Problemlösning är en central del av Lgr11 och dagens matematikundervisning. Detta gör att de läromedel som används i de svenska skolorna måste behandla problemlösning om de ska kunna ge eleverna möjlighet att nå de utsatta målen i Lgr11. I årskurs 6 ska eleverna få betyg i matematik vilket gör det viktigt att undersöka om läromedlen når upp till målen i lgr11 runt om problemlösning. Studien är gjord som en läromedelsanalys, av Matte Direkt Borgen 6a och 6b. Min studie är en kvantitativ studie i två delar. Först analyserade jag hur många av de problem som enligt författaren anser är problem är problemuppgifter eller rutinuppgifter. Av det resultatet kunde jag sedan analysera hur väl problemlösningsförmågan, begreppsförståelse och resonemangsförmågan gick att öva via uppgifterna i läromedlet. Resultatet visade att bara 59 av de 137 uppgifter som författaren anser är problemuppgifter gick att klassificera som problemuppgifter. Förmågorna som övades via uppgifterna spelade dock ingen roll om det var problem- eller rutinuppgifter. Här övade alla uppgifter någon av de tre undersökta förmågorna. / Problem solving is a central part of Lgr11 and today's mathematics education. This allows the teaching materials used in the Swedish schools must treat the problem if they are to provide students with the knowledge to reach the vulnerable requirements of Lgr11. In Year 6, pupils get grades in mathematics, making it important to conduct research about learning reaches Lgr11 targets around the problem solving. The study is designed as a teaching material analysis, of Matte Direkt Borgen 6a and 6b. My study is a quantitative study in two parts. First, I analyzed how many of the problems according to the author considers to be problems are problems tasks or routine tasks. Of the result, I could then analyze how well the problem-solving ability, conceptual understanding and reasoning ability went to practice using the information in the teaching material. The results showed that only 59 of the 137 tasks which the author believes is the problem tasks could be classified as problem tasks. The abilities who was exercised by the data, however, does not matter if it was a problem or routine tasks. Here practiced all the information any of the three investigated abilities.

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This mixed-methods study investigated the relationship between self-concept and problem-solving style and how these two constructs compared and contrasted in regards to a participant's perception of his or her problem-solving ability. The 86 study participants were high-achieving rising 11th and 12th grade students attending a summer enrichment program for agriculture. This study used a concurrent triangulation mixed methods design. The quantitative aspect of the study employed two instruments, SDQ III to test perceived self-concept and the VIEW to determine the perceived problem-solving style. Concurrent with this data collection, 13 open-ended interviews were conducted to explored the description of the problem-solving process during a problem-solving event. The reason for collection of both quantitative and qualitative data was to bring together the strengths of both forms of research in order to merge the data to make comparisons and further the understanding of problem-solving ability of high-achieving youth. The study discovered that self-concept and problem-solving style have a weak relationship for many of the constructs and a negative relationship between two of constructs. The qualitative component revealed that high-achieving youth had clear definitions of problem-solving, a rich and descriptive heuristic approach, a clear understanding of which resources provided key information, and a strong depiction of themselves as problem-solver. An emergent concept from the research was the participants' perceptions of the team-based structure and how the inclusion of multiple ability levels versus high ability levels affected the participants' perceptions of solving a problem in a team situation. The mixing component of the study depicted the influence of self-concept on the problem-solving style. This study was an initial exploration of the relationship between self-concept and problem-solving and compared the current results with previous research. It extended and connected the previous research areas of self-concept and problem-solving style. As an initial study, it led to recommendations for further research across education as well as additional exploration of the emergent relationships identified. Finally, the study denoted the importance of mixed-methods research due to the interconnectivity between self-concept and problem-solving style and the participant descriptions of themselves as problem-solvers. / Ph. D.

