Thesis (Ph. D.)--University of Toronto, 2007. / Source: Dissertation Abstracts International, Volume: 68-06, Dec 2007. Includes bibliographical references (leaves 193-209).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1974. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

No description available.

This case study centres round an afterschool intervention programme aimed at enhancing mental computation skills of Grade 8 learners at a secondary school in the Erongo educational region of Namibia. Nine research participants took part in the study, and the mental computational strategies exhibited by these participants constitutes the unit of analysis. The study is anchored within an interpretive paradigm and is theoretically underpinned by constructivist epistemology. Kilpatrick, Swafford and Findell’s (2001) model of mathematical proficiency provides the conceptual framework supporting the study. The research was carried out in four sequential phases – an initial pre-test, the intervention itself, a follow-up post-test, and a focus group discussion. The study highlights the underdevelopment of mental computation skills and the associated lack of appropriate mental computational strategies in secondary school learners. It is recommended that appropriate time within the school curriculum be allocated for the development of learners’ mental computation skills.

No description available.

Studien utgår från en kvalitativt inriktad analys och metod, där syftet är att undersöka vilka huvudräkningsstrategier som 3 svenska respektive 3 engelska lärare undervisar i, inom addition. Det empiriska materialet består av intervjuer som sedan har transkriberats och analyserats. Studien har låtit sig inspireras av ett hermeneutiskt perspektiv kombinerat med Grounded Theory. Hermeneutiskt perspektiv innebär att all data som finns i studien har tolkats och analyserats. Grounded Theory är ett vanligt sätt att analysera kvalitativ data och genom denna teori har kategorier skapats utifrån det resultat som framkommit. Resultatet av studien visar att de svenska lärarnas vanligaste val av strategier är: talsorter var för sig och algoritmer. De engelska lärarnas vanligaste val av strategier är: tiokamrater, additionstabellen och algoritmer. Av resultatet framkommer även de skillnader som finns mellan de intervjuade lärarnas val av strategier. / The study is based on a qualitatively directed method and the main aim is to investigate, and examine the mental arithmetic strategies of both Swedish and English teachers. In particular, the methods they use, to teach addition. The empirical data within this research is based on first hand interviews with six teachers; three from Sweden, and three from England. The study is inspired by a Hermeneutic Perspective in combination with Grounded Theory. The word hermeneutic, means that all of the data contained in the study has been interpreted and analyzed by the researcher. Grounded Theory is a common method used to analyze qualitative data. With this theory, categories have been created on the basis of the results obtained within this study. The results of the study show that Swedish teachers' most common choices of strategies are; partitioning method, and algorithms. In contrast, the English teachers’ strategies are the following; number bonds, the additiontable and algorithms. The results of this study also illustrate the differences between the Swedish and the English teachers’ choices of strategies.

Thesis advisor: Marina Vasilyeva / The ability to mentally store and manipulate information, termed working memory (WM), is essential to mathematical performance. Yet, little research has investigated the mechanisms through which WM capacity is related to mathematical performance in children. Furthermore, the extent to which children utilize specific WM resources when executing mathematical tasks is poorly understood. Addressing these gaps, this research investigated the nature of relations between WM and children's mathematical performance. Participants were 56 second and 32 fourth grade students from public and private elementary schools. Students completed tasks measuring their visuospatial-WM and verbal-WM capacities, the strength of their spatial and symbolic representations of numerical magnitude, and arithmetic performance. Arithmetic strategies were also assessed. In a dual-task condition, children's WM resources were experimentally manipulated: children completed mathematical tasks while retaining visuospatial and verbal stimuli in memory. Results showed that the relation between visuospatial-WM capacity and arithmetic accuracy was mediated by children's spatial numeric representations and the frequency of using a decomposition strategy in solving arithmetic problems. Conversely, the relation between verbal-WM and arithmetic accuracy was mediated by the frequency of using retrieval strategies in solving arithmetic problems. Additionally, the extent to which specific WM resources were involved in children's math performance varied by math task and children's skill level. Verbal-WM resources appeared to be minimally involved in children's spatial numerical representations, but highly involved in symbolic numerical representations and arithmetic calculations. On all math tasks, visuospatial-WM resources were involved to a greater extent among highly skilled children than low-skill children. The results suggest that WM capacity might improve spatial numerical representations and lead children to use memory-based arithmetic strategies more frequently, resulting in better arithmetic performance. Regardless of WM capacity, children who heavily use visuospatial-WM resources are more successful in executing mathematical tasks than children who rely on these resources minimally. These findings contribute to our understanding of how WM can facilitate children's mathematical performance. Implications for identifying specific challenges in children's mathematical learning are discussed. / Thesis (PhD) — Boston College, 2014. / Submitted to: Boston College. Lynch School of Education. / Discipline: Counseling, Developmental and Educational Psychology.

