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  • 1.
    Dahl, Thomas
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Problem-solving can reveal mathematical abilities: How to detect students' abilities in mathematical activities2012Licentiatavhandling, monografi (Övrigt vetenskapligt)
    Abstract [en]

    Dahl, Thomas (2012). Problemlösning kan avslöja matematiska förmågor. Att upptäcka matematiska förmågor i en matematisk aktivitet (Problem-solving can reveal mathematical abilities: How to detect students‟ abilities in mathematical activities). Linnéuniversitetet 2012; ISBN:978-91-86983-28-4. Written in Swedish.The thesis deals with the problem of identifying and classifying components of mathematical ability in students‟ problem-solving activities. The main theoretical framework is Krutetskii‟s theory of mathematical abilities in schoolchildren. After a short historical background focusing on the question of differentiation or integration among students on the basis of their various aptitudes for studies, the theory of mathematical ability and especially the Krutetskiian theory are described. According to Krutetskii mathematical ability should be looked upon as a structure of seven or eight different components called abilities which may appear and be subject to analysis during a mathematical activity.Krutetskii used school pupils and experimental problems to establish the relevance of his structure of abilities. However, in this work the theme is approached from the opposite perspective: If a problem and an experimental person are given, which mathematical abilities will appear and in what ways do they appear in the mathematical activity? The empirical study uses three so called “rich mathematics problems” and 98 students of which 37 study at the lower secondary school, 39 at the upper secondary school and 22 at the teacher education programme. The output data is either the written outcomes of the students‟ individual work on a problem or the recordings from small groups of students solving a problem in cooperation with their peers.In order to identify and classify abilities, the separate components of mathematical ability must be interpreted and adapted to the specific problem on which the students are working. I call this process of conformation of the abilities operationalization and the question in focus is if such an operationalization can be done successfully. The results indicate that it could be done and several examples are given which show how one or several mathematical abilities may come out more or less strongly in the mathematical activity of problem solving. The results also indicate that even low or average achieving students may show significant creative abilities. Another observation from the empirical study is that creative abilities do not seem to be more abundant among upper than lower secondary students. These two observations point out possible pathways to proceed further in the study of mathematical abilities.

  • 2.
    Ebbelind, Andreas
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Analysing the Discourse of Teacher Training2012Konferensbidrag (Refereegranskat)
  • 3.
    Ebbelind, Andreas
    et al.
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Roos, Helena
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Nilsson, Per
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Learning fractions: transformations between representations from a social semiotic perspective of multimodality2012Ingår i: Proceedings of Norma 11: The Sixth Nordic Conference on Mathematics Education / [ed] Gunnarsdottir, Hreinsdottir, Palsdottir, Hannula, Hannula-Sormunen, Jablonka, Jankvist, Ryve, Valero and Waege., University of Iceland Press, 2012, s. 217-226Konferensbidrag (Refereegranskat)
    Abstract [en]

    This study presents a tentative framework for studying the learning of fractions in the context of transformations between different forms of representations. The framework is used in an empirical sample of how eight 10-year-old students express understanding of activities which were developed to challenge them to reflect on different ways of representing aspects of the concept of fractions. The framework is based on a social semiotic perspective of multimodality.

    The analysis discloses how the framework helps in structuring our understanding of the interplay between representations in the learning of fractions. Specifically, we saw how concrete physical material and gestures complemented the symbolic and spoken language in the students’ solution strategies of different tasks. 

  • 4.
    Lennerstad, Håkan
    et al.
    BTH.
    Olteanu, Constanta
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Åtta IKT-projekt för matematiken i skolan: empiri och analys2012Rapport (Refereegranskat)
    Abstract [sv]