The purpose of the present study was to use an alternate psychoeducational assessment method to examine learning potential of Indian students in an academic domain, specifically Algebra. The study examined six Indian adolescents early in their Year Seven Mathematics. For the purpose of this study, the students were classified as achievers or non-achievers based on Canadian Test of Basic Skills (CTBS) grade equivalent scores, and Grade 7 Mathematics marks on the First Report Card.<p> A cross-case analysis of verbal and nonverbal protocol data gathered from the six Indian achieving and non-achieving Grade Seven students, and reduced through use of a technique developed by Giorgi, yielded information regarding the subjects' internalization processes of algebraic concepts. Vygotsky's zone of proximal development methodology, which was employed in the study, permitted the researcher to investigate processes used by the students during learning, maintenance, and near and far transfer tasks. While verbal and nonverbal communication styles appeared to distinguish achieving from non-achieving students, those same traits did not seem to affect efficiency in problem solving as observed during the present study. Other characteristics such as language usage, questioning techniques, and risk taking were the traits which most clearly affected the students' problem solving skills.<p> During the present study, formal metacognitive data proved hard to collect. This may be attributed to the reluctance of some students to participate in the questioning, and to the difficulty other students experienced In understanding the questions. All students had difficulty at some stage of the study in generating a rule to explain how they had solved the problems.<p> The results of the present study indicated that there were qualitative differences in problem solving between subjects. Those qualitative differences did not follow a pattern of achievement versus non-achievement as delineated by CTBS scores and classroom evaluation in Mathematics. Zone proximal development methodology provided a process assessment which uncovered learning potential profiles that were masked by static standardized tests.

The purpose of the present study was to use an alternate psychoeducational assessment method to examine learning potential of Indian students in an academic domain, specifically Algebra. The study examined six Indian adolescents early in their Year Seven Mathematics. For the purpose of this study, the students were classified as achievers or non-achievers based on Canadian Test of Basic Skills (CTBS) grade equivalent scores, and Grade 7 Mathematics marks on the First Report Card.<p> A cross-case analysis of verbal and nonverbal protocol data gathered from the six Indian achieving and non-achieving Grade Seven students, and reduced through use of a technique developed by Giorgi, yielded information regarding the subjects' internalization processes of algebraic concepts. Vygotsky's zone of proximal development methodology, which was employed in the study, permitted the researcher to investigate processes used by the students during learning, maintenance, and near and far transfer tasks. While verbal and nonverbal communication styles appeared to distinguish achieving from non-achieving students, those same traits did not seem to affect efficiency in problem solving as observed during the present study. Other characteristics such as language usage, questioning techniques, and risk taking were the traits which most clearly affected the students' problem solving skills.<p> During the present study, formal metacognitive data proved hard to collect. This may be attributed to the reluctance of some students to participate in the questioning, and to the difficulty other students experienced In understanding the questions. All students had difficulty at some stage of the study in generating a rule to explain how they had solved the problems.<p> The results of the present study indicated that there were qualitative differences in problem solving between subjects. Those qualitative differences did not follow a pattern of achievement versus non-achievement as delineated by CTBS scores and classroom evaluation in Mathematics. Zone proximal development methodology provided a process assessment which uncovered learning potential profiles that were masked by static standardized tests.

This study is centred on an analysis of pupils' lived experience while engaged in the generalisation of linear sequences/progressions presented in a pictorial context. The study is oriented within the conceptual framework of qualitative research, and is anchored within an interpretive paradigm. A case study methodological strategy was adopted, the research participants being the members of a mixed gender, high ability Grade 9 class of 23 pupils at an independent school in South Africa. The analytical framework is structured around a combination of complementary multiple perspectives provided by three theoretical ideas, enactivism, figural apprehension, and knowledge objectification. An important aspect of this analytical framework is the sensitivity it shows to the visual, phenomenological and semiotic aspects of figural pattern generalisation. It is the central thesis of this study that the combined complementary multiple perspectives of enactivism, figural apprehension and knowledge objectification provide a powerful depth of analysis to the exploration of the inter-relationship between the embodied processes of pattern generalisation and the visualisation of pictorial cues. The richly textured tapestry of activity captured through a multi-systemic semiotic analysis of participants' generalisation activity stands testament to this central thesis. Insights gleaned from this study are presented as practical strategies which support and encourage a multiple representational approach to pattern generalisation in the pedagogical context of the classroom.

