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  • 1.
    Johansson, Helena
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.
    Dependence between creative and non-creative mathematical reasoning in national physics tests2017In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 22, no 2, p. 93-119Article in journal (Refereed)
    Abstract [en]

    It is known from previous studies that a focus on rote learning and procedural mathematical reasoning hamper students’ learning of mathematics. Since mathematics is an integral part of physics, it is assumed that mathematical reasoning also influences students’ success in physics. This paper aims to study how students’ ability to reason mathematically affects their success on different kinds of physics tasks. A descriptive statistical approach is adopted, which compares the ratio between conditional and unconditional probability to solve physics tasks requiring different kinds of mathematical reasoning. Tasks from eight Swedish national physics tests for upper secondary school, serve as a basis for the analysis. The result shows that if students succeed on tasks requiring creative mathematical reasoning, the probability to solve the other tasks on the same test increases. This increase is higher than if the students succeed on tasks not requiring creative mathematical reasoning. This result suggests that if students can reason mathematically creatively, they have the ability to use their knowledge in other novel situations and thus become more successful on tests.

  • 2.
    Johansson, Helena
    Göteborgs universitet, Institutionen för matematiska vetenskaper.
    Mathematical Reasoning: In physics and real-life context2015Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis is a compilation of four papers in which mathematical reasoning is examined in various contexts, in which mathematics is an integral part. It is known from previous studies that a focus on rote learning and procedural mathematical reasoning hamper students’ learning of mathematics. The aims of this thesis are to explore how mathematical reasoning affects upper secondary students’ possibilities to master the physics curricula, and how real-life contexts in mathematics affect students’ mathematical reasoning. This is done by analysing the mathematical reasoning requirements in Swedish national physics tests; as well as by examining how mathematical reasoning affects students’ success on the tests/tasks. Furthermore, the possible effect of the presence of real-life contexts in Swedish national mathematics tasks on students’ success is explored; as well as if the effect differs when account is taken to mathematical reasoning requirements. The framework that is used for categorising mathematical reasoning, distinguishes between imitative and creative mathematical reasoning, where the latter, in particular, involves reasoning based on intrinsic properties. Data consisted of ten Swedish national physics tests for upper secondary school, with additional student data for eight of the tests; and six Swedish national mathematics tests for upper secondary school, with additional student data. Both qualitative and quantitative methods were used in the analyses. The qualitative analysis consisted of structured comparisons between representative student solutions and the students’ educational history. Furthermore, various descriptive statistics and significance tests were used. The main results are that a majority of the physics tasks require mathematical reasoning, and particularly that creative mathematical reasoning is required to fully master the physics curricula. Moreover, the ability to reason mathematically creatively seems to have a positive effect on students’ success on physics tasks. The results indicate additionally, that there is an advantage of the presence of real-life context in mathematics tasks when creative mathematical reasoning is required. This advantage seems to be particularly notable for students with lower grades.

  • 3.
    Johansson, Helena
    Göteborgs universitet, Institutionen för matematiska vetenskaper.
    Mathematical Reasoning in Physics Tests: Requirements, Relations, Dependence2013Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    By analysing and expanding upon mathematical reasoning requirements in physics tests, this licentiate thesis aims to contribute to the research studying how students’ knowledge in mathematics influence their learning of physics. A sample of physics tests from the Swedish National Test Bank in Physics was used as data, together with information of upper secondary students’ scores and grades on the tests. First it was decided whether the tasks in the tests required mathematical reasoning at all and if they did, that reasoning was characterised. Further, the relation between students’ grades and mathematical reasoning requirements was examined. Another aim in this thesis is to try out if the Mantel-Haenszel procedure is an appropriate statistical method to answer questions about if there is a dependence between students’ success on different physics tasks requiring different kinds of mathematical reasoning. The results show that 75% of the tasks in the physics tests require mathematical reasoning and that it is impossible to pass six out of eight tests without mathematical reasoning. It is also revealed that it is uncommon that a student gets a higher grade than Pass without solving tasks that require the student to come up with not already familiar solutions. It is concluded that the Mantel-Haenszel procedure is sensitive to the number of students each teacher accounts for. If there are not too few students, the procedure can be used. The outcome indicates that there is a dependence between success on tasks requiring different kinds of reasoning. It is more likely that a student manages to solve a task that requires the produce of new reasoning if the student has solved a task that is familiar from before.

