacerja

    Suela Kacerja has a postdoc position in mathematics education at the Western Norway University of Applied Sciences. She has a background as mathematics teacher educator from Albania and Norway. Her research interests are: developing critical mathematics education possibilities in teacher education and in schools, in intersection with real-life contexts in learning mathematics, as well as pre-service teachers’ reflections about their own practice.

    Toril Eskeland Rangnes

    Toril Eskeland Rangnes is associate professor in mathematics education. She works at the Department of Teacher Education Study in Mathematics, Western Norway University of Applied Sciences. Rangnes has a background as primary school teacher, textbook author and editor for Tangenten. Her main research interests are critical mathematics education, teacher professional development and language diversity in mathematics classrooms.

    Rune Herheim

    Rune Herheim is associate professor at Western Norway University of Applied Sciences. His research focuses on connections between communication qualities and learning in mathematics with a particular focus on argumentation and agency in real-life contexts and when students use digital learning tools. Herheim is the Editor in chief for Tangenten, a Norwegian journal on mathematics teaching.

    Meinrad Pohl

    Meinrad Pohl is associate professor in history. He works at the Department of Social Science, Western Norway University of Applied Sciences, Bergen. His main research interests are early modern economic theory and economic policy, trade history and mining history.

    Inger Elin Lilland

    Inger Elin Lilland is associate professor at the Western Norway University of Applied Sciences, where she works at the Department of Teacher Education Study in Mathematics. She has previous experience as mathematics teacher at the upper secondary school level. Her main research interests are critical mathematics education and mathematics teacher professional development.

    Ragnhild Hansen

    Ragnhild Hansen is associate professor at the Department of Teacher Education Study in Mathematics at Western Norway University of Applied Sciences (HVL). She received her master and PhD degrees from the University of Bergen within applied mathematics. Hansen has a background in as a researcher in different modelling projects. Her main research interests are critical mathematics education and teacher professional development.

    Skapad: 2018-01-04 kl. 00:00

  5. NOMAD 22(4), 2017

    Finnish entry-level students’ views of teacher knowledge and the characteristics of a good mathematics teacher

    Mervi A. Asikainen, Antti Viholainen, Mika Koponen and Pekka E. Hirvonen

    Abstract

    This paper reports a study of the views held by Finnish students at the start of their university studies concerning their understanding of the knowledge and characteristics of a good mathematics teacher. A total of 97 students following a basic university course responded to a questionnaire. The results showed that a knowledge of teaching mathematics was more often used to describe the good mathematics teacher than a knowledge of mathematics. According to the students’ views, mathematics teachers need to be able to take the level of understanding of individual students into account in their teaching. Good mathematics teachers were also considered to be skilled in explaining, simplifying and transforming mathematical contents for their students. A good mathematics teacher was often described by the respondents as a patient, clear, inspiring and consistent person. On the other hand, characteristics such as humorous, likeable, empathetic, or fair were seldom used in the students’ responses to describe a good mathematics teacher. Those respondents who planned to become teachers demonstrated a more learner-centred concept of a good mathematics teacher than did those who were aiming at some other subject specialist profession than that of teaching.

    Mervi A. Asikainen

    Docent Mervi A. Asikainen is a senior lecturer at the UEF Department of Physics and Mathematics. Asikainen directs the UEF physics and mathematics education research group. Her current field of interest include teacher knowledge of mathematics and physics teachers, teaching and learning of physics in higher and secondary education, and research-based development of STEM education.

    Antti Viholainen

    Antti Viholainen is a senior lecturer in mathematics / mathematics education at University of Eastern Finland. His research areas are mathematical beliefs, mathematics teacher education, learning materials (textbooks etc.) in mathematics, and mathematical argumentation.

    Mika Koponen

    Mika Koponen is a postdoctoral researcher at the University of Eastern Finland. He has used Mathematical Knowledge for Teaching (MKT) framework for evaluating and improving mathematics teacher education. In his dissertation study, he presented a novel approach for investigating teacher knowledge and its interconnections by making use of network analysis methods. His postdoctoral research continues from this work by focusing on how the components of teacher knowledge are interconnected.

    Pekka E. Hirvonen

    Docent Pekka E. Hirvonen is a senior lecturer at the UEF Department of Physics and Mathematics. Hirvonen has published more than 30 peer-reviewed articles in international journals, books, and proceedings.

