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  1. NOMAD 17(3-4), 2012.

    How mathematics students perceive the transition from secondary to tertiary level with particular reference to proof

    Fulvia Furinghetti, Chiara Maggiani and Francesca Morselli

    Abstract

    This paper reports on a research project concerning the difficulties met by undergraduate students in mathematics during the first year of university. Our aim is to provide elements for studying the transition from secondary to tertiary level as perceived by the students who live it. The combination of different analytical tools (questionnaires, interviews, problem solving and proving activities) allows shedding light on aspects which are not purely cognitive, but also pertain to the affective domain.

    Fulvia Furinghetti

    Fulvia Furinghetti is full professor (retired) in the University of Genoa. She teaches Mathematics Education in the Department of Mathematics of this University. Her research concerns beliefs, images of mathematics in society, proof, problem solving, use of history of mathematics in teaching, teacher professional development, and history of mathematics education. In 2000–2004 she chaired HPM (the International Study Group on the relations between History and Pedagogy of Mathematics affiliated to ICMI).

    Chiara Maggiani

    Chiara Maggiani graduated in Mathematics at the University of Genoa discussing a dissertation on the problems encountered by mathematics students in the transition from secondary school to university. At present she is going to obtain her specialization in mathematics teaching.

    Francesca Morselli

    Francesca Morselli is assistant professor at the Department of Philosophy and Education of the University of Turin. She teaches Mathematics Education to prospective primary teachers. Her research interests concern the intertwining of affect and cognition in mathematics teaching and learning, and the teaching and learning of mathematical proof.

    Skapad: 2013-08-20 kl. 01:00

  2. NOMAD 17(3-4), 2012.

    Interplay of cognition and affect in undergraduate math students’ careers: insights from recursive partitioning

    Chiara Andrà and Guido Magnano

    Abstract

    Data collected in entrance tests for undergraduate curricula in mathematics at the University of Turin are analysed using the recursive partition method, to obtain classification trees for different ”response variables” describing academic achievement or drop-out. The input factors include both math abilities and several affective and motivational factors, the latter having being assessed using internationally validated questionnaires. We argue that classification trees can provide unexpected insight into the interplay of such factors for academic success or failure, specifically for math students.

    Chiara Andrà

    Chiara Andrà is Lecturer at the University of Torino. She teaches Mathematics Education at the Department of Philosophy and Education in Torino, and Statistics at the Department of Mathematics. Her research interests regard early probabilistic thinking, undergraduate students’ difficulties about mathematics and its learning, and semiotics. Her research is framed within the paradigm of the embodied cognition.

    Guido Magnano

    Guido Magnano is associate professor of Mathematical Physics at the University of Torino. Since 2001 he has supervised the design and the administration of student entrance tests at his university, and participated to various research projects, both at regional and at national level, aimed at measuring mathematical ability and other relevant dimensions in students’ transition from high school to undergraduate studies. A significant part of his recent research activity is devoted to Item response theory, in connection with item validation and reliability issues in multiple-choice testing.

    Skapad: 2013-08-20 kl. 01:00

  3. NOMAD 17(3-4), 2012.

    Primary teachers’ affect: a crucial variable in the teaching of mathematics

    Cristina Coppola, Pietro Di Martino, Tiziana Pacelli and Cristina Sabena

    Abstract

    Mathematics education is strongly interested in defining ”what is necessary for teaching mathematics effectively”. The main directions of research emphasize the cognitive side of the answer to this question, trying to describe what kind of knowledge is needed in order to teach mathematics effectively. Starting from the point that teachers’ affect plays a crucial role in determining the quality of teaching, we discuss this issue from a theoretical point of view, introducing the construct of ”attitude towards mathematics teaching”. Within this theoretical framework we conducted a study with 189 primary school pre-service teachers, investigating teachers’ emotions, beliefs and attitudes. In this paper, we analyze and discuss the relationship among the participants’ emotional disposition towards mathematics and towards the idea of having to teach it, their past experiences as math-students and the current perceived competence in mathematics.

    Cristina Coppola

    Cristina Coppola has got a research fellowship at Dipartimento di Matematica of Università degli Studi di Salerno. Her main research interests are: future teachers’ attitudes and emotions towards mathematics; the study of different aspects regarding the relationship between mathematical logic and language, with particular attention to the development of logical tools in primary school children, to the semiotic coordination with secondary school children in mathematical learning processes and to undergraduate students’ reasoning in logical tasks; the use of e-learning in mathematics education.

    Pietro Di Martino

    Pietro Di Martino is a Researcher in Mathematics Education at Dipartimento di Matematica of Università degli Studi di Pisa. His main research interests regard: the role of affective factors in the teaching/learning of mathematics, with particular attention to the theoretical aspects related to the definition of the construct ”attitude towards mathematics”; the study of the difficulties related to the transition between secondary and tertiary transition in mathematics; mathematics teachers development, with particular attention to the development of future primary teachers, and the study of their emotions beliefs and attitudes towards mathematics.

    Tiziana Pacelli

    Tiziana Pacelli has got a research fellowship at Dipartimento di Matematica of Università degli Studi di Salerno. Her main research interests are: analysis of emotions, beliefs and attitudes towards mathematics in future primary teachers; the exploration of the relationship between language and the development of logical tools in students at different school levels, in particular through cooperative and linguistic-manipulative activities with primary school children, through activities about semiotic coordination with secondary school children, through logical tasks with undergraduate students; analysis of the use of e-learning in mathematics education.

    Cristina Sabena

    Cristina Sabena is a researcher in Mathematics Education at Dipartimento di Filosofia e Scienze dell’Educazione of Università degli Studi di Torino. Her main research interests regard: the multimodality of mathematics learning and teaching, with particular attention to the role of gestures, analysed with a semiotic lens; the argumentation processes from primary to secondary school; teachers’ and future teachers’ attitudes and emotions towards mathematics.

    Skapad: 2013-08-20 kl. 01:00

  4. NOMAD 17(3-4), 2012.

    Dialogue between past and future mathematical identities

    Sonja Lutovac and Raimo Kaasila

    Abstract

    Pre-service teachers’ school-time experiences have been addressed much in mathematics

    education research. These experiences have been shown to have a central meaning for pre-service teachers’ views of mathematics and their present mathematical identities. However, the identity is not only bound to the past and present, but it also extends to the future. Further, pre-service teachers’ anticipations of the future have been overlooked in the research on identity in a mathematics education context. We focus here on the mathematical identity work of two pre-service teachers and its dialogue between the past and the future. We compare the cases of one Finnish and one Slovenian pre-service teacher, who reported having had negative experiences with mathematics during their school years. Based on the results, two different types of mathematical identity work were identified; resulting from the different facilitators used in mathematics education courses.

    Sonja Lutovac

    Sonja Lutovac is a doctoral candidate in Education at the University of Maribor (Slovenia) and University of Lapland (Finland). Her research interests are in the field of elementary teacher education, especially in mathematics education and in the use of qualitative research methods, such as narrative and rhetorical approaches. She is mostly interested in pre-service teachers’ identity and identity work in mathematics education context.

    Raimo Kaasila

    Ph.D. Raimo Kaasila is a Professor of Education, especially studying and developing teacher education at the University of Oulu (Finland). His main research areas are pre-service teachers’ identity formation and reflective processes during teacher education, especially in the mathematics education context. He has also studied affective domain in teacher education and mathematics education, and the use of narrative, rhetorical and discursive approaches in teacher education.

    Skapad: 2013-08-20 kl. 01:00

  5. NOMAD 17(3-4), 2012.

    (In)consistent? The mathematics teaching of a novice primary school teacher

    Hanna Palmér

    Abstract

    This article focuses on the mathematics teaching of Helena, a Swedish novice teacher. Helena is one of seven teachers in a case study of primary school mathematics teachers’ professional identity development. She is also an example of a teacher whose mathematics teaching, from an observer’s perspective, may appear inconsistent with her talk about mathematics teaching. However, in this article a conceptual framework aimed at analysing professional identity development will be used making the process of her mathematics teaching visible and then her mathematics teaching appear as consistent.

    Hanna Palmér

    Hanna Palmér is a postgraduate student in mathematics education at Linnaeus University, Sweden. Her main research interest is the professional identity development of mathematics teachers and the work with and learning of mathematics of children in pre-school, pre-school class and lower primary school.

