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Olteanu, Constanta
Publications (10 of 108) Show all publications
Olteanu, C. & Olteanu, L. (2019). Examples in mathematics: Difference and repetition. In: Mellony Graven, Hamsa Venkat, Anthony A Essien, Pamela Vale (Ed.), Proceedings of the 43rd Conference of the International Groupfor the Psychology of Mathematics Education: Pretoria, South Africa, 7 – 12 July 2019. Paper presented at The 43rd Conference of the International Group for the Psychology of Mathematics Education - Improving access to the power of mathematics, Pretoria, South Africa, 7 – 12 July 2019 (pp. 169-176). IGPME, 3
Open this publication in new window or tab >>Examples in mathematics: Difference and repetition
2019 (English)In: 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, Published 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.

Place, publisher, year, edition, pages
IGPME, 2019
Series
Proceedings of the International Groups for the Psychology of Mathematics Education, ISSN 0771-100X
Keywords
variation theory, examples, mathematics, difference, repetition
National Category
Didactics
Research subject
Mathematics, Mathematical Education
Identifiers
urn:nbn:se:lnu:diva-86247 (URN)978-0-6398215-4-2 (ISBN)978-0-6398215-5-9 (ISBN)
Conference
The 43rd Conference of the International Group for the Psychology of Mathematics Education - Improving access to the power of mathematics, Pretoria, South Africa, 7 – 12 July 2019
Available from: 2019-07-08 Created: 2019-07-08 Last updated: 2019-08-30Bibliographically approved
Olteanu, C. & Olteanu, L. (2019). Programmering för matematiklärare: Årskurs 1-6 (1ed.). Malmö: Studentlitteratur AB
Open this publication in new window or tab >>Programmering för matematiklärare: Årskurs 1-6
2019 (Swedish)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.

Place, publisher, year, edition, pages
Malmö: Studentlitteratur AB, 2019. p. 128 Edition: 1
National Category
Didactics
Research subject
Mathematics, Mathematical Education
Identifiers
urn:nbn:se:lnu:diva-82281 (URN)9789144127125 (ISBN)
Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-05-06Bibliographically approved
Olteanu, L., Karlsson, N. & Olteanu, C. (2019). Programming and angles: patterns of variation. In: Mellony Graven, Hamsa Venkat, Anthony A Essien, Pamela Vale (Ed.), Proceedings of the 43rd Conference of the International Groupfor the Psychology of Mathematics Education: Pretoria, South Africa, 7 – 12 July 2019. Paper presented at Proceeding of the 43rd Conference of the International Group for the Psychology of Mathematics Education - Improving access to the power of mathematics, Pretoria, South Africa, 7 – 12 July 2019 (pp. 81-81). , 4
Open this publication in new window or tab >>Programming and angles: patterns of variation
2019 (English)In: 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, 2019, Vol. 4, p. 81-81Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

In several countries including Sweden programming is introduced to secondary students mainly as a part of the mathematics curriculum. “Scratch” is used as a tool inprogramming and this has become a common trend in many countries. However, teaching mathematics using “Scratch” is not appropriate for in-service teachers.

Several research findings show that angle, as a mathematical concept, is difficult to teach and learn (Mitchelmore & White, 2004). We conducted a study in which researchers worked with 32 in-service mathematics teachers in grades 7-9. Because angles are essential characteristics of two- and three-dimensional geometrical objects,the aim of this study was to give in-service teachers the opportunity to improve their experience of using “Scratch” in order to enhance students understanding of angles. Observation, tasks used, video samples and field notes were used as data collecting tools.

The data gathered were analysed in a qualitative way using concepts of the variation theory (Marton, 2015). The variation theory was also used to focus teachers’ attentionon aspects that were possible to discern by using “Scratch”. Angle is a geometric concept but it possesses properties that can be found in various other contexts. The variation theory of learning stems from the concept of phenomenography (e. g.,Marton, 2015). It emphasizes variation as a necessary condition for learners to be ableto discern new aspects of a subject of study.

Based on a preliminary analysis, we could discern three concepts of angle: (1) angle asa movement (in rotation or sweep), (2) angle as a geometric shape (a partitioning of space by two intersecting beams), and (3) angle as a unit for measure. There appears to be an alignment between in-service teachers using “Scratch” and their instructional practices that will be discussed in this presentation in detail. The use of patterns of variation in programming will also be presented.

