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  1. NOMAD 19(3-4), 2014

    Teachers’ mathematical knowledge for teaching in relation to the inclusion of history of mathematics in teaching

    Bjørn Smestad, Uffe Thomas Jankvist and Kathleen Clark

    Abstract

    This article discusses how the inclusion of history of mathematics in mathematics education draws heavily on a teacher’s mathematical knowledge for teaching, in particular horizon content knowledge, in the context of curricular changes. We discuss the role of history of mathematics in school curricula, its inclusion in textbooks and its consequences for the mathematical knowledge needed for teaching. We address the matter from three national settings (Denmark, Norway and the United States). These settings exemplify how, in particular, teachers’ horizon content knowledge needs to be broader than what is necessary for only the current curriculum.

    Bjørn Smestad

    Bjørn Smestad is an associate professor of mathematics education at Oslo and Akershus University College of Applied Sciences, Department of Primary and Secondary Teacher Education. His main research interests are the role of history of mathematics in teaching and teacher education, ICT in teaching mathematics and school placement as part of teacher education.

    Uffe Thomas Jankvist

    Uffe Thomas Jankvist is an associate professor of mathematics education at Aarhus University, Department of Education, Campus Emdrup, Denmark. His research interests include the use of history of mathematics, applications of mathematics, and philosophy of mathematics in mathematics education, both from a theoretical and an empirical point of view, including also students’ beliefs about and images of mathematics as a (scientific) discipline, as well as interdisciplinary teaching and learning. Also, he is involved in educating Danish ”maths counsellors” for upper secondary school at Roskilde University.

    Kathleen Clark

    Kathleen Clark is an associate professor in the College of Education at Florida State University. Her primary research interests lie in two fields, mathematics education and history of mathematics. In the former, her research investigates ways in which prospective and in-service mathematics teachers use history of mathematics in teaching and the ways in which the study of history of mathematics impacts mathematical knowledge for teaching. In the latter, her historical research is focused on 17th and 18th century mathematics, with a particular emphasis on the early development of logarithms.

    Skapad: 2014-10-22 kl. 01:00

  2. NOMAD 19(3-4), 2014

    Knowledge used when orchestrating mathematical discourses – doing, guiding and requesting

    Ove Gunnar Drageset

    Abstract

    There is a need to understand more about which types of knowledge teachers use when orchestrating mathematical discourses. This article combines models for mathematical knowledge for teaching with a recent framework that describes the actions that teachers typically use during classroom discourses in mathematics. By looking into what knowledge each action demands from the teacher, three areas related to mathematical knowledge for teaching are described: doing, guiding and requesting. Doing describes different ways the teachers are doing the mathematical work themselves. Guiding describes how the teachers help, while leaving most of the work to the students. Requesting describes different ways teachers asked the students to explain or contribute to the discourse.

    Ove Gunnar Drageset

    Ove Gunnar Drageset has a PhD in Mathematics Education from the University of Oslo (2013) and is currently working as associate professor at UiT ( The Arctic University of Norway) and as a program leader for master of teacher education for grades 5 to 10. The main research interests are communication in the classroom, mathematical knowledge for teaching, and teaching and learning of numbers and operations at grades 1 to 10.

    Skapad: 2014-10-22 kl. 01:00

  3. NOMAD 19(3-4), 2014

    The teaching of mathematical knowledge for teaching – a learning study of primary school teacher education

    Jorryt van Bommel

    Abstract

    A group of Swedish teacher educators conducted a learning study in order to identify critical features concerning the teaching and learning of Mathematical knowledge for teaching (MKT). Three seminars and 300 tests were analysed using variation theory revealing four critical features to take into account in teaching student teachers in mathematics education: namely their need to i) formulate proper goals for a lesson, ii) outline the lesson plan in detail, iii) shift perspective from the role of being a teacher to being a mathematics teacher, and iv) understand the underlying mathematics of the lesson topic at hand. Thus, these are the four features of importance to the learning and teaching of MKT.

    Jorryt van Bommel

    Jorryt van Bommel is a lecturer at Karlstad University and works mainly with in-service and pre-service teacher training. Her research interests concern mathematics teacher training and professional development of mathematics teachers.

    Skapad: 2014-10-22 kl. 01:00

  4. NOMAD 19(3-4), 2014

    When does a variable vary? Identifying mathematical content knowledge for teaching variables

    Cecilia Kilhamn

    Abstract

    In what sense is x in the expression x + 2 a variable? What do teachers need to know about variables in order to create optimal learning conditions for students? The aim of this study is to understand the mathematical issues and demands of teaching the concept of variables, to outline a body of Specialized content knowledge for teaching (SCK). Data from two lessons in two Swedish grade 6 classrooms, with complimentary focus group interviews, were analysed using the Mathematical knowledge for teaching framework. Findings suggest some aspects of SCK to be an awareness of the different roles of the algebraic letter x in the expression x + 3, the equation x + 3 = 8 and the formula x + 3 = y, an appropriate use of the terms unknown and variable, and the importance of mathematical contexts for expressions.

    Cecilia Kilhamn

    Cecilia Kilhamn is a teacher and a senior lecturer in Mathematics Education in the Faculty of Education at Gothenburg University.

    Skapad: 2014-10-22 kl. 01:00

  5. NOMAD 19(3-4), 2014

    Norwegian mathematics teachers’ and educational researchers’ perception of MPCK items used in the TEDS-M study

    Hege Kaarstein

    Abstract

    This paper presents how Norwegian teachers and educational researchers categorized a collection of items used in the international TEDS-M study. The teachers categorized the items according to their own prototype understanding of mathematical content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK), while the researchers categorised them after discussing how to understand MCK and MPCK and agreeing on what categorisation criteria to use. The results show that the item categorisation depended on the item characteristics. For example, multiple-choice items were associated with MCK and items asking the respondents to rewrite or reword a mathematical task were associated with MPCK. Furthermore, the results indicate a common Norwegian understanding of MPCK as the teachers’ and researchers’ categorisation largely coincided.

    Hege Kaarstein

    Hege Kaarstein was a member of the Norwegian TEDS-M group and she is currently working as a researcher for the Norwegian TIMSS 2015 group at the Department of Teacher Education and School Research, University of Oslo. The focus of her research is measurement of mathematical knowledge for teaching.

