This research was undertaken to determine the influence of a video class system on the strategic teaching and learning of school mathematics. A literature investigation served as a frame of reference for the planning, execution and assessment of the empirical investigation. Some of the approaches which have the greatest influence on the learning of school mathematics, namely the behaviourist, cognitive and constructivist approaches, are described and, where necessary, critically assessed. Factors which influence the learning of school mathematics are discussed in an interrelated manner and are used to identify the features of the strategic learning of school mathematics. It is then attempted to determine how teaching should take place to enable the strategic learning of school mathematics. To reach this objective, different approaches to the teaching of mathematics are discussed, based on approaches to the learning of mathematics, and the influence of these on the teaching of school mathematics is determined, based on the literature investigation. Different factors which influence the teaching of mathematics are identified and used to describe the characteristics of the effective teacher, who teaches mathematics for the strategic learning of the subject. The empirical investigation involved a quantitative as well as a qualitative investigation. In the quantitative investigation an actual experimental design with a pre-test and post-tests was used. Video recordings were made with one experimental group (video recording class) and delivered (played back) with another experimental group (video delivery class). The control group received conventional mathematics teaching. A quantitative field investigation was undertaken by means of an adapted LASSI-HS to establish the influence of the video class system used in the investigation on the study and learning strategies of the learners. In this way the influence on the strategic learning of mathematics could be determined. At the same time the influence of the video class system on the mathematics performance of the learners was established, in order to determine the extent of success of the use of the video class system. A qualitative investigation by means of an observation schedule, together with the analysis of video recordings of mathematics lessons, was used to determine the influence of the video class system on the teaching of mathematics. The video class system did not have a negative or a positive influence on the performance of either the video recording classes, the video delivery classes or the control classes of the schools who participated in the research. Neither did the video class system have a positive or a negative influence on the use of learning and study strategies (concerning mathematics) of the different class groups who participated in the research. That means that the video class system did not negatively influence strategic learning in learners who may use it. / Thesis (Ph.D. (Education))--Potchefstroom University for Christian Higher Education, 2003

Cooperative learning has emerged to be a preferred teaching-learning model in South Africa since the inception of Curriculum 2005 (C2005) emphasising Outcomes-based education (OBE). However, the documented success rate of cooperative learning in mathematics was experienced in small group sizes (emanating h m small class size) of about five learners. This study, therefore, aims at affording mathematics teachers and learners of crowded classes an opportunity to effectively use cooperative learning, namely the Hour-glass model in mathematics lessons. The prevalence of crowded classes in the majority of South African schools seems to inhibit the effectiveness of cooperative learning in mathematics. The big cooperative group size of about eight learners in South African context results in very complex lines of communication between learners. The teacher spends more time trying to manage off-task behaviour of learners instead of engaging them in active participation in the learning of mathematics. The combined quantitative and qualitative research methods were used. For the former, the study orientation in mathematics (SOM) questionnaire and the mathematics academic achievement test were used to collect data with regard to the influence of the Hour-glass model on the learners' learning skills in mathematics, and on the mathematics academic achievement respectively. A specific true experimental design, namely, the Solomon Four-group design, was used because of a large sample size (n > 500), and its credited ability to control the sources of threats to internal validity. For the latter the lesson observation and interviews were conducted to collect information about the influence of the Hour-glass model on learners' social skills during cooperative learning in mathematics. The groups that received the treatment (i.e. Hour-glass model) achieved higher scores of practical significance in mathematics academic achievement test than the groups that did not receive the treatment The Hour-glass model also yielded positive social skills among learners during mathematics learning. The teachers who applied the Hour-glass model revealed that they coped easier with crowded mathematics classes when using cooperative small groups. However, the Hour-glass model did not significantly influence learners' learning skills in mathematics. Certain logistical and administrative limitations emerged with regard to the implementation of the Hour-glass model in the usual school setting. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2004.