    Denna rapport presenterar empiri och analys av en granskning av åtta projekt som mottagit medel från Skolverket för att tillämpa IKT i skolans matematikundervisning. Empirin är organiserad enligt aktivitetsteorin, vilken sätter relationerna mellan människa, miljö, aktiviteter och mål i förgrunden. Empirin som presenteras är till stor del sammanställda repliker från lärare och elever vid intervjuerna, organi¬sera¬de för att belysa verksamhetens olika relationer. Det betyder att presentationen är till stor del på de verksammas villkor, och på deras språk.Ett stort antal konkreta slutsatser framkommer ur detta material. En av dem är att klass¬upp-sätt¬ningar av datorer är sällan framgångsrika, på grund av att teknisk support ofta var otillräcklig, och att lärarna inte kan veta hur mycket eleverna använder datorerna till icke-skol-verk¬sam¬het. Dessa problem finns inte för interaktiva skrivtavlor. De framstår däremot som ett socialt verktyg, som gör utbyte och dialog om ämnet lättare att få till stånd. I flera fall framkom indirekt, men ändå tydligt, att utbildningen på tekniken hade varit otillräcklig, trots att lärarna inte uttryckte ett tydligt missnöje med den. Skrivtavlan ökade lärarnas motivation för samarbete. En framåtriktad slutsats är att en lärargrupp som har ett fungerande samarbete och goda didaktiska, ämnesmässiga, ledar- och relationella kompe¬tenser med en interaktiv skrivtavla har en möjlighet att komma längre med elevernas måluppfyllelse.

  • 5.
    Lindström, Torsten
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Investeringar blir till konsumption2012Övrigt (Övrig (populärvetenskap, debatt, mm))
    Abstract [sv]

    Att lära sig räkna övningsexempel i matematikmed digitala hjälpmedel saknar bildningsvärde och gör kunskapen teknikberoende. Kunskapen föråldras på det här viset fort.

  • 6.
    Nilsson, Gunilla
    et al.
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Olteanu, Constanta
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Sällström, Karin
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Att initiera en learning study2012Ingår i: Matematikbiennalen, 2012, 2012, s. 506a-Konferensbidrag (Övrigt vetenskapligt)
    Abstract [sv]

    Linnéuniversitetet genomförde på uppdrag av Skolverket en fördjupad utvärdering av ett urval projekt inommatematiksatsningen 2009-2010. Det övergripande syftet med vår presentation är att lyfta fram konkretasituationer för att genomföra en bra learning study utifrån skolornas förutsättningar och behov. Fokus kommeratt ligga på organisation och nödvändiga villkor för att initiera en learning study. Presentationen utgår ifrånmaterialet som Linnéuniversitetet samlade in vid olika skolbesök och analysen av videoinspelade lektioner.

  • 7.
    Nilsson, Per
    et al.
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Lindström, Torsten
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Connecting Swedish compolsory schoolteachers' content knowledge of probability to their level of education, teaching years and self-assessments of probability concepts2012Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper reports on a survey on teachers’ content knowledge of probability and with connecting such knowledge to the teachers’ level of education, teaching years and self-assessments of probability concepts. Twenty-nine teachers in compulsory school answered a questionnaire calling for reflection on these issues. The teachers’ responses disclose that the teachers find probability to be a difficult subject. The survey reports that the teachers have low confidence in understanding key concepts of probability and that they have difficulties in applying the concepts in probability tasks. The test indicates no correlation between teaching years and confidence or between teaching years and results on the probability tasks. 

  • 8.
    Nilsson, Per
    et al.
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Sällström, Karin
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Nilsson, Gunilla
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    On the relationship between deterministic and probabilistic reasoning in modelling the chance of a natural phenomenon2012Ingår i: Proceedings of Norma 11: the sixth Nordic Conference on Mathmatics Education in Reykjavik, May 11-14, 2011, 2012Konferensbidrag (Refereegranskat)
    Abstract [en]

    This study aims at investigating the relationship between deterministic and probabilistic reasoning when students are asked to model and predict the outcomes of a real-world situation involving uncertainty. Twelve students, aged 8-9 years, participated in an outdoor located teaching activity which called for reflection on the growing of sunflowers. Based on the analysis, and previous research, the study suggests to structure an analysis on the relationship between deterministic and probabilistic reasoning according to four analytical relationships: Deterministic model and deterministic behaviour; Deterministic model and probabilistic behaviour; Probabilistic model and deterministic behaviour; Probabilistic model and probabilistic behaviour.

