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  • 1.
    Kilhamn, Cecilia
    et al.
    Göteborgs universitet.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics Education.
    Olika sätt att lösa ekvationer2013Other (Other academic)
  • 2.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    An iterative mapping strategy for improved teaching and learning of mathematics2011In: The World Association of Lesson Studies 2011, 2011Conference paper (Other academic)
  • 3.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Olteanu, Lucian
    Changing teaching practice and students’ learning of mathematics2010In: Education Inquiry, E-ISSN 2000-4508, Vol. 1, no 4, p. 381-397Article in journal (Refereed)
    Abstract [en]

    This article forms part of a larger study aimed at supporting teachers in understanding their practiceand improving it. Students’ tests, an examination of students’ mathematical work, teachers’ lessons plans and reports of the lessons’ instructions are the base data for this article. The analysis indicated that the teachers were unable to describe the critical aspects in students’ learning at the beginning of the project. By giving teachers the training that allows them to become theorising teachers, they also obtain the possibility, as professional decision-makers, to develop the ability to identify the critical aspects of students’ learning and consider how opportunities for learning can be enhanced. The findings suggest that developing an understanding of students’ critical aspects can be a productive basis for helping teachers to make fundamental changes in their instructions and to improve mathematical communication in the classroom.

  • 4.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Connections promote sense-making and reasoning in algebra: A qualitative study of tasks assemblage among elementary school students.2021In: Revisiting Lesson and Learning Studies: Accessibility, Quality, and Sustainability, World Association of Lesson Studies, Macau and Hong Kong, 2021Conference paper (Refereed)
  • 5.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Difference and repetition: instructional examples2018In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education / [ed] Umeå Universitet, 2018Conference paper (Refereed)
  • 6.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics, Department of Mathematics Education.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics, Department of Mathematics Education.
    Enhancing mathematics communication using critical aspects and dimensions of variation2013In: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 44, no 4, p. 513-522Article in journal (Refereed)
    Abstract [en]

    This article deals with two prominent topics in the field of mathematics education: the communication in mathematics and its teaching and learning and the continuous professional development of mathematics teachers. In this article, a framework is proposed for analysing the effectiveness of communication in mathematics classrooms. The presentation is based on data collected, during a 3-year period, while different objects of learning is presented in nine classes, and it includes 22 teachers and 884 students. Among other things, the data consist of the students’ tests, the teachers’ lessons plan and reports of the lessons’ instructions. 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 real critical aspects in student learning as its starting point. Also, the results show that teachers develop new strategies to present the contents by having the focus to open up dimensions of variation.

  • 7.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Equations, functions, critical aspects and mathematical communication2012In: International Education Studies, ISSN 1913-9020, E-ISSN 1913-9039, Vol. 5, no 5, p. 69-78Article in journal (Refereed)
    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.

  • 8.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Examples in mathematics: Difference and repetition2019In: Proceedings of the 43rd Conference of the International Groupfor the Psychology of Mathematics Education: Pretoria, South Africa, 7 – 12 July 2019 / [ed] Mellony Graven, Hamsa Venkat, Anthony A Essien, Pamela Vale, IGPME , 2019, Vol. 3, p. 169-176Conference paper (Refereed)
    Abstract [en]

    The availability of instructional examples in the mathematics classroom challenges theway teachers confront students with several aspects of the content, which cancontribute to designating the generality of mathematical concepts. Using the theory ofvariation and Deleuze’s philosophical concepts as the main interpretative framework,this study investigates what is involved in repetition and the nature of its interiority,what we understand by conceptual difference and difference without concept in adevelopment study. The data consisted of 36 teachers’ lesson plans. Qualitativeanalysis of these data led to the identification of events types and the characteristics ofrepetition.

  • 9.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Improvement of effective communication: the case of subtraction2012In: International Journal of Science and Mathematics Education, ISSN 1571-0068, E-ISSN 1573-1774, Vol. 10, no 4, p. 803-826Article in journal (Refereed)
    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.