    Skapad: 2013-08-20 kl. 01:00

  6. NOMAD 17(3-4), 2012.

    Prospective mathematics teachers’ metaphors for mathematics, teaching, and the teacher’s role

    Päivi Portaankorva-Koivisto

    Abstract

    This study sheds light on Finnish preservice mathematics teachers’ (n = 16) views of mathematics, teaching, and the teacher’s role. Data was gathered via metaphors at three time points during teacher students’ pedagogical studies, in academic year 2011–2012. The analysis was conducted inductively, but based on categories found in previous studies. The results indicated that prospective mathematics teachers’ metaphors for mathematics mostly involved picturing the self-existent quality of mathematics. Their metaphors for teaching referred to the ups and downs in teaching, and their metaphors for the teacher’s role were involved with the characteristics of the teacher’s personality. One possible explanation for these results centres round mathematics student teachers’ life situations. They have studied mathematics as their major at the department of mathematics for 2–3 years just before they started their pedagogical studies, and they have just experienced their very first and overwhelming lessons as teachers.

    Päivi Portaankorva-Koivisto

    Päivi Portaankorva-Koivisto is university lecturer (PhD) at the University of Helsinki. Her research interests are Experiential mathematics teaching; Teachers’ professional development; Metaphors in teacher education context; and Using photos and pictures to support reflective thinking in teacher education.

    Skapad: 2013-08-20 kl. 01:00

  7. NOMAD 17(3-4), 2012.

    Comparing mathematics teachers’ beliefs about good teaching: the cases of Estonia, Latvia and Finland

    Madis Lepik, Anita Pipere and Markku S. Hannula

    Abstract

    The article presents results from a cross-cultural NorBa project Mathematics teachers’ educational beliefs. We report on Estonian, Latvian and Finnish lower secondary mathematics teachers’ espoused beliefs about good teaching. A principal component analyses identified a two-component structure of teachers’ beliefs about good teaching: (1) Reasoning and conceptual understanding and (2) Mastery of skills and facts. Cross-cultural differences were identified in both of these dimensions. Latvian teachers indicated the strongest agreement with reasoning and conceptual understanding, Estonian teachers with mastery of skills and facts, while Finnish teachers scored lowest on both dimensions. Moreover, we analysed the amount of teachers with different profiles with regard to these two dimensions. The results suggest both common conceptual core of teachers’ beliefs on mathematics teaching and certain cultural influence on the profile of these beliefs.

    Madis Lepik

    Madis Lepik is associated professor of mathematics education at the Department of Mathematics, Tallinn University, Estonia. His research interests include teachers’ beliefs and professional development, textbook studies, and proof and proving.

    Anita Pipere

    Anita Pipere is professor of educational psychology at the Institute of Sustainable Education, Faculty of Education and Management, Daugavpils University, Latvia. Her research interests include professional identity, teachers’ beliefs and teaching approaches, dialogical self, and education for sustainable development.

    Markku S. Hannula

    Markku S. Hannula is professor in mathematics education at the Department of Teacher Education at the University of Helsinki in Finland. His research interests include motivation, beliefs, emotions, problem solving, and gender in mathematics education.

    Skapad: 2013-08-20 kl. 01:00

  8. NOMAD 18(1), 2013.

    Student teachers’ work on instructional explanations in multiplication – representations and conversions between them

    Anita Valenta and Ole Enge

    Abstract

    In this study we are analysing student teachers’ instructional explanations. The study is based on student teachers’ written work on two different tasks about different strategies and properties in multiplication and explaining these. Our research questions concern the type of representation registers student teachers use in their explanations. In explanations where several representation registers are used, we analyse what can be challenges in conversions between representations. Data is analysed using the framework of Duval’s cognitive analysis, and analyses and discussions are related to development of mathematical knowledge for teaching.

    Anita Valenta

    Anita Valenta is Associate Professor in mathematics education at Sør-Trøndelag University College in Trondheim, Norway. Her main interest is in developing a knowledge base for mathematics teacher education, research in student teachers’ mathematical knowledge for teaching and algebra in the early grades.

    Ole Enge

    Ole Enge is Associate Professor in mathematics education at Sør-Trøndelag University College in Trondheim, Norway. He is interested in developing a knowledge base for mathematics teacher education, research on instructional routines in mathematics teaching and students’ proportional reasoning.

    Skapad: 2013-05-15 kl. 01:00

  9. NOMAD 18(1), 2013.

    Making sense of a ”misleading” graph

    Oduor Olande

    Abstract

    Given the importance of a critical-analytical disposition in the case of graphical artefacts, this paper explores graphicacy based on students’ answers to an item from PISA survey test. Primarily, results from the written test were analyzed using PISA’s doubledigit rubrics or coding. In evaluating these categories, it is observed that just a small percentage of students are able to produce answers that reflect a critical-analytical approach with respect to the use of statistical/mathematical operators and forms of expressions. Secondly, video observation shows that students tend to employ what is perceived as an ”identification approach” while discussing the task. Whereas elements of mathematical and statistical ideas can be identified in the students’ discussion, these are not explicitly stated and are largely submerged in everyday concerns and forms of expression.

    Oduor Olande

    Oduor Olande is a Ph. D. candidate in the didactics of mathematics at the Department of Applied Science and Design, Mid Sweden University (Mittuniversitetet), Sweden. His special research interest is in interactions (sense making and analysis) with graphical artefacts. He is also interested in issues concerning stochastic thinking.

    Skapad: 2013-05-15 kl. 01:00

  10. NOMAD 18(1), 2013.

    I need advanced mathematics to pursue the career of my choice”. Norwegian students’ motivations for enrolling in mathematics and plans for post-secondary studies

    Ida Friestad Pedersen

    Abstract

    Participation in advanced science and mathematics courses in upper secondary school is a gateway to tertiary education and career opportunities in the STEM fields (Science, Technology, Engineering, and Mathematics). The purpose of this study is to investigate Norwegian final-year upper secondary school students’ motivations for choosing to enroll in the most advanced mathematics course offered (3MX), as well as to ascertain their plans for post-secondary education. Since females are underrepresented in mathematics and mathematics-related fields of study, special attention is paid to the gender perspective. The analyses are based on questionnaire data from the large-scale international achievement study TIMSS Advanced, and are framed by the expectancy-value model developed by Eccles and her colleagues (1985). Results show that the subject’s utility value was the primary reason for students’ enrollment in mathematics; that interest in mathematics as a school subject is somewhat more important to the girls than to the boys; and that there are some gender differences in students’ plans for post-secondary studies in the STEM fields.

    Ida Friestad Pedersen

    Ida Friestad Pedersen is a PhD-student in the doctoral program at the University of Oslo, and works as a lecturer at the University of Tromsø. Her research interests include students’ mathematical competence, with an emphasis on algebra, and their motivations for choosing mathematics in upper secondary school and beyond.

    Skapad: 2013-05-15 kl. 01:00

  11. NOMAD – 18(1), 2013


    Tidigare nummerPrevious issues
    Array

    Nummer/Issue

    Volume 18, No 1, March 2013

    Ledare/Editorial

    Editorial

    Oduor Olande

    Making sense of a ”misleading” graph

    [PDF]

    Anita Valenta and Ole Enge

    Student teachers’ work on instructional explanations in multiplication – representations and conversions between them

    [PDF]

    Ida Friestad Pedersen

    ”I need advanced mathematics to pursue the career of my choice”. Norwegian students’ motivations for enrolling in mathematics and plans for post-secondary studies

    [PDF]

    Innehåll: JH

    Skapad: 2013-05-15 kl. 01:00

  12. NOMAD 17(2), 2012. Upper secondary school students’ gendered conceptions about affect in mathematics

    Upper secondary school students’ gendered conceptions about affect in mathematics

    Lovisa Sumpter

    Abstract

    This study explores upper secondary school students’ conceptions about gender and affect in mathematics. Two groups of students from Swedish Natural Science Programme each answered a questionnaire; the first with a focus on boys and girls in general and the other with a focus on individuals themselves. The results from two questionnaires were compared. The first questionnaire revealed a view of rather traditional femininities and masculinities, a result that did not repeat itself in the second questionnaire. There was a discrepancy between traits students ascribed as gender different and traits students ascribed to themselves.

    Lovisa Sumpter

    Lovisa Sumpter is lecturer and researcher at Dalarna University, Falun, Sweden. Her research interests are mathematical reasoning, affect and gender.