  • 9.
    Olteanu, Constanta
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Critical aspects as a means to develop students learning to simplify rational expressions2012Ingår i: The 12th International Congress on Mathematical Education (ICME-12), 2012, s. 1-10Konferensbidrag (Refereegranskat)
  • 10.
    Olteanu, Constanta
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Dimensions of variation and student learning2012Ingår i: The 12th International Congress on Mathematical Education (ICME-12), 2012, s. 1-10Konferensbidrag (Refereegranskat)
  • 11.
    Olteanu, Constanta
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Forskare och lärare: kollegial samverkan2012Ingår i: Skolforum, 2012, 2012Konferensbidrag (Övrigt vetenskapligt)
  • 12.
    Olteanu, Constanta
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Learning study in mathematics education: opportunities and challenges2012Ingår i: The World Association of Lesson Studies 2012, 2012Konferensbidrag (Övrigt vetenskapligt)
  • 13.
    Olteanu, Constanta
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Utvärdering– learning/lesson study2012Ingår i: Matematikbiennalen, 2012, 2012, s. 413b-Konferensbidrag (Övrigt vetenskapligt)
    Abstract [sv]

    Linnéuniversitetet genomförde på uppdrag av Skolverket en fördjupad utvärdering av ett urval projekt inommatematiksatsningen 2009-2010. Det övergripande syftet är att utvärdera genomförda utvecklingsinsatserseffekter med avseende på kvaliteten i matematikundervisningen. Utvärderingen har en huvudsaklig kvalitativinriktning, och bygger på fördjupade samtal (gruppintervjuer, individuella intervjuer), projektdokumentationoch lärares fördjupade dokumentation. Viss kvantitativ information kommer också att samlas in för att belysakommunernas/skolornas förutsättningar.

  • 14.
    Olteanu, Constanta
    et al.
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Holmqvist, Mona
    University of Gothenburg.
    Differences in success in solving second-degree equations due to differences in classroom instruction2012Ingår i: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 43, nr 5, s. 575-587Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The point of departure in this study is that differences in solving second-degree equations result from differences in what is presented to the students in a learning situation. However, the specified aim is to describe what kind of differences seem to be crucial for learning, and what does seem fruitless. The study is carried out in an upper secondary school in Sweden. Data consist of video-recorded lessons and tests. Two teachers and 45 students participated in this study. The analysis has been made with the aid of variation theory. The results show that the teachers focused on different aspects of a second-degree equation, and that this implied different learning outcomes as some of the aspects were not critical to promoting learning while others were.

  • 15.
    Olteanu, Constanta
    et al.
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Olteanu, Lucian
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Equations, functions, critical aspects and mathematical communication2012Ingår i: International Education Studies, ISSN 1913-9020, E-ISSN 1913-9039, Vol. 5, nr 5, s. 69-78Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The purpose of this paper is to present the mechanism for effective communication when the mathematical objects of learning are equations and functions. The presentation is based on data collected while the same object of learning is presented in two classes, and it includes two teachers and 45 students. Among other things, the data consists of video-recordings of lessons and tests. In the analysis, concepts relating to variation theory have been used as analytical tools. The results show that effective communication occurs in the classroom if it has the critical aspects in students learning as its starting point. The communication in the classroom succeeds or not if the aspects of the content supposed to be treated is the same as or different from the aspects of the content of the teacher’s representation, and if the aspects of the content of the teacher’s representation are the same as or different from the aspects discerned by the students. The results also show that the students cannot make sense of the difference between the highest/lowest value of a quadratic function and the maximum/minimum point; the difference between a quadratic equation and function; the students also have difficulties in solving a quadratic equation if it appears in a new context. The argument of the functions is identified as critical aspect in this study.

  • 16.
    Olteanu, Constanta
    et al.
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Olteanu, Lucian
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Improvement of effective communication: the case of subtraction2012Ingår i: International Journal of Science and Mathematics Education, ISSN 1571-0068, E-ISSN 1573-1774, Vol. 10, nr 4, s. 803-826Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The research study this article is based on aims to implement researchknowledge to teaching, that is, the concept of critical aspects and dimensions of variationused in the variation theory. To do this, the researchers worked with willing teachers toexplore how to make mathematics teaching more effective. This paper illustrates howteachers make use of a learning theory, the variation theory, as well as their ownprofessional expertise and collaboration to help students improve their mathematicalunderstanding of subtraction as well as their learning of it. The students’ tests,examinations of students’ mathematical work, the teachers’ lessons plan and reports ofthe instructions for lessons form the data base for the article. The analysis indicates thatone of the critical aspects in the process of implementation of the variation theory in theteachers’ practice was to identify the critical aspects in students’ learning. Another criticalaspect in the implementation of the variation theory was to open up dimensions ofvariation in the identified critical aspects of the students. By giving teachers the possibilityto develop the ability to identify critical aspects in students’ learning, dimensions ofvariation are opened up in these aspects, and by applying this knowledge in the dailyteaching, they have the possibility to improve students’ learning. The findings suggest thatdeveloping an understanding of the students’ critical aspects can be a productive basis inhelping teachers make fundamental changes in their instructions and improve students’learning.

