Syftet med denna studie var att undersöka elevers användning av lösningsstrategier i subtraktion samt lärares och läromedlens framställning av dessa, för att kunna komma fram till hur en framgångsrik undervisning i subtraktion, med fokus på lösningsstrategier, kan se ut. Undersökningen genomfördes i tre klasser i åk 3. Metoder i studien var elevenkät, intervju med lärare och läromedelsgranskning. Data bearbetades med hjälp av en egenkonstruerad begreppsmodell utifrån olika lösningsstrategier. Resultatet visar på en större variation av lösningsstrategier i undervisningen än i elevernas uträkningar. Eleverna använder sig oftast av enbart en av lösningsstrategierna, så kallad ”talsortsvis beräkning”. Strategin leder till många fel i elevernas uträkningar. / The purpose of this study was to investigate how pupils use solution strategies for subtraction, and how those are presented by teachers and textbooks in order to find out how successful teaching in subtraction, with focus on solution strategies, might look. The study was carried out on three groups in the 3rd grade. The methods of this study consisted of a pupil survey, interviews with teachers and a review of textbooks. The data were processed using a self-constructed conceptual model based on different solution strategies. The results indicate a larger variation of solution strategies in the teaching than in the pupils´ calculations. The pupils typically use only one of the solution strategies, a so-called "number-splitting calculation". This strategy leads to many errors in the pupils' calculations.

This paper presents an innovat ive cons t ruct ion of a probabilistic model for predicting chance situations. It describes the construction of a four phase model, derived from an intense qualitative analysis of the written responses of 94 mathematically talented middle school students to the probabilistic compound event problem: “How many doubles are expected when rolling two dice fifty times?” We found that the students’ comprehension process of compound event situations can be broken down into a four phase model: beliefs, subjective estimations, chance estimations and probabilistic calculations. The paper focuses on the development of the model over the course of the experiment, identifying the process the students underwent as they attempted to answer the question. We explain each phase as it was reflected in the students\' rationalizations. All phases, including their definitions and students’ citations, will be presented in the paper. While not every student necessarily goes through all four phases, an awareness and understanding of them all allows for efficient, effective intervention during the learning process. We found that guidance and learning intervention helped shorten the preliminary phases, leading to more relative time spent on probabilistic calculations.

This paper presents an innovat ive cons t ruct ion of a probabilistic model for predicting chance situations. It describes the construction of a four phase model, derived from an intense qualitative analysis of the written responses of 94 mathematically talented middle school students to the probabilistic compound event problem: “How many doubles are expected when rolling two dice fifty times?” We found that the students’ comprehension process of compound event situations can be broken down into a four phase model: beliefs, subjective estimations, chance estimations and probabilistic calculations. The paper focuses on the development of the model over the course of the experiment, identifying the process the students underwent as they attempted to answer the question. We explain each phase as it was reflected in the students\'' rationalizations. All phases, including their definitions and students’ citations, will be presented in the paper. While not every student necessarily goes through all four phases, an awareness and understanding of them all allows for efficient, effective intervention during the learning process. We found that guidance and learning intervention helped shorten the preliminary phases, leading to more relative time spent on probabilistic calculations.