Worldwide the teaching and learning of mathematics pose a great challenge to mathematics teachers as learners' performance in the subject leaves much to be desired. This is particularly the case in South Africa where there was a great disparity in the development of teachers in the past. Extensive research has shown that many teachers in South Africa are under-qualified, especially in the teaching of mathematics at secondary schools. Those who are regarded as well qualified for teaching mathematics at secondary schools still experience problems in teaching certain sections of the syllabus, for example geometry, which is not offered at tertiary institutions. It is for this reason that the researcher, together with colleagues at an experimental school, joined forces to share the teaching of mathematics in what they referred to as "collaborative teaching". This work therefore involves a case study, which resulted after three teachers successfully achieved good matric results on employing this approach between 1993 and 1996. The study is based on an experimental design where both quantitative and qualitative methods were used. The aim of the study was to measure the extent to which collaboration between teachers affects the learning of mathematics in Grades 12. Two schools, the experimental school and a control school were involved. Learners from the experimental school were taught according to a collaborative approach whereas learners at the control school were taught conventionally (one teacher teaching all sections alone). This happened over a period of six months in 2001. Learners who were taught collaboratively outperformed those who were taught conventionally especially in the most problematic areas of the syllabus, namely geometry and trigonometry. The teachers who were involved in this approach, that is, collaborators, loved it to the extent that one of them applied it in another school where it improved their Grade 12 results tremendously. Learners who were taught according to this approach greatly appreciated it and wished they had been taught the same way in other subjects. This approach did not, however, significantly influence learners in their problem solving and information processing skills. In addition, one of the most serious limitations of this approach is to find a substitute for a teacher who leaves the team. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2006.

Syftet med detta arbete är att få kunskap om hur pedagoger i förskoleklass samt årskurserna 1-3 som har tillgång till iPads i sin matematikundervisning ser på användandet av dessa. Hur resonerar pedagoger när de använder iPadsen och finns det en tanke bakom hur iPadsen används när det gäller matematiska mål i Lgr 11? Metoden som användes för att få svar på frågeställningarna var dels en enkätundersökning för att nå ut till många pedagoger och därefter fördjupande intervjuer som baserade på enkätfrågornas resultat.

This study investigates the ways in which parents' and teachers' experiences and representations mediate their child's mathematics learning as they make the transition between home and school to either a multiethnic or mainly white school. In particular, it examines if the forms of mediation they adopt can shed light on the academic success of the child in school mathematics. The focus on mathematics learning has been chosen for the study because of its relative neglect, until recent times, to be seen as a subject influenced by cultural representations. Furthermore, there are significant implications in the relative neglect of understanding the achievement of ethnic minority pupils in mathematics. The research was framed by Vygotskian sociocultural theory and Wenger's (1998) communities of practice to explore the construction of meaning, identity and representations of practice. The amalgam of Wenger's communities of practice with sociocultural theory provided three key theoretical facets: (i) multiple levels of understanding in the form of meaning, practice and identity, (ii) the scope to explore the social and cultural worlds of the learner and (iii) understanding the ways that past experiences impact on current practice. Three different forms of qualitative data collection were used within the context of an ethnographic approach: (i) investigations in the form of classroom observations, (ii) in-depth semi-structured interviews and (iii) a child identity task. Twenty-two parents, eight teachers and fifty-eight children took part in the interviews, which form the main part ofthe data analysis. Out ofthese fifty-eight children, twenty-seven undertook the child identity task. The research took place in three schools with different ethnic make-up: a multicultural school, a mainly white school and a predominantly South Asian school. Two year groups were chosen, year 2 (ages 6/7 years) and year 6 (10/11 years), balancing high and low achievers. This study has provided data, which suggests that the way parents and teachers mediate the child's learning involves more than representations of mathematics. In making meaning of the mathematical, they draw on wider representations of the educational world, which include aspects like child development, notions of achievement, past experiences and the child's projected futures. This complex picture emerged from studying the highly interwoven aspects ofthe construction of meaning, identity and representations of practice. Representations of learning can be borrowed from both communities, providing the ethnic minority pupil with the potential to create hybrid representations of learning as they make the transition between home and school, which may be attributed a cultural status within the home. Each social actor has the potential to borrow from the home or school community to a greater or lesser degree. lfthe gap between the shared representations of the home and school are large, then this increases the likelihood of difficulties for the child in transition. However, the data suggests that even if the cultural representations of the home are very different from the school, the identification of high achievement and the engagement in mathematical activity at home can still provide success in learning. From the school community perspective, classrooms were represented by the teacher informants as 'cultureless' in both the multi ethnic and mainly white school. For example, in the multicultural school the teachers felt that there were so many ethnicities that differences were not visible. In the mainly white school, there were so few ethnic minority children that teachers also struggled to identify issues of culture. In the predominantly South Asian school, issues surrounding culture were brought to the forefront of the teacher discourse. However, in many ethnic minority homes, parents described how culture was influential in mediating representations ofleaming. This has implications in the educational arena with respect to the teachers' understanding of the transitional process that ethnic minority children undergo and the levels of visibility that culture and ethnicity is given in the school community.