  • 17.
    Olteanu, Lucian
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    A case study of proportional reasoning2012Ingår i: International Conference of the World Association of Lesson Studies, 28-30 November, 2012, 2012, s. 1-10Konferensbidrag (Refereegranskat)
  • 18.
    Olteanu, Lucian
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Proportioner och den gyllene regeln2012Ingår i: Matematikbiennalen,  26-27 Jan, 2012, Umeå, 2012Konferensbidrag (Övrigt vetenskapligt)
  • 19.
    Palmér, Hanna
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Assessment as a tool in the professional identity development of novice mathematics teachers.2012Ingår i: Proceedings of MADIF8: Evaluation and Comparison of Mathematical Achievement: Dimensions and Perspectives / [ed] Bergsten, C.; Jablonka, E. & Raman, M., Svensk förening för MatematikDidaktisk Forskning - SMDF, 2012, s. 161-170Konferensbidrag (Refereegranskat)
    Abstract [en]

    The empirical material and the results presented in this paper are taken from a study investigating novice primary school mathematics teachers’ professional identity development. This paper focuses on how the novice primary school mathematics teachers in the study use assessments as a tool in professional identity development. The respondents equate pupils’ results in assessments with understanding and learning and they use the assessments primarily as confirmation in identity development as mathematics teachers and not as material for planning lessons. In this paper, confirmation through assessment is illustrated by the case of Helena, one of the respondents in the study.  

  • 20.
    Palmér, Hanna
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    (In)consistent? The mathematics teaching of a novice primary school teacher.2012Ingår i: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 17, nr 3-4, s. 141-157Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 21.
    Palmér, Hanna
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Telling identities in self-recordings2012Ingår i: Proceedings of Norma 11: The sixth nordic conference on mathematics education in Reykjavik, May 11-14, 2011 / [ed] Gunnarsdottir, G.H.; Hreinsdottir, F.; Palsdottir, G.; Hannula, M.; Hannula-Sormunen, M.; Jablonka, E.; Jankvist, U.T.; Ryve, A.; Valero, P.; Wæge, K., University of Iceland Press, 2012, s. 493-502Konferensbidrag (Refereegranskat)
    Abstract [en]

    The focus of this paper is on self-recording, a method for collecting empirical data. The context for the method is a study of the professional identity development of novice primary school mathematics teachers as seen from the perspective of the teachers themselves. The background for using the method is based on theoretical and methodological issues as well as problems regarding data collection in this study. Self-recordings were tried as a complement to observations and interviews and contributed with data of original character, e.g. data regarding current happenings and data giving insights into day-to-day work from the perspective of the informants. In this paper, the theoretical and methodological starting points, the method as such and examples of the empirical outcome will be presented and discussed

  • 22.
    Palmér, Hanna
    et al.
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Ebbelind, Andreas
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Matematiklärande2012Ingår i: Förskoleklassens Didaktik: Möjligheter och Utmaningar / [ed] Katarina Herrlin, Elisabeth Frank, Helena Ackesjö, Stockholm: Natur och kultur, 2012, s. 134-184Kapitel i bok, del av antologi (Övrigt vetenskapligt)
  • 23.
    Peng, Aihui
    et al.
    Umea University.
    Nyroos, Mikaela
    Umea University.
    Values in effective mathematics lessons in Sweden: what do they tell us?2012Ingår i: The Montana Mathematics Enthusiast, ISSN 1551-3440, E-ISSN 1551-3440, Vol. 9, nr 3, s. 409-429Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This study aims to examine values in effective mathematics lessons in Sweden from the perspectives of students in different groups and their teachers. By using methods with lesson observations, student focus group interviews and teacher interviews, it shows that instructional explanation and classroom atmosphere with quietness are shared-values of students and their teachers. The findings propose some crucial issues which related to how mathematics teaching could be adjusted to different students’ learning conditions and whether it needs more instructional explanation in mathematics teaching in Sweden.