  • 10.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Investigating Difference and Repetition in Mathematics Teachers’ Professional Development2018In: Philosophy of Mathematics Education Journal, ISSN 1465-2978, Vol. 33, p. 1-11Article in journal (Refereed)
  • 11.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Kommunicera med entydiga instruktioner2018Other (Other academic)
  • 12.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics. Linnaeus University, Linnaeus Knowledge Environments, Education in Change.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics. Linnaeus University, Linnaeus Knowledge Environments, Education in Change.
    Kommunicera med entydiga instruktioner: Programmering i grundsärskolan, åk 1-32020Other (Other academic)
  • 13.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics. Linnaeus University, Linnaeus Knowledge Environments, Education in Change.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics. Linnaeus University, Linnaeus Knowledge Environments, Education in Change.
    Kommunicera med entydiga instruktioner: Programmering i grundsärskolan, åk 4-62020Other (Other academic)
  • 14.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Kommunikation i olika programmeringsmiljöer2018Other (Other academic)
  • 15.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics. Linnaeus University, Linnaeus Knowledge Environments, Education in Change.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics. Linnaeus University, Linnaeus Knowledge Environments, Education in Change.
    Kommunikation i programmering: Programmering i grundsärskolan, åk 7-92020Other (Other academic)
  • 16.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Kommunikation i visuella programmeringsmiljöer2018Other (Other academic)
    Abstract [sv]

    Ingår i Lärportalen för matematik, Grundskolan årskurs 4-6 ; Modul: Algebra ; Del 7 : Kommunikation och programmering i algebraklassrummet

  • 17.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics, Department of Mathematics Education.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics, Department of Mathematics Education.
    Mathematics communication and critical aspects2015In: 39th Meeting of the International Group for the Psychology of Mathematics Education (PME39), Tasmania, Australia, 2015, Vol. 3, p. 329-336Conference paper (Refereed)
  • 18.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics Education.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics Education.
    Planering och genomförande av undervisningen (åk 1-3)2013Other (Other academic)
  • 19.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics Education.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics Education.
    Planering och genomförande av undervisningen (åk 4-6)2013Other (Other academic)
  • 20.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics Education.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics Education.
    Planering och genomförande av undervisningen (åk 7-9)2013Other (Other academic)
  • 21.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Pre-Service Teachers’ Reasoning and Sense-Making of Growing Patterns2023In: Proceedings of The 6th World Conference on Research in Education, 2023, Diamond Scientific Publishing , 2023Conference paper (Refereed)
    Abstract [en]

    In this study, we aimed to present the features of pre-service teachers’ reasoning and sense making in the process of exploring growing patterns tasks. Participants were 79 pre-service primary teachers in Sweden. The analysis was grounded in the concept of critical aspects from variation theory and the concepts of assemblage, lines of flight, segmentarity, and rupture from a post-structuralist philosophical perspective. Results indicate that the concepts of assemblage, line of flight, rupture, and segmentarity can be useful tools for analyzing analysing reasoning and sense making in mathematics. The results also show that in mathematics, the line of flight can be seen in moments of creativity and innovation. Furthermore, the results show that rupture can be seen in the connection of concepts or ideas that challenge established mathematical structures and ways of thinking. Further, the results shows that segmentarity creates disciplinary boundaries and inhibits reasoning and sense making. Therefore, it is important to recognize and break down these boundaries to facilitate more creative and innovative reasoning and sense making in mathematics.