  • 4.
    Johansson, Helena
    Göteborgs Universitet, Institutionen för matematiska vetenskaper.
    Mathematical Reasoning Requirements in Swedish National Physics Tests2016In: International Journal of Science and Mathematics Education, ISSN 1571-0068, E-ISSN 1573-1774, Vol. 14, no 6, p. 1133-1152Article in journal (Refereed)
    Abstract [en]

    This paper focuses on one aspect of mathematical competence, namelymathematical reasoning, and how this competency influences students’ knowing ofphysics. This influence was studied by analysing the mathematical reasoning requirementsupper secondary students meet when solving tasks in national physics tests.National tests are constructed to mirror the goals stated in the curricula, and these goalsare similar across national borders. The framework used for characterising the mathematicalreasoning required to solve the tasks in the national physics tests distinguishesbetween imitative and creative mathematical reasoning. The analysis process consistedof structured comparisons between representative student solutions and the students’educational history. Of the 209 analysed tasks, 3/4 required mathematical reasoning inorder to be solved. Creative mathematical reasoning, which, in particular, involvesreasoning based on intrinsic properties, was required for 1/3 of the tasks. The results inthis paper give strong evidence that creative mathematical reasoning is required toachieve higher grades on the tests. It is also confirmed that mathematical reasoning isan important and integral part of the physics curricula; and, it is suggested that theability to use creative mathematical reasoning is necessary to fully master the curricula

  • 5.
    Johansson, Helena
    Göteborgs Universitet.
    Mathematical reasoning requirements to solve tasks in physics tests2012In: Evaluation and Comparison of Mathematical Achievement: Dimensions and Perspectives: Proceedings of MADIF 8, The Eighth Mathematics Education Research Seminar / [ed] Christer Bergsten, Eva Jablonka & Manya Raman, Linköping: Svensk förening för matematikdidaktisk forskning (SMDF) , 2012, p. 211-212Conference paper (Other academic)
  • 6.
    Johansson, Helena
    Göteborgs universitet, Institutionen för matematiska vetenskaper.
    Relation between imitative and creative mathematical reasoning when solving physics tasks2013In: Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education / [ed] Anki M. Lindmeier & Aiso Heinze, Kiel, Germany: PME , 2013, Vol. 5, p. 80-80Conference paper (Refereed)
  • 7.
    Johansson, Helena
    Göteborgs Universitet, Institutionen för Matematiska vetenskaper.
    Relation between mathematical reasoning ability and national formal demands in physics courses2015In: Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education / [ed] Kim Beswick, Tracey Muir, & Jill Wells, Hobart, Australia: PME , 2015, Vol. 3, p. 121-128Conference paper (Refereed)
    Abstract [en]

    It is widely accepted that mathematical competence is of great importance whenlearning physics. This paper focuses on one aspects of mathematical competence,namely mathematical reasoning, and how this competency influences students’ successin physics. Mathematical reasoning required to solve tasks in physics tests, within anational tests system, is separated in imitative and creative mathematical reasoning.The result shows that students lacking the ability to reason mathematically creativelyare more likely not to do well on national physics test, thus not fully mastering thephysics curricula. It is further discussed how the high demands of creativemathematical reasoning in physics tests stand in contrast to what is known about theeducational practices in mathematics and physics in upper secondary school

  • 8.
    Johansson, Helena
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Kilhamn, Cecilia
    Nationellt Centrum för Matematikutbildning, NCM, Göteborgs Universitet.
    Grade 6 teachers’ objectification of the algebra discourse2019In: Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education / [ed] Graven, M., Venkat, H., Essien, A. & Vale, P, Pretoria, South Africa: PME , 2019, Vol. 4, p. 51-51Conference paper (Refereed)
    Abstract [en]

