The purpose of the study is to investigate factors of 7th graders learning attitude in mathematics. According to the result of this study, the research provides some suggestions for the education authorities, the schools and future study. The approaches used in this research are Questionnaire on Mathematics Learning Attitude. 168 7th graders were randomly sampled at a Junior High School in Kaohsiung City. The feedback undergoes a descriptive statistics, two-sample independent Student t test, Pearson Correlation among other statistical methods. The following are conclusions of the research: 1. Factors of influencing 7th graders Attitude in Mathematics are the following eight elements. They are confidence of learning, influence of teachers, concept about value of mathematics, influence of the art of teaching, efficacy of self-learning, effect of learning, pressure of learning, and fearlessness. 2. Confidence of learning, influence of teachers, concept about value of mathematics, efficacy of self-learning, effect of learning, fearlessness, and grades in mathematics have moderate related. 3. Concept about value of mathematics, effect of learning, influence of teachers, efficacy of self-learning, fearlessness, confidence of learning demonstrate significantly different degrees of respect on students whose grades between above 70 and under 70. 4. Confidence of learning, influence of teachers, concept about value of mathematics, efficacy of self-learning, effect of learning, fearlessness can forecast learning grades in mathematics. Ultimately, based up on the above findings, the researcher of this study proposed 3 suggestions for the authorities concerned and official staffs.

It has been shown in experiments that a method of teaching where students are encouraged to create their own solution methods to mathematical problems (creative mathematically founded reasoning, CMR) results in better learning and proficiency than one where students are provided with solution methods for them to practice by repetition (algorithmic reasoning, AR). The present study investigated whether students in an AR practice condition pay less attention to information relevant for mathematical problem solving than students in a CMR condition. To test this, attentional behavior during practice was measured using eye-tracking equipment. These measurements were then associated with task proficiency in a follow-up test one week after the practice session. The findings support the theory and confirm previous studies in that CMR leads to better task performance in the follow-up test. The findings also suggest that students within the CMR condition whom focus less on extraneous information perform better. / Experiment har visat att en undervisningsmetod i vilken elever uppmuntras att själva komma på lösningsmetoder till matematiska problem (creative mathematically founded reasoning, CMR) resulterar i bättre inlärning och färdighet än en metod i vilken eleverna ges en färdig en lösningsmetod att öva på genom repetition (algorithmic reasoning, AR). Denna studie undersöker om elever under en AR-träningsbetingelse ägnar mindre uppmärksamhet åt information som är relevant för matematisk problemlösning än vad elever under en CMR-träningsbetingelse gör. För att testa detta mättes elevernas uppmärksamhetsbeteende under träning med hjälp av ögonrörelsekamera. Måtten ställdes sedan i relation till uppgiftsfärdighet i ett uppföljningstest en vecka efter träningssessionen. Resultaten stödjer teorin och bekräftar tidigare studier som visat att CMR leder till bättre prestation i uppföljningstestet. Resultaten tyder även på att de elever under CMR-betingelsen som fokuserar minst på ovidkommande information presterar bättre.

