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

Mokyklinės matematikos mokymo(si) priemonė skirta vyresniųjų klasių moksleiviams, kurioje pateikta matematikos mokyklinio brandos egzamino temų teorija ir uždavinių pavyzdžiai, savikontrolės uždaviniai ir kontroliniai testai. / The mathematics tool for learning is targeted to the students of higher forms and includes the theory of particular topics and task examples, self-monitoring, check tests and assessment tasks.

Det finns en problematik i övergången för svenska studenter mellan gymnasiet och högskolan. En faktor i den problematiken är att bevis och bevisföring hanteras på olika sätt på de olika utbildningsnivåerna. Dessutom är forskning kring hur läroböcker hanterar bevis och bevisföring begränsad. I denna studie undersöks två vanliga läroböcker på gymnasiet med avseende på bevis och bevisföring. Utifrån de i ämnesplanen befintliga ämnesområdena granskas teoriavsnitten i läroböckerna med fokus på bevis och bevisföring. Dessutom undersöks bevisföringsuppgifter med utgångspunkt i G. Stylianides (2009) ramverk. Resultaten visar att läroböckerna är inkonsekventa i sitt hanterande av bevis och att bevis ofta osynliggörs i teoriavsnitten. Ett annat resultat är att den matematiska strukturen är svår att följa. Läroböckerna innehåller 6,7 % respektive 13,7 % bevisföringsuppgifter och vi har funnit 19 olika typer av bevisföringsuppgifter varav två typer är väldigt dominerande. Vi argumenterar att didaktiskt värdefulla syften kan uppnås genom att synliggöra bevis bättre i läroböcker. / There exists a problem in Swedish students’ transition between high school and college. One factor of this problem stems from the fact that proofs and proving are handled in different ways at these different levels of education. In addition, research on how textbooks deal with proofs and proving is limited. This study examines proofs and proving in two common math textbooks intended for upper secondary high school students in Sweden. Based on the contents of the curriculum, the theoretical sections in the textbooks are examined with an added focus on proofs and proving. Also, the textbooks’ tasks are examined with the help of a modified framework based on G. Stylianides (2009) framework. The results show that the textbooks are inconsistent in their handling of proofs and that proofs are often made invisible in the theoretical sections. Another result is that the mathematical structure is difficult to follow. The textbooks contain 6.7% and 13.7% proving tasks respectively and we have found 19 different types of proving tasks among which two types are very dominant. We argue that didactically valuable objectives can be achieved by making proofs more visible in textbooks.

Traditionally, geometry at school starts on a formal level, largely ignoring prerequisite skills needed for formal spatial reasoning. Ignoring that geometry has a sequential and hierarchical nature causes ineffective teaching and learning. The Van Hiele theory postulates learner progression through levels of geometry thinking, from a Gestalt-like visual level through increasing sophisticated levels of description, analysis, abstraction, and proof. Progression from one level to the next does not depend on biolog~caml aturation or development only, but also on appropriate teachingllearning experiences. A higher thinking level is achieved through the application of a series of learning phases, consisting of suitable learning activities. The teacher plays an important facilitating role during this process. In accordance with the social cognitive learning perspective on self-regulated learning, geometry learners must direct their thoughts and actions while completing activities in order for effective learning to take place. Learners can be described as being selfregulated to the degree that they are metacognitively, motivationally, and behaviorally active in their own learning. The social cognitive theory assumes that students enter learning activities to acquire knowledge, learning how to solve' problems and completing learning activities. Self-regulated learners are aware of strategic relations between self-regulatory processes and learning outcomes and feel self-efficacious about using strategies. Self-regulation is similar to metacognitive awareness, which includes task and personal knowledge. Self-regulated learning requires that learners understand task demands, their personal qualities, and strategies for completing a task. A Van Hiele-based geometry learning and teaching program was designed (with a problem solving context in mind) and implemented in four Grade 7 classes (133 learners) at two schools. The study investigated factors and conditions influencing the effective learning and teaching of spatial concepts, processes and skills in different contexts. Results suggest that the implementation of a Van Hiele based geometry learning and teaching program in a problem solving context had a positive effect on the learners' concentration, when working on academic tasks, and level of geometric thought. The higher levels of geometric thought included higher categories of thought within these levels. Learners who completed the program reasoned on a higher level, ,gave more complete answers, demonstrated less confusion, and generally exhibited higher order thinking skills than their counterparts who did not take part in the program. The only prerequisite' is that the teacher should consistently teach from a learner-centered approach as the program will deliver little or no advantages if the program is presented in a teacher-centered content-based context. / Thesis (M.Ed.)--Potchefstroom University for Christian Higher Education, 2000.