    Skapad: 2014-10-22 kl. 01:00

  6. NOMAD 19(3-4), 2014

    Studying teachers’ knowledge by the use of multiple-choice items: the case of ”I’m not sure”

    Janne Fauskanger and Reidar Mosvold

    Abstract

    The mathematical knowledge for teaching (MKT) measures have been widely adopted by researchers in several countries. This article reports on a study on the connection between teachers’ responses to multiple-choice MKT items, and in particular where they select the suggested solution ”I’m not sure”, and their written responses to corresponding open-ended questions (long responses). The findings from our analysis of 15 teachers’ responses indicate that their long responses and their multiple-choice responses do not always correspond. Some teachers who selected ”I’m not sure” showed uncertainty also in their long responses, whereas other teachers revealed instrumental and even relational understanding of the content.

    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.

    Skapad: 2014-10-22 kl. 01:00

  7. NOMAD 19(3-4), 2014

    Exploring the mathematical knowledge of prospective elementary teachers in Iceland using the MKT measures

    Björg Jóhannsdóttir and Berglind Gísladóttir

    Abstract

    This article reports findings from a study carried out with prospective teachers at the University of Iceland. The study explores the mathematical content knowledge of participants, with a special focus on the understanding of numbers, operations, patterns, functions, and algebra. The mathematical knowledge is measured with interviews and a survey, translated and adapted from the MKT measures designed by Ball and the research team at the University of Michigan. The findings indicate that prospective teachers’ knowledge is procedural and related to the ”standard algorithms” they learned and used in elementary school. Findings also indicate that prospective teachers have difficulty evaluating alternative solution methods, and working with and understanding fractions.

    Björg Jóhannsdóttir

    Björg Jóhannsdóttir graduated with a PhD in Mathematics Education from Teachers College, Columbia University in May 2013. Dr. Jóhannsdóttir is an assitant professor of mathematics at California State University Stanislaus. Her main research interests lie within elementary mathematics education, especilly elemenatry teacher education, and in ways to assist students in experiencing mathematics as alive and creative subject.

    Berglind Gísladóttir

    Berglind Gísladóttir is a researcher at Reykjavík University, where she focuses on research. She got her PhD in Mathematics Education from Teachers College, Columbia University 2013. Dr. Gísladóttir’s research interests are, among others, teacher education and mathematics education, inparticular how social factors affect mathematics learning.

    Skapad: 2014-10-22 kl. 01:00

  8. NOMAD – 19(3-4), 2014


    Tidigare nummerPrevious issues
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    Nummer/Issue

    Volume 19, No 3-4, October 2014

    Editorial

    Mark Hoover, Reidar Mosvold and Janne Fauskanger

    Common tasks of teaching as a resource for measuring professional content knowledge internationally

    [PDF]

    Björg Jóhannsdóttir and Berglind Gísladóttir

    Exploring the mathematical knowledge of prospective elementary teachers in Iceland using the MKT measures

    [PDF]

    Janne Fauskanger and Reidar Mosvold

    Studying teachers’ knowledge by the use of multiple-choice items: the case of ”I’m not sure”

    [PDF]

    Hege Kaarstein

    Norwegian mathematics teachers’ and educational researchers’ perception of MPCK items used in the TEDS-M study

    [PDF]

    Cecilia Kilhamn

    When does a variable vary? Identifying mathematical content knowledge for teaching variables

    [PDF]

    Frode Opsvik og Leif Bjørn Skorpen

    Matematisk kvalitet i undervisning

    [PDF]

    Bodil Kleve and Ida Heiberg Solem

    Aspects of a teacher’s mathematical knowledge in his orchestration of a discussion about rational numbers

    [PDF]

    Arne Jakobsen, C. Miguel Ribeiro and Maria Mellone

    Norwegian prospective teachers’ MKT when interpreting pupils’ productions on a fraction task

    [PDF]

    Ove Gunnar Drageset

    Knowledge used when orchestrating mathematical discourses – doing, guiding and requesting

    [PDF]

    Bjørn Smestad, Uffe Thomas Jankvist and Kathleen Clark

    Teachers’ mathematical knowledge for teaching in relation to the inclusion of history of mathematics in teaching

    [PDF]

    Jorryt van Bommel

    The teaching of mathematical knowledge for teaching – a learning study of primary school teacher education

    [PDF]

    Innehåll: JH

    Skapad: 2014-10-22 kl. 01:00

  9. NOMAD 19(3-4), 2014

    Common tasks of teaching as a resource for measuring professional content knowledge internationally

    Mark Hoover, Reidar Mosvold and Janne Fauskanger

    Abstract

    In the United States, extensive time and money has been invested in developing and validating measures of mathematical knowledge for teaching (MKT). Although studies of adaptation of these measures generally conclude that they are useable in other countries, cultural differences in teaching prompt questions about whether theories and measures of knowledge for teaching are culturally specific. This article argues that the issue turns on the meaning of ”teaching” and ”tasks of teaching” and it recommends increased efforts to identify professionally defensible mathematical tasks of teaching that can serve as a common foundation for conceptualizing and measuring mathematical knowledge for teaching internationally.

    Mark Hoover

    Mark Hoover is Assistant Research Scientist in Educational Studies at the University of Michigan, Ann Arbor, MI. His research investigates the practice of teaching mathematics, including research on equitable teaching, measures of teacher knowledge and designs for collective work on teaching.

    Reidar Mosvold

    Reidar Mosvold is Associate Professor in mathematics education at the University of Stavanger, Norway. His research interests are related to mathematical knowledge for teaching, teacher beliefs and use of history of mathematics in mathematics education.

    Janne Fauskanger

    Janne Fauskanger is Assistant Professor in mathematics education at the University of Stavanger, Norway. Her main research interests are related to teachers’ beliefs and mathematical knowledge for teaching and their influence on teaching practice.

    Skapad: 2014-10-22 kl. 01:00

  10. NOMAD 19(2), 2014

    View of mathematics – an investigation of Estonian university students

    Indrek Kaldo

    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. This paper documents and analyses the data from the study. In this study students agreed that mathematics is an important and valuable subject. Female students have a more positive view of mathematics than male students. Science students have a more positive view of mathematics than non-science students.

    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 14 years experiences as lecturer in mathematics at university level.

