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Publications (10 of 34) Show all publications
Gunnarsson, R., Runesson, U. & Håkansson, P. (2019). Identifying what is critical for learning ‘rate if change’: Experiences from a learning study in Sweden. In: R. Huang, A. Takahashi & J. P. da Ponte (Ed.), Theory and practice of lesson study in mathematics: An international perspective (pp. 441-456). Cham: Springer
Open this publication in new window or tab >>Identifying what is critical for learning ‘rate if change’: Experiences from a learning study in Sweden
2019 (English)In: Theory and practice of lesson study in mathematics: An international perspective / [ed] R. Huang, A. Takahashi & J. P. da Ponte, Cham: Springer, 2019, p. 441-456Chapter in book (Refereed)
Abstract [en]

Learning study is an adapted version of lesson study developed in Hong Kong and Sweden. It has commonalities with lesson study but is framed within a specific pedagogical learning theory – variation theory. Central in variation theory is the object of learning and what is critical for students’ learning. Hence, as with lesson study, it is a collective and iterative work where teachers explore how they can make the object of learning available to students, but what characterises learning study is the use of a specific learning theory. In this process, special attention is paid to the critical aspects of the object of learning. We argue that to identify the aspects that are critical, the aspects need to be verified and refined in classrooms. In this chapter, we demonstrate how teachers gain knowledge about such critical aspects. Particularly, we show how these critical aspects cannot be extracted only from the mathematical content or the students pre-understanding alone, but evolve during the learning study cycles. For this we use a learning study about the mathematical topic of rate of change in grade 9 in Sweden as an illustration. We describe how an analysis of how students solved tasks in pre- and post-test and during the lessons, as well as how the mathematical content was presented in lessons, helped the teachers identify what was critical for learning to understand and express the rate of change for a dynamic situation.

Place, publisher, year, edition, pages
Cham: Springer, 2019
Series
Advances in Mathematics Education, ISSN 1869-4918
Keywords
Learning study; Critical aspects; Rate of change
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-42201 (URN)10.1007/978-3-030-04031-4 (DOI)978-3-030-04030-7 (ISBN)978-3-030-04031-4 (ISBN)
Available from: 2018-12-03 Created: 2018-12-03 Last updated: 2019-06-03Bibliographically approved
Gunnarsson, R. & Papadopoulos, I. (2019). Pairing numbers: An unconventional way of evaluating arithmetic expressions. In: : . Paper presented at CERME 11, Eleventh congress of the European Society for Research in Mathematics Education, Utrecht, NL, 6-10 February 2019.
Open this publication in new window or tab >>Pairing numbers: An unconventional way of evaluating arithmetic expressions
2019 (English)Conference paper, Published paper (Refereed)
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-42222 (URN)
Conference
CERME 11, Eleventh congress of the European Society for Research in Mathematics Education, Utrecht, NL, 6-10 February 2019
Available from: 2018-12-06 Created: 2018-12-06 Last updated: 2018-12-06
Håkansson, P. & Gunnarsson, R. (2018). Frågan är vad frågan gör – olika frågeställningars betydelse för hur elever uttrycker och använder förändringstakt i matematik. Forskning om undervisning och lärande, 6(2), 44-62
Open this publication in new window or tab >>Frågan är vad frågan gör – olika frågeställningars betydelse för hur elever uttrycker och använder förändringstakt i matematik
2018 (Swedish)In: Forskning om undervisning och lärande, ISSN 2000-9674, E-ISSN 2001-6131, Vol. 6, no 2, p. 44-62Article in journal (Refereed) Published
Abstract [sv]

Syftet med denna studie är att jämföra olika frågeställningars betydelse för hur elever relaterar och uttrycker relationer mellan olika storheter i uppgifter om förändringstakt i matematik. Genom en kvalitativ analys jämför vi hur elever i årskurs 9 besvarar två olika typer av uppgifter om hur snabbt vätskevolymen i två medicinska droppåsar förändras. Analysen pekar bland annat på att en jämförande uppgift (”vilken förändras snabbast?”) kan öppna ett brett utfallsrum, där vi kunde observera fem kvalitativt skilda sätt att lösa uppgiften. Vidare verkar en uppgift som efterfrågar ett värde (”hur snabbt förändras den?”) kunna leda eleverna mot multiplikativa jämförelser, som ligger nära den vedertagna matematiska innebörden i begreppet förändringstakt. Avslutningsvis diskuterar vi de olika frågeställningarnas potential för att lyfta olika aspekter av begreppet förändringstakt och hur de skulle kunna användas av lärare för olika syften i undervisningen.