Developmental dyscalculia (DD) is a learning disability that is characterized by severe difficulties with acquiring age-appropriate mathematical skills that cannot be attributed to insufficient education, language skills, or motivation. The prevalence rate is estimated at 3-6%, meaning that a substantial portion of the population struggles to learn mathematics to such a large degree that it affects overall well-being and academic prospects. However, our understanding of the etiology of DD is incomplete and there are competing hypotheses regarding the characteristics of DD and its underlying causal factors. The purpose of the current thesis is to contribute to our understanding of DD from the perspective of cognitive psychology and cognitive neuroscience. To this end, we identify children with DD to identify the cognitive determinants of DD that hamper their ability to learn basic mathematics. It is believed that human beings are endowed with an innate ability to represent numerosities, an ability phylogenetically shared with other species. We investigate whether the purported innate number system plays a role in children with DD insofar as  failures in this system may undermine the acquisition of symbolic representations of number. Although some researchers believe DD is a monolithic learning disability that is genetic and neurobiological in origin, the empirical support for various hypotheses suggests that DD may be shaped by heterogeneous characteristics and underlying causes. The present thesis, and the studies presented therein, provides support for the notion that DD is indeed heterogeneous. We identify at least two subtypes of DD that are characterized by specific deficits in number processing, and one subtype that could more aptly be labelled as a mathematical learning disability, the causal factors of which are likely limited to deficits in non-numerical abilities. In addition, we locate candidate neurocognitive correlates that may be dysfunctional in DD. / Dyskalkyli är en specifik inlärningssvårighet som karaktäriseras av stora svårigheter med att tillgodogöra sig matematikkunskaper som inte kan härledas till bristande undervisningsmöjligheter, språkfärdigheter, eller motivation. Prevalensen av dyskalkyli uppskattas till 3-6%, vilket innebär att en ansenlig andel av populationen har sådana besvär att lära sig matematik att det påverkar deras allmänna välbefinnande och akademiska möjligheter. Förståelsen för dyskalkyli är emellertid knapphändig, men ett flertal konkurrerande hypoteser har föreslagits avseende dess karaktäristika och kausala faktorer. Syftet med denna avhandling är att öka vår förståelse av dyskalkyli utifrån ett kognitionspsykologiskt perspektiv och utifrån kognitiv neurovetenskap. Följaktligen identifierade vi skolbarn med specifika och stora matematiksvårigheter för att sedermera undersöka vilka kognitiva faktorer som underminerar deras förmåga att förvärva grundläggande matematikfärdigheter. Rådande uppfattning är att människan är utrustad med en medfödd förmåga att uppfatta och representera antal, vilket är en förmåga som vi fylogenetiskt delar med andra arter. Vi undersöker huruvida detta medfödda antalsuppfattningssystem är involverat vid utvecklandet av dyskalkyli hos barn, där ett dysfunktionellt antalsuppfattningssystem kan underminera förmågan att tillgodogöra sig symboliska representationer av antal. Gängse uppfattning gör gällande att dyskalkyli är en enhetlig och homogen inlärningssvårighet som genetiskt och neurobiologiskt betingad. Dock har ett flertal hypoteser angående orsaken till dyskalkyli fått empiriskt stöd, vilket möjliggör tolkningen att dyskalkyli snarare är en heterogen inlärningssvårighet med olika kausala faktorer och egenskaper. Föreliggande avhandling ger stöd för denna senare tolkning. Vi identifierar åtminstone två  subtyper av dyskalkyli, som vardera karaktäriseras av specifika svårigheter med numeriska färdigheter, samt en subtyp som mer korrekt bör benämnas som matematiska inlärningssvårigheter där bidragande faktorer sannolikt kan härledas till icke-numeriska förmågor. Vidare så identifierar vi potentiella neurokognitiva korrelat som är dysfunktionella vid dyskalkyli.

Fifty-eight children of varying math abilities, ranging in age from 7 to 8 years, were tested to investigate the influence of certain low-level cognitive abilities on their use of spatial representations of number magnitude (i.e., the so-called mental number line). A number-line estimation task and a number comparison task were administered to measure their use of the mental number line. A combined spatial-cueing and flanker task was used to assess three attention networks: executive functioning, alerting, and visual attention orienting. Visuospatial working memory was assessed with a mental rotation task, and intelligence was measured with a short-form IQ test. Regression results showed that visuospatial working memory ability was related to performance on the mental number line tasks. Hence, children with stronger visuospatial working memory ability are able to more efficiently manipulate the mental number line, and thus perform better on tasks involving understanding of number magnitude. / October 2015