    Skapad: 2018-01-04 kl. 00:00

  6. NOMAD 22(4), 2017

    A study of students’ concept images of inverse functions in Ireland and Sweden

    Sinéad Breen, Niclas Larson, Ann O’Shea and Kerstin Pettersson

    Abstract

    In this paper we focus on first-year university students’ conceptions of inverse function. We present results from two projects, conducted in Ireland and Sweden respectively. In both countries, data were collected through questionnaires, as well as through student interviews in Sweden. We draw on the notion of concept image and describe the components of students’ evoked concept images. The students’ responses involved e.g. ”reflection”, ”reverse”, and concrete ”examples”, while just a few students gave explanations relating to the definition of inverse functions. We found that the conceptions of inverses as reflections and reverse processes are important and relatively independent of local factors, and the data seemed to suggest that a ”reverse” conception is linked to an appreciation of injectivity more than a

    ”reflection” conception.

    Sinéad Breen

    Sinéad Breen holds a PhD in Mathematics (on Asymptotic Analysis) from Dublin City University and has recently returned there as an Assistant Professor in the School of Mathematical Sciences. She conducts research in mathematics education, her main interest being in the teaching and learning of mathematics at undergraduate level.

    Niclas Larson

    Niclas Larson is an associate professor at the Department of Mathematical Sciences, University of Agder, Kristiansand, Norway. His research interest lies in the teaching and learning of mathematics at secondary or university level. Current projects, both comparative, deal with students’ understanding of proof by mathematical induction and student teachers’ explanations of solutions to linear equations respectively. His methodological and theoretical standpoints are varied and driven by current research questions.

    Ann O’Shea

    Ann O’Shea is a Senior Lecturer in the Department of Mathematics and Statistics at the Maynooth University in Ireland. She received a PhD in Mathematics from the University of Notre Dame, Indiana in 1991. Currently her research interests lie in Mathematics Education, especially at undergraduate level.

    Kerstin Pettersson

    Kerstin Pettersson is an associate professor at the Department of Mathe-matics and Science Education, Stockholm University, Sweden. Her research interests concern university students’ conceptions of thres-hold concepts. Current projects deal with students’ learning in small groups teaching and students’ understanding of proof by mathematical induction.

    Skapad: 2018-01-04 kl. 00:00

  7. NOMAD 22(4), 2017

    Oral presentations as a tool for promoting metacognitive regulation in real analysis

    Margrethe Naalsund and Joakim Skogholt

    Abstract

    Real Analysis is for many students their first proof-based mathematics course, and many find it challenging. This paper studies how oral presentations of mathematical problems for peers can contribute to students’ metacognitive reflections. The paper discusses several aspects tied to preparing for, and carrying out, oral presentations, that seem to spur important sub-components of metacognitive regulation such as planning, monitoring, and evaluating. Thoughtful guidance from an expert encouraged the students to further monitor their cognition, and evaluate their arguments and cognitive processes when expressing their reasoning to their peers.

    Margrethe Naalsund

    Margrethe Naalsund is associate professor in Mathematics Education. She works at Faculty of Science and Technology (Section for Learning and Teacher Education) at Norwegian University of Life Sciences (NMBU). Her main research interests are learning and teaching algebra at primary and secondary school, and learning and teaching real analysis at university level.

    Joakim Skogholt

    Joakim Skogholt is PhD-student in Mathematics. He works at Faculty of Science and Technology (Section for Applied Mathematics) at Norwegian University of Life Sciences (NMBU). His main research interests are applied linear algebra, and learning and teaching real analysis at university level.

    Skapad: 2018-01-04 kl. 00:00

  8. NOMAD – 22(4), 2017


    Tidigare nummerPrevious issues
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    Nummer/Issue

    Volume 22, No 4, December 2017

    Editorial

    Simon Goodchild and Barbara Jaworski

    Developing practice through research into university mathematics education

    [PDF]

    Angeliki Mali and Georgia Petropoulou

    Characterising undergraduate mathematics teaching across settings and countries: an analytical framework

    [PDF]

    Suela Kacerja, Toril Eskeland Rangnes, Rune Herheim, Meinrad Pohl, Inger Elin Lilland and Ragnhild Hansen

    Stimulating critical mathematical discussions in teacher education: use of indices such as the BMI as entry points

    [PDF]

    Mervi A. Asikainen, Antti Viholainen, Mika Koponen and Pekka E. Hirvonen

    Finnish entry-level students’ views of teacher knowledge and the characteristics of a good mathematics teacher

    [PDF]