The purpose of the study was to investigate the high school students&#039 / beliefs about mathematics and the teaching of mathematics. The study was conducted in Ankara with 425 tenth-grade students enrolled to general, Anatolian, foreign language and vocational high schools. Two measuring instruments were utilized: 1.Beliefs about Mathematics Scale (BaMS) / 2.Beliefs about the Teaching of Mathematics Scale (BTMS). The validity and reliability of these scales were tested. The design of the present research is a casual-comparative study. The hypotheses of the present study were tested by using multivariate analysis of variance at the significance level 0.05. The results of the study indicated that:1. There are statistically significant differences among the mean scores of students enrolled to different kinds of high schools with respect to beliefs about mathematics and beliefs about the teaching of mathematics / 2. There are statistically significant mean differences among students who have different mathematics achievement levels in terms of beliefs about mathematics and beliefs about the teaching of mathematics / 3. There are statistically significant mean differences among students who are in different branches in terms of beliefs about mathematics and beliefs about the teaching of mathematics / 4.There is no statistically significant mean difference between the male and female students on beliefs about mathematics. On the other hand, there is statistically significant mean difference between the male and female students on beliefs about the teaching of mathematics in the favor of female students.

In this paper, the psychological aspects of clearness in teaching mathematics are considered and some suggestions for the achieve the clearness are given.

This study focused on the teacher interpersonal behaviour in the teaching of Mathematics, compared to English. It investigated: differences between student perceptions of their Mathematics and English teachers' interaction styles using the actual and ideal QTI; investigate associations between students' attitudes to Mathematics and English and their perceptions of the teachers' interpersonal behaviour; investigate whether any factors exist that contribute to students' perceptions of teachers' interpersonal behaviour, determine what the typical Mathematics and English teacher in Singapore is like; and what makes an effective teacher from students' and teachers' viewpoints. The QTI, together with the Attitude to Mathematics and Attitude to English, was administered to 913 students and 37 mathematics and English teachers from an independent school in Singapore. Student and teacher interviews were conducted to further substantiate the quantitative results. Both QTI and attitudinal scales were found to be valid and reliable instruments with alpha coefficients ranging from 0.69 to 0.92. In terms of leadership, helping/friendly, understanding and student responsibility, teacher behaviour as perceived by students, fell short of the ideal. Positive associations were found between students' attitudes to Mathematics and English and their perceptions of the teachers' interpersonal behaviour. Teacher experience and students' grade level were factors that contributed to students' perceptions of teachers' interpersonal behaviour. The typical Singaporean Mathematics teacher is that of the directive and authoritative type and the English teacher is the tolerant-authoritative type. Finally, an effective teacher is one who, besides having the positive qualities of good leadership, helping/friendly, understanding, has a good sense of humour and a passion to make a difference.

