The rationale behind this study concerns the issues school administrators and teachers of expatriate students face over the progress and placement of the growing number of these students in mathematics classrooms in various countries brought about by the demographical changes occurring in this globalization era. This study aimed to present a method of examining lower secondary school mathematics textbooks with the purpose of evaluating students' expected past learning and comparing students' expected mathematics learning across the different curricula. It is anticipated that such an investigation will be of value to those responsible for the correct level of placement of these students.Six sets of textbooks from four countries on the Asia-Pacific rim, namely Australia, Brunei, China and Singapore, were selected for this study. The textbook content of each country was analyzed in terms of strand weighting and content details, and then coupled with information gained from interviews with teachers. This led to the findings which addressed the various issues raised.The findings facilitated a comparison of the learning paths offered by the various textbooks, fleshed out the differences and similarities of the various curricula and made available detailed comparisons of the textbooks' content in terms of topics covered. The analytical procedure of the examination of text content as presented in this study is itself a diagnostic technique for assessment of the students' past learning, which addressed the main objective of the study.The findings will be of interest to all who are interested in the mathematics taught in the countries involved. / Outcomes will be particularly useful to curriculum planners and textbook writers as well as the administrators and teachers of International Schools and other schools enrolling expatriate students from these countries. The study offers a 'simplistic' way of evaluating textbooks to assess students' learning progress, and highlights the traits of the countries' curricula to provide a general idea of the mathematics ability expected from the expatriate students residing in these countries.

As a result of two years working with the pre-service primary teachers in a College in Fiji I became aware of the difficulty many of the students were having understanding the primary school mathematics they would be required to teach. During that time I had attempted to help them overcome the difficulties by using different teaching approaches and activities but was far from satisfied with my efforts. Hence I decided to make a concerted effort to help the students by planning, implementing and partially evaluating a mathematics education unit, known as the Teaching Program for the first semester of their course. This work formed the basis of my study. For the Teaching Program I chose a constructivist teaching approach with number sense as the underlying theme. To examine the aspects of the Program I used my observations and those of the students especially ones reported in their mathematics journals. To evaluate the effectiveness of the Teaching Program I collected and analysed quantitative data from traditional testing of the class of forty students as well as data from case studies of six of the pre-service teachers in the class. To determine what features of the Teaching Program were linked to positive changes my main source of data was the case studies, especially entries from their journal writings. The findings suggested that a significant development of the cognitive aspects of the students’ number sense did occur during the time of the Teaching Program but not as much as was hoped for. As a result of the analysis of the data I came to a greater realisation of the importance of the non-cognitive aspects of number sense and the necessity for a greater consideration of them in the development of a Program. I also realise now that a major development that did occur was in my understanding of the knowledge and learning of mathematics. My ideas of a teaching paradigm of social constructivism had not guided me sufficiently to incorporate activities and procedures to develop the non-cognitive aspects. I suggest that a paradigm which extends the theory of social constructivism to give greater consideration of these aspects of learning in general, and hence numeracy and number sense in particular, was needed. As a result of this study, my introduction to the theory of enactivism appears to be giving me some direction in this search at this stage.

Achievement and the experiences of women in secondary school mathematics have been well documented in the research literature (e.g., Benbow & Stanley, 1980, 1983; Tartre & Fennema, 1995; Sherman, 1982; Ryckman & Peckham, 1987; Keller & Dauenheimer, 2003). With respect to achievement, the research literature primarily focuses on how women are deficient to men (e.g., Benbow & Stanley, 1980, 1983) and the roles affective attributes (e.g., Sherman, 1982; Fennema, Petersen, Carpenter & Lubinski, 1990) and stereotype threat (e.g., Quinn & Spencer, 2001; Steele & Aronson, 1995) have played in women’s deficiencies. Despite the perspective and nature of this research, there are, however, women who have achieved at extraordinarily high levels in the secondary mathematics classroom. It is important to examine this historical research as it has impacted the views of teachers, researchers, and media with regard to female mathematics students’ opportunities. By reflecting upon the research literature and its far reaching impacts, high-achieving women in mathematics can begin to reverse the perceptions that limit their opportunities. Thus, the purpose of this study was to explore, through the experiences and stories relayed by the study’s participants, how young women might negotiate the (historic all male) mathematics domain. Employing a qualitative research designed within a phenomenological framework and analyzed through a combination of postmodern and standpoint feminisms, I examined the stories of four undergraduate female students who were identified as being high-achieving in secondary school mathematics. These young women, by reflecting upon their secondary school experiences, and by reflecting upon their experiences within the context of the existing research literature, not only identified the aspects of their lives they felt had the greatest impact upon their opportunities but also examined their personal definitions of success and the impacts their gender had on their (socially defined) achievements within secondary school mathematics.