    Skapad: 2014-06-25 kl. 01:00

  11. NOMAD – 19(2), 2014


    Tidigare nummerPrevious issues
    Array

    Nummer/Issue

    Volume 19, No 2, June 2014

    Editorial

    Indrek Kaldo

    View of mathematics – an investigation of Estonian university students

    [PDF]

    Eugenia Koleza

    Students’ conceptions about the formula for a rectangle’s area and some similarities to its historical context

    [PDF]

    Andreas Lorange and Reinert A. Rinvold

    Students’ strategies of expanding fractions to a common denominator – a semiotic perspective

    [PDF]

    Kristina Juter and Jan-Fredrik Olsen

    ”Just-in-time teaching” in undergraduate mathematics

    [PDF]

    Innehåll: JH

    Skapad: 2014-06-25 kl. 01:00

  12. NOMAD 19(2), 2014

    Students’ strategies of expanding fractions to a common denominator – a semiotic perspective

    Andreas Lorange and Reinert A. Rinvold

    Abstract

    The aim of this article is to identify students’ strategies while solving tasks which involve the expansion of fractions to a common denominator. In this case study we follow two groups of 11 year old students and their use of the artifact multilink cubes in the solution process. The analysis of the students’ strategies is based upon a semiotic-cultural framework. Five different types of strategies are reported: trial-and-error, factual, contextual, embodied-symbolic and symbolic. The concept of semiotic contraction is also used in the analysis.

    Andreas Lorange

    Andreas Lorange is Assistant Professor at NLA University College in Bergen. His main research interest is related to how physical and visual artefacts can be used in connection with the learning of mathematics.

    Reinert A. Rinvold

    Reinert A. Rinvold is Associate Professor at Hedmark University College in Hamar. His main research interest is multimodal mathematical thinking and learning.

    Skapad: 2014-06-25 kl. 01:00

  13. NOMAD 19(2), 2014

    ”Just-in-time teaching” in undergraduate mathematics

    Kristina Juter and Jan-Fredrik Olsen

    Abstract

    We compared five groups of students to investigate the effects of ”Just-in-time teaching” (JiTT), a method designed to both help students keep up with the often fast pace of undergraduate calculus and to deepen their learning. In total, 137 students participated in the study. The outcome is discussed in terms of conceptual and procedural knowledge in relation to examination and other assessment tasks. We observed an improvement on the assessed items and a shift in study habits.

    Kristina Juter

    Kristina Juter works as an associate professor in mathematics education at Kristianstad University in Sweden. She got her doctoral degree in mathematics and learning at Luleå University of Technology in 2006. Her research interests are, among others, students’ conceptual development at undergraduate calculus courses and mathematics teacher identity.

    Jan-Fredrik Olsen

    Jan-Fredrik Olsen has a PhD in pure mathematics from NTNU in Norway (2009), and is currently working as an associate professor in mathematics at Lund University in Sweden. While his research interests lie primarily in the meeting point between complex analysis and Fourier analysis, he has a strong interest in undergraduate mathematics education and the potential of technology to improve student motivation and learning.

    Skapad: 2014-06-25 kl. 01:00

  14. NOMAD 19(2), 2014

    Students’ conceptions about the formula for a rectangle’s area and some similarities to its historical context

    Eugenia Koleza

    Abstract

    In this paper, we focus on a debate between grade 6 students about the formula for a rectangle’s area, emerging during a 2-hours teaching, and raising questions about the possibility of using history in order to design a hypothetical learning/teaching trajectory of rectangle’s area, and we analyse students’ conceptions/misconceptions in relation to the historical context of area measurement.

    Eugenia Koleza

    Eugenia Koleza is Professor of Mathematics Education at the Department of Primary Education, University of Patras, Greece. She is member of the International Scientific Committee of the International Journal for Mathematics in Education and of the Editorial Board of the journal Mathematical Review. She is one of the Editors of the journal Critical Science & Education and Vice-President of the Hellenic Society of History, Philosophy and Didactics of the Sciences.

    Skapad: 2014-06-25 kl. 01:00

  15. NOMAD – 19(1), 2014


    Tidigare nummerPrevious issues
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    Volume 19, No 1, March 2014

    Editorial

    Indrek Kaldo and Markku S. Hannula

    Gender differences favouring females in Estonian university students’ views of mathematics

    [PDF]

    Hege Kaarstein

    A comparison of three frameworks for measuring knowledge for teaching mathematics

    [PDF]

    Raymond Bjuland, Arne Jakobsen og Elaine Munthe

    Muligheter og begrensninger for studenters læring i praksisopplæring – eksempel fra en førveiledningsdialog i matematikk

    [PDF]

    Christer Bergsten

    News from Nordic mathematics education

    Innehåll: JH

    Skapad: 2014-03-20 kl. 00:00

  16. NOMAD – 1(1), 1993

    Tidigare nummerPrevious issues
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    Nummer
    Issue

    Volume 1, No 1, October 1993

    Ledare/Editorial
    En ny nordisk forskningstidskrift

    Ole Björkqvist

    Social konstruktivism som grund för matematikundervisning

    [PDF]

    Morten Blomhøj

    Modellerings betydning for tilegnelsen af matematiske begreber

    [PDF]

    Inger Wistedt

    Elevers svårigheter att formulera matematiska problem

    [PDF]

    Bengt Johansson

    Matematikdidaktik – nordiskt samarbete i historisk belysning

    [PDF]

    Gunhild Nissen

    Nordisk Forskernetværk – Initiativet Matematikundervisning og Demokrati

    [PDF]

    Ole Björkqvist

    Litteraturanmälningar. Mobilisering av krafter för bättre utvärdering

    [PDF]

    Skapad: 2014-03-19 kl. 00:00

  17. NOMAD – 19(1), 2014


    Tidigare nummerPrevious issues
    Array

    Nummer/Issue

    Volume 19, No 1, March 2014

    Editorial

    Indrek Kaldo and Markku S. Hannula

    Gender differences favouring females in Estonian university students’ views of mathematics

    [PDF]

    Hege Kaarstein

    A comparison of three frameworks for measuring knowledge for teaching mathematics

    [PDF]

    Raymond Bjuland, Arne Jakobsen og Elaine Munthe

    Muligheter og begrensninger for studenters læring i praksisopplæring – eksempel fra en førveiledningsdialog i matematikk

    [PDF]

    Christer Bergsten

    News from Nordic mathematics education

    Innehåll: JH

    Skapad: 2014-03-04 kl. 00:00

  18. NOMAD 19(1), 2014

    Muligheter og begrensninger for studenters læring i praksisopplæring – eksempel fra en førveiledningsdialog i matematikk

    Raymond Bjuland, Arne Jakobsen og Elaine Munthe

    Sammanfattning

    Denne artikkelen presenterer resultater fra en førveiledningsdialog mellom en grunnskolelærerstudent og hennes praksislærer fra en ordinær fjerde semesters praksisopplæringsperiode. Ved hjelp av en dialogisk tilnærming forsøker analysen å identifisere dialogsekvenser som inneholder ytringer som er støttende eller begrensende med tanke på å hjelpe studenten til å rette oppmerksomheten mot elevers læring av likeverdige brøker på 7. trinn. Inspirert av perspektiver som fremmer et positivt læringsmiljø i klasserommet (Bransford, Brown & Cocking, 2000) blir ytringer innenfor en dialogsekvens kategoriserte som elevsentrerte, kunnskapssentrerte og vurderingssentrerte med tanke på å planlegge en undervisningsøkt. Dette danner et grunnlag for å diskutere styrker og svakheter ved førveiledningsdialogen.