    Skapad: 2013-02-13 kl. 00:00

  13. NOMAD 17(2), 2012. Innovative approaches to teaching mathematics in higher education: a review and critique

    Innovative approaches to teaching mathematics in higher education: a review and critique

    Mahmoud Abdulwahed, Barbara Jaworski and Adam R. Crawford

    Abstract

    This paper provides a snapshot of emerging trends in mathematics teaching in higher education for STEM subjects (Science, Technology, Engineering and Mathematics). Overwhelmingly, papers identify a focus on conceptual understandings of mathematics in comparison to understanding that is instrumental or procedural. Calls for reform of mathematics teaching have been the basis for a range of studies; responses to these calls have embraced innovative methods for implementing changes in learning and teaching of mathematics, sometimes rooted in constructivist ideology. Observed trends have been categorised in six groups. In many studies, technology is being used as an enabler of reforms. Constraints to implementing new approaches in mathematics teaching are indicated. Discussion of contemporary research questions that could be asked as a result of the shift towards teaching mathematics in innovative ways is provided and is followed by a critique of the underlying theoretical positions, essentially that of constructivism.

    Mahmoud Abdulwahed

    Mahmoud Abdulwahed is Assistant Professor and Acting Head of the College Requirement Unit at the College of Engineering, Qatar University, Qatar. He was formerly a researcher and developer in ICT, STEM Education, and Innovation at Loughborough University, where he earned his PhD.

    Barbara Jaworski

    Barbara Jaworski is a Professor of Mathematics Education and Director of Research at the Mathematics Education Centre, Loughborough University, UK, formerly a Professor of Mathematics Education at the University of Agder, Norway, where she recently was awarded an Honorary Doctorate.

    Adam Crawford

    Adam Crawford is based within the School of Civil and Building Engineering at Loughborough University, UK, formerly Manager of the Engineering Centre for Excellence in Teaching and Learning at the University.

    Skapad: 2013-02-13 kl. 00:00

  14. NOMAD – 17(2), 2012


    Tidigare nummerPrevious issues
    Array

    Nummer/Issue

    Volume 17, No 2, June 2012

    Ledare/Editorial

    Editorial

    Indrek Kaldo and Markku S. Hannula

    Structure of university students’ view of mathematics in Estonia

    [PDF]

    Lovisa Sumpter

    Upper secondary school students’ gendered conceptions about affect in mathematics

    [PDF]

    Mahmoud Abdulwahed, Barbara Jaworski and Adam R. Crawford

    Innovative approaches to teaching mathematics in higher education: a review and critique

    [PDF]

    Christer Bergsten

    News from Nordic mathematics education

    Innehåll: JH

    Skapad: 2013-02-13 kl. 00:00

  15. NOMAD 17(2), 2012. Structure of university students’ view of mathematics in Estonia

    Structure of university students’ view of mathematics in Estonia

    Indrek Kaldo and Markku S. Hannula

    Abstract

    This study reports on first-year Estonian university students’ view of mathematics. The data was collected from 970 university students of different disciplines. The participants filled out a Likert-type questionnaire that was developed using previously published instruments. The study confirmed that several different attitudes, beliefs, and motivational orientations can be identified and validly measured as separate components of Estonian university students’ view of mathematics. However, the low reliability of some scales highlights the necessity for careful testing of instruments in any new population.

    Indrek Kaldo

    Indrek Kaldo is a PhD student in mathematics education at the Institute of Educational Sciences, Tallinn University. His research interests are students’ beliefs, attitudes and motivation towards the teaching and learning of mathematics, particularly at the university level. He has also 11 years experiences as lecturer in mathematics at university level.

    Markku S. Hannula

    Markku S. Hannula is professor in mathematics education at the Department of Teacher Education at the University of Helsinki in Finland. His research interests include motivation, beliefs, emotions, problem solving, and gender in mathematics education.

    Skapad: 2013-02-13 kl. 00:00

  16. NOMAD 17(1), 2012. Interference of subtraction strategies

    Interference of subtraction strategies

    Per-Olof Bentley

    Abstract

    This study concerns a particular kind of mistake that a number of pupils made when subtracting two positive whole numbers. The aim was to analyse the cause behind this particular mistake. According to the pupils, the difference was equal to the subtrahend. It was found that the pupils counted down to the subtrahend. But instead of finding the answer as the number of steps between the two terms, the pupils applied the last-number-word rule and gave the subtrahend, which was the last mentioned number word, as the result. When seeing subtraction as a concept, it could be assumed that the lack of experience of subtraction as a comparison and as equalization played a decisive role for this mistake. A comparable mistake described in previous research is also analysed.

    Per-Olof Bentley

    Per-Olof Bentley is senior lecturer at Gothenburg University. He has a Ph D degree in mathematics education and has been responsible for the TIMSS project in Sweden from 2004 to 2008. He has made three indepth analyses of the Swedish pupils mathematical knowledge exposed in TIMSS 2007 and TIMSS Advanced 2008. During three and a half years he had also carried out a large interview study in which about 500 pupils were in-depth interviewed.

    Skapad: 2012-09-17 kl. 01:00

  17. NOMAD 17(1), 2012. Using strands of tasks to promote growth of students’ mathematical understanding

    Using strands of tasks to promote growth of students’ mathematical understanding

    John Francisco and Gunnar Gjone

    Abstract

    This article reports on the mathematical activity of a group of five high school students (15–16 year olds) who worked together on a series of challenging task in combinatorics and probability. The students were participants in an after-school, classroom-based, longitudinal research on students’ development of mathematical ideas and different forms of reasoning in several mathematical content strands. The purpose of the article is to contribute insights into how to promote growth of students’ mathematical understanding through problem-solving activities. In particular, the article shows that problem-solving activities involving strands of challenging tasks have the potential to promote growth of students’ mathematical understanding by providing opportunities for students to engage in reasoning by isomorphism. This is a type of reasoning whereby students rely on structural similarities, i.e., isomorphism among mathematical tasks to solve or deepen their understanding of the tasks. Implications for classroom teaching, and environmental conditions that promote reasoning by isomorphism are also discussed.

    John Francisco

    John Francisco is assistant professor in mathematics education in the School of Education at the University of Massachusetts at Amherst, USA. His research interests include students’ development of mathematical ideas and reasoning, personal epistemological beliefs and teacher learning.

    Gunnar Gjone

    Gunnar Gjone is professor of mathematics education at the University of Oslo, Norway, and guest professor at Karlstad University Sweden. His research interests are mathematics teaching and learning in lower and upper secondary school, as well as teacher training. He has special interest in the use of ICT in students’ learning of mathematical concepts.

    Skapad: 2012-09-17 kl. 01:00

  18. NOMAD 17(1), 2012. Methodological issues when studying the relationship between reading and solving mathematical tasks

    Methodological issues when studying the relationship between reading and solving mathematical tasks

    Magnus Österholm and Ewa Bergqvist

    Abstract

    In this paper we examine four statistical methods used for characterizing mathematical test items regarding their demands of reading ability. These methods rely on data of students’ performance on test items regarding mathematics and reading and include the use of regression analysis, principal component analysis, and different uses of correlation coefficients. Our investigation of these methods focuses on aspects of validity and reliability, using data from PISA 2003 and 2006. The results show that the method using principal component analysis has the best properties when taking into account aspects of both validity and reliability.

    Magnus Österholm

    Magnus Österholm has a PhD in mathematics education from Linköping University and now works as a research fellow at the Department of Science and Mathematics Education at Umeå University. He is also a member of Umeå Mathematics Education Research Centre (UMERC). During 2011 and 2012 he is a visiting scholar at Monash University in Melbourne, Australia. His research interests deal primarily with mathematics education at the upper secondary and university levels, where cognitive and metacognitive perspectives are of special interest, together with studying language and communication in the learning and teaching of mathematics.

    Ewa Bergqvist

    Ewa Bergqvist has a PhD in mathematics education from Umeå University and is an assistant professor at the Department of Science and Mathematics Education at Umeå University. She is a member of Umeå Mathematics Education Research Centre (UMERC) and a teacher in mathematics education for pre-service mathematics teachers. Her research focuses mainly on language, competencies, and reasoning in upper secondary and university level mathematics.