  • 22.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Programmering: centrala begrepp2018Other (Other academic)
  • 23.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Programmering för matematiklärare: hållbart för eleverna, lärarna, samhället och framtiden2020In: Matematikbiennalen- Hållbar matematikundervisning - hållbart för eleverna, lärarna, samhället och framtiden, 16-17 januari, Växjö, Växjö: Linnéuniversitetet , 2020Conference paper (Other academic)
  • 24.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Programmering för matematiklärare: Årskurs 1-62019 (ed. 1)Book (Other academic)
    Abstract [en]

    Att kunna förstå och använda programmering är en betydelse
full kompetens i dagens samhälle. Programmering finns numera med i skolans läroplaner och syftet är att ge elever grundläggande kunskaper i hur de kan lösa problem med hjälp av programmering.Denna bok vänder sig i första hand till matematiklärare i årskurs 1–6 och täcker in den programmering som finns definierad i kursplanen.

    Lärare behöver känna till vad, hur, varför och när man kan sammanväva matematiken med programmering för att kunna möta och utveckla elevens tankar, idéer och resonemang. Boken utgår från metodisk variation i syfte att utforma undervisningen i matematik med programmering och tvärtom.

    Programmering för matematiklärare presenteras en mängd konkreta exempel och förslag på aktiviteter, som visar på hur man kan arbeta med programmering i matematik i den visuella programmeringsmiljön Scratch.

    Boken vänder sig till lärarutbildare, verksamma lärare,lärarstuderande och övriga med intresse för att utveckla program
meringen i grundskolans årskurser F–6.

  • 25.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Programmering och programmeringsprocessen2018Other (Other academic)
  • 26.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics. Linnaeus University, Linnaeus Knowledge Environments, Education in Change.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics. Linnaeus University, Linnaeus Knowledge Environments, Education in Change.
    Programmering som språk: Programmering i grundsärskolan, åk 1-32020Other (Other academic)
  • 27.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics. Linnaeus University, Linnaeus Knowledge Environments, Education in Change.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics. Linnaeus University, Linnaeus Knowledge Environments, Education in Change.
    Programmering som språk: Programmering i grundsärskolan, åk 4-62020Other (Other academic)
  • 28.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics. Linnaeus University, Linnaeus Knowledge Environments, Education in Change.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics. Linnaeus University, Linnaeus Knowledge Environments, Education in Change.
    Programmering som språk: Programmering i grundsärskolan, åk 7-92020Other (Other academic)
  • 29.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Programmering som språk2018Other (Other academic)
  • 30.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics. Linnaeus University, Linnaeus Knowledge Environments, Education in Change.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics. Linnaeus University, Linnaeus Knowledge Environments, Education in Change.
    Rational Expressions and Critical Aspects2021In: ICMSE 2021 : International Conference on Mathematics, Science, and Education, Cancun, Mexico, april 5-6, World Academy of Science, Engineering and Technology , 2021Conference paper (Refereed)
  • 31.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Sense making and reasoning in algebra2022In: Proceedings of the 45th Conference of the International Groupfor the Psychology of Mathematics Education: Alicante, Spain, July 18 – 23, 2022 / [ed] Ceneida Fernández, Salvador Llinares, Ángel Gutiérrez, Núria Planas, Alicante: Universidad de Alicante, 2022, Vol. 4, p. 270-Conference paper (Refereed)
    Abstract [en]