    Abstract

    This article presents results from analyses of a mentoring session between a student teacher and her mentor teacher which took place prior to instruction during a fourth semester field practice placement. Using a dialogic approach, the analyses identify utterances that are perceived as supportive or constraining in relation to enabling the student to direct attention towards pupils’ learning about fractions in grade 7. Bransford mfl.’s (2000) approaches to learning have inspired the development of analytical categories to assess the degree of learner centered, knowledge centered and assessment centered utterances, and thus to discuss strengths and weaknesses in the mentoring session.

    Raymond Bjuland

    Raymond Bjuland is Professor of Mathematics Education at the Univer- sity of Stavanger (UiS), Norway. He is the leader of the research project: Teachers as Students at the Department of Education and Sports Science, University of Stavanger. His interests are related to students’ collaborative problem solving in small groups, the use of gestures in teacher-student dialogues, classroom research and mathematical knowledge for teaching.

    Arne Jakobsen

    Arne Jakobsen is Associate Professor of Mathematics at the University of Stavanger, Norway. He has experience from several international research projects in Mathematics Education, and is the leader of the NORHED project “Improving quality and capacity of mathematics teacher education in Malawi”. His interests are mathematics, mathematical knowledge for teaching, and quantitative studies in mathematics education.

    Elaine Munthe

    Elaine Munthe is Professor of Education and Dean of the Faculty of Education & Arts, University of Stavanger (UiS), Norway. She is Chair of a national panel appointed by the Ministry of Education and Research to follow up the teacher education reform which started in 2010, and is also Chair of the board of a funding program for educational research administered by the Norwegian Research Board. She has led several research projects investigating classroom practices and teachers’ professional work.

    Skapad: 2014-03-04 kl. 00:00

  19. NOMAD 19(1), 2014

    A comparison of three frameworks for measuring knowledge for teaching mathematics

    Hege Kaarstein

    Abstract

    This paper presents a comparison of three different frameworks used in research projects aimed at measuring knowledge for teaching mathematics. As the included cases all build on Shulman’s theoretical framework for teacher knowledge, in which the categories subject matter content knowledge (CK) and pedagogical content knowledge (PCK) are central, his framework was used as a reference. To enable comparison across the frameworks, each framework’s categories were analysed and organized taxonomically. The results indicate agreement on a superordinate level. However, important differences were found in the operationalisation of the basic level cat- egories mathematics CK and mathematics PCK. As the basic level normally represents clear communication of categories, this paper suggests that more attention to the operationalisation of basic level categories is needed.

    Hege Kaarstein

    Hege Kaarstein is a PhD student at the Department of Teacher Education and School Research, University of Oslo. Her focus is mathematical knowledge for teaching – the concept, its categorization and operationalization.

    Skapad: 2014-03-04 kl. 00:00

  20. NOMAD 19(1), 2014

    Gender differences favouring females in Estonian university students’ views of mathematics

    Indrek Kaldo and Markku S. Hannula

    Abstract

    This study reports on first-year Estonian university students’ views of mathematics. The data were collected from 970 university students of different disciplines. The participants completed a Likert-type questionnaire that was compiled from previously published instruments. The results reveal the importance of Mastery Goal Orientation as central to the structure of their views of mathematics. In this study, in five of six dimensions, females hold a more positive view of mathematics than do male students. Performance-Approach Goal Orientation was the only dimension in which we found no statistically significant gender difference. In all the other dimensions, the female respondents expressed a more positive affect towards mathematics: They showed a more powerful mastery orientation, valued mathematics more, felt more competent, perceived their teacher more positively, and cheated less frequently.

    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 14 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. He feels comfortable with both quantitative and qualitative research methods and enjoys the challenges of synthesizing research findings across different research paradigms and theoretical frameworks.

    Skapad: 2014-03-04 kl. 00:00

  21. NOMAD 18(4), 2013

    The first foci of elementary school students dealing with prognosis tasks in interviews

    Judith Stanja

    Abstract

    The nature of stochastics is not only characterized by its relationship as a model of the real phenomena described by it as well as by its usage to find hypotheses to be tested in reality, but also by its peculiar characteristic of modeling the relation between model and real phenomena. Stochastic prognoses can be one key concept for ele- mentary school stochastics to implement the fundamental idea of the specific nature of stochastics. Stochastic prognoses may be characterized as reflexive statements containing the structural components focus, evaluation and justification. Examples are given to illustrate these components. The paper outlines some a priori determined conceptional requirements for stochastic prognoses to give a first orientation of what can be expected from primary school children. It is assumed that the topics, ques- tions and problems stochastics is concerned with, are part of a culture that a child is just entering. To learn more about the ways in which primary school students under- stand and express stochastic prognoses, a series of half-structured interviews with 3rd graders (age 8-9) were videotaped and transcribed before and after a series of lessons. This contribution concentrates on the foci that children might adopt when dealing with prognosis tasks in interviews for the first time. An overview of the reconstructed types of foci is given and illustrated by examples. The stochastic foci reconstructed so far may be classified as simple foci that could be further described as sequential or aggregate foci. A case study of one child in a pre-interview shows what and how foci might be articulated when being confronted with the new semiotic means of a list.

    Judith Stanja

    Judith Stanja studied mathematics and history of science at the Georg- August University of Göttingen (Germany) and at Lund University (Sweden) with an emphasis on stochastics. Currently, she is working on her Phd in mathematics education at the University of Duisburg-Essen (Germany). Her research interests include early stochastic learning, con- straints for the development of stochastic knowledge, and representations.