Thesis (M.A.)--Carleton University, 2004. / Includes bibliographical references (p. 56-60). Also available in electronic format on the Internet.

Huvudräkning är den av de matematiska förmågorna vi lär oss i skolan som vi sedan oftast använder utanför och efter skolan. Därför är det ur ett samhällsperspektiv viktigt att alla skolelever får lära sig huvudräkning. Studiens syfte är att undersöka hur elever i åk 8 gör när de löser additions- och subtraktionsuppgifter med huvudräkning samt hur de kommunicerar om sitt arbete med huvudräkningen. Empiriska data samlades in genom intervjuer med 11 elever där eleverna fick lösa 11 huvudräkningsuppgifter och svara på frågor om hur de upplevde arbetet med att lösa uppgifterna. Huvudräkningsuppgifter kan lösas med hjälp av talfakta, uppräkning, visualiserad uppställning eller en sekvens av åtgärder, ofta kallat att använda strategier. Flexibel huvudräkning består av talfakta, förmåga, förståelse och attityd. Intervjudata sorterades och analyserades utifrån dessa fyra komponenter. Resultaten från studien visar att alla eleverna har tillräckligt god kunskap om talfakta för att lösa uppgifterna under intervjun. Förmåga består av kunskap om metoder och procedurer samt kommunikativ förmåga. Eleverna visade olika grad av procedurförmåga. De använde mellan fem och nio olika strategier för att lösa de 11 uppgifterna. Den kommunikativa förmågan var avsevärt lägre än procedurförmågan hos alla elever. Det märktes inte minst av att eleverna hade svårt att hitta rätt begrepp när de skulle berätta om sina lösningar. Förståelse har i det här arbetet brutits ner i taluppfattning, flexibelt eller mekaniskt val av strategi, mentala bilder och medvetenhet i val av strategi. Vissa elever väljer strategi efter talens beskaffenhet och numeriska relationer, medan andra i möjligaste mån håller sig till de bäst inövade strategierna oavsett talen i uppgiften. Under intervjuerna framkom att de flesta eleverna hade någon form av mentala bilder till hjälp när de räknade. Ingen av eleverna förklarade hur de gjorde när de bestämde vilken strategi de skulle använda, vilket tolkats som att de valde strategi undermedvetet. I komponenten attityd ingår tillit till sin egen förmåga och hur ansträngande huvudräkningsuppgifterna i intervjun upplevdes. Ansträngningen skattades av eleverna på en skala 1-10 och svaren varierade mellan 1-8. Flera elever uppgav en skattning för själva arbetet att räkna och en högre skattning när momentet att förklara sina beräkningar inkluderades. Ett problem ur ett samhällsperspektiv är att drygt två tredjedelar av eleverna i studien har så låg tillit till sin förmåga att räkna huvudräkning. Komponenten attityd befanns vara den svagaste delen i elevernas huvudräkning, följt av förståelse. För att stärka elevernas självförtroende är det viktigt att de får känna att de lyckas. Ett sätt att uppnå det är att arbeta mer med muntlig kommunikation, så att idéer får prövas och tankar utvecklas. / Arithmetic is one of the mathematical skills we learn in school, which we most frequently use outside and in our grown up life. Therefore, from a societal perspective, it is important that all school students learn arithmetic. The purpose of the study is to investigate how students in year 8 do when they solve addition and subtraction problems with mental arithmetic and how they communicate about their work with mental arithmetic. Empirical data were collected through interviews with 11 students where the students had to solve 11 mental arithmetic problems and answer questions about how they experienced the work of solving the problems. Mental arithmetic can be done using number facts, counting, a mental representation of a written procedure or by constructing a sequence of transformations, often called using strategies. Flexible mental arithmetic consists of four components: number facts, ability, understanding and attitude. The interview data were sorted and analyzed based on these four components. The results from the study show that all students have sufficient knowledge of number facts to solve the problems presented at the interview. Ability consists of knowledge of methods and procedures as well as communicative ability. The students showed different degrees of procedural ability. They used between five and nine different strategies to solve the 11 problems. The communicative ability was significantly lower than the procedural ability of all students. It was not least noticed that the students had difficulty finding the right concepts when they had to talk about their solutions. Understanding has here been broken down into number perception, flexible or instrumental choice of strategy, mental images and awareness in choice of strategy. Some students choose strategy according to the nature of the numbers and numerical relations, while others, as far as possible, stick to the best practiced strategies regardless of the numbers in the problem. During the interviews, it emerged that most students had some form of mental pictures to help when they calculated. None of the students explained how they did when deciding which strategy to use, which was interpreted as them choosing strategy subconsciously. The attitude component includes confidence in one's own abilities and how strenuous the interview tasks were experienced. The effort was rated by the students on a scale of 1-10 and the answers varied between 1-8. Several students stated one estimate for the actual work of calculating and a higher estimate when the element of explaining their calculations was included. A problem from a societal perspective is that just over two thirds of the students in the study have such low confidence in their ability to do mental arithmetic. The attitude component was found to be the weakest part of students' mental arithmetic, followed by comprehension. To strengthen students' self-confidence, it is important that they feel that they are succeeding. One way to achieve this is to work more with oral communication, so that ideas can be tested and thoughts developed.