    Researchers note that algebraic reasoning and sense making is essential for buildingconceptual knowledge in school mathematics. Consequently, pre-service teachers’own reasoning and sense making are useful in fostering and developing students’algebraic reasoning and sense making. We report here the features of pre-serviceteachers’ reasoning and sense making in algebra, specifically in the process ofanalysing problem posing, with a focus on first-degree equations. The followingresearch questions served as a guide in the analysis of data: What are the characteristicsof the problem-posing tasks used for reasoning and sense making of first-degreeequations? What are the characteristics of pre-service teachers’ reasoning and sensemaking in problem-posing tasks?This study is part of ongoing research carried out with pre-service teachers enrolled inthe abovementioned mathematics teacher education course. All the pre-serviceteachers were older than 19, from diverse socio-economic backgrounds and attendedclass for all 10 weeks of the semester, including the seven weeks in which data wascollected. Sixty-six pre-service primary teachers participated in an anonymous writtenexam and were informed about our research (characteristics, aim, confidentialityissues, etc.). The data analysis adopted a qualitative/interpretative approach, and theunit of analysis has three dimensions: reasoning, sense making and critical aspects.According to Olteanu (2020), reasoning and sense making are closely related to eachother and to these dimensions in the manner of a ‘rhizome’ (Deleuze & Guattari, 1987).Results revealed that the pre-service teachers create a rhizomatic reasoning and sensemaking that is characterized by lines of rupture. Those lines interconnect and arise fromincorrect translations of rhizomatic problem-posing task (RPPT) into mathematicalnotations and the failure to discern the difference between variables and variables asunknown numbers; i.e., between algebraic expression and equation. The characteristicsof reasoning in RPPT and of pre-service teachers are selecting, exploring,reconfiguring, encoding, abstracting, and connecting to highlight associations andrelationships between different content, and the characteristics of sense making arerecognition, relationships, profiling, comparing, laddering, and verifying.  

  • 32.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Similarity as a dimension of variation and its importance for students learning2011In: Nordic Conference on Mathematics Education (NORMA11), Iceland, 2011, p. 1-10Conference paper (Refereed)
  • 33.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Olteanu, Lucian
    Subtraction: the improvement of communication through critical aspects2010In: Proceedings of The 14th World Multi-Conference on Systemics, Cybernetics and Informatics: WMSCI 2010., 2010, Vol. 4, p. 90-95Conference paper (Refereed)
    Abstract [en]

    The research study, this article is based on, aims to develop principles to enable the transfer of research knowledge to teaching. In this article are presented the design and implementations of a research project intended to support teachers in understanding their practice and improve it. Furthermore, the central idea was to improve the communication in mathematics between teachers and teachers-students. Issues that arose from practice were framed in terms of learning. In addition, the variation theory formed the background to our work. The students’ tests, examination of students’ mathematical work, the teachers’ lessons plan and reports of the lessons’ instructions are the data base for this article. The analysis indicated that teachers were not able to describe the critical aspects in students’ learning in the beginning of the project. By giving teachers the training that allows them to become reflective teachers, they also get the possibility, as professional decision makers, to develop the ability to identify the critical aspects in students’ learning and consider how opportunities for learning can be enhanced. Furthermore, if the teachers base their instructions on the identified critical aspects and open up dimensions of variation in these aspects, the students’ learning seems to be facilitated. The findings suggest that developing an understanding of the students’ critical aspects can be a productive basis in helping teachers to make a fundamental change in their instructions and to improve the mathematical communication in the classroom.

  • 34.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics. Linnaeus University, Linnaeus Knowledge Environments, Education in Change.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics. Linnaeus University, Linnaeus Knowledge Environments, Education in Change.
    Tasks assemblage, sense-making, and reasoning in algebra: Creating Lesson Study in Sustaining Community and Providing Quality Education2022In: International Conference of the World Association of Lesson Studies, Universiti Kebangsaan, Malaysia, 2022Conference paper (Refereed)
  • 35.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    The design and implementations of a research project intended to support teachers in understanding their practice and improve it2010In: The World Association of Lesson Studies 2010, 2010Conference paper (Other academic)
  • 36.
    Olteanu, Constanta
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Variation and algebra2017In: Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education (PME41) / [ed] Kaur, B., Ho, W.K., Toh, T.L., & Choy, B.H., Singapore: IGPME - The International group of the Psychology of Mathematics Education , 2017, Vol. 3, p. 337-344Conference paper (Refereed)
    Abstract [en]

    The aim of this article is to contribute to understanding the relationship between teaching and learning algebra at school in order to identify how schools can be supported to improve students’ learning outcomes. The students’ tests and examinations of their mathematical work and the teachers’ lessons plan and reports on the lessons’ instructions were the base data for this article. The analysis indicated that, if the teachers base their instructions on the critical aspects identified in students’ learning and open up patterns of variation in these aspects, they seem to facilitate students’ learning. The findings suggest that helping teachers develop an understanding of the students’ critical aspects can be a productive basis for helping them to make fundamental changes to their instructions and to improve their mathematical communication in the classroom.

