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.

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.

The purposes of this study were 1) to determine the effect upon the arithmetic computation, concepts, and application skills of pupils when the regular instructional program in arithmetic at the fifth- and seventh-grade levels was supplemented with the Cyclo-Teacher (2) programmed materials; 2) to determine the effect upon the arithmetic computation, concepts, and application skills of pupils when the regular instructional program in arithmetic at the fifth- and seventh-grade levels was supplemented with the Mental Computation (6) materials.

The purpose of this research is to explore preservice teachers’ attitudes and beliefs towards mathematics, mental and written computations, and mental computation anxiety, to investigate their use of different mental computation strategies using different approaches (i.e., Direct Teaching (DT) and Open-Approach (OA)) among the three different groups, and to identify how the use of preservice teachers’ mental computation strategies affects their flexibility regarding mental computation. The participants were preservice teachers (PTS). Three classes were used for this study: two classes in a mathematics class (Course A) for experimental groups and one class for the control group. One class from professional education courses was selected. A mixed methods design was used, more specifically, the Mathematics Attitude Survey (MAS) was administrated before and after intervention to examine PTS’ attitudes towards mathematics, mental and written computation, and mental computation anxiety. In addition, to determine whether there is any statistically significant difference among the three groups, the one-way analysis of variance (ANOVA) was used. Then, the MAS was analyzed descriptively. Next, a pre-and post-Mental Computation Test (MCT) was given to investigate PTS’ mental computation knowledge in relation to whole numbers, integers, and rational numbers (i.e., fractions, decimals, and percentages). A one-way analysis of covariance (ANCOVA) was conducted to determine if there were significant differences in mental computation performance among the three groups (i.e., DT, OA, and Control) with different instructions. Further, before and after intervention, face-to-face interviews were given to both the experimental and control groups to identify how they arrived at their answers. During interviews, 38 interviewees in the pre-interviews and 36 in the post-interviews for all groups participated. The interview items were selected from the pre-and post-MCT problems. Three levels of problems (i.e., high, medium, and low difficulty) for each operation were selected. The results of the MAS showed that with respect to the attitudes towards mathematics, PTS were generally shown positive attitudes towards learning mathematics and were aware of the importance of learning mathematics; however, in reality, about half of them did not want to spend time on learning or studying mathematics. In terms of PTS’ attitudes towards mental and written computation, PTS were aware that learning mental computation is more useful in real life situations and provides benefits in their mathematics learning. However, they do not feel comfortable and safe when using mental computation because of their lack of confidence and teaching abilities. For the mental computation, PTS showed slightly higher anxiety levels from pre-to post-tests. The findings of Mental Computation Test (MCT) revealed that there was a statistically significant difference in post-MCT scores between the different instructional groups when adjusted for pre-MCT scores. In particular, PTS using Open-Approach (OA) performed better than the PTS in the group using Direct Teaching (DT). The PTS in the control group performed worst. Significant differences between pre-and post-MCT performance were found among the three groups in solving multiplication, fraction, and decimal operations. The results of interviews suggest that there was an association between each interviewee’s quintile level and their flexibility in the use of the mental computation strategies. Regarding the whole number operation strategies, the results revealed that the interviewees in the middle and upper quintiles in both DT and OA used more than two different strategies with higher accuracy and were more likely to use the strategies. Interviewees in the middle and upper quintiles for the DT and OA groups were more likely to use the strategies that reflect efficient number facts or number-sense (e.g., Adding by place, Decomposing, & Compensation). The mental image of the Traditional method was frequently observed in the OA group. In contrast, for the lower quintiles, alternative strategies were not provided for both groups. The interviewees in the control group offered the smallest range of strategies. For the integer and rational operations, the interviewees in the DT group showed strategies that focused more on conceptual understanding. Surprisingly, the interviewees in the OA group were more likely to apply teacher-taught methods, including the Traditional method. The control group was not able to provide any alternative strategies. Plans for future research are set forth to add to the body of knowledge that exists regarding mental computation.

This study was conducted to analyse aspects of mental computation within primary school mathematics curricula and to formulate recommendations to inform future revisions to the Number strand of mathematics syllabuses for primary schools. The analyses were undertaken from past, contemporary, and futures perspectives. Although this study had syllabus development in Queensland as a prime focus, its findings and recommendations have an international applicability. Little has been documented in relation to the nature and role of mental computation in mathematics curricula in Australia (McIntosh, Bana, & Farrell, 1995,p. 2), despite an international resurgence of interest by mathematics educators. This resurgence has arisen from a recognition that computing mentally remains a viable computational alternative in a technological age, and that the development of mental procedures contributes to the formation of powerful mathematical thinking strategies (R. E. Reys, 1992, p. 63). The emphasis needs to be placed upon the mental processes involved, and it is this which distinguishes mental computation from mental arithmetic, as defined in this study. Traditionally, the latter has been concerned with speed and accuracy rather than with the mental strategies used to arrive at the correct answers. In Australia, the place of mental computation in mathematics curricula is only beginning to be seriously considered. Little attention has been given to teaching, as opposed to testing, mental computation. Additionally, such attention has predominantly been confined to those calculations needed to be performed mentally to enable the efficient use of the conventional written algorithms. Teachers are inclined to associate mental computation with isolated facts, most commonly the basic ones, rather than with the interrelationships between numbers and the methods used to calculate. To enhance the use of mental computation and to achieve an improvement in performance levels, children need to be encouraged to value all methods of computation, and to place a priority on mental procedures. This requires that teachers be encouraged to change the way in which they view mental computation. An outcome of this study is to provide the background and recommendations for this to occur. The mathematics education literature of relevance to mental computation was analysed, and its nature and function, together with the approaches to teaching, under each of the Queensland mathematics syllabuses from 1860 to 1997 were documented. Three distinct time-periods were analysed: 1860-1965, 1966-1987, and post-1987. The first of these was characterised by syllabuses which included specific references to calculating mentally. To provide insights into the current status of mental computation in Queensland primary schools, a survey of a representative sample of teachers and administrators was undertaken. The statements in the postal, self-completion opinionnaire were based on data from the literature review. This study, therefore, has significance for Queensland educational history, curriculum development, and pedagogy. The review of mental computation research indicated that the development of flexible mental strategies is influenced by the order in which mental and written techniques are introduced. Therefore, the traditional written-mental sequence needs to be reevaluated. As a contribution to this reevaluation, this study presents a mental-written sequence for introducing each of the four operations. However, findings from the survey of Queensland school personnel revealed that a majority disagreed with the proposition that an emphasis on written algorithms should be delayed to allow increased attention on mental computation. Hence, for this sequence to be successfully introduced, much professional debate and experimentation needs to occur to demonstrate its efficacy to teachers. Of significance to the development of efficient mental techniques is the way in which mental computation is taught. R. E. Reys, B. J. Reys, Nohda, and Emori (1995, p. 305) have suggested that there are two broad approaches to teaching mental computation,,Ya behaviourist approach and a constructivist approach. The former views mental computation as a basic skill and is considered an essential prerequisite to written computation, with proficiency gained through direct teaching. In contrast, the constructivist approach contends that mental computation is a process of higher-order thinking in which the act of generating and applying mental strategies is significant for an individual's mathematical development. Nonetheless, this study has concluded that there may be a place for the direct teaching of selected mental strategies. To support syllabus development, a sequence of mental strategies appropriate for focussed teaching for each of the four operations has been delineated. The implications for teachers with respect to these recommendations are discussed. Their implementation has the potential to severely threaten many teachersf sense of efficacy. To support the changed approach to developing competence with mental computation, aspects requiring further theoretical and empirical investigation are also outlined.