Abstract [en]

The aim of this study is to compare the impact of different phrasings of questions as of how students relate and express relations between different quantities in student tasks concerning rate of change. Through a qualitative analysis we compare how students in ninth grade (age 15) respond to two different framings of questions, concerning how fast the volume of fluid in two medicine bags change. The analysis indicates that a comparing question (”which changes fastest?”) can open up a wide outcome space, in which we could observe five qualitatively distinct ways of solving the task. Furthermore, a question that requests a value (“how fast does it change?”) seem to encourage students to make multiplicative comparisons, which is close to the mathematical meaning of rate of change. Finally, we discuss the potential of each question for pointing to different aspects of rate of change, and how they could be used by teachers for different purposes in teaching situations.

Place, publisher, year, edition, pages
Stiftelsen SAF i samverkan med Lärarförbundet, 2018
Keywords
Rate of change, Mathematics teaching, Task design, Proportionality, förändringstakt, matematikundervisning, uppgiftsdesign, proportionalitet
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-41821 (URN)
Available from: 2018-10-11 Created: 2018-10-11 Last updated: 2018-12-06Bibliographically approved
Gunnarsson, R., Hellquist, B., Strömdahl, H. & Zelic, D. (2018). Secondary school science teachers’ arguments for the particulate nature of matter. Journal of Research in Science Teaching, 55(4), 503-525
Open this publication in new window or tab >>Secondary school science teachers’ arguments for the particulate nature of matter
2018 (English)In: Journal of Research in Science Teaching, ISSN 0022-4308, E-ISSN 1098-2736, Vol. 55, no 4, p. 503-525Article in journal (Refereed) Published
Abstract [en]

How do secondary school science teachers justify the model of a particulate nature of matter, and how do the arguments they use relate to historical arguments? To find out, we individually interviewed 11 in-service secondary school science teachers (certified to teach chemistry and/or physics in secondary school, and with 2–30 years of teaching experience) regarding their arguments for the particulate nature of matter and experiments that could demonstrate the existence of particles. The collected data were qualitatively analyzed. Three qualitatively different categories of arguments could be constructed from data: philosophical argumentsindirect experimental arguments, and direct experimental arguments. The indirect experimental arguments, which is the largest category, could be further divided into qualitatively different subcategories: non-specific research and experiments, and chemical, physical and subatomic experiments. Even though several experiments and arguments were suggested by the informants in our study, the arguments regarding the validity of the experiments were quite uncertain and vague. The experiments and arguments were used to corroborate the particulate nature of matter and taken for granted in advance rather than used to justify a model with particles. The outcome was discussed in relation to scientific arguments and experiments and in view of results from previous science education research. Based on our data, teacher education and in-service teacher training, as well as teacher guides, were suggested to be more elaborate regarding contemporary knowledge, with direct experimental evidence for the particulate nature of matter being presented. 