    In tackling the well-known challenges of learning algebra, Sfard (2008) highlights the need for objectification of mathematical discourse. Teachers can support students in this objectification by modelling the discourse they want students to develop (Sfard, 2016). Our study uses Sfard’s (2008) definition of objectification in order to analyse grade 6 teachers’ algebra discourse. The purpose is to understand if and how objectification occurs in the discourse when algebra is introduced, and how this might influence students’ understanding of algebra. Data consist of video recordings from three Swedish teachers’ introductory lessons in algebra with 12-year old students, with four consecutive introductory algebra lessons for each teacher. The recordings are from a larger international video study. Teachers’ discourse about algebraic entities was analysed concerning word-use, visual mediators, routines, and endorsed narratives (Sfard, 2008). Preliminary results show that there were mainly three algebraic entities that were in focus in the lessons, described as equations, expressions and variables. Generally, we note that as more formal algebraic symbols were introduced and used by two of the teachers, the more objectified became their discourse. This objectification did not occur in the third teacher’s discourse, which lacked an early introduction of formal symbols. This could imply that symbols reinforce objectification. Particularly, the progression of the objectification process concerning expressions was very prominent over the course of one teacher’s four lessons. The word use clearly changed from treating the introduced symbols as processes, where an expression was “to describe something with the help of a variable”; to objects, where an expression was “a system of symbols” that “could be used in an equation”. A more comprehensive discussion of the results, including routines and endorsed narratives, will be included in our presentation.

  • 9.
    Johansson, Helena
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Oskarsson, Magnus
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Nyström, Peter
    NCM, Göteborgs Universitet.
    Fysikbegreppets flyktighet: En konsekvens av kursplaneförändringar?2019In: Från forskning till fysikundervisning: Bidrag från konferensen 10-11 april 2018 i Lund arrangerad av Nationellt Resurscentrum för Fysik / [ed] K. Stolpe, G. Höst, & A. Larsson, Linköping, Sverige: Linköping University Electronic Press, 2019, p. 33-46Conference paper (Refereed)
    Abstract [sv]

    TIMSS Advanced är en internationell studie om gymnasieelevers kunskaperi avancerad matematik och fysik. Studien har genomförts tregånger, 1995, 2008 och 2015, och Sverige har deltagit alla tre gångerna.Resultaten från senaste studien visade att svenska gymnasieeleverpresterade bättre i matematik men sämre i fysik jämfört med resultatenfrån 2008. Normalt brukar prestationerna i matematik och fysikföljas åt och det är därför intressant att undersöka tänkbara orsakertill de försämrade fysikresultaten. Resultatet visar för det första på försämraderesultat på uppgifter som tidigarelagts i undervisningen närde nya ämnesplanerna i fysik infördes 2011 och för det andra på försämraderesultat på uppgifter som mäter begreppsbildning i fysik.Detta kan tyda på att eleverna hade glömt områden som behandlades iundervisningen året innan provet gick, men kan också tyda på att elevernaskunskaper var alltför ytliga. Slutsatsen blir att man tydligarebör studera vad som händer när kurser och kursinnehåll förändras.

  • 10.
    Johansson, Helena
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Oskarsson, Magnus
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Nyström, Peter
    Göteborgs Universitet.
    Glömska eller ytliga fysikkunskaper: Fördjupad analys av svenska elevers sjunkande fysikresultat i TIMSS Advanced 20152018Report (Other academic)
    Abstract [sv]

    TIMSS Advanced (Trends in Mathematics and Science Study ) är en internationell studie som undersöker gymnasieelevers kunskaper i avancerad matematik och fysik. TIMSS Advanced har genomförts tre gånger, 1995, 2008 och 2015, och Sverige har deltagit varje gång. I 2015 års studie deltog svenska elever i årskurs 3 på naturvetenskaps-och teknikprogrammet som slutfört eller håller på att slutföra kursen matematik 4 respektive fysik 2. Resultaten visade att Sverige förbättrat sina resultat i matematik medan resultaten i fysik försämrats. Dessa resultat brukar normalt följas åt och denna rapport undersöker möjliga orsaker till de sjunkande fysikresultaten i TIMSS Advanced.