    Skapad: 2014-01-09 kl. 00:00

  22. NOMAD – 18(4), 2013


    Tidigare nummerPrevious issues
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    Nummer/Issue

    Volume 18, No 4, December 2013

    Editorial

    Theodosia Prodromou

    A modelling approach to probability – analysing students’ conceptual structures

    [PDF]

    Judith Stanja

    The first foci of elementary school students dealing with prognosis tasks in interviews

    [PDF]

    Per Nilsson and Torsten Lindström

    Prolifing Swedish teachers’ knowledge base in probability

    [PDF]

    Innehåll: JH

    Skapad: 2014-01-09 kl. 00:00

  23. NOMAD 18(4), 2013

    Prolifing Swedish teachers’ knowledge base in probability

    Per Nilsson and Torsten Lindström

    Abstract

    This paper aims at profiling Swedish teachers’ knowledge base in probability. 43 teachers in compulsory school answered a questionnaire on probability estimation tasks and concept tasks. In the concept tasks, they were challenged to explain their solutions and the content involved in the probability estimation tasks. We distin- guish five patterns in the teachers’ knowledge profile: 1) a basic understanding of the theoretical interpretation of probability, 2) problems with structuring compound events, 3) difficulty with conjunction and conditional probability, 4) a higher degree of common content knowledge than of specialized content knowledge and 5) limited understanding of random variation and principles of experimental probability.

    Per Nilsson

    Per Nilsson is professor in mathematics education at the School of Science and Technology, Örebro University and associated professor at Linnaeus University. His research interests concern classrooms communication in mathematics, the nature of mathematical reasoning and knowledge for teaching probability.

    Torsten Lindström

    Torsten Lindström is professor in mathematics at the Department of Mathematics, Linnaeus University. His research interests concern dynamical systems with applications to biology. He has a teacher’s exam in mathematics, physics, and chemistry.

    Skapad: 2014-01-09 kl. 00:00

  24. NOMAD 18(4), 2013

    A modelling approach to probability – analysing students’ conceptual structures

    Theodosia Prodromou

    Abstract

    This research study investigates how middle school students use probability to model random behaviour in real-world contexts and how they articulated fundamental prob- abilistic concepts to show aspects of the mental models that they generated. This article is concerned with the conceptual structures that the students develop when exploring computer-based simulations. The results suggest that the students relied on their experience to provide a context reality from which to construct their mental model of the situation, from which they then defined the probability model. While the students attempted to build mental models, they checked the adequacy of the mapping between their probability models and reality by interrogating the context of their personal experiences. The results also suggest that the way students express this relationship between signal and noise seems to have a particular importance in building comprehensive models that link observed data to modelling distributions.

    Theodosia Prodromou

    Dr Theodosia Prodromou is a mathematician, statistician and educator. She lectures mathematics education at the University of New England (UNE) in New South Wales, Australia. Her research interests are focused on exploring the relationship between technology and mathematical thinking – especially statistical thinking and probabilistic thinking. She is very interested in statistics education.

    Skapad: 2014-01-09 kl. 00:00

  25. Workshop April 17, 2018

    NOMAD as a resource for mathematics education research in the Nordic countries

    Workshop for doctoral students in mathematics education

    The 7th workshop for doctoral students led by the editors of NOMAD will be held in Gothenburg April 17, 2018. PhD students in mathematics education from the Nordic and Baltic countries are invited to submit a draft of a paper for NOMAD, which they will have the opportunity to present and discuss during the workshop.
    The deadline for submissions is set to March 15, 2018. The submitted papers will be distributed among the participants shortly after submission, and each participant will be asked to make a review of one other paper before the workshop, according to certain guidelines. Each paper will also be read by one or more of the editors of NOMAD, who during group discussions will give feedback on the paper considering a possible publication in NOMAD.
    More information is provided in the Invitation

    Skapad: 2013-11-28 kl. 00:00

  26. NOMAD 18(3), 2013

    An analysis of mathematical modelling in Swedish textbooks in upper secondary school

    Peter Frejd

    Abstract

    A new national curriculum has recently been implemented in the Swedish upper secondary school where one of the goals to be taught is modelling ability. This paper presents a content analysis of 14 ”new” mathematical textbooks with the aim to investigate how the notion of mathematical modelling is presented. An analytic scheme is developed to identify mathematical modelling in the textbooks and to analyse modelling tasks and instructions. Results of the analysis show that there exist a variety of both explicit and implicit descriptions, which imply for teachers to be attentive to complement the textbooks with other material.

    Peter Frejd

    Peter Frejd is a PhD-student in mathematics education at the Department of Mathematics, Linköping University, Sweden. His main research interest is on how different actors interpret and work with mathematical modelling in and out of school settings.

    Skapad: 2013-11-19 kl. 00:00

  27. NOMAD 18(3), 2013

    Arithmetic textbooks in Estonia, Iceland and Norway – similarities and differences during the nineteenth century

    Kristín Bjarnadottír, Andreas Christiansen and Madis Lepik

    Abstract

    This paper identifies similarities and eventual differences in the development of public mathematics education in the nineteenth century in three Northern-European countries: Estonia, Iceland and Norway. Special attention is paid to how these developments were reflected in the first arithmetic textbooks written in the vernacular in these countries. By the end of the century, all three countries had taken serious steps to develop public education, and arithmetic textbooks, meant for self-instruction or for use in elementary schools, had been published. The content and style of presentation of these textbooks in Estonia, Iceland and Norway are described and compared in the paper, revealing their roots in Northern-European culture: Lutheran Protestantism, Enlightenment and pedagogical currents initiated by Comenius, Pestalozzi and Spencer, emphasizing meaningful learning. Their educational aims were important driving forces in growing national movements in the respective countries by contributing to capability to manage own resources and use of own vernacular, resulting in increased self-esteem.

    Kristín Bjarnadóttir

    Kristín Bjarnadóttir is associate professor at the School of Education, University of Iceland. Her research interests concern the history of mathematics education and its socio-economic context.

    Andreas Christiansen

    Andreas Christiansen is assistant professor at the Department of Teacher Education and Cultural Studies at Stord/Haugesund University College in Norway. His research interests are history of mathematics, and history of mathematics education.

    Madis Lepik

    Madis Lepik is associate 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.