  • 37.
    Olteanu, Lucian
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    A case study of proportional reasoning2012In: International Conference of the World Association of Lesson Studies, 28-30 November, 2012, 2012, p. 1-10Conference paper (Refereed)
  • 38.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics Education.
    Annulleringsmetoden (åk 7-9)2013Other (Other academic)
  • 39.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Construction of tasks and classroom communication in mathematics2015In: Focused learning in mathematics (FLM1), August 13-15, 2015, Växjö, 2015Conference paper (Other academic)
  • 40.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics, Department of Mathematics Education.
    Construction of tasks in order to develop and promote classroom communication in mathematics2015In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 46, no 2, p. 250-263Article in journal (Refereed)
    Abstract [en]

    In this article, the focus is on task construction and the importance of this process to develop and promote classroom communication in mathematics. The students’ tests, examination of students’ mathematical work, the teachers’ lesson plans, and reports of the lessons’ instructions are the basic data for this article. The analysis indicated that teachers develop their professional decision-makers through developing the ability to construct relevant tasks for identifying the critical aspects in students’ learning. The findings suggest that construction of tasks can be a productive basis in helping teachers to make fundamental changes in their understanding of what they should focus on in a teaching situation to improve mathematical communication. In this process, the teachers integrate, in a natural way, the research results from mathematics education.

  • 41.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Critical aspects and rational expressions2018In: International Congress of Mathematicians (ICM 2018), 1-9 August, 2018, Rio de Janeiro, Brazil, 2018Conference paper (Refereed)
  • 42. Olteanu, Lucian
    Den gyllene regeln2009In: SMaL, 2009Conference paper (Other (popular science, discussion, etc.))
  • 43.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics Education.
    Designing mathematical tasks to improve the communication in the classroom2015In: World Association of Lesson Studies (WALS) International Conference: Lesson study for improvement of classroom quality, Khon Kaen University , 2015, p. 69-69Conference paper (Refereed)
  • 44.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Distributive law as object of learning through direct and inverse tasks2017In: International Journal for Lesson and Learning Studies, ISSN 2046-8253, E-ISSN 2046-8261, Vol. 6, no 1, p. 56-65Article in journal (Refereed)
    Abstract [en]

    Purpose – Problem solving is a skill in mathematics which although always relevant has heightened priority due to the changes in the new mathematics GCSE (Department for Education, 2013). It has previously been a skill which is deemed underdeveloped within mathematics and therefore is a theme which teachers are seeking to improve and nurture in order to align with the new changes. The GCSE is the formal qualification that students take at the end of Key Stage 4 (KS4) in the UK. The paper aims to discuss these issues.

    Design/methodology/approach – The focus of the enquiry was to explore, using lesson studies, the differences in students’ approaches to problem solving. Consequently, key themes relating to the mediation of gender, ability, and academic motivation surfaced. Considering these themes, the paper subsequently reflects upon pedagogical practices which might effectively develop students’ ability to problem solve. The study took part in a mixed gender comprehensive secondary school with students taking part in the observation lesson ranging in age from 11 to 12 years old. The authors are the teachers who took part in the lesson study. The teachers implemented observation techniques in the form of video and peer observation with the accompanying teacher. In addition, students provided feedback on how they approached the problem-solving tasks through a form of semi-structured interviews, conducted via the use of video diaries where no teachers were present to prevent power bias. Following this, a thematic analysis of both the observations and student video diaries generated conclusions regarding how said key themes shaped the students’ approaches to problem solving.

    Findings – Students’ frustration and competitive need to find a specific answer inhibited their ability to thoroughly explore the problem posed thus overseeing vital aspects needed to solve the problem set. Many students expressed a passion for problem solving due to its freedom and un-rigid nature, which is something teachers should nurture.