  • 11.
    Johansson, Helena
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Österholm, Magnus
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education. Umeå universitet, Umeå.
    Objectification of upper-secondary teachers’ verbal discourse in relation to symbolic expressions2019In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 56, article id 100722Article in journal (Refereed)
    Abstract [en]

    Research literature points to the importance of objectification when learning mathematics, and thereby in the discourse of mathematics. To increase the field's understanding of aspects and degrees of objectification in various mathematical discourses, our study uses the combination of two sub-processes of objectification in order to analyse upper-secondary teachers’ word use in relation to any type of mathematical symbols. Our results show that the verbal discourse around symbols is very objectified. This can put high demands on students understanding of their teacher, since it might be needed that the students have reached a certain degree of objectification in their own thinking in order to be able to participate in a more objectified discourse. The results also show that there exist patterns in the variation of the degree of objectification, in particular that the discourse tends to be more objectified when more familiar symbols are used. This exploratory study also reveals several phenomena that could be the focus of more in-depth analyses in future studies. 

  • 12.
    Johansson, Helena
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Österholm, Magnus
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Upper-secondary teachers' objectification of symbols by their use of language2017In: Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education / [ed] Kaur, B., Ho, W.K., Toh, T.L., & Choy, B.H., Singapore: PME , 2017, Vol. 1, p. 215-215Conference paper (Refereed)
  • 13.
    Johansson, Helena
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Österholm, Magnus
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Flodén, Liselott
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Heidtmann, Pia
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Teachers’ and students’ perception of the gap between secondary and tertiary mathematics2018In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education / [ed] Bergqvist, E., Österholm, M., Granberg, C., & Sumpter, L., Umeå, Sweden: PME , 2018, Vol. 5, p. 77-77Conference paper (Refereed)
  • 14.
    Nyström, Peter
    et al.
    Göteborgs Universitet.
    Kjellson Lind, Annika
    Umeå Universitet.
    Dahlberg, Ulrica
    Göteborgs Universitet.
    Johansson, Helena
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.
    Hur samstämmiga är svenska styrdokument och nationella prov med ramverk och uppgifter i TIMSS Advanced 2015?2016Report (Other academic)
    Abstract [sv]

    TIMSS Advanced (Trends in Mathematics and Science Study ) är en internationell studie som undersöker gymnasieelevers kunskaper i avancerad matematik och fysik. TIMSS Advanced har genomförts tre gånger, 1995, 2008 och 2015, och Sverige har deltagit varje gång. I 2015 års studie deltog svenska elever i årskurs 3 på naturvetenskaps- och teknikprogrammet som slutfört eller håller på att slutföra kursen matematik 4 respektive fysik 2. Studien ger möjlighet att analysera förändringar i motsvarande elevgruppers kunskaper över tid inom dessa områden, men också möjlighet att jämföra svenska resultat med resultat från andra länder. TIMSS Advanced 2015 har genomförts av Skolverket i samarbete med Nationellt Centrum för Matematikutbildning (NCM) vid Göteborgs universitet. Skolverket har sammanställt en nationell huvudrapport med resultaten från TIMSS Advanced 2015. En viktig utgångspunkt för tolkning och analys av resultaten är att veta i vilken utsträckning svenska elever fått möjlighet att lära sig det som prövas i TIMSS Advanced. I denna rapport analyseras därför samstämmigheten mellan TIMSS Advanced 2015 och svenska ämnesplaner, nationella prov och bedömningsstöd. Mot bakgrund av ämnenas kopplingar mellan varandra genomförs också en analys som särskilt fokuserar på inslaget av matematik i fysikuppgifterna.

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CiteExportLink to result list
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