    Skapad: 2012-09-17 kl. 01:00

  19. NOMAD – 17(1), 2012


    Tidigare nummerPrevious issues
    Array

    Nummer/Issue

    Volume 17, No 1, March 2012

    Ledare/Editorial

    A new editorial team

    Magnus Österholm and Ewa Bergqvist

    Methodological issues when studying the relationship between reading and solving mathematical tasks

    [PDF]

    John Francisco and Gunnar Gjone

    Using strands of tasks to promote growth of students’ mathematical understanding

    [PDF]

    Per-Olof Bentley

    Interference of subtraction strategies

    [PDF]

    Innehåll: JH

    Skapad: 2012-09-17 kl. 01:00

  20. NOMAD 16(4), 2011. Does the format matter? How the multiple-choice format might complicate the MKT items

    Does the format matter? How the multiple-choice format might complicate the MKT items

    Janne Fauskanger, Reidar Mosvold, Raymond Bjuland and Arne Jakobsen

    Abstract

    In order to design appropriate professional development programs for teachers, an instrument has been developed in the U.S. to measure teachers’ mathematical knowledge for teaching. The process of translating and adapting these measures for use in other countries involves several challenges. This article focuses on issues related to the multiple-choice format of the items. Analyses of focus-group interviews reveal that the multiple-choice format may complicate the items. The teachers’ reflections about the format in this Norwegian case contribute to the understanding of this important challenge.

    Janne Fauskanger

    Janne Fauskanger is Assistant Professor in mathematics education at the University of Stavanger, Norway. Her main interest is related to primary school teachers’ mathematical knowledge for teaching and their practice.

    Reidar Mosvold

    Reidar Mosvold is Associate Professor in mathematics education at the University of Stavanger, Norway. His interests are related to teachers’ beliefs and knowledge of mathematics, and their influence on practice.

    Raymond Bjuland

    Raymond Bjuland is Associate Professor in mathematics education at the University of Stavanger, Norway. His interests are related to students’ collaborative problem solving in small groups, the use of gestures in teacher-student dialogues, and mathematical knowledge for teaching.

    Arne Jakobsen

    Arne Jakobsen is Associate Professor in mathematics at the University of Stavanger, Norway. His interests are mathematics, mathematical knowledge for teaching, and quantitative studies in mathematics education.

    Skapad: 2012-03-06 kl. 00:00

  21. NOMAD 16(4), 2011. Comparing perceptions of mathematics: Norwegian and Finnish university students‘ definitions of mathematics

    Comparing perceptions of mathematics: Norwegian and Finnish university students‘ definitions of mathematics

    Miika Vähämaa and Kennet Härmälä

    Abstract

    The article presents a comparison between Norwegian and Finnish university students’ perceptions of what mathematics is. To carry out the comparison, a mix of qualitative – the creation of abstract and concrete categories for mathematics representations – and quantitative (regression modeling) methods was used in the study. The main result of the study is that Norwegian students were more homogenous in their responses and the vast majority perceived mathematics in concrete terms. The Finnish students, on the contrary, showed greater variety in their responses. There are not many comparative studies among Nordic countries regarding students’ perceptions of mathematics. Therefore this study contributes to improving our knowledge about the possible differences and similarities on students’ perceptions of mathematics among Nordic students. A total of 239 students were asked how they perceive mathematics, numbers and personal applicability of mathematics via an open questionnaire. We propose that the divergent perceptions of mathematics stem from different types of communication cultures that surround mathematics. The argument is made that perceptions of mathematics should be treated as a type of mathematical knowledge that is valuable whenever mathematics is communicated.

    Miika Vähämaa

    Miika Vähämaa is a doctoral student in social psychology at the Department of Social Research at the University of Helsinki, Finland. Vähämaa’s research interests include group epistemologies, heuristics and decision making in groups.

    Kennet Härmälä

    Kennet Härmälä is a project researcher at the Aalto University School of Arts, Design and Architecture, Finland. Härmälä’s research interests include group epistemologies and precarious employment.

    Skapad: 2012-03-06 kl. 00:00

  22. NOMAD – 16(4), 2011


    Tidigare nummerPrevious issues
    Array

    Nummer/Issue

    Volume 16, No 4, December 2011

    Ledare/Editorial

    About this issue

    Tom Rune Kongelf

    What characterises the heuristic approaches in mathematics textbooks used in lower secondary schools in Norway?

    [PDF]

    Janne Fauskanger, Reidar Mosvold, Raymond Bjuland and Arne Jakobsen

    Does the format matter? How the multiple-choice format might complicate the MKT items

    [PDF]

    Miika Vähämaa and Kennet Härmälä

    Comparing perceptions of mathematics: Norwegian and Finnish university students‘ definitions of mathematics

    [PDF]

    Barbro Grevholm

    Network for research on mathematics textbooks in the Nordic countries

    Christer Bergsten

    News from Nordic mathematics education

    Innehåll: JH

    Skapad: 2012-03-06 kl. 00:00

  23. NOMAD 16(4), 2011. What characterises the heuristic approaches in mathematics textbooks used in lower secondary schools in Norway?

    What characterises the heuristic approaches in mathematics textbooks used in lower secondary schools in Norway?

    Tom Rune Kongelf

    Abstract

    In this paper I present findings of an analysis of how mathematics textbooks treat heuristic approaches. The aim of this analysis is to give a characterisation of the occurrence of nine well-known heuristic approaches by analysing 740 examples presented in six ninth grade textbook series. The findings show that many of the problems in the examples are being solved by using one or more heuristic approaches, but the characteristics of the examples and the textbooks’ lack of discussion of the approaches themselves make it challenging to teach and learn these in school. The heuristic approaches seem to be used rather incidentally, which is supported by the fact that none of the textbooks explicitly treat or mention problem solving.

    Tom Rune Kongelf

    Tom Rune Kongelf is a Ph. D. student in the doctoral program at University of Agder in Kristiansand and works as lecturer at Sogn og Fjordane University College in Sogndal. His main research interests concerns textbooks in mathematics in lower secondary school, with an emphasis on heuristic approaches, algebra and tasks.

    Skapad: 2012-03-06 kl. 00:00

  24. NOMAD – 16(3), 2011


    Tidigare nummerPrevious issues
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    Nummer/Issue

    Volume 16, No 3, October 2011

    Ledare/Editorial

    About this issue

    Anne Birgitte Fyhn

    Introduksjon til vektorer i norske lærebøker og i en undervisningsfilm

    [PDF]

    Joakim Samuelsson

    Development of self-regulated learning skills in mathematics in lower secondary school in Sweden

    [PDF]

    Laia Saló i Nevado, Gunilla Holm and Leila Pehkonen

    Farmers do use mathematics: the case of animal feeding

    [PDF]

    Simon Goodchild

    Mathematics education PhD summer school 2011

    Innehåll: JH

    Skapad: 2011-12-21 kl. 00:00

  25. NOMAD 16(3), 2011. Introduksjon til vektorer i norske lærebøker og i en undervisningsfilm

    Introduksjon til vektorer i norske lærebøker og i en undervisningsfilm

    Anne Birgitte Fyhn

    Sammendrag

    Vektorer introduseres andre år på videregående skole i Norge. Denne teksten undersøker hvordan læreverkene og en klatrefilm introduserer dette emnet og hvorvidt filmen kan supplere bøkene. Film og lærebøker undersøkes ut fra samme kriterier. Fordi bøkene bygger på læreplanen, presenteres først en oversikt over vektorers plass i norske læreplaner. Analysene viser at filmen kan supplere lærebøkene ved å utfordre elevenes matematiske tenking i forhold til relasjoner mellom vektor og vinkel. Analysene indikerer også en svakhet ved læreplanen: Læreplanens kompetansemål med hensyn på vektorer fokuserer kun på regning og prosedyrer uten at disse eksplisitt inngår i en sammenheng. Kompetansemålene sier heller ikke noe om forståelse.

    Anne Birgitte Fyhn

    Anne Birgitte Fyhn har PhD i matematikkdidaktikk fra det matematisk-

    naturvitenskapelige fakultet (nå: NT-fakultetet) ved Universitetet i Tromsø, Norge. Hun er tilsatt som førsteamanuensis i matematikkdidaktikk ved Institutt for lærerutdanning og pedagogikk ved Universitetet i Tromsø. Hun leder forskningsprosjektet Strukturer og mønstre i samisk ornamentikk som basis for undervisning i matematikk på ungdomstrinnet. Prosjektet er finansiert av Norges Forskningsråd.