Series
Proceedings of the International Groups for the Psychology of Mathematics Education, ISSN 0771-100X
Keywords
programming, angles, variation theory, patterns of variation
National Category
Didactics
Research subject
Mathematics, Mathematical Education
Identifiers
urn:nbn:se:lnu:diva-86248 (URN)978-0-6398215-6-6 (ISBN)978-0-6398215-7-3 (ISBN)
Conference
Proceeding of the 43rd Conference of the International Group for the Psychology of Mathematics Education - Improving access to the power of mathematics, Pretoria, South Africa, 7 – 12 July 2019
Available from: 2019-07-08 Created: 2019-07-08 Last updated: 2019-08-30Bibliographically approved
Karlsson, N., Kilborn, W. & Olteanu, C. (2019). Teachers and student-teachers' challenges with addition and multiplication strategy problems. In: Mellony Graven, Hamsa Venkat, Anthony A Essien, Pamela Vale (Ed.), Proceedings of the 43rd Conference of the International Groupfor the Psychology of Mathematics Education: Pretoria, South Africa, 7 – 12 July 2019. Paper presented at The 43rd Conference of the International Group for the Psychology of Mathematics Education - Improving access to the power of mathematics, Pretoria, South Africa 7 – 12 July 2019 (pp. 53-53). IGPME, 4
Open this publication in new window or tab >>Teachers and student-teachers' challenges with addition and multiplication strategy problems
2019 (English)In: 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. 4, p. 53-53Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

The Swedish National Agency for Education emphasizes that students in grades 1-3 should be able to develop addition and multiplication strategies based on the properties of these operations before focusing on standard algorithms. This means that teachers need to understand student perceptions of these concepts in order to be able to develop instructions for promoting such strategies. According to Ball, Thames and Phelps (2008) teachers need mathematical knowledge to be able to meet such a demand. Other researchers recommend carrying out qualitative studies investigating a field experience of pre-service and in-service teachers. Since the in-service teachers’ knowledge depends on what they were taught in school themselves, we studied the teaching process in grade 3 in order to learn how they were initially introduced to addition and multiplication (Van Dooren, De Bock, & Verschaffel, 2010).

The teaching process and teachers’ understanding of problems with multiplication content was studied in 3rd grade mathematics classrooms. This study investigated challenges faced by teachers when they went from interpretation to formulation of the multiplication problems. Data is drawn from three main sources: observation, interviews, field notes and video recordings. The data was analysed in a qualitative way, using variation theory (Marton, 2015). The analysis reveals that the participating teachers were more successful in using addition strategies than multiplication ones in problem development. For example, most teachers identified multiplication as a repeated addition. Consequently, they often missed important multiplication structures and their link to division. The results explain some reasons for difficulties in elementary mathematics experienced by in-service teachers and the consequences they lead to in their teaching. Teachers' understanding of mathematical concepts is crucial for their interpretation and setting of the example problems.

Place, publisher, year, edition, pages
IGPME, 2019
Series
Proceedings of the International Groups for the Psychology of Mathematics Education, ISSN 0771-100X
Keywords
mathematical knowledge, multiplikation, addition, variation theory
National Category
Didactics
Research subject
Mathematics, Mathematical Education
Identifiers
urn:nbn:se:lnu:diva-86250 (URN)978-0-6398215-6-6 (ISBN)978-0-6398215-7-3 (ISBN)
Conference
The 43rd Conference of the International Group for the Psychology of Mathematics Education - Improving access to the power of mathematics, Pretoria, South Africa 7 – 12 July 2019
Available from: 2019-07-08 Created: 2019-07-08 Last updated: 2019-08-30Bibliographically approved
Olteanu, C. (2018). Designing examples to create variation patterns in teaching. In: International Congress of Mathematicians (ICM 2018), 1-9 august, 2018, Rio de Janeiro, Brazil: . Paper presented at International Congress of Mathematicians(ICM 2018)1-9 august, 2018, Rio de Janeiro, Brazil.
Open this publication in new window or tab >>Designing examples to create variation patterns in teaching
2018 (English)In: International Congress of Mathematicians (ICM 2018), 1-9 august, 2018, Rio de Janeiro, Brazil, 2018Conference paper, Oral presentation with published abstract (Refereed)
Keywords
variation theory, schematic picture, rhizomatic thinking
National Category
Didactics
Research subject
Mathematics, Mathematical Education
Identifiers
urn:nbn:se:lnu:diva-77053 (URN)
Conference
International Congress of Mathematicians(ICM 2018)1-9 august, 2018, Rio de Janeiro, Brazil
Note

Ej belagd 180911

Available from: 2018-08-03 Created: 2018-08-03 Last updated: 2018-09-11Bibliographically approved
Olteanu, C. (2018). Designing examples to create variation patterns in teaching. International journal of mathematical education in science and technology, 49(8), 1219-1234
Open this publication in new window or tab >>Designing examples to create variation patterns in teaching
2018 (English)In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 49, no 8, p. 1219-1234Article in journal (Refereed) Published
Abstract [en]

This paper uses a post-qualitative philosophical perspective to find new ways of understanding teaching and learning. The paper presents a series of examples that were used in a longitudinal study, with the aim of creating variation patterns that would make it possible for students to discern the use of the four basic arithmetic operations in different situations. The focus of this article is the potential of the examples to systematically create variation patterns that students need to perceive in order to make generalizations. The result demonstrates that well-thought-out examples help identify the correct arithmetic operation in different situations, and provide a basis from which students can discern the connection between text and the use of operation in mathematical example. The result also demonstrates that students develop rhizomatic thinking through the creation of new links between aspects of the object of learning, association and linking of different aspects to each other and the creation of a whole with unique and specific characteristics that cannot be explained by simply adding the characteristics of the individual parts.