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

<p>This thesis investigates grade seven learners perceived experiences in learning algebra.Things that learners do and say during algebra lessons and about algebra were investigated. The study was done at one of the previously disadvantaged schools in Cape Town, South Africa.The data were collected through observations, a questionnaire and interviews. Observations were made from the day the topic was started in two grade seven classes. Two different teachers taught the two classes. Focus group interviews were conducted, two group of learners, ten learners from each of the two classes were interviewed. Learners devised a number of strategies for solving problems related to sums and differences. The principal learning difficulties experienced by learners in algebra related to the transition from arithmetic conventions to those of algebra, the meaning of literal symbols and the recoginition of structures. It became obvious then that developing algebraic thinking is not necessarily dependent upon algebraic notation and that the presence of algebraic notation says little about the level of problem solving.</p>

This study aimed to develop a teaching and learning model, based on principles derived from the fields of constructivist theory, schema theory, critical literacy theory, and design theory, to inform the development of hypermedia-mediated learning environments that facilitate the construction of mathematical knowledge by secondary school students in Thailand. In this study, the participants were a group of three secondary school students from the Demonstration school attached to the Faculty of Education at Khon Kaen University (Thailand). In order to ascertain how mathematical learning could be facilitated by the process of designing a web page that could be used to introduce other students to analytic geometry, all three participants were asked to work collaboratively to design an analytic geometry web page. The process of designing the web page was informed by a theoretical model derived from an analysis and synthesis from the research literature on constructivist theory, schema theory, critical literacy theory, and design theory. Findings from the study indicated that the creation of a web page facilitated and enhanced the Thai students' learning about analytic geometry. The major outcomes from the study are a revised theoretical framework to inform the integration of the design of mathematical web pages into Thai mathematics classrooms and a conceptual map framework to assess qualitative and quantitative changes to students' repertoires of knowledge about analytic geometry that emerge during the process of designing a webpage.

Educators need clear, actionable data to help them understand students' current levels of performance and students' probable trajectory toward college- and career-readiness in math if they are to make informed programmatic decisions to shape that trajectory. This study explored the relation between CBM-math in Grade 7 as a one-point, teacher accessible measure of student math skill and the students' performance on the Grade 8 EXPLORE-math test, a large-scale achievement test linked to one set of college- and career-readiness benchmarks. Results indicated that a moderate positive correlation and predictive relation exist between CBM-math and EXPLORE-math. Information was disaggregated by gender and for subgroups, including students eligible for special education, free or reduced meals, and English language development services. No difference in means for male and female students on either measure was identified, but eligibility for special education or for free or reduced lunch was associated with lower performance on both measures. Insufficient numbers of ELD students hindered detailed analysis, but none of the ELD students included in the study achieved the EXPLORE benchmark or the CBM normalized cut score based on the 40th percentile. An ROC analysis showed that easyCBM consistently predicted students who did not meet the EXPLORE benchmark, although results indicated that a higher cut score on easyCBM may be a more consistent predictor. The study adds to validity research on CBM and may be useful for educators seeking to identify students at risk of missing achievement benchmarks and make programmatic decisions to ensure students are on track to be college- and career-ready in math.