    Skapad: 2013-11-19 kl. 00:00

  28. NOMAD 18(3), 2013

    Barns bruk av digitale verktøy i barnehagen: muligheter for å gjøre seg matematiske erfaringer

    Martin Carlsen

    Sammanfattning

    Denne artikkelen har som mål å studere hvordan barnehagebarn gjør seg matematiske erfaringer gjennom å bruke digitale verktøy. Ved å ta et sosiokulturelt perspektiv på læring og utvikling studeres den sosiale interaksjonen mellom barn og voksne når disse diskuterer og samhandler med ulike digitale verktøy. Analysene av transkriberte dialoger i to grupper, hver bestående av en voksen og to barn, gir innblikk i det matematiske læringspotensialet som oppstår når barna interagerer med de digitale verktøyene. Dette læringspotensialet knytter seg til de matematiske begrepene telling og tallsymbol, deriblant matematiskteoretiske komponenter som sortering, subitizing, parkobling og kardinalprinsipp. Samtidig viser analysen at interaksjonen med de digitale verktøyene har potensiale til å gi ytterligere næring til approprieringsprosessen av de implisitte matematiske begrepene som finnes i applikasjonene.

    Abstract

    This study aims at illuminating aspects of how kindergarten children make mathematical experience through the use of digital tools. By taking a sociocultural perspective on learning and development the social inter- action amongst children and adults is studied when these discuss and collaborate in using different digital tools. The analyses of transcribed dialogues in two groups comprising one adult and two children show the learning potential that unfolds when the children interact with the digital tools. This learning potential is relative to the mathematical con- cepts of counting and number digits, including mathematical theoretical components of sorting, subitizing, one-to-one correspondence and cardinality. Furthermore, the analyses show that interaction with the digital tools carries potentials regarding how to further nurture the appropriation process with respect to the implicit mathematical concepts inherent in the applications.

    Martin Carlsen

    Martin Carlsen er førsteamanuensis i matematikkdidaktikk ved Universitetet i Agder, Norge. Hans forskningsinteresser er innenfor temaet i denne artikkelen, barns læring av matematikk i barnehagen med og uten bruk av digitale verktøy. Hans forskningsinteresse handler også om før- skolelæreres orkestrering av matematikkaktiviteter i barnehagen. Han er i tillegg interessert i læring av matematikk gjennom problemløsning i smågrupper. Han identifiserer seg med et sosiokulturelt perspektiv på læring og utvikling, og forskningen hans er situert innen dette teoretiske rammeverket.

    Skapad: 2013-11-19 kl. 00:00

  29. NOMAD – 18(3), 2013


    Tidigare nummerPrevious issues
    Array

    Nummer/Issue

    Volume 18, No 3, October 2013

    Editorial

    Martin Carlsen

    Barns bruk av digitale verktøy i barnehagen: muligheter for å gjøre seg matematiske erfaringer

    [PDF]

    Kristín Bjarnadottír, Andreas Christiansen and Madis Lepik

    Arithmetic textbooks in Estonia, Iceland and Norway – similarities and differences during the nineteenth century

    [PDF]

    Peter Frejd

    An analysis of mathematical modelling in Swedish textbooks in upper secondary school

    [PDF]

    First Announcement – NORMA 14, June 3rd–6th 2014

    Innehåll: JH

    Skapad: 2013-11-19 kl. 00:00

  30. NOMAD 18(2), 2013

    Att ändra arbetssätt och kultur inom den inledande aritmetikundervisningen

    Dagmar Neuman

    Sammanfattning

    Utgående från den holistiska kunskapssyn som representerar fenomenologin och den fenomenografiska forskningsansatsen diskuterar jag i den här artikeln observationer redovisade i min nu drygt tjugosex år gamla avhandling, i boken Räknefärdighetens rötter samt i en senare studie av hur barn dividerar. Observationerna gäller dels elever som deltar i specialundervisning i matematik i grundskolan, samt elever i gymnasieskolan som anser sig lida av matematiksvårigheter, och dels skolnybörjare som ännu inte har undervisats i matematik. De visar

    – att det som främst tycks förorsaka grava eller specifika matematiksvårigheter är att eleverna saknar talföreställningar samt förståelse för sambandet mellan de fyra räknesätten

    – att sådana begrepp och föreställningar knappast utvecklas genom skolans tabellträning

    – att många barn intuitivt börjar utveckla talföreställningar före skolstarten, samtidigt med att de formar konkreta representationer som blir till abstrakta föreställningar om tal.

    Avslutningsvis ställer jag frågan: skulle den stora andel elever som nu lämnar grundskolan utan godkänt betyg i matematik möjligen kunna reduceras genom ett paradigmskifte inom den kultur som styr hur den grundläggande aritmetiken behandlas under de första skolåren?

    Abstract

    Setting out from the holistic view of knowledge representing pheno- menology and the phenomenographic research approach, I have in this article revisited the observations presented in my now twenty-six year old dissertation The origin of arithmetic skills, the Swedish book Räknefärdighetens rötter and a later study of how children divide. One side of the observations concerns elementary and middle school pupils who take part in special education as well as high school pupils who believe they suffer from severe math difficulties; the other concerns seven year old first year pupils without any formal education in the field of mathematics. These observations show

    – that the primary cause of severe or specific math difficulties seems to be the absence of numerical representations and of the concep- tual understanding of the inverse relation between addition and subtraction

    – that those concepts and representations are probably not developed through the table-training usually used at school; but

    – that many children intuitively begin to use those concepts or arith- metic laws before they enter school, whilst simultaneously crea- ting numerical representations, which in due time become tools for thinking in numerical terms.

    Finally, the question is posed: would a shift of paradigm within the culture now ruling the ways in which arithmetic is introduced to first year pupils possibly reduce the great number of pupils who now fail mathematics when leaving school at the end of grade nine?

    Dagmar Neuman

    Dagmar Neuman doktorerade vid Göteborgs universitet år 1987, avgick med pension från universitetet år 1991 och har därefter huvudsakligen ägnat sig åt fortbildning inom ämnet matematik, med inriktning mot förskollärare och lärare för de första skolåren.

    Skapad: 2013-10-15 kl. 01:00

  31. NOMAD 18(2), 2013

    Preparing future teachers for interdisciplinarity: designing and implementing a course for pre-service upper secondary teachers

    Uffe Thomas Jankvist, Jan Alexis Nielsen and Claus Michelsen

    Abstract

    Educational researchers and policy-makers have for some time touted the need for interdisciplinary teaching. But while there are many educational, democratic, and economic arguments for bringing an increased attention to interdisciplinary teaching, there has been a striking lack of exposure of the question of how future teachers, who are largely educated in a mono-disciplinary fashion, can best become equipped to introduce genuinely interdisciplinary teaching activities to their future students. This article presents some preliminary reflections upon a graduate course at the University of Southern Denmark, which aims to prepare future science and mathematics teachers for interdisciplinary teaching, and which has been designed on the basis of influential theoretical expositions of the concept of interdisciplinarity.