    Originality/value – Generally, teachers are led by a culture in which attainment is the key. However, an atmosphere should be developed where the answer is not the key and students can explore the vibrant diversity mathematics and problem solving can offer.

  • 45.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics Education.
    Effective communication and test construction: 2013In: WALS,The World Association of Lesson Studies International Conference 2013, Lesson and Learning Study as Teacher Research: 5-9 September 2013: Conference Programme & Abstracts of Papers, 2013, p. 120-121Conference paper (Refereed)
  • 46.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics, Department of Mathematics Education.
    Effective communication, critical aspects and compositionality in algebra2014In: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 45, no 7, p. 1021-1033Article in journal (Refereed)
    Abstract [en]

    This paper contains a discussion of how the concept of critical aspects and the principle of compositionality can provide a powerful tool to analyse and understand the communications that occur in the classroom. It is grounded in data collected in a longitudinal study. The content chosen is algebra. It is argued that the critical aspects and the principle of compositionality should be considered as a methodological principle that describe how communication in the classroom should be designed. Here, I present the power of using variation theory whose main purpose is to generate an understanding of critical aspects and compositionality in practice.

  • 47.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics Education.
    Ekvationslösningsresonemang (åk 7-9)2013Other (Other academic)
  • 48.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics Education.
    First-degree equations: critical aspects and the principle of compositionality2014In: World Association of Lesson Studies (WALS), Becomming Reflective Educators and Professionals of Learning, 25-28 November, 2014, Bandung, 2014, p. -8Conference paper (Other academic)
  • 49. Olteanu, Lucian
    Framgångsrik kommunikation i matematikklassrummet2016Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The research for this thesis was done to examine, describe and understand the ways in which mathematical content (algebra) is communicated in classrooms. It also sought to identify the opportunities that allow successful classroom communication.

    The educational design research approach in this study was used to understand the connection between teaching, communication and students' learning. The empirical material consisted of video-recorded lessons, observations, students’ tests and teachers’ written reports of the instructions for lessons. The empirical material was analysed using concepts relating to variation theory, strong compositionality and research results found in mathematics education.

    Some important findings have been found in this thesis. Communicative success is linked to a hierarchic structure of communicative events with a strong compositionality. It is also linked to the discernment of the structure of algebraic objects. This structure is a relation between para- and proto-mathematical concepts and a form of composition with a semantic character. Teachers support successful classroom communication by using research results found in mathematics education to open up patterns of variation in the critical aspects of an object of learning. Similarity is a pattern identified in this study, and it is defined as the property of two or more expressions to adapt the same meaning. Teachers also support successful classroom communication through a systematic analysis of the parts of an object of learning, relations between parts, how to relate the parts to each other in different ways, the relation between the parts, the relation between the parts and the whole as well as the relation between different wholes. Through and around tasks, teachers and students are communicating successfully or not according to the opportunities provided in the classroom to work out the meaning of the whole by understanding the meaning of the simple parts, the semantic significance of a finite number of syntactic modes of composition, and by recognizing how the whole is made up out of simple parts. If the choice/construction of tasks is focused on what may vary and what stays invariant, students' opportunities to distinguish aspects that could lead to algebraic generalizations are improved. One of the values of this study is in the design of the project that contributes to integration of research results found in mathematics education, in teachers' practice. In addition, a value of the study lies in its operational definition of the concept of communication, which can be used to study successful communication. Communication is a collectively performed patterned activity in which an aspect that is critical for one or more students (A) is focused on by the action of the teacher or other students (B) so that A discerns the aspects focused on by B.

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  • 50.
    Olteanu, Lucian
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Framgångsrik kommunikation i matematikklassrummet.: Lärarutbildare i matematik, LUMA 20172017In: Lärarutbildare i matematik, LUMA, 2017Conference paper (Other academic)
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