Esta dissertação apresenta um estudo sobre a construção de histórias em quadrinhos (HQs), inspiradas em contos do livro O Homem que Calculava, de Malba Tahan, e a exploração de conceitos matemáticos na leitura desses contos e na produção dessas histórias por alunos do Ensino Fundamental. Ela oferece uma contextualização das HQs desde sua origem, ressaltando seu surgimento e seu desenvolvimento no Brasil, além de sua presença na educação matemática escolar. Além disso, enfoca um grande autor e professor de Matemática brasileiro, apresentando sua trajetória e utilizando uma de suas obras como provocação à produção escrita discente. O estudo foi realizado na Escola Municipal de Ensino Fundamental Almirante Raphael Brusque, em Pelotas, RS, ao longo de 20 encontros semanais e envolveu uma turma de oitava série do Ensino Fundamental, cujos discentes residem na Colônia de Pescadores Z3. Em seu planejamento, definimos algumas etapas que reuniram atividades ligadas às áreas de Literatura, Matemática e Artes. Para a aplicação dessas atividades, desenvolvidas em sala de aula por três grupos, totalizando 13 alunos, consideramos a leitura de alguns contos narrados pelo personagem Beremiz, a interpretação dos correspondentes problemas matemáticos, e a criação de novas histórias e sua transformação em HQs, inspiradas nesses contos, que incluíram algumas características socioculturais da Colônia de Pescadores Z3. Durante o desenvolvimento das atividades, observamos o empenho e o progresso dos alunos na execução das diferentes tarefas que deram suporte a este estudo, que resultou na produção escrita discente de três livros de HQs. / This dissertation presents a study on the making of comic books inspired in some of the short stories of MalbaTahan’s The Man Who Counted and the exploration of mathematical concepts in the reading and production of these stories by elementary school students. It offers a contextualization of comic books from their origin, emphasizing their emergence and development in Brazil, besides their presence in school mathematics education. The dissertation also focuses on an important Brazilian author, writer and mathematics teacher, presenting his trajectory and using one of his works to instigate the written production of students. The study took place in the Almirante Raphael Brusque Elementary Education Municipal School, located in the city of Pelotas, RS, Brazil, during 20 weekly meetings and involved a class of eight graders who live in the Z3 fisher Colony. In its planning we defined some phases which brought together activities related to the fields of literature, mathematics and arts. Regarding the application of these activities in the classroom, which were developed by three groups adding up to 13 students, we considered the reading of some short stories narrated by the character Beremiz, the interpretation of their corresponding mathematical problems, and the creation of new stories, including their transformation to comic book format. The new stories were inspired in those stories and included some sociocultural characteristics of the Z3 fisher Colony. During the development of the activities we observed the commitment and the progress of the students while engaged in the several tasks that provided support for this study, which resulted in the written production of three comic books.

Esta dissertação apresenta um estudo sobre a construção de histórias em quadrinhos (HQs), inspiradas em contos do livro O Homem que Calculava, de Malba Tahan, e a exploração de conceitos matemáticos na leitura desses contos e na produção dessas histórias por alunos do Ensino Fundamental. Ela oferece uma contextualização das HQs desde sua origem, ressaltando seu surgimento e seu desenvolvimento no Brasil, além de sua presença na educação matemática escolar. Além disso, enfoca um grande autor e professor de Matemática brasileiro, apresentando sua trajetória e utilizando uma de suas obras como provocação à produção escrita discente. O estudo foi realizado na Escola Municipal de Ensino Fundamental Almirante Raphael Brusque, em Pelotas, RS, ao longo de 20 encontros semanais e envolveu uma turma de oitava série do Ensino Fundamental, cujos discentes residem na Colônia de Pescadores Z3. Em seu planejamento, definimos algumas etapas que reuniram atividades ligadas às áreas de Literatura, Matemática e Artes. Para a aplicação dessas atividades, desenvolvidas em sala de aula por três grupos, totalizando 13 alunos, consideramos a leitura de alguns contos narrados pelo personagem Beremiz, a interpretação dos correspondentes problemas matemáticos, e a criação de novas histórias e sua transformação em HQs, inspiradas nesses contos, que incluíram algumas características socioculturais da Colônia de Pescadores Z3. Durante o desenvolvimento das atividades, observamos o empenho e o progresso dos alunos na execução das diferentes tarefas que deram suporte a este estudo, que resultou na produção escrita discente de três livros de HQs. / This dissertation presents a study on the making of comic books inspired in some of the short stories of MalbaTahan’s The Man Who Counted and the exploration of mathematical concepts in the reading and production of these stories by elementary school students. It offers a contextualization of comic books from their origin, emphasizing their emergence and development in Brazil, besides their presence in school mathematics education. The dissertation also focuses on an important Brazilian author, writer and mathematics teacher, presenting his trajectory and using one of his works to instigate the written production of students. The study took place in the Almirante Raphael Brusque Elementary Education Municipal School, located in the city of Pelotas, RS, Brazil, during 20 weekly meetings and involved a class of eight graders who live in the Z3 fisher Colony. In its planning we defined some phases which brought together activities related to the fields of literature, mathematics and arts. Regarding the application of these activities in the classroom, which were developed by three groups adding up to 13 students, we considered the reading of some short stories narrated by the character Beremiz, the interpretation of their corresponding mathematical problems, and the creation of new stories, including their transformation to comic book format. The new stories were inspired in those stories and included some sociocultural characteristics of the Z3 fisher Colony. During the development of the activities we observed the commitment and the progress of the students while engaged in the several tasks that provided support for this study, which resulted in the written production of three comic books.