Place, publisher, year, edition, pages
John Wiley & Sons, 2018
Keywords
chemistry education, particulate nature of matter, secondary school, teachers’ arguments
National Category
Didactics
Identifiers
urn:nbn:se:hj:diva-38456 (URN)10.1002/tea.21428 (DOI)000427126100002 ()2-s2.0-85034215273 (Scopus ID)
Available from: 2018-01-11 Created: 2018-01-11 Last updated: 2018-06-28Bibliographically approved
Gunnarsson, R. & Papadopoulos, I. (2018). The impact of number pairing on students' ideas on how to evaluate numerical expressions. In: E. Bergqvist, M. Österholm, C. Granberg & L. Sumpter (Ed.), Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education: Vol. 5. Paper presented at PME 42, the 42nd Conference of the International Group for the Psychology of Mathematics Education, July 3-8, Umeå, Sweden (pp. 238-238). Umeå: PME
Open this publication in new window or tab >>The impact of number pairing on students' ideas on how to evaluate numerical expressions
2018 (English)In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education: Vol. 5 / [ed] E. Bergqvist, M. Österholm, C. Granberg & L. Sumpter, Umeå: PME , 2018, p. 238-238Conference paper, Poster (with or without abstract) (Refereed)
Place, publisher, year, edition, pages
Umeå: PME, 2018
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-42205 (URN)
Conference
PME 42, the 42nd Conference of the International Group for the Psychology of Mathematics Education, July 3-8, Umeå, Sweden
Available from: 2018-12-04 Created: 2018-12-04 Last updated: 2018-12-06Bibliographically approved
Papadopoulos, I. & Gunnarsson, R. (2018). The use of ‘mental’ brackets when calculating arithmetic expressions. In: E. Bergqvist, M. Österholm, C. Granberg & L. Sumpter (Ed.), Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education: Vol. 3. Paper presented at PME 42, the 42nd Conference of the International Group for the Psychology of Mathematics Education, July 3-8, Umeå, Sweden (pp. 451-458). Umeå: PME
Open this publication in new window or tab >>The use of ‘mental’ brackets when calculating arithmetic expressions
2018 (English)In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education: Vol. 3 / [ed] E. Bergqvist, M. Österholm, C. Granberg & L. Sumpter, Umeå: PME , 2018, p. 451-458Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Umeå: PME, 2018
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-42203 (URN)
Conference
PME 42, the 42nd Conference of the International Group for the Psychology of Mathematics Education, July 3-8, Umeå, Sweden
Available from: 2018-12-04 Created: 2018-12-04 Last updated: 2018-12-06Bibliographically approved
Håkansson, P. & Gunnarsson, R. (2018). What is critical in order to learn the average rate of change?. In: E. Bergqvist, M. Österholm, C. Granberg & L. Sumpter (Ed.), Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education: Vol. 5. Paper presented at PME 42, the 42nd Conference of the International Group for the Psychology of Mathematics Education, July 3-8, Umeå, Sweden (pp. 55-55). Umeå: PME
Open this publication in new window or tab >>What is critical in order to learn the average rate of change?
2018 (English)In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education: Vol. 5 / [ed] E. Bergqvist, M. Österholm, C. Granberg & L. Sumpter, Umeå: PME , 2018, p. 55-55Conference paper, Oral presentation with published abstract (Refereed)
Place, publisher, year, edition, pages
Umeå: PME, 2018
National Category
Didactics Mathematics
Identifiers
urn:nbn:se:hj:diva-42204 (URN)
Conference
PME 42, the 42nd Conference of the International Group for the Psychology of Mathematics Education, July 3-8, Umeå, Sweden
Available from: 2018-12-04 Created: 2018-12-04 Last updated: 2018-12-06Bibliographically approved
Gunnarsson, R. (2016). Arithmetic expressions with multiple operations - How to solve it?. In: Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education, Volume 2: . Paper presented at 40th Annual Meeting of the International Group for the Psychology of Mathematics Education (PME 40) (pp. 298). , 1
Open this publication in new window or tab >>Arithmetic expressions with multiple operations - How to solve it?
2016 (English)In: Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education, Volume 2, 2016, Vol. 1, p. 298-Conference paper, Published paper (Refereed)
National Category
Didactics
Identifiers
urn:nbn:se:hj:diva-32021 (URN)
Conference
40th Annual Meeting of the International Group for the Psychology of Mathematics Education (PME 40)
Available from: 2016-10-19 Created: 2016-10-19 Last updated: 2016-10-26Bibliographically approved
Gunnarsson, R., Wei Sönnerhed, W. & Hernell, B. (2016). Does it help to use mathematically superfluous brackets when teaching the rules for the order of operations?. Educational Studies in Mathematics, 92(1), 91-105
Open this publication in new window or tab >>Does it help to use mathematically superfluous brackets when teaching the rules for the order of operations?
2016 (English)In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 92, no 1, p. 91-105Article in journal (Refereed) Published
Abstract [en]

The hypothesis that mathematically superfluous brackets can be useful when teaching the rules for the order of operations is challenged. The idea of the hypothesis is that with brackets it is possible to emphasize the order priority of one operation over another. An experiment was conducted where expressions with mixed operations were studied, focusing specifically on expressions of the type a ± (b × c) with brackets emphasizing the multiplication compared to expressions of the type a ± b × c without such brackets. Data were collected from pen and paper tests, before and after brief (about 7 min) instructions, of 169 Swedish students in year 6 and 7 (aged 12 to 13). The data do not seem to support the use of brackets to detach the middle number (b) from the first operation (±) in a ± b × c type of expressions.

Place, publisher, year, edition, pages
Springer Netherlands, 2016
Keywords
Mathematics education; Brackets; Order of operations
National Category
Didactics
Identifiers
urn:nbn:se:hj:diva-28767 (URN)10.1007/s10649-015-9667-2 (DOI)000374412500006 ()2-s2.0-84955269808 (Scopus ID)
Available from: 2015-12-27 Created: 2015-12-27 Last updated: 2017-12-01Bibliographically approved
Gunnarsson, R., Ekdahl, A.-L., Landén, J. & Tegnefur, J. (2016). Students’ strategies to continue geometric number sequences. In: : . Paper presented at MADIF-10. Tionde matematikdidaktiska forskningsseminariet. 26-27 jan 2016. Karlstad..
Open this publication in new window or tab >>Students’ strategies to continue geometric number sequences
2016 (English)Conference paper, Published paper (Refereed)
Abstract [en]

Number sequences can be useful tools for teaching generalization, functions, or variables, for instance. Consequently, there are many studies that have studied students’ perception of number sequences and the strategies used to continue those sequences. However, a large part of the studies have been using arithmetic or quadratic number sequences. In this paper we present a study of students’ strategies to continue non-contextualized geometric number sequences. Interview data from 18 students in grades 9 to 12(age 15-19) (in Sweden) was analysed. Five qualitatively different strategies have been discerned in the data. These strategies are not completely overlapping the strategies previously described in literature.

National Category
Didactics
Identifiers
urn:nbn:se:hj:diva-28768 (URN)
Conference
MADIF-10. Tionde matematikdidaktiska forskningsseminariet. 26-27 jan 2016. Karlstad.
Available from: 2015-12-27 Created: 2015-12-27 Last updated: 2015-12-27
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-2199-1627

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