Students’ understandings of multiplication

0 Skriv ut

Vad visar elevers lösningar till olika typer av multiplikativa uppgifter, inom multiplikation med flersiffriga tal och decimaltal, av deras förståelse av multiplikation? Den frågan utforskar Kerstin Larsson i sin avhandling.

Abstract in English:

Multiplicative reasoning permeates many mathematical topics, for example fractions and functions. Hence there is consensus on the importance of acquiring multiplicative reasoning. Multiplication is typically introduced as repeated addition, but when it is extended to include multi-digits and decimals a more general view of multiplication is required.

There are conflicting reports in previous research concerning students’ understandings of multiplication. For example, repeated addition has been suggested both to support students’ understanding of calculations and as a hindrance to students’ conceptualisation of the two-dimensionality of multiplication. The relative difficulty of commutativity and distributivity is also debated, and there is a possible conflict in how multiplicative reasoning is described and assessed. These inconsistencies are addressed in a study with the aim of understanding more about students’ understandings of multiplication when it is expanded to comprise multi-digits and decimals.

Understanding is perceived as connections between representations of different types of knowledge, linked together by reasoning. Especially connections between three components of multiplication were investigated; models for multiplication, calculations and arithmetical properties. Explicit reasoning made the connections observable and externalised mental representations.

Twenty-two students were recurrently interviewed during five semesters in grades five to seven to find answers to the overarching research question: What do students’ responses to different forms of multiplicative tasks in the domain of multi-digits and decimals reveal about their understandings of multiplication? The students were invited to solve different forms of tasks during clinical interviews, both individually and in pairs. The tasks involved story telling to given multiplications, explicit explanations of multiplication, calculation problems including explanations and justifications for the calculations and evaluation of suggested calculation strategies. Additionally the students were given written word problems to solve.

The students’ understandings of multiplication were robustly rooted in repeated addition or equally sized groups. This was beneficial for their understandings of calculations and distributivity, but hindered them from fluent use of commutativity and to conceptualise decimal multiplication. The robustness of their views might be explained by the introduction to multiplication, which typically is by repeated addition and modelled by equally sized groups. The robustness is discussed in relation to previous research and the dilemma that more general models for multiplication, such as rectangular area, are harder to conceptualise than models that are only susceptible to natural numbers.

The study indicated that to evaluate and explain others’ calculation strategies elicited more reasoning and deeper mathematical thinking compared to evaluating and explaining calculations conducted by the students themselves. Furthermore, the different forms of tasks revealed various lines of reasoning and to get a richly composed picture of students’ multiplicative reasoning and understandings of multiplication, a wide variety of forms of tasks is suggested.

 

FAKTA

Disputation
2016-12-12
Titel (sv):
Titel (eng):
Students' understandings of multiplication
Författare
Kerstin Larsson
Handledare:
Associate professor Kerstin Pettersson, Stockholms universitet Professor Paul Andrews Stockholms universitet
Opponent:
Professor Lieven Verschaffel, Katholieke Universiteit, Leuven, Belgium
Institution:
Institutionen för matematikämnets och naturvetenskapsämnenas didaktik
Lärosäte:
Stockholms universitet
RELATERAT

Inlärningssvårigheter i matematik och läsning hänger ihop

Intervju

image descriptionSambandet mellan inlärningssvårigheter i matematik och inlärningssvårigheter i läsning är starkare än jag trodde, säger Johan Korhonen. Hans forskning visar också att dessa svårigheter ökar risken för skolavbrott.

Svenska elever har svårt att läsa och förstå matteuppgifter

Intervju

image descriptionNär elever stöter på många ord som de inte känner igen från sina matteböcker, finns det en risk att det är deras läsförmåga som testas istället för deras matematiska förmåga. Det visar Anneli Dyrvolds avhandling.

Bedömning FÖR och AV lärande, 2-3 feb i Stockholm

Arrangemang

image descriptionBedömning kan liknas vid att lägga pussel av elevers kunskapsutveckling, det är en komplex men viktig del av lärararbetet och inkluderar planering och genomförande såväl som kartläggning och utvärdering. Ta del av aktuell forskning och inspirerande praktiska inslag för att stödja dig i din bedömningskompetens.

Gymnasielärare i svenska, 30-31 jan 2017 i Stockholm

Arrangemang

image descriptionSvenskämnet är mångfacetterat med en bred variation av arbetsområden. Välkommen till en fördjupande tvådagarskonferens som bland annat behandlar ämnen som hur man kan undervisa elever i källkritik, retorik, vetenskapligt skrivande samt hur man kan uppmuntra och motivera skönlitterär läsning.

 
Annons