Utan förmågan att uppleva vare sig stress eller smärta hade mänskligheten inte överlevt fram tills idag. Dessvärre uppstår stress- och/eller smärtreaktioner för oss människor vid icke livshotande situationer och tenderar i vissa fall att få motsatt effekt. Detta bidrar till lidande på individnivå, men leder också till stora kostnader för samhället, framförallt i form av sjukskrivning. Problemen hänger ofta ihop, många arbetstagare lider både av stress- och smärtproblematik. Enligt den transdiagnostiska modellen vidmakthåller liknande (s.k. transdiagnostiska) faktorer både stress- och smärtrelaterad ohälsa. Det skulle vara användbart ur flera olika perspektiv att undersöka och förstå mer exakt vilka transdiagnostiska faktorer som förekommer vid stress- och smärtproblematik samt hur kopplingen till arbetsförmåga ter sig. Föreliggande studie utgick från tvärsnittsdata, N=139 (100% kvinnor) svarade via internetbaserade enkäter. Analysen visar samband mellan stress och/eller smärta och arbetsförmåga, både stress och smärta visar unika negativa effekter på arbetsförmåga. Vi fann tre olika undergrupper baserat på relativa nivåer av stress- och smärtproblematik. Gruppen med höga nivåer av självskattad stress- och smärtproblematik visade låga nivåer av problemlösningsförmåga och höga nivåer av katastrofiering. Det diskuterades kring dessa transdiagnostiska faktorers koppling till stress- och smärtproblematik. Transdiagnostiska faktorer kan med fördel beaktas för effektivare behandling och bör undersökas vidare i framtida forskning. / Without the ability to experience neither stress nor pain, humanity would not survive. Unfortunately, stress and pain reactions sometimes occur in non-life-threatening situations and seem to be less functional in some cases. This contributes to suffering for individuals and enormous costs for society. The problems are often related, many workers suffer from both stress and pain problems. Similar (so-called transdiagnostic) factors maintain both stress and pain related illness according to the transdiagnostic model. It would be useful from several perspectives to investigate and understand which transdiagnostic factors are present in stress and pain problems, as well as how the connection to work ability expresses itself. This study was based on cross-sectional data, N=139 (100% females) responded to an internet-based survey. Analysis shows that pain and stress together predict work ability, both stress and pain show unique negative effects on work ability. We found three subgroups, one of the groups stood out from the others with high levels of stress and pain. The same group showed low problem-solving ability and high on catastrophizing, which are theoretical transdiagnostic factors. These factors and their relationship to stress and pain problems were discussed. Future research and eventual treatment need to take transdiagnostic factors into consideration.

Syftet med studien var att undersöka vad elever i årskurs 6 upplever vid arbete med problemlösning inom matematik. Studiens frågeställningar var följande: Vilka upplevelser ger eleverna uttryck för vid problemlösning och påverkar dessa upplevelser eventuellt deras resultat samt upplever eleverna svårigheter vid problemlösning, i så fall vilka? För att besvara syftet fick tio årskurs 6-elever en problemlösningsuppgift från ett gammalt nationellt prov. Sedan utfördes kvalitativa intervjuer med eleverna. Insamlade data bearbetades genom tematisk analys där koder hittades som sedan skapade olika kategorier och underkategorier. Det som framkom var arbetsprocess, information och upprepad läsning, bildlig representation, elevernas inställning, kognitiva aspekter, tankeprocess samt tidigare kunskaper och förståelse. Tillsammans med studiens bakgrund och kognitivismen bearbetades resultatet. Eleverna visade ofta en, men olika upplevelser, varav några visade flera upplevelser. Vi ansåg att elevernas upplevelser påverkade deras resultat på olika sätt. Inom de framkomna kategorierna ansåg vi att faktorerna oförståelse, negativ inställning och bristande tidigare kunskaper var svårigheter som eleverna upplevde. / The purpose of the study was to investigate what students' in year six experience  while working with problem solving in mathematics. The research questions were: what experiences do the students express in problem solving and does these experiences affect their results and also do the students experience difficulties in problem solving, if so which ones? To answer the purpose, ten sixth grade students were given a problem solution from an old national test. Qualitative interviews were then conducted with the students. Collected data were processed through thematic analysis where codes were found, which then created different categories and subcategories. The outcome was work process, repeated reading and information,  image representation, students' attitudes, cognitive aspects, thought process  and previous knowledge and understanding. The results were processed through the studies literature and the cognitive perspective. The students showed different experiences, some of which showed several. We felt that students' experiences affected their results in different ways. From the categories, we believe that the factors of incomprehension, negative attitude and lack of previous knowledge were difficulties that the students experienced.

