| 1. |
- Petersson, Jöran
(författare)
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A fit model for model fitting : an a-didactical situation for model building
- 2019
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Ingår i: NOFA7 Abstracts, Stockholm University, 13 - 15 May 2019. ; , s. 169-169
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Konferensbidrag (refereegranskat)abstract
- Mathematical modelling in school mathematics encompasses a wide range of questions such as curricular aspects, mathematical concepts involved, orchestrating lesson activities, and many more. When building models, one approach is to use epistemological arguments and another approach is to base the model on empirical data. In the latter case, we can either focus on applying the resulting model to real life problems or we can focus on the mathematical methods needed to find the resulting model. In this empirical study, students in school year 10 in Sweden were asked “How do you think a digital tool calculates the fitted curve?” Doing so, the students were given an open-response task where they themselves are expected to develop mathematical knowledge that is new to them. One outcome of the students’ work was the following: They suggested mathematical methods corresponding to those analytical and geometrical methods that have been developed and used through the history of mathematics. Moreover, they suggested both discrete and continuous metric spaces as a means for measuring the distance between data and model. They also suggested modern methods from exploratory data analysis such as trimming the empirical data before fitting the model to them. Another outcome was that the tasks for the students were formulated so that they promoted and enthused the students’ mathematical creativity and reasoning in a way that in this mathematical area reached far beyond the curriculum for secondary school mathematics.
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| 2. |
- Petersson, Jöran
(författare)
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A PhD-project in multiculturalism : Ethnomathematics, language or educational systems
- 2010
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Ingår i: Mathematics and mathematics education: Cultural and social dimensions. - Linköping : Svensk förening för matematikdidaktisk forskning, Linköping universitet. - 9197393460 ; , s. 275-276
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Konferensbidrag (refereegranskat)abstract
- What could a PhD-project within a multicultural perspective on mathematics education comprise? So far a literature survey suggests three possible aspects, namely ethno-mathematics, multilingualism or educational systems.
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| 3. |
- Petersson, Jöran
(författare)
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Components of knowledge in solving linear equations
- 2021
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Ingår i: Sustainable mathematics education in a digitalized world. - 9789198402445 ; , s. 41-50
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Konferensbidrag (refereegranskat)abstract
- This article identifies knowledge components needed for successfully solving linear equations. Data for this purpose is 359 Swedish year 9 students’ written responses to the test task ”solve the equation 2x + 3 = 11”. The following set of knowledge components were identified; arithmetic knowledge, parsing knowledge, balancing equations, giving a value to the unknown, not omitting parts and the habit of verifying the solution. This paper discusses for which of these knowledge components, students could discover and correct their own errors if they would both solve an equation and verify its solution.
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| 4. |
- Petersson, Jöran, et al.
(författare)
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Content Analysis of Mathematics Textbooks and Adapted Lorentz Curves
- 2021
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Ingår i: <em>Proceedings of the Eighth Conference on Research in Mathematics Education in Ireland</em>. - Dublin. ; , s. 356-363
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Konferensbidrag (refereegranskat)abstract
- In this paper, we introduce an adaption of the Lorenz curve as a powerful tool for graphicallypresenting content analyses of mathematics textbooks. Three textbooks currently used withyear-one children in Sweden, one Swedish-, one Finnish and one Singaporean-authored, wereanalysed against the eight categories of Foundational Number Sense (FoNS), which is a set ofliterature-derived and instruction-dependent competences that all children need to acquire ifthey are to become successful learners of mathematics. The adapted Lorenz curvehighlighted, inter alia, major differences in the distribution of FoNS-related tasks across thethree textbooks. In general, the Swedish-authored textbook offers repeated cycles of FoNSrelated opportunities, the Finnish-authored textbook offers such opportunities continuously,and the Singaporean-authored textbook typically offers FoNS-related opportunities onlywithin its earlier pages.