Place, publisher, year, edition, pages
Taylor & Francis, 2018
Keywords
arithmetic; example; schematic picture; variation theory; rhizomatic thinking
National Category
Didactics
Research subject
Mathematics, Mathematical Education
Identifiers
urn:nbn:se:lnu:diva-71809 (URN)10.1080/0020739X.2018.1447151 (DOI)000446502800006 ()2-s2.0-85044463710 (Scopus ID)
Available from: 2018-03-26 Created: 2018-03-26 Last updated: 2019-08-29Bibliographically approved
Olteanu, C. & Olteanu, L. (2018). Difference and repetition: instructional examples. In: Umeå Universitet (Ed.), Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education: . Paper presented at International Group for the Psychology of Mathematics Education (PME42) - Delight in Mathematics Education, 3-8 July, 2018, Sweden.
Open this publication in new window or tab >>Difference and repetition: instructional examples
2018 (English)In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education / [ed] Umeå Universitet, 2018Conference paper, Published paper (Refereed)
Series
Proceedings of the International Groups for the Psychology of Mathematics Education, ISSN 0771-100X
National Category
Didactics
Research subject
Mathematics, Mathematical Education
Identifiers
urn:nbn:se:lnu:diva-76743 (URN)
Conference
International Group for the Psychology of Mathematics Education (PME42) - Delight in Mathematics Education, 3-8 July, 2018, Sweden
Available from: 2018-07-10 Created: 2018-07-10 Last updated: 2019-01-18Bibliographically approved
Olteanu, C. (2018). Essential role of invariance in mathematics. In: World Association of Lesson Studies (WALS)
International Conference 2018- Lesson Study and Teacher Education:International Dialogue, Beijing Normal University, China.: . Paper presented at World Association of Lesson Studies (WALS)
International Conference 2018- Lesson Study and Teacher Education:International Dialogue, 23-26 November, Beijing Normal University, China. , Article ID I0065.
Open this publication in new window or tab >>Essential role of invariance in mathematics
2018 (English)In: World Association of Lesson Studies (WALS)
International Conference 2018- Lesson Study and Teacher Education:International Dialogue, Beijing Normal University, China., 2018, article id I0065Conference paper, Oral presentation with published abstract (Refereed)
Keywords
variation, invariance, examples, mathematics
National Category
Didactics
Research subject
Mathematics, Mathematical Education
Identifiers
urn:nbn:se:lnu:diva-79052 (URN)
Conference
World Association of Lesson Studies (WALS)
International Conference 2018- Lesson Study and Teacher Education:International Dialogue, 23-26 November, Beijing Normal University, China
Available from: 2018-12-03 Created: 2018-12-03 Last updated: 2018-12-10Bibliographically approved
Olteanu, C. & Olteanu, L. (2018). Investigating Difference and Repetition in Mathematics Teachers’ Professional Development. Philosophy of Mathematics Education Journal, 33, 1-11
Open this publication in new window or tab >>Investigating Difference and Repetition in Mathematics Teachers’ Professional Development
2018 (English)In: Philosophy of Mathematics Education Journal, ISSN 1465-2978, E-ISSN 1465-2978, Vol. 33, p. 1-11Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Exeter: University of Exeter Press, 2018
Keywords
repetition, difference, variation theory, function, patterns of variation
National Category
Didactics
Research subject
Mathematics, Mathematical Education
Identifiers
urn:nbn:se:lnu:diva-69591 (URN)
Available from: 2018-01-06 Created: 2018-01-06 Last updated: 2018-02-01Bibliographically approved
Olteanu, C. & Olteanu, L. (2018). Kommunicera med entydiga instruktioner. Skolverket
Open this publication in new window or tab >>Kommunicera med entydiga instruktioner
2018 (Swedish)Other (Other academic)
Place, publisher, year, pages
Skolverket, 2018. p. 10
Keywords
programmering, algebra
National Category
Didactics
Research subject
Mathematics, Mathematical Education
Identifiers
urn:nbn:se:lnu:diva-73746 (URN)
Note

Ingår i Lärportalen för matematik, Grundskolan årskurs 1-3 ; Modul: Algebra ; Del 7: Kommunikation och programmering i algebraklassrummet

Available from: 2018-04-30 Created: 2018-04-30 Last updated: 2018-09-11Bibliographically approved
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