Syftet med studien är att undersöka om problemlösningsuppgifter i läroböcker ger möjlighet till utveckling av problemlösningsförmågan. I studien har innehållsanalys valts som metod och med hjälp av Schoenfeld’s ramverk och Skolverkets kommentarmaterial har ett resultat skrivits fram. I resultatet framgår det att förekomsten av problemlösningsuppgifter i läromedlet Favorit matematik för årskurs 3 är låg. Vidare visar resultatet att majoriteten av problemlösningsuppgifterna ger elever möjlighet att utveckla fyra av de fem delförmågorna i problemlösningsförmågan samtidigt. Studiens slutsats är att läroböcker i matematik bör analyseras för att ge elever möjlighet att arbeta med problemlösningsuppgifter och säkerställa deras utveckling av problemlösningsförmågans olika delar. / The purpose of the study is to investigate whether problem-solving tasks in textbooks provide an opportunity for the development of problem-solving ability. In the study, content analysis has been chosen as the method and with the help of Schoenfeld's framework and the Swedish National Agency for Education's commentary material a result has been produced. In the result appears that the occurrence of problem-solving tasks in the learning material Favorit matematik for grade 3 is low. Furthermore, the results show that most of the problem-solving tasks give pupils the opportunity to develop four of the five sub-skills in the problem-solving ability at the same time. The study's conclusion is that textbooks in mathematics should be analyzed to give pupils the opportunity to work with problem-solving tasks and ensure their development of the different parts of problem-solving ability.

Tidigare studier har visat att matematiken i svenska skolan till övervägande del handlar om att räkna i läroboken samtidigt som det också påvisats att dessa i för låg utsträckning innehåller uppgifter som låter eleverna arbeta med problemlösning. Forskning menar att problemlösningsförmågan handlar om att ha en bred repertoar av strategier och en förståelse för hur dessa hänger samman och hur de kan användas. Förmågan förklaras som att kunna tänka kreativt och värdera sina kunskaper för att på bästa sätt angripa ett problem. För att utveckla detta måste eleverna få diskutera, konstruera egna problem och lösa problem på många sätt. De måste också få lösa många problem under en lång period. Denna studie har jämfört två läroböcker i årskurs fem som används i skolor och tittat på deras innehåll och uppbyggnad för att se hur de möjliggör utvecklingen av problemlösningsförmågan. Studien visade att båda läromedlen innehåller en låg andel matematiska problem och eleverna uppmanas att diskutera mycket lite. Eleverna ombeds aldrig att lösa ett problem på fler än ett sätt och bara i det ena läromedlet får eleverna träna på att skapa egna problem. Slutsatsen blev att båda läromedlen behöver kompletteras med annan undervisning om eleverna ska utveckla problemlösningsförmågan i matematik. / Previous studies have shown that mathematics in Swedish school for most part consists of calculating in the textbook when it at the same time has been proven that the textbooks in a too low extent contains tasks that allow the pupils to work with problem solving. Research mean that the problem-solving ability is about having a broad repertoire of strategies and an understanding for how these are associated and how they can be used. The ability is described as being able to think creatively and to evaluate one’s knowledges to tackle a problem as good as possible. To develop this, the pupils need to get the opportunity to discuss, create own problems and solve problems in many ways. They also must get to solve many problems during a long period of time. This study has compared two textbooks for grade five which are used in Swedish schools and has looked at their content and structure to see how they enable the development of the problem-solving ability. The study showed that both textbooks contain a low proportion of mathematical problems and the pupils are encouraged to discuss very little. The pupils are never asked to solve a problem in more than one way and only in one of the teaching materials the pupils get to practice making own problems. The conclusion was that both teaching materials need to be complemented by other education if the pupils are to develop the problem-solving ability in mathematics.