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| 5. |
- Petersson, Jöran
(författare)
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Late-arrived immigrants in school and performance in algebra
- 2013
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Ingår i: Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education. - : International Group for the Psychology of Mathematics Education. ; , s. 143-143
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Konferensbidrag (refereegranskat)abstract
- This paper reports from a study on immigrant and native students tested in algebra asone of several topics in school mathematics. In general immigrant students performlower the later they have immigrated (Böhlmark, 2008). Students often find workingwith algebra difficult and Kieran (1992) noted that new-beginners in algebra oftenread algebraic expressions from left to right and might ignore the brackets.In this study 358 school year 9 students in six Swedish schools, with an over averagepercentage of immigrants, took a test. Several test problems were formulated so thatthey were likely to not cause too much of language obstacles for second languagelearners. In this report the test problem “a = 2, b = 4. What is a(b+2)+b?” is in focus.This problem was characterized in Duval’s (2006) semiotic registers as mainly“computations” and scarcely dependent on natural language.An important result is that the students who immigrated during school years 8 – 9performed better than the native students and much better than students whoimmigrated during school years 1 – 7. Most wrong solutions among all studentcategories were due to misuse of the distributive law in line with Kieran (1992).There were few arithmetic errors.In this on-going research project one conclusion is that there seems to be a need tosee early and late immigrants as having different challenges in being second languagelearners. The former have difficulties in following some advanced topics inmathematics teaching and the latter have difficulties in understanding some testquestions. A second conclusion is that there is a need in research to look at specifictopics in mathematics, especially advanced compulsory school mathematics such asnegative numbers and algebra, for these student categories.
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| 6. |
- Petersson, Jöran
(författare)
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Late-arrived immigrants in school and performance in arithmetic for negative numbers
- 2013
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Ingår i: Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education. - : International Group for the Psychology of Mathematics Education. ; , s. 252-252
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Konferensbidrag (refereegranskat)abstract
- This paper reports from a study on immigrant and native students tested in negative number arithmetic as one of several topics in school mathematics. In general immigrant students perform lower the later they have immigrated (Böhlmark, 2008). Students often find working with negative numbers difficult and Vlassis (2004) identified two kinds of conceptual changes needed for productive use of the minus and subtraction sign. First, the arithmetic rules are different for addition and subtraction. For example, subtraction is not commutative. Second, the minus sign has a flexible use exemplified by the expression (-23) + 9 = 9 – 23 = -(23 – 9). The expression uses the minus sign as a signed integer (non-operational), a subtraction (operational) and a reflection (operational) and a flexible change between these.In this study 356 school year 9 students in six Swedish schools, with an over average percentage of immigrants, took a test. Several test problems were formulated so that they were likely to not cause too much of language obstacles for second language learners. In this report the test problem “Calculate 12 – 23 + 9” is in focus. This problem was characterized in Duval’s (2006) semiotic registers as mainly “computations” and scarcely dependent on natural language. One result is that about half of the solutions contained sign errors. There were few arithmetic errors and few other unclassified errors. A second result is that the students who immigrated during school years 1 – 7 clearly underperformed compared to the other students while those who immigrated during school years 8 – 9 performed slightly better than the native students. In this on-going research project one conclusion is that there seems to be a need to see early and late immigrants as having different challenges in being second language learners. The former have difficulties in following some advanced topics in mathematics teaching and the latter have difficulties in understanding some test questions. A second conclusion is that there is a need in research to look at specific topics in mathematics, especially advanced compulsory school mathematics such as negative numbers and algebra, for these student categories.
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| 7. |
- Petersson, Jöran, et al.