Στην παρούσα εργασία θα παρουσιαστεί μία νέα διδακτική προσέγγιση για τη διδασκαλία των μαθηματικών και της πληροφορικής, η οποία αναπτύχθηκε με τη βοήθεια του συστήματος εκπαιδευτικής ρομποτικής LEGO Mindstorms, με σκοπό να αξιοποιηθεί τόσο στη διδασκαλία της ενότητας των Μαθηματικών της Β΄ Γυμνασίου και συγκεκριμένα στο μάθημα: «Καρτεσιανό Σύστημα Συντεταγμένων », όσο και στη διδασκαλία της ενότητας της Πληροφορικής της Γ΄ Γυμνασίου, που αφορά στην έννοια της αντιμετάθεσης, ως ενδιαφέρουσας διαθεματικής εφαρμογής. Τα LEGO Mindstorms είναι εύκολα προγραμματιζόμενα ρομπότ με αισθητήρες, τα οποία περιλαμβάνουν μια μεγάλη ποικιλία από τουβλάκια, κινητήρες, αισθητήρες και άλλα εξαρτήματα με τα οποία μπορεί κανείς να κτίσει φυσικά μοντέλα. Τα ρομπότ με τη χρήση κατάλληλων περιβαλλόντων ανάπτυξης προγραμμάτων μπορούν να προγραμματιστούν ώστε να εκτελούν μία σειρά ενεργειών και να αντιδρούν σε ερεθίσματα που δέχονται οι αισθητήρες τους. Η εφαρμογή αυτή στόχευε να αναδείξει τη σημασία της ύπαρξης επαρκών γνώσεων, εμπειριών και εργαλείων στην αντιμετώπιση προβλημάτων που συνδέονται με το σύστημα ορθογωνίων αξόνων και το ορθοκανονικό σύστημα αξόνων, τα τεταρτημόρια, την τετμημένη, την τεταγμένη, τις συντεταγμένες ενός σημείου στο επίπεδο, τον υπολογισμό περιμέτρων, την μετατροπή σε απόσταση περιμέτρου κύκλου (τροχού) καθώς και την επιβεβαίωσή της, αλλά και την κατανόηση μιας δύσκολης έννοιας στην πληροφορική, της έννοιας της αντιμετάθεσης, με την εμπλοκή των μαθητών και την κατασκευή κατάλληλων τύπων ρομπότ, χρησιμοποιώντας τόσο τις γνώσεις που απέκτησαν, όσο και την κατασκευαστική τους ικανότητα και τη φαντασία τους. Η υλοποίηση αυτής της εργασίας πραγματοποιήθηκε στο 17ο Γυμνάσιο Πατρών και διήρκεσε 20 διδακτικές ώρες συνολικά. Η παρατήρηση και η αξιολόγηση των ενεργειών των μαθητών έδειξαν πώς η εργασία αυτή τους βοήθησε να κατανοήσουν τις παραπάνω έννοιες, ενώ ταυτόχρονα συνεργάστηκαν μεταξύ τους ανταλλάσοντας εμπειρίες και δεξιότητες και δοκιμάζοντας νέους τρόπους μάθησης ενδυναμώνοντας την αυτοεκτίμησή και την αυτοπεποίθησή τους. Από τη συμμετοχή και τις απαντήσεις των μαθητών στα ερωτηματολόγια βγάζουμε το συμπέρασμα ότι διαμόρφωσαν θετικές στάσεις έναντι της εκπαιδευτικής ρομποτικής και θα ήθελαν να συμμετέχουν στο μέλλον σε παρόμοια προγράμματα. / --

Submitted by Ricardo Sampaio null (cobraxms@yahoo.com.br) on 2018-04-02T17:22:08Z No. of bitstreams: 1 Ricardo Sampaio - Matrizes no estudo e na resolução de sistemas lineares.pdf: 1339231 bytes, checksum: c27b73e8517bd73345ca823cfeecf3e5 (MD5) / Approved for entry into archive by Elza Mitiko Sato null (elzasato@ibilce.unesp.br) on 2018-04-03T12:04:18Z (GMT) No. of bitstreams: 1 sampaio_r_me_sjrp.pdf: 1130997 bytes, checksum: 82f22c665b2241146e03d978ffb2e926 (MD5) / Made available in DSpace on 2018-04-03T12:04:18Z (GMT). No. of bitstreams: 1 sampaio_r_me_sjrp.pdf: 1130997 bytes, checksum: 82f22c665b2241146e03d978ffb2e926 (MD5) Previous issue date: 2018-03-01 / Os sistemas de equações lineares são muito úteis, pois podem modelar matematicamente diversos problemas em Estatística, Física, Química, Engenharia, Administração, Economia, enfim, em várias áreas do conhecimento. Historicamente, o cálculo de soluções desse tipo de sistema pelos chineses motivou o surgimento das matrizes, que, grosseiramente falando, são tabelas de elementos distribuídos em linhas e colunas. O uso de matrizes facilita o estudo e também a resolução de sistemas lineares, pois simplificam a notação e padronizam os procedimentos. O método do escalonamento de matrizes, por exemplo, é uma técnica que pode ser utilizada em sistemas lineares em geral, além de ser facilmente automatizada devido ao seu algoritmo. O objetivo deste trabalho é apresentar alguns conceitos e resultados sobre matrizes e sistemas lineares e abordar a relação entre eles, além de propor alguns problemas que podem ser resolvidos utilizando esses resultados. Professores do Ensino Médio podem utilizar tais problemas em sala de aula para trabalhar esse assunto com seus alunos. / The systems of linear equations are very useful because they can mathematically model several problems in Statistics, Physics, Chemistry, Engineering, Administration, Economics, and finally, in various areas of knowledge. Historically, the computation of solutions of this type of system by the Chinese motivated the emergence of matrices, which, roughly speaking, are tables of elements distributed in rows and columns. The use of matrices facilitates the study and the resolution of linear systems because they simplify the notation and standardize the procedures. The Echelonment method, for example, is a technique that can always be used in linear systems in general, besides being easily automated due to its algorithm. The objective of this work is to present some concepts and results about matrices and linear systems and to approach the relation between them, besides proposing some problems that can be solved using these results. High school teachers may use such problems in the classroom to work on this subject with their students.