    Skapad: 2011-12-21 kl. 00:00

  26. NOMAD 16(3), 2011. Development of self-regulated learning skills in mathematics in lower secondary school in Sweden

    Development of self-regulated learning skills in mathematics in lower secondary school in Sweden

    Joakim Samuelsson

    Abstract

    In this study, the development of 219 students’ self-regulated learning skills in lower secondary school across ability groups were investigated and related to measures of students’ performance in mathematics. Self-regulated learning skills were assessed with a questionnaire originally designed and used in PISA 2003. Pre-testing was performed during the first two weeks in school in seventh grade. The first post-test was performed after one term in eighth grade, in January 2008. The second post-test was performed during the last two weeks in grade 9, in June 2009. All testing was performed by the class teacher. However, the result states that internal motivation, instrumental motivation as well as self-concept decline across year in lower secondary school. The development of interest and enjoyment of mathematics, self-concept in mathematics and anxiety in mathematics was similar in each ability group. No interaction effects across groups were significant in the study. This study highlights the importance of taking affective factors into account in discussions about the results of mathematics teaching and learning. The strong correlation between affective factors and achievement in mathematics helps us to identify some weaknesses in the Swedish education system.

    Joakim Samuelsson

    Joakim Samuelsson is associated professor at the Department of Behavioural Sciences and Learning at Linköping University. His research focuses on issues related mathematics teaching and learning in compulsory school.

    Skapad: 2011-12-21 kl. 00:00

  27. NOMAD 16(3), 2011. Farmers do use mathematics: the case of animal feeding

    Farmers do use mathematics: the case of animal feeding

    Laia Saló i Nevado, Gunilla Holm and Leila Pehkonen

    Abstract

    This article presents findings from a study on the use of mathematics in the context of a farm. Ethnographic methods were used for the data collection and ethnomathematics provides the theoretical framework guiding the analysis. We present two different situations, as examples of ethnomathematics, in which the farmers make use of mathematics in daily life situations on a farm. The first situation has to do with how one of the farmers dealt with a barn as a space for feeding calves. The second situation is about the use of different objects as measuring tools.

    Laia Saló i Nevado

    Laia Saló i Nevado is doctoral student in the Institute of Behavioural Sciences at the University of Helsinki. Her research interests are focused on the everyday uses of mathematics and adults learning mathematics.

    Gunilla Holm

    Gunilla Holm is professor of education in the Institute of Behavioural Sciences at the University of Helsinki. Her research interests are focused on photography as a data collection method as well as issues in education related to race, ethnicity, class, and gender. She has published widely on multicultural education and on schooling in popular culture and has co-edited several books.

    Leila Pehkonen

    Leila Pehkonen is senior lecturer of education in the Institute of Behavioural Sciences at the University of Helsinki. Her current research interests include teaching and learning in higher education, mathematics education and teachers’ agency in vocational education.

    Skapad: 2011-12-21 kl. 00:00

  28. NOMAD 16(1-2), 2011. Structure of students’ view of mathematics in the Estonian Business School

    Structure of students’ view of mathematics in the Estonian Business School

    Indrek Kaldo

    Abstract

    Students’ mathematics-related beliefs are a decisive parameter for engagement and success in school. In the present research the students’ attitudes, beliefs and motivations regarding mathematics at an Estonian university was explored. The paper focuses on describing such a view of mathematics. By means of a confirmatory factor analysis, seven factors were confirmed. The data were collected from 93 first-year mathematics course students in the Estonian Business School through a questionnaire using a Likert-type scale. The study confirmed most of the components identified in earlier studies. It validates the use of the instrument in further studies of beliefs, attitudes and motivation at the university level in Estonia.

    Indrek Kaldo

    Indrek Kaldo is a PhD student in mathematics education at the Institute of Educational Sciences, Tallinn University. His research interests are students’ beliefs, attitudes and motivation towards the teaching and learning of mathematics, particularly at the university level. He has also 11 years experiences as lecturer in mathematics at university level.

    Skapad: 2011-06-30 kl. 01:00

  29. NOMAD 16(1-2), 2011. Students’ mathematical identity formations in a Swedish multilingual mathematics classroom

    Students’ mathematical identity formations in a Swedish multilingual mathematics classroom

    Eva Norén

    Abstract

    In this article I explore how students’ mathematical identities are formatted in a multilingual mathematics classroom. The study has been conducted in a group of ten multilingual Arabic and Swedish speaking students in grade eight and nine. In the article the focus is on two of the students. Students’ mathematical identity formations are effects of exercise of a variety of discourses available in the mathematics classroom. In discourses promoting multilingualism and social relations students’ possibilities to positively build upon opportunities in the mathematics classroom seem to enhance and identity formations as engaged mathematics learners is not an obstacle.

    Eva Norén

    Eva Norén is PhD in mathematics education at Stockholm University, the Department of mathematics and science education, where she also teaches. Her research interest is in mathematics education related to multilingual and multicultural issues. She has been a teacher in primary school for many years and her practice as a teacher has inspired her to use ethnographic research methods, spending time in classrooms with students and teachers.

    Skapad: 2011-06-30 kl. 01:00

  30. NOMAD 16(1-2), 2011. From beliefs to patterns of participation – shifting the research perspective on teachers

    From beliefs to patterns of participation – shifting the research perspective on teachers

    Jeppe Skott, Dorte Moeskær Larsen and Camilla Hellsten Østergaard

    Abstract

    Belief research was introduced to mathematics education in the early 1980s. It challenged the primarily cognitive and mathematical agenda of the time by investigating the character and significance of mental meta-constructs called beliefs. Particular attention has ever since been paid to teachers’ beliefs and their role in instruction.

    Belief research has been troubled by conceptual and methodological problems since its early beginnings, and most of these are still unresolved. This indicates that it may be time to adopt a different perspective, if we are to understand the role of the teacher for the practices of the mathematics classroom.

    Elsewhere we have discussed the problems of belief research at some length and suggested an alternative that we call patterns-of-participation research (e.g. Skott, 2009, 2010). In the present article we briefly recapitulate some of the arguments underlying this suggestion, but our main interest is to use the patterns-of-participation approach for empirical purposes. Consequently the article consists of two main sections. First we summarise some of the problems of belief research and present the contours of our alternative, patterns-of-participation research. Second, we in a much longer section present and analyse data on the case of a teacher, Susanne, whom we follow prior to and after her graduation from college. The overall intention is to suggest a change of research perspective from beliefs to patterns of participation.

    Jeppe Skott

    Jeppe Skott, PhD, is a professor of mathematics education at the Linnaeus University, Sweden, and an associate professor in the same field at the Danish School of Education. His main research interest is in the teacher’s role for classroom interaction, but he has also written on theory-practice relationships in mathematics education. Besides he has been involved in educational development in different countries in Europe, Africa, and Asia.

    Dorte Moeskær Larsen

    Dorte M. Larsen, MA, is a lecturer at University College Capital, Copenhagen. She teaches mathematics and mathematics education to prospective and practising teachers. Her main research interest is teacher development during their pre-service education and immediately after their graduation, especially the role of the practicum for the students’ professional development.

    Camilla Hellsten Østergaard

    Camilla Hellsten Østergaard, MA, is a lecturer at University College Capital, Copenhagen. She teaches mathematics and mathematics education to prospective teachers. Her main research interest is teacher development during their pre-service education and especially how they change their participation in the social practices at their schools in the first few year after their graduation.