(författare)
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Methods for visual and statistical comparison of the distribution of codes from content analyses
- 2019
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Ingår i: NOFA7 Abstracts, Stockholm University, 13 - 15 May 2019. - Stockholm : HSD, Stockholm University. ; , s. 170-170
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Konferensbidrag (refereegranskat)abstract
- The FoNS-project (Foundational Number Sense) in Mathematics education at Stockholm University aims to compare different countries with respect to opportunities for acquiring FoNS in first school year. We do this by analysing textbooks, teachers’ classroom activities and parent engagement with respect to mathematics. This means that the FoNS-project focuses less on the pupils themselves, but more on the mathematical education environment the pupils meet. One part of the FoNS-project is to compare textbooks through content analysis. The generated data are a sequence of codes from each textbook. In the generated data, the authors found that besides comparing frequencies, there is also much to be found in comparing the distribution of the codes for different textbooks. For this purpose we developed a novel method that allows a visual comparison of how the content in each textbook is distributed and we present this method and compare it with other methods found in a literature review. Another challenge is to make statistical inference tests on the generated data.Typically, the generated data set is large and a drawback is that with large data sets even small differences can result in statistically significant but in practice irrelevant differences. The authors will also compare various statistical methods for dealing with this challenge for both the case of comparing frequency and for comparing distribution of the data.
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| 8. |
- Petersson, Jöran, et al.
(författare)
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Opportunities for year-one children to acquire foundational number sense : comparing English and Swedish adaptations of the same Singapore textbook
- 2019
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Ingår i: Proceedings of the Seventh Conference on Research in Mathematics Education in Ireland (MEI7). - Dublin : Institute of Education, Dublin City University. - 9781873769959 ; , s. 251-258
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Konferensbidrag (refereegranskat)abstract
- In this paper we compare adaptations of a Singaporean year-one mathematics textbook for use in England and Sweden respectively. The texts were analysed in two different ways against the eight dimensions of Foundational Number Sense (FoNS), a set of core competences that the literature has shown to be necessary for year-one children’s later mathematical learning. The first analysis, based on frequencies, showed that neither adaptation incorporated any opportunities for children to acquire the two FoNS competence relating to estimation and number patterns respectively. They also showed that the English adaptation comprised significantly more tasks than the Swedish, particularly with respect to systematic counting, where the former comprises 26% more tasks than the latter. The second analysis, based on moving averages, showed that across five of the six FoNS categories for which there were data, the temporal location and emphases of FoNS-related learning were comparable, with, in particular, no such opportunities after the mid-point of the school year in either book. However, the English adaptation’s presentation of systematic counting, occurring at various points throughout the school year, was substantially different from the Swedish adaptation, highlighting differences due, we speculate, to interpretations of local didactical traditions.
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| 9. |
- Petersson, Jöran
(författare)
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Rare mathematics – a needle eye for mathematics teachers of second language learners
- 2012
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Ingår i: Proceedings of Norma 11. - Reykjavik : University of Iceland Press. - 9789979549659 ; , s. 483-492
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Konferensbidrag (refereegranskat)abstract
- This paper compares performance in a Swedish national test in mathematics of second language learners and students without another mother tongue than Swedish. The result is that some test problems had statistically significant and large differences between the student groups. Using discourse as an analytical tool, the suggested explanation is that second language learners for different reasons have less frequent access to the teaching of mathematical concepts or activity fields that occur rarely in the mathematics teaching and textbooks.
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| 10. |
- Petersson, Jöran
(författare)
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Recent and early immigrants’ achievements in mathematics
- 2015
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Ingår i: Nordic Conference on Subject Education. - : University of Helsinki. ; , s. 111-111
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Konferensbidrag (refereegranskat)abstract
- Achievement in mathematics, science and language is often used as national indicators and a personal bridge for future opportunities to work and education. One Swedish school law defines a ‘recent immigrant’ as the first four semesters during school years 6-9 of immigrated students. In an ongoing research project, the distribution of students’ different solving strategies in a multilingual classroom is studied through a test. Preliminary results are that students who immigrated in school years 8-9 in many cases show higher mathematical quality than those who immigrated during school years 1-7. This can be interpreted as a partial exclusion from taking a productive part in the mathematics classroom due to being second language learner. This raises questions of extending the definition of recent immigrants to all newly immigrated students disregarding their age and thus allow all newcomers extra support needed to include them in the mathematics classroom.
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