Under den verksamhetsförlagda tiden väcktes intresset för huvudräkning hos mig, ef­tersom eleverna valde att använda sig av miniräknare trots att de hade kunskap om olika huvudräk­ningsstrategier. Enligt skolverket (2011b) skall eleverna vid huvudräkning ta del av olika strategier för att stärka självsäkerheten och tilltron till sin förmåga. Syftet med studien var att undersöka vilken eller vilka strategier som några elever i grundskolan föredrog vid huvudräk­ning inom addition och subtraktion. Undersökningen byggde på en kvalitativ metod och her­meneutiken som teoretisk forskningsansats. Urvalet bestod av ett målinriktat urval kombinerat med ett bekvämlighetsurval och resulterade i tre elever från vardera tre olika skolor och skol­områden. Huvudräkningsuppgifter samt intervjuer användes som datainsamlingsmetod. Data­bearbetningen av intervjuerna har utförts under inspiration av hermeneutiken som bygger på tolkningar. Resultatet av studien visade att inom addition är det strategin talsorter var för sig, algoritm och dubbla som elever föredrar helst. Inom subtraktion varierade eleverna mer vid valet av huvudräkningsstrategier, där de helst föredrar räkna uppåt, algoritm, jämföra, tals­orter var för sig, komplettera, lägga till och räkna neråt. Resultatet visade även att skillnaden mellan skolorna inte var så stor, dock fanns det en liten skillnad mellan skola II och skola III vad gäller strategin räkna uppåt. Skillnaden var att skola II föredrar flera olika strategier av­seende subtraktion. Det framgår tydligt att eleverna har en god kunskap om olika huvudräk­ningsstrategier vid addition och subtraktion. Enligt eleverna är det på grund av att lärarna i sin undervisning hade gått igenom olika strategier inom huvudräkning. / During my practical training periods I became interested in mental arithmetic because I expe­rienced that the students chose calculators despite their knowledge of mental arithmetic strat­egies. According to skolverket (2011b) students shall take part of different strategies to strengthen their selfconfidence and belief in their own ability. The purpose of this study was to identify which strategies some students in middle school choose when they are practising mental arithmetic in addition and subtraction. The study was based on a qualitative method and hermeneutic as a theoretical approach. The sample consisted of a targeted selection in combination with a convenience selection and resulted in three students from each of three different schools and school areas. Mental arithmetic tasks and interviews were used as data collection method. Data processing of the interviews has been processed using hermeneutics method and is based on interpretation. The result of the study showed that partitioning num­bers, algorithm and double was the most common mental arithmetic strategies in addition. When it comes to strategies in subtraction the students varied more and the most common was counting upwards, algorithm, compare, partitioning numbers, complementary addition and counting back from. The result also showed that there was no significant difference between the schools except school II and III when it comes to the strategy counting upwards. The dif­ference was that school II uses several different strategies when performing subtractions. It was rather clear that the students in this study had a good knowledge of various mental arithmetic strategies for addition and subtraction, and according to themselves it was a consequence of the various strategies in mental arithmetics, that their teachers had taught them.