  • 24.
    Perez, Miguel
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Mathematical Knowledge Requirements for Learning Activity Design Supported by ICT2012Ingår i: Proceedings of MADIF8, 2012Konferensbidrag (Refereegranskat)
  • 25.
    Perez, Miguel
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Scaffolding Teachers’ Construction of A Learning Trajectory for Mathematics Supported by ICT2012Ingår i: Doctoral Student Consortia Proceedings of the20th International Conference on Computers in Education ICCE 2012 / [ed] Weiqin Chen, Hiroaki Ogata, Chen-Chung Liu, Gautam Biswas, Lung-Hsiang Wong, Tsukasa Hirashima, Wenli Chen, Asia-Pacific Society for Computers in Education, 2012, , s. 4s. 21-24Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper, we present preliminary results related to a developmental project where we explore how technology can be used to improve teachers’ teaching practices and their students’ learning of mathematics. We have adopted a teacher-centered, collaborative approach that challenges the participating researcher to develop strategies for finding different forms of scaffolding to support the teachers’ participation in this project. So far, we have used the software GeoGebra to provide competence development for the teachers in terms of mathematical representations. This software will also have a central role when investigating how the teachers perceive and make use of different affordances provided by technologies when addressing a specific learning goal related to the teaching of algebra at a lower secondary school.

  • 26.
    Perez, Miguel
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Theoretical underpinnings for a co-design process for the learning of mathematics2012Konferensbidrag (Refereegranskat)
  • 27.
    Sollervall, Håkan
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Affordances and their mediating artifacts as instruments for the collaborative design of innovative mathematical learning activities2012Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    The unfolding of an affordance, as an opportunity for action, during a learningactivity requires the learner to interact with mediating artifacts. The design of alearning activity involves appropriating affordances and embedding them in theactivity in such a manner that the learner is invited to unfold the affordances,through interaction with their mediating artifacts in accordance with pre-definedhypothetical learning trajectories. In this paper, the notion of affordances is usedexplicitly in the discussion of two previous research efforts. We argue that thenotion of affordances, which was tacitly used in these efforts and aligns well withthe methodology of scenario-based design, may be used as an instrument for thecollaborative design of innovative mathematical learning activities.

  • 28.
    Sollervall, Håkan
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM. Halmstad University, Sweden.
    Collaborative mathematical inquiry with augmented reality2012Ingår i: Research and Practice of Technology Enhanced Learning, ISSN 1793-2068, Vol. 7, nr 3, s. 153-173Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we describe and reflect on the design of a mathematical learning activity developed incollaboration between teachers, researchers and technical developers. By making use of augmentedreality (AR) as a technology supporting augmentation of a real-world projection with computergene-rated images, we have designed an activity that promotes unique action and learningtrajectories. These trajectories require the learners to engage in interactive-constructive actions thatinvolve and stimulate the development of their self-regulatory skills by inviting them to vary andcoordinate across the contextual affordances of the technologies and the physical resources in theclassroom. Our learning activity is designed as a collaborative guided inquiry, implemented in aregular classroom and involved mathematical problem solving in relation to the geometric conceptof scale. In order to successfully complete the activity, the learners are challenged to coordinateaffordances from three distinct referential contexts by involving physical and virtual artifacts. In thedesign process, we identify critical aspects of the activity and embed affordances for correspondingscaffolding actions which turn out to play a crucial role when the activity is implemented with agroup of four 15-year-old students. Although the AR technology has served us well in developingthis particular activity, this specific technology appears to have limited applicability in mathematicseducation beyond geometry. We recommend that future research efforts move beyond AR andconsider the broader context of embodied design with tangible user interfaces, that have recentlyshown great potential for the design of innovative activities for the learning of mathematics.

  • 29.
    Sollervall, Håkan
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    From Euclid to GPS: designing an innovative spatial coordination activity with mobile technologies2012Ingår i: Proceedings of th 36th Conference of the International Group for the Psychology of Mathematics Education: Opportunities to Learn in Mathematics Education / [ed] Tai-Yih Tso, 2012, s. 4:107-4:114Konferensbidrag (Refereegranskat)
    Abstract [en]

    Guided by the notion of design research we develop a learning activity for 12 year old students, who are asked to coordinate themselves physically in terms of distances with respect to two given points in an outdoor setting. The outdoor activity, as well as its continuation into the mathematics classroom, involves mobile software applica-tions specifically developed to support this activity. In this paper, we argue that the design of innovative learning activities is enhanced by the coordination of expertise and knowledge from several research domains, whose collaboration is facilitated by using affordances for representation and communication as design instruments. We present a case where ancient Greek mathematics, modern psychology and techno-logical affordances guide the design of an innovative spatial coordination activity.