The purpose of the present study is (1) to investigate factors that influence mathematical problem solving competence for elementary students, (2) to understand the current studies regarding the development of mathematical problem solving competence, and (3) to probe background factors that affect the development of mathematical problem solving competence. The subjects of the study included 710 fifth-graders in Tainan city. The surveys of Thinking Style Inventory, Mathematical Learning Perception Check List as well as Mathematical Problem Solving Competence Test were used as instruments for data collection. A total of 710 questionnaires were delivered and 587valid questionnaires were collected, with fairly high 82.60% return rate. The collected data was tested with descriptive analysis, independent t test¡BANOVA¡Bproduct-moment correlation coefficient,multiple correlation and multiple regression. Based on the data analysis, the six findings of this study are summarized as follows: 1. The low satisfaction with mathematics class was revealed from the analysis of students¡¦ Mathematical Learning Perception Check List. It is suggested boosting subjects¡¦ satisfaction with the mathematics class will enhance the development of mathematical problem solving competence. 2. The positive correlation between administration style and mathematical problem solving competence was shown eminently among all types of thinking styles. The result indicated different function of the thinking styles influenced the development of mathematical problem solving competence in a varied degree. 3. From the analysis of students¡¦ background factor and mathematics problem solving competence, the statistic indicated the length of extra curriculum students devoted to does not affect their mathematical problem solving competence. The factors that influence students¡¦ mathematical problem solving competence the most were shown in the following order: administration district, the social status of father, the social status of mother, gender and the size of school. 4. The comparative variance of the mathematics learning achievement and mathematics problem solving competence was 24.3%. It implied the two influences each other. Students with low mathematical learning achievement show low mathematical problem solving competence and vice versa. 5. When predicting students¡¦ development of mathematical problem solving competence via the data of parents¡¦ social status and mathematical learning perception check list, the result showed the prediction via parents¡¦ social status is less significant. Yet the prediction via mathematical learning perception check list gained the highest variance ratio in this case. 6. In terms of the distribution of parents¡¦ social status, East, North and Middle East were of eminent as compared to South, An-Ping and An-Nan district in Tainan city. The finding implied parents¡¦ social status was a major factor that influence students¡¦ mathematics problem solving ability in administration district, as the £b2 ¡]Eta Squared¡^¡×25.3¢H shown in this study.

The purpose of the present thesis was to test and contrast hypotheses about the cognitive conditions that support the development of mathematical learning disability (MLD). Following hypotheses were tested in the thesis: a) domain general deficit, the deficit is primarily located in the domain general systems such as the working memory, b) number sense deficit, the deficit is located in the innate approximate number system (ANS), c) numerosity coding deficit, the deficit is located to a exact number representation system, d) access deficit, the deficit is in the mapping between symbols and the innate number representational system (e.g., ANS), e) multiple deficit hypothesis states that MLD could be related to more than one deficit. Three studies examined the connection between cognitive abilities and arithmetic. Study one and three compared different groups of children with or without MLD (or risk of MLD). Study two investigated the connection between early number knowledge, verbal working memory and the development of arithmetic ability. The results favoring the multiple deficit hypothesis, more specifically the result indicate that number sense deficit together with working memory functions constitutes risk-factors to the development of MLD in children. A simple developmental model that is based on von Asters and Shalev´s (2007) model and the present results is suggested, in order to understand the development of MLD in children. / Avhandlingens syfte var att testa och kontrastera hypoteser om vilka kognitiva förutsättningar som är centrala för utvecklandet av matematiska inlärningssvårigheter (MLD) hos barn. De hypoteser som prövas i avhandlingen är följande: a) den domängenerella hypotesen, detta innebär att den förmodade störningen/nedsättningen finns primärt i barnets generella förmågor, främst då i arbetsminnes funktioner. b) en nedsättning i den medfödda approximativa antalsuppfattningen. c) nedsättning i den exakta antalskodningen. d) nedsättning gällande kopplingen mellan den kulturellt betingande symboliska nivå (räkneord och siffror) samt den medfödda antalsuppfattningen (eller antalskodningen). e) slutligen prövas även hypotesen att MLD kan härröras från flera nedsättningar i dessa förmågor. I tre studier undersöktes kopplingen mellan kognitiva förmågor och aritmetik. i studie1 och 3 jämfördes grupper av barn med MLD (eller risk för MLD) med grupper av barn som inte hade MLD i studie 2 undersöktes kopplingen mellan förmågorna verbalt arbetsminne och tidig sifferkunskap samt tidig aritmetiskförmåga. Sammantaget indikerar resultaten från denna avhandling att det kan vara både multipla och enstaka kognitiva förmågor, primärt i den approximativa antalsuppfattningen samt i arbetsminnesfunktioner, som kan fungera som riskförutsättningar för utvecklande av MLD hos barn. Dock måste dessa förmågor samspela med andra faktorer som kan fungera kompensatoriskt eller riskhöjande för utvecklandet av MLD. En förenklad utvecklingsmodell med utgångspunkten i resultaten från studierna samt von Asters och Shalevs (2007) modell föreslås. Syftet med modellen är att den ska kunna användas som teoretiskt ramverk för att förstå utvecklingen av MLD hos barn.