    Skapad: 2011-06-30 kl. 01:00

  31. NOMAD – 16(1-2), 2011


    Tidigare nummerPrevious issues
    Array

    Nummer/Issue

    Volume 16, No 1-2, June 2011

    Ledare/Editorial

    Belief research in mathematics education

    Peter Liljedahl

    The theory of conceptual change as a theory for changing conceptions

    [PDF]

    Jeppe Skott, Dorte Moeskær Larsen and Camilla Hellsten Østergaard

    From beliefs to patterns of participation – shifting the research perspective on teachers

    [PDF]

    Magnus Österholm

    To translate between different perspectives in belief research: a comparison between two studies

    [PDF]

    Indrek Kaldo

    Structure of students’ view of mathematics in the Estonian Business School

    [PDF]

    Eva Norén

    Students’ mathematical identity formations in a Swedish multilingual mathematics classroom

    [PDF]

    Frode Rønning

    News from Nordic mathematics education

    Innehåll: JH

    Skapad: 2011-06-30 kl. 01:00

  32. NOMAD 16(1-2), 2011. The theory of conceptual change as a theory for changing conceptions

    The theory of conceptual change as a theory for changing conceptionst

    Peter Liljedahl

    Abstract

    It has become widely accepted that what and how mathematics teachers teach is linked to what it is they believe. What teachers believe, however, is not always in alignment with contemporary notions of mathematics and the teaching and learning of mathematics. As such, it is important for teacher educators to help facilitate changes in teachers’ beliefs in ways that will enable them to become more effective teachers of mathematics. In this article I present the results of a research project designed to examine the feasibility of using the theory of conceptual change as a theory for changing mathematics teachers’ conceptions about key aspects of mathematics and the teaching and learning of mathematics. The results indicate both that the theory of conceptual change is a viable theory for designing interventions for the purpose of changing beliefs, and that the implementation of these aforementioned interventions resulted in the rejection of participants’ a priori beliefs.

    Peter Liljedahl

    Dr. Peter Liljedahl is an Associate Professor of Mathematics Education in the Faculty of Education and an associate member in the Department of Mathematics at Simon Fraser University in Vancouver, Canada. He is a co-director of the David Wheeler Institute for Research in Mathematics Education. His research interests are creativity, insight, and discovery in mathematics teaching and learning; the role of the affective domain on the teaching and learning of mathematics; the professional growth of mathematics teachers; mathematical problem solving; and numeracy.

    Skapad: 2011-06-30 kl. 01:00

  33. NOMAD 16(1-2), 2011. To translate between different perspectives in belief research: a comparison between two studies

    To translate between different perspectives in belief research: a comparison between two studies

    Magnus Österholm

    Abstract

    A common problem in belief research seems to be a missing link between aspects of theory and empirical analyses and results. This issue highlights a question of how dependent empirical studies about beliefs actually are on the theoretical perspective described in the study. In this paper, I examine relationships between two different perspectives. One perspective focuses on belief change, and seems to rely on a type of cognitive perspective, where beliefs can be characterized as mental objects. The other perspective argues for moving away from such cognitive perspective and instead to adopt a participatory perspective in the analysis of mathematics teaching. The results show that the study about belief change is not dependent on seeing beliefs as mental objects, but that this study could as well have been located within a participatory perspective.

    Magnus Österholm

    Magnus Österholm has a PhD in mathematics education from Linköping University and now works as a research fellow at the Department of Science and Mathematics Education at Umeå University. He is also a member of Umeå Mathematics Education Research Centre (UMERC). During 2011 and 2012 he is a visiting scholar at Monash University in Melbourne, Australia. His research interests deal primarily with mathematics education at the upper secondary and university levels, where cognitive and metacognitive perspectives are of special interest, together with studying language and communication in the learning and teaching of mathematics.

    Skapad: 2011-06-30 kl. 01:00

  34. NOMAD 15(4), 2010. Different views – some Swedish mathematics students’ concept images of the function concept

    Different views – some Swedish mathematics students’ concept images of the function concept

    Olov Viirman, Iiris Attorps and Timo Tossavainen

    Abstract

    This study analyses what kind of concept images a group of engineering and teacher students have of the function concept, and how these concept images are related to the historical development of this concept. The study was conducted using questionnaires, and 34 students at a Swedish university participated. It is found that the students primarily rely on operational conceptions of the function concept, with only a minority of students possessing structural conceptions. The definitions given by the students mostly resemble an 18th or 19th century view of functions. The study also indicates that the character of the definitions given in the textbooks used by the students affect their concept images.

    Olov Viirman

    Olov Viirman is a graduate student in mathematics education at the department of Electronics, Mathematics and Science, University of Gävle, and the department of Mathematics, Karlstad University. His research interests are the teaching and learning of mathematical concepts, particularly at the university level.

    Iiris Attorps

    Iiris Attorps is senior lecturer in mathematics education at the Department of Electronics, Mathematics and Science, University of Gävle. Research interest: learning and teaching mathematical concepts from preschool to university level.

    Timo Tossavainen

    Timo Tossavainen is senior lecturer in mathematics at the University of Eastern Finland and docent of mathematics education at the University of Tampere. He has got a Ph.D. in mathematics and his research interests cover function theory and mathematics education at secondary and tertiary levels. He is a co-author of several mathematics textbooks for upper secondary schools and universities.

    Skapad: 2011-05-20 kl. 01:00

  35. 15(4), 2010. Assessment of university students’ understanding of abstract binary operations

    Assessment of university students’ understanding of abstract binary operations

    Timo Ehmke, Martti E. Pesonen and Lenni Haapasalo

    Abstract

    This paper presents the results of a study on the use of interactive online tasks to assess students’ conceptual understanding of abstract binary operations in a first-year linear algebra course. The assessment consists of recognition, identification and production tasks and uses verbal, graphic and symbolic representations of binary operations in numerous point set contexts. The aim of the study is to directly assess the students’ understanding of binary operations and – more indirectly – to identify different profiles for the students’ procedural and conceptual knowledge levels. A latent class analysis revealed different levels in students’ conceptual understanding. Implications will be drawn for teaching abstract binary operations – and other similar concepts. Finally, some suggestions about conceptual qualifications for mathematics teacher education will be discussed.

    Timo Ehmke

    Timo Ehmke, Dr. habil., works as a research scientist at the Leibniz Institute for Science Education (IPN) in Kiel, Germany. He studied Mathematics, Technology and Education at the Universities of Kiel and Flensburg in Germany. He received the state examination in Mathematics and Technology Education in 1997 and a Ph.D. in Education in 2001. Since 2001 he has been working at the Department of Education at the IPN Kiel in the field of Educational Research. In 2007, he finished his habilitation (postdoctoral lecture qualification) in Educational Research at the University of Kiel.

    Martti E. Pesonens

    Martti E. Pesonen, Ph.D., acts as senior lecturer at the University of Eastern Finland (Joensuu campus). He studied mathematics and physics in Joensuu and Paris and got the doctor’s degree in mathematics in 1986. He achieved the pedagogical competence of mathematics and physics subject teacher in 1997. He teaches mostly the first year university mathematics courses including basic relational concepts, discrete mathematics and axiomatic approach to linear algebra.

    Lenni Haapasalo

    Prof. Dr. Lenni Haapasalo worked at the University of Jyväskylä, at first 9 years as mathematician, and after that18 years as Senior Lecturer/Associate Professor in Mathematics Education. Since 1999 he is full-time Professor of Education at the University of Eastern Finland. His research interest is to develop practical theories based on modern socio-constructivist views, emphasizing technology-based self-determined learning environments, links between conceptual and procedural knowledge, and the genesis of sustainable heuristic processes.

    Skapad: 2011-05-20 kl. 01:00

  36. NOMAD – 15(4), 2010

    Nummer/Issue

    Volume 15, No 4, December 2010

    Ledare/Editorial

    Nordic mathematics education in Europe

    Olov Viirman, Iiris Attorps and Timo Tossavainen

    Different views – some Swedish mathematics students’ concept images of the function concept

    [PDF]

    Timo Ehmke, Martti E. Pesonen and Lenni Haapasalo

    Assessment of university students’ understanding of abstract binary operations

    [PDF]

    Hanna Palmér

    Identity development in limbo: teacher transition from education to teaching

    [PDF]

    Innehåll: JH

    Skapad: 2011-05-20 kl. 01:00

  37. 15(4), 2010. Identity development in limbo: teacher transition from education to teaching

    Identity development in limbo: teacher transition from education to teaching

    Hanna Palmér

    Abstract

    The theories and results discussed in this article are from a study investigating the identity development of novice primary mathematics teachers. The article has two aims: first, to elaborate the notion of beliefs in relation to the notions of identity and identity development, with the purpose of developing a framework to investigate the process of becoming and being a teacher of mathematics; and second, to offer an example of the use of this framework in a study of novice primary mathematics teachers. The core of the example is the case of Jenny, a Swedish novice primary mathematics teacher. Jenny’s case, however, is not simply about her but also about identity development when the formal aspect of employment is missing, a case not rare in Sweden.