  • 30.
    Sollervall, Håkan
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Nurturing self-regulating learners by guided mathematical inquiry in a TEL environment2012Ingår i: Proceedings of the 20th International Conference on Computer Education ICCE 2012 / [ed] Gautam, Biswas, Lung-Hsiang Wong, Tsukasa Hirashima, Wenli Chen, 2012, s. 423-425Konferensbidrag (Refereegranskat)
    Abstract [en]

    We design and evaluate a curriculum-based mathematical learning activity involvingsecondary students’ geometrical constructions, mathematical modeling and algebraicvalidation of hypotheses based on hands-on explorations with the interactive geometryapplication GeoGebra available on individual laptops. We argue that guided inquiries in atechnology-enhanced learning environment that invites blending of interactive technologiesand traditional resources may be an efficient means for developing self-regulatory skills.

  • 31.
    Sollervall, Håkan
    et al.
    Högskolan i Halmstad, Sektionen för lärarutbildning (LUT), Forskning om utbildning och lärande inom lärarutbildningen (FULL).
    Milrad, Marcelo
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Theoretical and methodological considerations regarding the design of innovative mathematical learning activities with mobile technologies2012Ingår i: International Journal of Mobile Learning and Organisation, ISSN 1746-725X, E-ISSN 1746-7268, Vol. 6, nr 2, s. 172-187Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The design of innovative learning activities supported by mobile technologies calls for the coordination of theories and methodologies from several research domains. The authors of this paper have been engaged in several collaborative research efforts involving expertise in mathematics education and technology–enhanced learning as well as in–service mathematics teachers. Within the methodological framework of design research, we coordinate and make use of specific theoretical and methodological constructs in order to stimulate the collaborative creation of innovative trajectories for the learning of mathematics. We illustrate this design approach by accounting for a specific activity designed to support a learning progression over time and across contexts, aiming at enacting the learning of geometry in an outdoors context. The outcomes of these efforts have provided us with valuable insights into how collaborative design research and mobile technologies can be used in school contexts to guide and support novel ways to enact mathematical learning.

  • 32.
    Sollervall, Håkan
    et al.
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Otero, Nuno
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Milrad, Marcelo
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Johansson, David
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Vogel, Bahtijar
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Outdoor activities for the learning of mathematics: Designing with mobile technologies for transitions across learning contexts2012Ingår i: Proceedings 2012 Seventh IEEE International Conference on Wireless, Mobile and Ubiquitous Technology in Education (WMUTE 2012), Takamatsu, Kagawa, Japan: IEEE, 2012, s. 33-40Konferensbidrag (Refereegranskat)
    Abstract [en]

    Guided by design-based research and the notion of seamless learning, we have designed a learning activity in mathematics where mobile and web technologies support transitions between outdoor and indoor learning contexts. The students' initiatives during the self-regulated outdoor part of the activity are scaffolded by the use of mobile technologies and activity prompts which provide means and demands for on-the-spot oral and visual recordings of the groups' experiences and strategies. We argue that the high quality of mathematical content in the recordings is due to several contributing factors: the choice of appropriate technological support, the informal settings, the availability of relevant physical references, and the immediate recording based on fresh experiences. Our data suggests that the rich nature of the recordings contributes to the effective transition and communication of the outdoor experiences to the classroom's learning context where these experiences are shared and discussed with peers. Finally, we discuss design issues related to the role of the teacher, as well as the structure of the entire activity and the implications for future design iterations.

  • 33.
    Sollervall, Håkan
    et al.
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Stadler, Erika
    Stockholm University.
    Instruments for improving teachers' use of artefacts for the learning of mathematics2012Konferensbidrag (Refereegranskat)
  • 34. Wee, Seah
    et al.
    Peng, Aihui
    Southwest University, Chongqing, People’s Republic of China.
    What students outside Asia value in effective mathematics lessons: a scoping study2012Ingår i: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704, Vol. 44, s. 71-82Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This article reports on a scoping study conducted in Australia and Sweden to facilitate the understanding of the values that are associated with effective learning of mathematics in Asian classrooms. Nineteen ‘Western’ values have been identified, of which three (explanation, sharing and fun) were commonly embraced in the two countries. It is also evident that traits that are valued can be and are demonstrated in different forms. The implications for improving mathematics education through the harnessing of values are discussed. The distinction made between what is valued and the forms the value can take should empower classroom teachers to incorporate values flexibly in different classroom contexts.

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