This study investigates the relationship between the beliefs of early childhood education teachers and their use of the teaching strategies instruction and negotiation in relation to the scaffold process. Consideration of thinking skills and the ability to problem solve through the vehicle of play provided the background to the research focus. The research was undertaken in two differently structured early childhood education centres in New Zealand with a case study design framing the gathering of data through observations and interviews. It is a small qualitative study driven by socio-cultural theory and therefore considered from a social constructivist position. The main findings from observations and interviews revealed that not all teachers had congruency between their beliefs and practice, that instruction could be the only mediation within a scaffolding process and by considering the power relations in the learning and teaching situation, a model of how different teaching strategies could be related to different states of thinking. A key finding was that of a definition of negotiation as a teaching strategy.

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Previous research showed that the use of laboratory materials, cooperative learning or rich mathematical problems promotes problem solving teaching and has a significant role in student learning. That is why the intention of this study was to investigate how the three concepts are used in problem solving teaching and how they can promote this type of mathematics teaching. In order to produce results for the purpose of the study, eight interviews were conducted with eight active primary school teachers to answer the following questions: 1) How do teachers describe their use of laboratory material, cooperative learning and rich mathematical problems in problem-solving teaching? 2) What opportunities and difficulties do teachers see with the use of these concepts? The results showed that the integration of laboratory material in the form of everyday materials, pedagogical materials and digital materials in problem solving teaching has a positive impact on students' problem solving skills and contributes to increased interest in mathematics teaching. It also appeared that the use of these materials enables the students to understand the abstract mathematical content in a clear way. The results of the study showed that the use of cooperative teaching is beneficial for students' development in problem solving. Through this way of working, the students' participation and activity in the classroom is strengthened and increased, which contributes to the students being able to achieve a desired result together. The results analysis clarified that the use of certain criteria for rich mathematical problems are important and necessary to be met in problem solving, while other criteria may be difficult to meet. But previous research showed that all seven criteria for rich math problems are necessary in problem solving tasks.

Syftet med denna studie är att undersöka hur matematiklärare beskriver digitala lärresursers användbarhet i sin problemlösningsundervisning. För att undersöka detta har flera kvalitativa semistrukturerade intervjuer genomförts. De genomförda intervjuerna med lärarna har analyserats med hjälp av TPACK-ramverket och visar att problemlösning med digitala lärresurser har både fördelar och nackdelar. De fördelar som lärarna lyfter fram berör i huvudsak individualisering och differentiering, exempelvis att det är enkelt att hitta och anpassa uppgifter till respektive elevs nivå. Nackdelarna handlar främst om digitala läromedlens funktion, bland annat att det finns för få och för enkla problemuppgifter. Digitala lärresurser möter delvis lärarnas förväntningar, men resultatet visar också på vilken utvecklingspotential som finns. / The purpose of this study is to examine how mathematical teachers describe digital teaching resources usefulness in their problem-solving teaching. To examine this, we have conducted several qualitative semi-structured interviews. The completed interviews with the teachers have been analyzed using the TPACK-framework and show that problem-solving using digital resources have both pros and cons. According to the teachers the advantages are mainly connected to individualization and differentiation, for example it is easy to find and adjust tasks to each pupil’s level. The disadvantages concern the function of digital teaching aids, among other things, there are too few and too simple problem-solving tasks. Overall digital resources match the teacher’s expectations, but the result also indicate the potential for development.

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