    Uffe Thomas Jankvist

    Uffe Thomas Jankvist is associate professor of mathematics education at Aarhus University, Department of Education, Campus Emdrup, Denmark. In addition to the topic of interdisciplinarity, his research interests include the use of history of mathematics, applications of mathematics, and philosophy of mathematics in mathematics education, both from a theoretical and an empirical point of view, including also students’ beliefs about and images of mathematics as a (scientific) discipline. Besides being an editor of Nomad, he is currently involved in a new initiative at Roskilde University to design and implement an educational program for in-service upper secondary school mathematics teachers to become ”math counselors”.

    Jan Alexis Nielsen

    Jan Alexis Nielsen is postdoc at Department of Science Education, University of Copenhagen. His research focus lies in student argumentation in interdisciplinary contexts and in competence assessment – in particular assessment of competencies that are ill-defined and manifest in processes. He has taught several courses in education and communication at bachelor, master and post-graduate levels.

    Claus Michelsen

    Claus Michelsen is associate professor of mathematics education at University of Southern Denmark, Department of Mathematics and Computer Science. He is associate dean and head of the Ph.D.-school at The Faculty of Science at University of Southern Denmark. In addition to the topic of interdisciplinarity, his research interests include students’ interest in science and mathematics, informal learning in mathematics and science, teacher education and in-service teacher training.

    Skapad: 2013-10-15 kl. 01:00

  32. NOMAD – 18(2), 2013


    Tidigare nummerPrevious issues
    Array

    Nummer/Issue

    Volume 18, No 2, June 2013

    Editorial

    Dagmar Neuman

    Att ändra arbetssätt och kultur inom den inledande aritmetikundervisningen

    [PDF]

    Markus Hähkiöniemi, Henry Leppäaho and John Francisco

    Teacher-assisted open problem solving

    [PDF]

    Uffe Thomas Jankvist, Jan Alexis Nielsen and Claus Michelsen

    Preparing future teachers for interdisciplinarity: designing and implementing a course for pre-service upper secondary teachers

    [PDF]

    Christer Bergsten

    News from Nordic mathematics education

    Innehåll: JH

    Skapad: 2013-10-15 kl. 01:00

  33. NOMAD 18(2), 2013

    Teacher-assisted open problem solving

    Markus Hähkiöniemi, Henry Leppäaho and John Francisco

    Abstract

    Previous research has developed several problem-solving models and suggested that the teacher plays a crucial role in guiding students’ problem solving. However, less is known about the particularities of problem solving and teacher guidance when dealing with open problems which include multiple possible solution pathways. The aim of this study is to understand students’ open problem-solving processes and teachers’ ways of supporting them. Data collection involved videotaping one 9th grade mathematics lesson with two video cameras and capturing the screens of the students’ computers. Seven student pairs worked on an open problem using GeoGe- bra under the guidance of a teacher trainee. We found that students had various kinds of problem-solving processes and that the teacher had a crucial role in guiding them. We elaborate on 9 ways how the teacher guided students to change between phases in open problem solving.

    Markus Hähkiöniemi

    Dr. Markus Hähkiöniemi is university lecturer in the Department of Teacher Education, University of Jyväskylä, Finland. He is interested in classroom interaction and students’ mathematical thinking. His current project focuses on pre-service mathematics teachers’ technology-enriched inquiry-based mathematics teaching in grades 7 to 12.

    Henry Leppäaho

    Dr. Henry Leppäaho is university lecturer on the pedagogy of mathematics in the Department of Teacher Education, University of Jyväskylä, Finland. His research is focused on mathematical problem solving.

    John Francisco

    Dr. 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.

    Skapad: 2013-10-15 kl. 01:00

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

    Research on mathematical beliefs. The birth and growth of the MAVI group in 1995–2012

    Erkki Pehkonen

    Abstract

    In the 1980s the meaning of beliefs for teaching and learning aroused also to the con- sciousness of mathematics educators. Therefore, here it is firstly sketched the research field of mathematical beliefs, in order to understand why belief research has been a topic for an international research group for more than 30 years. The aim of the paper is to have a look at the history of MAVI and to describe its development within the years 1995–2012. A special look is given at the birth of the MAVI group in the middle of the 1990s and then its development through the last 18 years will be described. Also some statistics on the MAVI meetings and their participants are presented. And in the appendix the total list of the MAVI proceedings is documented.

    Erkki Pehkonen

    Dr. Erkki Pehkonen is a full professor (retired) in the field of mathematics and informatics education in the Department of Applied Sciences of Education at the University of Helsinki in Finland. He is interested in problem solving with a focus on motivating middle grade pupils, as well as in understanding pupils’ and teachers’ beliefs and conceptions about mathematics teaching.

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

  35. 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

  36. 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

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

    Affective pathways and interactive visualization in the context of technological and professional mathematical knowledge

    Inés Mª Gómez-Chacón

    Abstract

    This article reports the findings for a qualitative study on the use of dynamic geometry systems (DGS) and their impact on students’ affective pathways. The approach adopted is to view affect through the lens of a representational system. The participants, mathematics teacher trainees, were asked to solve geometric locus exercises using GeoGebra software. The results reveal a number of features that characterize subjects’ local and global affect. Future teachers’ local affect when using imagery in computerized environments was found to be impacted by the balance between their analytical-algebraic and graphic reasoning and their understanding of the tools at their avail and their use in the instrumental deconstruction of geometric figures. Evidence was observed that linked student teachers’ global affect, in turn, to their motivation as defined by their goals and self-concept.

    Inés Mª Gómez-Chacón

    Inés Mª Gómez-Chacón is Professor of Mathematics Education in the Faculty of Mathematics in Complutense University where she is Vicedean and Director of Cátedra Miguel de Guzmán about Mathematic Education. She develops basic research and applied research in different topics: relationship between knowledge and affectivity in mathematics, Sociology of mathematical education (the sociocultural environments and identity) and the development of new technologies as part of the curriculum and teacher training in these areas.