The aim of this study was to investigate which factors teachers and special needs education teachers view as being the main causes of mathematical learning difficulties and from these choose how to educate pupils with these difficulties. The aim was also to investigate how this education is organised at two different schools. An interview based investigation addressed these objectives by using three comprehensive questions: Which factors do the teachers and special needs teachers view as being the main reasons for mathematical learning difficulties? How do teachers and special needs teachers educate pupils with mathematical learning difficulties? How is the education organised for pupils with mathematical learning difficulties at two different schools? This study is based on four interviews of three teachers and one special needs teacher. The people interviewed work at two different primary schools in the same local authority. The results of the interviews show that it is the pupils’ experiences of the maths that affects how well they comprehend the subject. Furthermore factors such as reading and writing difficulties can cause problems with regards to understanding tasks in maths. Educationalists in this study regard a varied education with an element of group work, communication and experimental material as being beneficial for pupils with mathematical learning difficulties. How the education of pupils is organised depends on the extent of the learning difficulties of each pupil. The needs of pupils with mild learning difficulties can be met by the form teacher whereas pupils with more severe difficulties require assistance from special teachers.

This study is situated at the confluence of three calls for research within mathematics education: 1) work using novel approaches for studying students’ understanding of nonlinear meanings of multiplication; 2) work using discrete mathematics to explore social issues related to equity; and 3) work at the intersection of mathematical learning and critical race consciousness—specifically, social justice mathematics initiatives that explicitly address racism and the learners’ perspectives. The design research methodology of the study with 8th grade students provides practical curricular and pedagogical steps for doing work at the intersection of mathematical learning and race and racism; offers domain-specific learning insights; and merges theory and practice in conceptualizing the multiple complexities of learning and development in situ to create new possibilities for a more just mathematics education. Findings from this study offer insights at the intersection of the evolution of students’ establishment of nonlinear meanings of multiplication and critical race consciousness development. Specifically, this study identifies two schemes that students use to establish a nonlinear meaning of multiplication (SARC Scheme and RA Scheme), illustrates students’ growing racism awareness, and highlights how these initiatives can be mutually supportive in helping to normalize conversations about race and racism.

This literature review looks into the effects of integrating music in mathematics teaching andhow it influences the problem solving ability. A systematic search for scientific articles was madeto investigate the research area. All together 13 scientific articles were chosen, which presentedvarious ways to integrate music in mathematics teaching and which had found different resultsin their studies. Generally, the articles presented positive effects of integrating music inmathematics teaching to develop students’ problem solving ability and mathematical learning.Similarities and differences between the presented articles were compared in the results of thisstudy, which showed common features in the characters of music and mathematics. In this study,problem solving is used in a wide definition which includes arithmetic, communication,reasoning and mathematical concepts

