Hierarchical Linear Models were used to analyze data from one Texas school and identify effective and ineffective mathematics teachers using their students’ scores on two consecutive years of the state test (TAKS) over a three-year period. A model was developed which attempted to control for student grade level, as well as whether a class was an honors course. Special attention was paid to requiring statistically significant results. Results were minimal and may lack validity. The barriers to getting better results include missing data, the small sample size of students for an individual teacher, the non-random assignment of teachers to courses, and the extent of variability in the data. Most of these are beyond the control of educators. A better way of measuring student growth could reduce variability and improve the prospects of using a data driven approach to evaluate teachers. / text

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

The objective with this research was to establish the correlation between problem solving and the teaching and learning of mathematics in grade 4. The results of the Third International Mathematics and Science Study (TIMSS) showed that South Africa is behind other countries in terms of the teaching and learning of mathematics, especially with regard to problem solving. Because problem solving is an integral part of the teaching and learning of mathematics, a literature study was conducted (1) to investigate the learning of school mathematics and (2) to describe the manner in which problem solving can take place in the classroom. The learning of school mathematics was studied by focusing on different approaches to the learning of mathematics. The constructionist approach to learning was identified as the appropriate approach towards learning, which correlates with outcomes-based education (OBE) and with the approach currently taught in South African schools. Factors which contribute towards the meaningful learning of school mathematics, namely mathematical knowledge and skills, meta-cognition, learning strategies and tasks and assignments in mathematics, have been discussed. The role of problem solving in the learning of mathematics was studied by means of a possible problem-solving model which may be developed together with the learners. The teaching of problem solving was investigated by referring to the planning of a problem-based lesson and attention was paid to the learning content of the lesson and the planning of the teaching-learning activities. Together with the learners a problem-solving model was developed for the teaching of problem solving. The implementation of the teaching of problem solving was described with reference to the use of big-group presentations as well as problem solving in small groups. Attention was also paid to problem solving, and the use of different assessment techniques was discussed. The empirical investigation was done by means of a case study, and the focus was firstly on the influence of problem solving on the learning of mathematics, and secondly on the manner in which problem solving may be taught. Information was collected during the qualitative investigation by using a questionnaire which was completed by the learners, as well as an interview and observation schedule. The class work, homework and group work books of the learners were studied and transcribed. Video recordings were made of the learners' participation in the big group, small groups and written work, and the transcribed information was used to make deductions about the teaching of problem solving to the learners. From the empirical investigation it became clear that there is a correlation between problem solving and the teaching and learning of mathematics. Problem solving may be taught to learners by means of a problem-solving model, although this does not necessarily result in successful problem solving by all learners. While learners are solving problems, they are also learning mathematical concepts and acquiring and applying mathematical skills. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2005.

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

The objective with this research was to establish the correlation between problem solving and the teaching and learning of mathematics in grade 4. The results of the Third International Mathematics and Science Study (TIMSS) showed that South Africa is behind other countries in terms of the teaching and learning of mathematics, especially with regard to problem solving. Because problem solving is an integral part of the teaching and learning of mathematics, a literature study was conducted (1) to investigate the learning of school mathematics and (2) to describe the manner in which problem solving can take place in the classroom. The learning of school mathematics was studied by focusing on different approaches to the learning of mathematics. The constructionist approach to learning was identified as the appropriate approach towards learning, which correlates with outcomes-based education (OBE) and with the approach currently taught in South African schools. Factors which contribute towards the meaningful learning of school mathematics, namely mathematical knowledge and skills, meta-cognition, learning strategies and tasks and assignments in mathematics, have been discussed. The role of problem solving in the learning of mathematics was studied by means of a possible problem-solving model which may be developed together with the learners. The teaching of problem solving was investigated by referring to the planning of a problem-based lesson and attention was paid to the learning content of the lesson and the planning of the teaching-learning activities. Together with the learners a problem-solving model was developed for the teaching of problem solving. The implementation of the teaching of problem solving was described with reference to the use of big-group presentations as well as problem solving in small groups. Attention was also paid to problem solving, and the use of different assessment techniques was discussed. The empirical investigation was done by means of a case study, and the focus was firstly on the influence of problem solving on the learning of mathematics, and secondly on the manner in which problem solving may be taught. Information was collected during the qualitative investigation by using a questionnaire which was completed by the learners, as well as an interview and observation schedule. The class work, homework and group work books of the learners were studied and transcribed. Video recordings were made of the learners' participation in the big group, small groups and written work, and the transcribed information was used to make deductions about the teaching of problem solving to the learners. From the empirical investigation it became clear that there is a correlation between problem solving and the teaching and learning of mathematics. Problem solving may be taught to learners by means of a problem-solving model, although this does not necessarily result in successful problem solving by all learners. While learners are solving problems, they are also learning mathematical concepts and acquiring and applying mathematical skills. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2005.

<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>