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

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

    Emotional atmosphere in third-graders’ mathematics classroom – an analysis of pupils’ drawings

    Anu Laine, Liisa Näveri, Maija Ahtee, Markku S. Hannula and Erkki Pehkonen

    Abstract

    The aim of this study is to find out what kind of emotional atmosphere dominates in third-graders’ mathematics lessons. The analysis is based on pupils’ drawings. In total 133 drawings were analyzed by looking for content categories related to a holistic evaluation of emotional atmosphere during mathematics lesson. As a summary we can conclude that the emotional atmospheres in the mathematics lessons are mainly positive even though the differences between the classes are large. Furthermore, it can be said that asking pupils to do drawings is a good and many-sided method to collect data about the emotional atmosphere of a class.

    Anu Laine

    Anu Laine is adjunct professor in mathematics education and she is working as university lecturer at the Department of Teacher Education at the University of Helsinki in Finland. Her research interests include affects, communication and problem solving in mathematics education.

    Liisa Näveri

    Liisa Näveri is Ph.D. and working as a researcher at the Department of Teacher Education at the University of Helsinki in Finland. Her research interests include learning and problem solving in mathematics education.

    Maija Ahtee

    Maija Ahtee is professor emerita in mathematics and science education at the University of Jyväskylä, Finland. Her research interests have been more in science education.

    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.

    Erkki Pehkonen

    Erkki Pehkonen is a full professor (emeritus) in the field of mathematics and informatics education in the Department of Teacher Education at the University of Helsinki in Finland. He is interested in problem solving with a focus on motivating middle grade pupils, as well as in understanding pupils’ and teachers’ beliefs and conceptions about mathematics teaching.

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

  39. NOMAD – 17(3-4), 2012


    Tidigare nummerPrevious issues
    Array

    Nummer/Issue

    Volume 17, No 3-4, December 2012

    Ledare/Editorial

    Editorial

    Erkki Pehkonen

    Research on mathematical beliefs. The birth and growth of the MAVI group in 1995–2012

    [PDF]

    Peter Liljedahl, Susan Oesterle and Christian Bernèche

    Stability of beliefs in mathematics education: a critical analysis

    [PDF]

    Anu Laine, Liisa Näveri, Maija Ahtee, Markku S. Hannula and Erkki Pehkonen

    Emotional atmosphere in third-graders’ mathematics classroom – an analysis of pupils’ drawings

    [PDF]

    Inés Mª Gómez-Chacón

    Affective pathways and interactive visualization in the context of technological and professional mathematical knowledge

    [PDF]

    Chiara Andrà and Guido Magnano

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

    [PDF]

    Fulvia Furinghetti, Chiara Maggiani and Francesca Morselli

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

    [PDF]

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

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

    [PDF]

    Sonja Lutovac and Raimo Kaasila

    Dialogue between past and future mathematical identities

    [PDF]

    Hanna Palmér

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

    [PDF]

    Päivi Portaankorva-Koivisto

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

    [PDF]

    Madis Lepik, Anita Pipere and Markku S. Hannula

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

    [PDF]

    Igor’ Kontorovich and Boris Koichu

    Feeling of innovation in expert problem posing

    [PDF]

    Innehåll: JH

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

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

    Stability of beliefs in mathematics education: a critical analysis

    Peter Liljedahl, Susan Oesterle and Christian Bernèche

    Abstract

    The field of mathematics education has assumed for too long that stability is an inherent and definable characteristic of beliefs. In this article we explore the validity of this claim through the critical analysis of 92 journal articles, conference papers, and book chapters. Using a stringent definition of what it means for a belief to be stable, we conclude that the body of research on mathematical beliefs is inconsistent in its use of this construct. The aggregated results of our analysis also indicate that stability and instability are not mutually exclusive characteristics of beliefs.

    Peter Liljedahl

    Dr. Peter Liljedahl is an Associate Professor of Mathematics Education in the Faculty of Education at Simon Fraser University in Vancouver, Canada. He is a former high school mathematics teacher who has kept his research interests and activities close to the classroom. He regularly works closely with teachers, schools, school districts, and ministries of education on issues pertaining to the improvement of teaching and learning. His primary research interests are teacher beliefs, teacher education, and creativity in mathematics.

    Susan Oesterle

    Dr. Susan Oesterle is a Mathematics instructor in the Faculty of Science & Technology at Douglas College in New Westminster, Canada. Over the last few years she has been heavily involved in developing and teaching in a Graduate Diploma Program for Mathematics and Science Teaching, a two-year program which provides an opportunity for practicing elementary and middle school teachers to build their knowledge-base and improve their teaching of these subjects. Her current research interests include pre-service and in-service teacher education, teacher beliefs, and issues concerning mathematics teacher educators.

    Christian Bernèche

    Christian Bernèche is a PhD student in Mathematics Education at Simon Fraser University in Vancouver, Canada. He has been teaching for over two decades and is presently teaching Grade 6. He is a member of his local Professional Development Committee and strongly believes in selfdirected professional growth plans. His area of interest in research is student perceptions about learning and teaching mathematics.

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

  41. 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

  42. 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

  43. 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

  44. 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

  45. 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

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

    Feeling of innovation in expert problem posing

    Igor’ Kontorovich and Boris Koichu

    Abstract

    This paper is one of the reports on a multiple-case study concerned with the intertwining between affect and cognition in the mechanisms governing experts when posing new mathematical problems. Based on inductive analysis of a single case of an expert poser for mathematics competitions, we suggest that the desire to experience the feeling of innovation may be one of such mechanisms. In the case of interest, the feeling was realized through expert’s reflections on the problems he created in the past, by systematically emphasizing how a new problem was innovative in comparison with other familiar problems based on the same nesting idea. The findings are discussed in light of past research on expert problem posers and expert problem solvers.

    Igor’ Kontorovich

    Igor’ Kontorovich is a mathematics educator and a researcher, who has recently (in 2013) completed his Ph.D. studies at the Department of Education in Science and Technology at the Technion – Israel Institute of Technology. Assistant Professor Boris Koichu was his academic adviser. The Ph.D. research, of which this paper is a part, is concerned with mental mechanisms involved in expert problem posing.

    Boris Koichu

    Boris Koichu is an Assistant Professor at the Department of Education in Science and Technology at the Technion – Israel Institute of Technology. His research domain is mathematical problem solving and problem posing, with special attention to learning and teaching mathematics at secondary school and university. Some of his work concerns a question of how insights on problem solving and problem posing by the gifted and experts can be implemented in promoting regular students and in mathematics teacher education.

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

  47. 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

  48. 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

  49. 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

  50. 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

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