Στόχος της παρούσας έρευνας ήταν να διερευνηθούν οι επιδόσεις και τα είδη των στρατηγικών που χρησιμοποιούν οι μαθητές της Δ΄ τάξης του δημοτικού σχολείου, με και χωρίς μαθησιακές δυσκολίες στα μαθηματικά (ΜΜΔ), όταν υπολογίζουν νοερά προσθέσεις και αφαιρέσεις διψήφιων αριθμών και να διαπιστωθεί αν υπάρχει αξιόλογη διαφορά στην επίδοση μεταξύ των μαθητών αυτών. Προηγούμενες μελέτες που αφορούν στις ΜΜΔ έχουν ασχοληθεί με τις απλές (π.χ. 3+5) και όχι με τις διψήφιες νοερές προσθέσεις και αφαιρέσεις. Στην παρούσα έρευνα συμμετείχαν 85 μαθητές (40 με ΜΜΔ και 45 κανονικής επίδοσης στα μαθηματικά-ΚΕ), όπως προέκυψε από την αξιολόγησή τους με σταθμισμένες και μη δοκιμασίες. Επιπλέον, στους μαθητές αυτούς χορηγήθηκε δοκιμασία στους νοερούς υπολογισμούς. Τα αποτελέσματα της έρευνας έδειξαν ότι οι μαθητές ΚΕ χρησιμοποιούν, κατά κύριο λόγο, στρατηγικές υψηλού επιπέδου (αυτές που συντελούν στην καλύτερη κατανόηση των αριθμών) τόσο στην πρόσθεση όσο και στην αφαίρεση. Παρόλα αυτά, η χρήση στρατηγικών υψηλού επιπέδου είναι πιο έντονη στην πρόσθεση συγκριτικά με την αφαίρεση, γεγονός που υποδηλώνει τη δυσκολία της αφαίρεσης ως πράξη. Επιπλέον, οι αφαιρέσεις με κρατούμενο είναι πιο δύσκολες από αυτές χωρίς κρατούμενο και για τις δύο ομάδες. Επίσης, τα αποτελέσματα έδειξαν ότι οι επιδόσεις των μαθητών με ΜΜΔ γενικά σε όλες τις πράξεις είναι χειρότερες από αυτές των μαθητών ΚΕ. Τέλος, οι μαθητές με ΜΜΔ υπέπεσαν σε περισσότερα λάθη σε σχέση με τους μαθητές ΚΕ, ανάλογα με το είδος της πράξης, αλλά και σε περισσότερα είδη λαθών. Τα περισσότερα λάθη των μαθητών εντοπίστηκαν κυρίως στις αφαιρέσεις με κρατούμενο, όπου είτε αφαιρούσαν τις μονάδες του μειωτέου από τις μονάδες του αφαιρετέου είτε έκαναν κάποιο λάθος στο δανεισμό. Περαιτέρω έρευνες είναι απαραίτητες προκειμένου να διαπιστωθούν οι διαφορές που εντοπίζονται στην επίδοση, τις στρατηγικές και τα λάθη μεταξύ των παραπάνω μαθητών στις διψήφιες νοερές προσθέσεις και αφαιρέσεις. / The purpose of the present study was to investigate the performance and the kinds of strategies that students, with and without mathematical learning disabilities (MLD), attending fourth grade of elementary school (9 years old) use when they add and subtract two-digit numbers mentally and to find out whether there is any notable difference in the performance between these groups. Previous studies related to MLD have dealt with simple mental additions and subtractions (eg 3+5) and not with two-digit calculations. Eighty five students participated in the present study (40 with MLD and 45 normally achieving students – NA). All students completed tests, which evaluated their mathematical skills. The results from these tests led to the selection of the students that would form each one of the two groups. Moreover, students of both groups were assessed on a mental calculation task. The results of the study indicated that NA students tend to use sophisticated strategies (those that contribute to a better understanding of numbers) both in addition and subtraction. However, the percentage of sophisticated strategies appeared to be higher in addition than in subtraction, a fact that implies there is a particular difficulty in subtractions. Moreover, this study found that subtractions, which involve regrouping procedures (such as “carrying” or “borrowing”), are more complex than others for both groups. Furthermore, the results showed that the performance of MLD students on mental calculation tasks was worse than NA students. Last but not least, MLD children made more errors than NA children depending on the type of operation and they made more types-categories of errors than NA children. Most errors were made in subtractions with carrying digit. There either they subtracted minuend’s units from subtrahend’s units or they made an error with the carrying digit. Further research is necessary in order to investigate the performance and the kinds of strategies that students, with and without mathematical learning disabilities when they add and subtract mentally two-digit numbers.