    Hanna Palmér

    Hanna Palmér is a postgraduate student in mathematics education at Linnaues University, Sweden. Her main research interest is mathematics teacher education, and the becoming, being and mathematics teaching of primary teachers after graduation.

    Skapad: 2011-05-20 kl. 01:00

  38. NOMAD 15(3), 2010. Understanding and solving multistep arithmetic word problems

    Understanding and solving multistep arithmetic word problems

    Guri A. Nortvedt

    Abstract

    This article discusses the findings of a study in which the interplay between reading, numeracy, and strategies for working on multistep arithmetic word problems was researched through two approaches. The first approach involved analysing results on national tests in reading and numeracy for a representative sample of 1,264 grade 8 (13-years-old) students. A scale of ten multistep arithmetic word problems was identified in the numeracy test. Proficiency in reading explained 44 % of the variance in scores on this scale, indicating a positive relationship between reading comprehension and success in word problem solving. The second approach involved analysing verbal protocol data for 19 grade 8 students who worked on a collection of multistep arithmetic word problems. Protocols consisted of both independent and scaffolded work. Interpretive analysis of student work on one of the eight word problems given in the protocol sessions revealed three main areas of difficulties: representing quantities in the word problem text, retrieving number facts from memory, and performing basic operations. Difficulties within more than one area were frequent. To students with below-average numeracy skills, executing the basic operations was the main obstacle for this particular word problem.

    Guri A. Nortvedt

    Guri A. Nortvedt works at the University of Oslo. Her main research interests are 1) relationships between language and (learning and doing mathematics) and 2) assessment studies within mathematics education.

    The research reported in this article was carried out at the Department of Special Needs Eduaction, University of Oslo.

    Skapad: 2011-02-07 kl. 00:00

  39. NOMAD 15(3), 2010. Head teachers’ conception of gifted students in mathematics in Swedish upper secondary school

    Head teachers’ conception of gifted students in mathematics in Swedish

    upper secondary school

    Linda Mattsson

    Abstract

    The article presents a study of how Swedish upper secondary head teachers, working within mathematically intensive study programs, conceptualize giftedness in mathematics. The study is based on a survey of 34 randomly selected head teachers, in a population of about 400, who have answered questions about how they characterize and detect gifted mathematics students. The results show that teachers characterize such students as creative, strong in logical ability and keen in their motivation for mathematics. The teachers detect such students by the students’ own initiative for engaging in mathematics, their inclination to orally reason about mathematics and their successfulness on tests. The findings, which are in accordance with results from internationally published studies, are of importance to the current discussion on special provision for gifted students in Sweden.

    Linda Mattsson

    Linda Mattsson is PhD student at the Department of Mathematical Sciences, University of Gothenburg and Chalmers University of Technology. Her research focus lies within the field of gifted education in upper

    secondary school and on-going studies concern issues of nurturing gifted students in mathematics.

    Skapad: 2011-02-07 kl. 00:00

  40. NOMAD 15(3), 2010. Boganmeldelse

    Boganmeldelse: Forskeres og studerendes mulige udbytte af at læse Springes nye bog om teorier i matematikkens didaktik

    Uffe Thomas Jankvist

    Skapad: 2011-02-07 kl. 00:00

  41. NOMAD 15(3), 2010. Orchestrating mathematical activities in the kindergarten: the role of inquiry

    Orchestrating mathematical activities in the kindergarten: the role of

    inquiry

    Martin Carlsen

    Abstract

    The aim of my study is to address the role played by inquiry in orchestrating a mathematical activity in the kindergarten. The study takes the inquiry cycle as a methodological departure, i.e. the whole process of designing, acting, observing, reflecting, and feeding back. The subtleties of how the kindergarten teachers and a didactician reason in order to orchestrate the mathematical activity and the role played by inquiry in this orchestration are hence analysed. The analyses show how inquiry in every phase of the inquiry cycle, plays a significant role in the orchestration of the mathematical activity. The participants become co-learners in these processes, and are involved in appropriating the mathematical tools and concepts as well as didactical issues involved in orchestrating a mathematical activity in the kindergarten.

    Martin Carlsen

    The author’s research interests are within the scope of this paper, mathematical inquiry in the kindergarten. He is also particularly interested in mathematical appropriation through problem solving in collaborative small groups. He identifies with a sociocultural perspective on learning and development, and his research is taking place within this theoretical stance.

    Skapad: 2011-02-07 kl. 00:00

  42. NOMAD – 15(3), 2010


    Tidigare nummerPrevious issues
    Array

    Nummer/Issue

    Volume 15, No 3, October 2010

    Ledare/Editorial

    About this issue

    Linda Mattsson

    Head teachers’ conception of gifted students in mathematics in Swedish
    upper secondary school

    [PDF]

    Guri A. Nortvedt

    Understanding and solving multistep arithmetic word problems

    [PDF]

    Martin Carlsen

    Orchestrating mathematical activities in the kindergarten: the role of
    inquiry

    [PDF]

    Uffe Thomas Jankvist

    Boganmeldelse: Forskeres og studerendes mulige udbytte af at læse Springes nye bog om teorier i matematikkens didaktik

    [PDF]

    Frode Rønning

    News from Nordic mathematics education

    Innehåll: JH

    Skapad: 2011-02-07 kl. 00:00

  43. NOMAD 15(2), 2010. Learning opportunities offered by a classical calculus textbook

    Learning opportunities offered by a classical calculus textbooky

    Mira Randahl and Barbro Grevholm

    Abstract

    In this paper we present results of an analysis of what the textbook used by the first year engineering students offers the students, when they take a basic calculus course. The aim of this analysis is to examine as an entirety what students are offered by the book to learn about the concept of derivative. The results show that the presentation of the concept is formal and depends on students’ previous knowledge. The treatment of the concept emphasises procedural knowledge. It is not easy for students using the book to make connections between conceptual and procedural knowledge of the concept of derivative.

    Mira Randahl

    Mira Randahl has worked at Narvik University College and is enrolled in the doctoral programme at University of Agder. Earlier she has been mathematics teacher in compulsory school, upper secondary school and in teacher education in Norway.

    Barbro Grevholm

    Barbro Grevholm is professor of mathematics education at University of Agder and leader of the doctoral programme there. She is also professor II at Narvik University College.

    Skapad: 2010-10-01 kl. 01:00

  44. NOMAD 15(2), 2010. Affektive sider ved lærerstudenters arbeid med matematikk

    Affektive sider ved lærerstudenters arbeid med matematikk

    Leif Kværnes

    Sammenfattning

    Formålet med artikkelen er å belyse og drøfte sider ved allmennlærerstudenters utvikling av lærerkompetanse i matematikk. I empiriske analyser har jeg har valgt å fokusere på studenters affektive eller følelsesmessige forhold til læring av/arbeid med matematikk; som er sett som et delaspekt ved lærerkompetansen. I første del av artikkelen redegjør jeg for sentrale teoretiske utgangspunkt; et triadisk syn på læring og en kommunikativ tilnærming til analyser og beskrivelser av læring og undervisning. Andre delen av artikkelen starter med analyser og beskrivelser av affektive sider gjennom utvalgte eksempler fra studenters arbeid med matematikk. Disse beskrivelsene er utgangspunkt for en avsluttende problematisering og drøfting av hvordan affektive sider kan influere på studenters utvikling av lærerkompetanse i faget.

    Abstract

    My intention with this article is to discuss some aspects of teacher student’s development towards becoming mathematics teachers. My main focus is on the relations between affect and cognition. First part of the article will be theoretical. I will here outline how this relation is seen, and I also describe what may be called a communicative or discursive approach to this relation. In the second part I use this approach on student’s utterances while working with mathematics. My intentions are not to make representative or broad descriptions of relations between affect and cognition. The descriptions will be used as points of departure for discussing student’s development towards becoming mathematics teachers.

    Leif Kværnes

    Leif Kværnes er høgskolelektor i matematikk ved Høgskolen i Oslo, avdeling for lærerutdanning, hvor han underviser både grunnutdanningsstudenter, masterstudenter og lærere som søker etter- eller videreutdanning. Hans forskningsinteresse er knyttet til lærerutdanning og til utvikling av lærerkompetanse for undervisning i matematikk.

