Hoppa till sidinnehåll
Matematik

Att lära om statisk och dynamisk proportionalitet. En studie av den didaktiska transpositionen av svenska matematikuppgifter med proportionalitet

Publicerad: 2024-11-20
Uppdaterad: 28 januari

Anna L. V. Lundberg har forskat om hur proportionalitet behandlas av läromedelsförfattare, på nationella prov och av lärare och elever i matematikklassrummet.

Författare

Anna L. V. Lundberg

Handledare

Professor Roger Säljö, Göteborgs universitet

Opponent

Professor Magnus Österholm, Umeå universitet

Disputerat vid

Göteborgs universitet

Disputationsdag

2024-12-03

Abstract in English

The purpose of this study is to shed light on how static and dynamic proportionality is treated by authors of teaching materials, on national tests and by teachers and students in the classroom, as well as how students encounter mathematics tasks where proportional reasoning is an option. The research is based on two sets of empirical data. In concrete terms, the thesis includes three studies examining three themes that relate to proportionality in classroom interaction and in texts. The first study analyses how proportionality is presented in some Swedish textbooks, in curricular texts and national course tests in mathematics for students in upper secondary school. The second study is a case study of how a teacher instructs and explains a task in a class in Grade 6, where proportional reasoning is a possible solution technique. Finally, the third study concerns how students in Grade 6 handle proportional reasoning when they encounter a patterning task involving proportional relationships. The analyses of textbooks and national course tests show that proportionality is handled differently in these two settings in the context of “Mathematics A” at the upper secondary school. About a quarter of the tasks in the textbooks and the national course tests involved proportionality tasks of one specific kind (missing value). Other types of proportionality tasks were infrequent. The results of the classroom studies show that students are able to engage in early forms of proportional reasoning before being taught about proportionality as a mathematical concept. The concept of learning trajectory is used to identify situations in the learning process during instruction where students meet obstacles and need scaffolding and teacher support. It is shown how a teacher dealing with a mathematical task involving mixtures of liquids encounters a task that has the possibility of making proportional reasoning visible for the students, and how she struggles to make the modelling required intelligible to herself and to the students. The instructional strategy of using everyday problems as a basis for learning implies that the initial modelling phase becomes crucial, and the students have to be aware of the conditions and limitations under which proportional reasoning is applicable. In conclusion, students engage in early forms of proportional reasoning well ahead of formal instruction. The difficulties they experience as they are to develop their proficiency, and where they require support from the teacher, concern how to model the familiar, everyday situations they encounter in exercises in mathematically precise and productive ways. In addition, in textbooks and national course tests proportionality is presented in a standardized, and rather simplified, form, and it is not sufficiently connected to the various areas of mathematics teaching and learning where it is applicable

Dela via: 

Relaterade artiklar

Forskning och utveckling kategorier

Podcast: När matematik blir ett språkprov

2024-10-29
Hur ska man bedöma en elev i matematik om eleven inte förstår begrepp i uppgiften och saknar ord för att resonera och beskriva lösningen? Det har forskare och lärare undersökt i muntliga provsituationer med andraspråkselever i årskurs 9. Resultaten och slutsatserna delar de med sig av i det här avsnittet av Lärare & Forskning. (webbradio)

Avhandling om sex och samlevnad i biologiböcker utsedd till Lärarpanelens favorit

2024-05-16
Flera ämnen saknas i avsnitten om sexualundervisning i läroböckerna i biologi. Det visar Hannele Junkalas forskning i vilken hon har undersökt sexualundervisningens innehåll i ett antal biologiböcker för högstadiet, samt gjort observationer av biologilektioner i årskurs 8. Hennes avhandling är nu vald till Lärarpanelens favorit. 
Forskning och utveckling kategorier

Studie i Västerbotten visar: Vanligare med socioemotionella svårigheter hos barn till lågutbildade

2024-10-01
Nästan var tionde treåring i Västerbotten visar tecken på socioemotionella svårigheter. Svårigheterna är vanligare hos barn till föräldrar med låg inkomst och låg utbildning samt utlandsfödda. "Alla ska ha samma möjligheter, men här kan vi se att det skiljer sig redan i treårsåldern", säger Marie Lindkvist, forskare.
Forskning och utveckling kategorier

“With a twinkle in my eye”: vocational teachers’ relational work in schools in disadvantaged areas

11 februari
Research on teachers’ relational practices and how they develop relationships with their students is a growing field, internationally and in Scandinavia. However, research on teachers’ relational work in disadvantaged areas is rare. This study examines how vocational teachers in schools in disadvantaged areas describe their relational work with students. (pdf)

Relaterat innehåll

Senaste magasinen

Läs mer

Nyhetsbrev

Prenumerera på Skolportens nyhetsbrev!

Vi ger ut kostnadsfria nyhetsbrev dagligen, veckovis och månadsvis. Breven sammanfattar nyheter och forskning inom olika områden.