    Sinéad Breen, Niclas Larson, Ann O’Shea and Kerstin Pettersson

    A study of students’ concept images of inverse functions in Ireland and Sweden

    [PDF]

    Margrethe Naalsund and Joakim Skogholt

    Oral presentations as a tool for promoting metacognitive regulation in real analysis

    [PDF]

    Stephanie Treffert-Thomas, Olov Viirman, Paul Hernandez-Martinez and Yuriy Rogovchenko

    Mathematics lecturers’ views on the teaching of mathematical modelling

    [PDF]

    Ian Jones and David Sirl

    Peer assessment of mathematical understanding using comparative judgement

    [PDF]

    Barbro Grevholm

    Bokanmälan

    Innehåll: JH

    Skapad: 2018-01-04 kl. 00:00

  9. NOMAD 22(4), 2017

    Mathematics lecturers’ views on the teaching of mathematical modelling

    Stephanie Treffert-Thomas, Olov Viirman, Paul Hernandez-Martinez and Yuriy Rogovchenko

    Abstract

    The paper reports on the views and use of mathematical modelling (MM) in university mathematics courses in Norway from the perspective of lecturers. Our analysis includes a characterisation of MM views based on the modelling perspectives developed by Kaiser and Sriraman (2006). Through an online survey we aimed to identify the main perspectives held in higher education by mathematics lecturers and the underlying rationale for integrating (or not) MM in university courses. The results indicated that most respondents displayed a realistic perspective on MM when it came to their professional practice. There was a more varied response when it came to their views on MM in teaching. Regarding conditions influencing the use or non-use of MM in teaching, these mainly concerned the mathematical content and the institutional practices.

    Stephanie Treffert-Thomas

    Stephanie Treffert-Thomas is a lecturer at Loughborough University (UK) with experience of teaching mathematics at school level, tertiary (college) level and at university, mainly to engineering students. Her research interests are in university level mathematics teaching and learning using socio-cultural educational theories. She has a particular interest in the mathematical teaching practices of lecturers, including the use of mathematical modelling in teaching.

    Olov Viirman

    When the research reported on in this paper was conducted, Olov Viirman was a postdoctoral researcher within the MatRIC centre at the University of Agder, Norway. He has recently taken up a position as senior lecturer at the University of Gävle, Sweden. His research is in university mathematics education, mainly focusing on the discursive practices of lecturers and students, and on the teaching and learning of mathematics, for instance mathematical modelling, in other academic disciplines.

    Paul Hernandez-Martinez

    Paul Hernandez-Martinez is a senior lecturer in the Department of Mathematics at Swinburne University of Technology, Australia, and a visiting fellow in the Mathematics Education Centre at Loughborough University, UK. His research is in post-compulsory Mathematics Education, where he uses socio-cultural educational theories to investigate teaching-learning practices (e.g. Mathematical Modelling) that have the potential to develop in students rich mathematical meanings while at the same time create in them positive dispositions towards the subject.

    Yuriy Rogovchenko

    Yuriy Rogovchenko is a Professor of Mathematics at the University of Agder, Kristiansand, Norway. His research interests include qualitative theory of ordinary, functional and impulsive differential equations, mathematical modelling, and mathematics education related to teaching and learning of differential equations and mathematical modelling at university level.

    Skapad: 2018-01-04 kl. 00:00

  10. NOMAD 22(3), 2017

    The development of pre-service teachers’ self-efficacy in teaching mathematics

    Annette Hessen Bjerke

    Abstract

    Teacher efficacy has received much attention in the general field of educational research, but applications in mathematics teacher education are few. In order to deepen the understanding of the nature and development of self-efficacy in teaching mathematics (SETM) during teacher education, the study presented here followed over a period of two years pre-service teachers (PSTs) preparing to teach primary school mathematics in Norway (grades 1–7, ages 6–13). Their developing SETM was investigated by means of an instrument designed to target the core activity of teaching mathematics: helping a generic child with mathematics tasks. A comparison of responses collected from 191 novice PSTs with those from the same cohort two years later (n = 103) shows a rise in SETM in the typical PST, and indicates the nature of the development of SETM during teacher education.

    Annette Hessen Bjerke

    Annette Hessen Bjerke got her PhD degree in September 2017 and this article is a part of her thesis. She has worked as a teacher educator in mathematics at Oslo and Akershus University College since 2004, and is a textbook author in elementary school mathematics. Her research interest concerns how teacher education fosters future mathematics teachers.

    Skapad: 2017-09-21 kl. 01:00

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