    Skapad: 2010-10-01 kl. 01:00

  45. NOMAD 15(2), 2010. Cooperation and collaboration as zones of proximal development within the mathematics classroom

    Cooperation and collaboration as zones of proximal development within the mathematics classroom

    Sharada Gade

    Abstract

    Beyond understanding the Vygotskian construct of zone of proximal development or ZPD with reference to an individual student, this paper explores the formation of ZPD within the pedagogical constructs of cooperation, wherein students cooperate with each other within their groups; as well as collaboration, wherein students from different groups that constitute the classroom collaborate with each other. Identified on the basis of functions that are in the process of maturing, the formation of either ZPD is exemplified from a socio-cultural-historical study at an upper secondary mathematics classroom in Norway. An emphasis on what distinguishes events in instruction that are educational from those that are not is also explored, before illustrating what nature of ZPD is established. The role of guidance received, imitation and cultural resources in the development of higher mental functions is understood as these ZPD are formed, enabling students to act independently within the classroom teaching-learning of mathematics.

    Sharada Gade

    Sharada Gade combined her long teaching experience at Vidyaranya High School, Hyderabad, India with writing for teachers and popularisation. At University of Agder, Norway she pursued her doctorate in mathematics education with a classroom based thesis drawing upon sociocultural and activity theory perspectives. As Visiting fellow at Homi Bhabha Centre for Science Education, Mumbai, she taught master and doctoral courses and conducted narrative inquiry with middle school teachers about their experiences of classroom teaching-learning. Currently as postdoctoral researcher at Umeå University, Sweden, Sharada continues her pursuit of understanding classrooms as productive teaching-learning environments for students, their teachers and research.

    Skapad: 2010-10-01 kl. 01:00

  46. Clone of NOMAD 15(2), 2010. Affektive sider ved lærerstudenters arbeid med matematikk

    Affektive sider ved lærerstudenters arbeid med matematikk

    Leif Kværnes

    Sammenfattning

    Formålet med artikkelen er å belyse og drøfte sider ved allmennlærerstudenters utvikling av lærerkompetanse i matematikk. I empiriske analyser har jeg har valgt å fokusere på studenters affektive eller følelsesmessige forhold til læring av/arbeid med matematikk; som er sett som et delaspekt ved lærerkompetansen. I første del av artikkelen redegjør jeg for sentrale teoretiske utgangspunkt; et triadisk syn på læring og en kommunikativ tilnærming til analyser og beskrivelser av læring og undervisning. Andre delen av artikkelen starter med analyser og beskrivelser av affektive sider gjennom utvalgte eksempler fra studenters arbeid med matematikk. Disse beskrivelsene er utgangspunkt for en avsluttende problematisering og drøfting av hvordan affektive sider kan influere på studenters utvikling av lærerkompetanse i faget.

    Abstract

    My intention with this article is to discuss some aspects of teacher student’s development towards becoming mathematics teachers. My main focus is on the relations between affect and cognition. First part of the article will be theoretical. I will here outline how this relation is seen, and I also describe what may be called a communicative or discursive approach to this relation. In the second part I use this approach on student’s utterances while working with mathematics. My intentions are not to make representative or broad descriptions of relations between affect and cognition. The descriptions will be used as points of departure for discussing student’s development towards becoming mathematics teachers.

    Leif Kværnes

    Leif Kværnes er høgskolelektor i matematikk ved Høgskolen i Oslo, avdeling for lærerutdanning, hvor han underviser både grunnutdanningsstudenter, masterstudenter og lærere som søker etter- eller videreutdanning. Hans forskningsinteresse er knyttet til lærerutdanning og til utvikling av lærerkompetanse for undervisning i matematikk.

    Skapad: 2010-10-01 kl. 01:00

  47. NOMAD 15(2), 2010. Communication and learning at computers: an overview

    Communication and learning at computers: an overview

    Rune Herheim

    Abstract

    The article highlights key findings from a research literature overview within the field of learning and communication, for face-to-face small group settings in which pupils use a computer. The overview surveys articles with a general learning approach and articles from the field of mathematics education. The purpose of the overview is to locate the most significant literature of the field and qualitatively summarize these articles by identifying the issues that are their focus. In addition, the article presents some of the sceptical arguments presented in the literature, and finally some important issues for future work are singled out.

    Rune Herheim

    Rune Herheim is a PhD-candidate at the Department of Education, University of Bergen. Before this he has worked as a lecturer in mathematics education at Bergen University College and as a teacher in primary school. Herheim’s main research interests lie in ICT and education, collaborative learning, and the relationship between pupils’ communication and pupils’ learning.

    Skapad: 2010-10-01 kl. 01:00

  48. NOMAD – 15(2), 2010


    Tidigare nummerPrevious issues
    Array

    Nummer/Issue

    Volume 15, No 2, July 2010

    Ledare/Editorial

    Nomad – a regional journal
    in mathematics education research

    Mira Randahl & Barbro Grevholm

    Learning opportunities offered by a classical calculus textbook

    [PDF]

    Leif Kværnes

    Affektive sider ved lærerstudenters arbeid med matematikk

    [PDF]

    Sharada Gade

    Cooperation and collaboration as zones of proximal development within the mathematics classroom

    [PDF]

    Rune Herheim

    Communication and learning at computers: an overview

    [PDF]

    Barbro Grevholm & Frode Rønning

    Nordic collaboration in mathematics education research

    Innehåll: JH

    Skapad: 2010-10-01 kl. 01:00

  49. NOMAD 15(1), 2010. Theorising in mathematics education research: differences in modes and quality

    Theorising in mathematics education research: differences in modes and quality

    EVA JABLONKA & CHRISTER BERGSTEN

    Abstract

    In mathematics education research reports, we find a bewildering array of ”theories”, ”theoretical models” or ”theoretical frameworks”. The key notions and principles as well as the intellectual roots of these constructions are made more or less explicit, and the relations of theoretical entities to the empirical field under study are established in different ways. These differences imply discrepancies in quality. In this contribution we touch upon some of these issues. We attempt to show that an investigation of the relations between key concepts might help to read and evaluate theoretical underpinnings of research studies, and we argue that not all constructions that are labelled ”theoretical” meet the criteria we consider essential for productive theorising. We also allude to different modes of engaging with empirical material and different ways in which theories are used in research studies. The main part of our discussion is limited to examples of ”home-grown” theorising. The examples we have chosen to illustrate our points necessarily represent a biased selection.
    EVA JABLONKA

    Eva Jablonka is professor of mathematics education at Luleå University of Technology. Her research activities comprise studies of curriculum conceptions (mathematical modelling and mathematical literacy), international comparative classroom research, studies of the emergence of disparity in mathematics achievement and sociological theorizing in mathematics education.
    CHRISTER BERGSTEN

    Christer Bergsten is professor of mathematics education at Linköping University. His research has focused on mathematics teacher education, undergraduate mathematics education, semiotics, and the role of theory in mathematics education research.

    Skapad: 2010-06-01 kl. 01:00

  50. NOMAD 15(1), 2010. What is quality in a PhD dissertation in mathematics education?

    What is quality in a PhD dissertation in mathematics education?

    MOGENS NISS

    Abstract

    The present paper discusses the issue of quality in PhD dissertations in mathematics education on the basis of the author’s reflections, observations and experiences as a supervisor and as an assessor of PhD dissertations in several countries during the last three decades. Thus, the paper represents the personal stances and views of the author and does not claim to be written on behalf of any segment of the community of researchers in mathematics education. Two major components of quality in a PhD dissertation are being dealt with, quality of the underlying research, and quality of the dissertation as a reflective report of this research and its outcomes. Particular attention is being paid to the issue of what should cause a dissertation to be rejected. The paper emphasises, at the end, that because of the multiplicity of research paradigms and philosophies in research in mathematics education there is no royal road to quality in a PhD dissertation. Therefore, the student cannot avoid involving him- or herself in independent in-depth thinking.
    MOGENS NISS

    Mogens Niss is a professor of mathematics and mathematics education at Roskilde university, Denmark, where he has been working since 1972, the year the university was founded. He was a member of the Executive committee of ICMI, 1987–1991, the last eight years as the Secretary general of the commission. He is currently the chair of the ICMI Awards committee, a member of the Education committee of the European mathematical society, and a member of the board of National centre for mathematics education (NCM) in Sweden. His research interests and many publications focus on mathematics education, in particular mathematical competencies, mathematical modelling, the nature of mathematics education as a research discipline, and the justification problem of mathematics education in society.

    Skapad: 2010-06-01 kl. 01:00

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