Dyskalkyli (specifika räknesvårigheter) är en av flera orsaker till matematiksvårigheter. Studier har påvisat samband mellan dyskalkyli och dyslexi och att personer med dyskalkyli har svårt att klara skolmatematiken. Två skilda synsätt förklarar orsaken till dyskalkyli: systemteorin och modulärteorin. Dyscalculia Screener är ett screeningverktyg som bygger på modulärteorin och att dyskalkyli beror på svårigheter med grundläggande antalsuppfattning och ska urskilja personer med dyskalkyli från de som är dåliga på matematik av andra orsaker. Testet innehåller delar som testar reaktionstid (Simple Reaction Time), antalsuppfattning (Dot Enumeration och Numerical Stroop) och aritmetik (Addition och Multiplication). Denna studie undersökte hur svenska barn i årskurs 5 och 6 presterade på testet, för att ge referensdata för svenska förhållanden och undersöka hur väl de engelska normerna fungerar. Studien studerade även samband mellan avkodningsförmåga, av riktiga ord och non-ord (med testet LäSt) och prestation på Dyscalculia Screener samt samband mellan prestation i skolmatematik och resultat på respektive test. Studien innefattade 66 barn, 36 i årskurs 5 och 30 i årskurs 6. Svenska barns resultat skiljde sig till viss del från de engelska normvärdena. De presterade lägre än normvärdena på deltesten Simple Reaction Time och Multiplication. På Dot Enumeration och Numerical Stroop presterade barnen högre. På Addition låg barnen inom normvärdena. Samband mellan avkodningsförmåga och räkneförmåga kunde påvisas, framförallt för avkodning av non-ord. En skillnad i resultat fanns på deltesten Numerical Stroop, Addition och Multiplication mellan de som uppnådde målen i matematik och de som var tveksamma att uppnå eller inte uppnådde målen. / Dyscalculia (specific mathematics disorder) is one, among other causes of mathematical difficulties. Studies have indicated a correlation between dyscalculia and dyslexia and people with dyscalculia have problems managing school mathematics. Two different theories explain the cause of for dyscalculia: the system theory and the modular theory. Dyscalculia Screener is a screening tool based on the modular theory and that dyscalculia is caused by difficulties in basal number sense and should discriminate people with dyscalculia from those who are bad at mathematics for other reasons. The test includes parts that test reaction time (Simple Reaction Time), number sense (Dot Enumeration and Numerical Stroop) and arithmetics (Addition and Multiplication). This study investigated how Swedish children, in year 5 and 6, scored on the test, to get reference data for Swedish relations and see whether the normes from England could be used. The study also investigated correlations between decoding, of real words and non-words (with the test LäSt) and score on Dyscalculia Screener and correlations between ability to manage school mathematics and score on each test. The study included 66 children, 36 in year 5 and 30 in year 6. Swedish children scored different in some ways from the English norms. They scored lower than the norms on the testparts Simple Reaction Time and Multiplication. On Dot Enumeration and Numerical Stroop they scored higher. On Addition, they scored within the norms. A correlation between decoding and counting ability was found, especially for decoding of non-word. A difference in score was seen on the testparts Numerical Stroop, Addition och Multiplication between children that achieved the goals in mathematics and those who were unsure to achieve them or did not.

This study examined teachers' learning and understanding of mathematical representation through the Middle School Mathematics Project (MSMP) professional development, investigated teachers' use of mathematics representations in teaching fractions and algebraic functions, and addressed patterns of teachers' changes in learning and using representation corresponding to Teachers' Zone of Proximal Development (TZPD). Using a qualitative research design, data were collected over a 2-year period, from eleven participating 6th and 7th grade mathematics teachers from four school districts in Texas in a research-designed professional development workshop that focused on helping teachers understand and use of mathematical representations. Teachers were given two questionnaires and had lessons videotaped before and after the workshop, a survey before the workshop, and learning and discussion videotapes during the workshop. In addition, ten teachers were interviewed to find out the patterns of their changes in learning and using mathematics representations. The results show that all teachers have levels of TZPD which can move to a higher level with the help of capable others. Teachers' knowledge growth is measurable and follows a sequential order of TZPD. Teachers will make transitions once they grasp the specific content and strategies in mathematics representation. The patterns of teacher change depend on their learning and use of mathematics representations and their beliefs about them. This study advocates teachers using mathematics representations as a tool in making connections between concrete and abstract understanding. Teachers should understand and be able to develop multiple representations to facilitate students' conceptual understanding without relying on any one particular representation. They must focus on the conceptual developmental transformation from one representation to another. They should also understand their students' appropriate development levels in mathematical representations. The findings suggest that TZPD can be used as an approach in professional development to design programs for effecting teacher changes. Professional developers should provide teachers with opportunities to interact with peers and reflect on their teaching. More importantly, teachers' differences in beliefs and backgrounds must be considered when designing professional development. In addition, professional development should focus on roles and strategies of representations, with ongoing and sustained support for teachers as they integrate representation strategies into their daily teaching.

Thesis (Ed. D.)--West Virginia University, 2001. / Title from document title page. Document formatted into pages; contains xi, 156 p. Vita. Includes abstract. Includes bibliographical references (p. 125-138).

Students’ struggle with learning mathematics is often cast in a negative light. Mathematics educators and researchers, however, suggest that struggling to make sense of mathematics is a necessary component of learning mathematics with understanding. In order to investigate the possible connection between struggle and learning, this study examined students’ productive struggle as students worked on tasks of higher cognitive demand in middle school mathematics classrooms. Students’ productive struggle refers to students’ “effort to make sense of mathematics, to figure something out that is not immediately apparent” (Hiebert & Grouws, 2007, p. 287) as opposed to students’ effort made in despair or frustration. As an exploratory case study using embedded multiple cases, the study examined 186 episodes of student‐teacher interactions in order to identify the kinds and nature of student struggles that occurred in a naturalistic classroom setting as students engaged in mathematical tasks focused on proportional reasoning. The study identified the kinds of teacher responses used in the interaction with the students and the types of resolutions that occurred. The participants were 327 6th and 7th grade students and their six mathematics teachers from three middle schools located in mid‐size Texas cities. Findings from the study identified four basic types of student struggles: get started, carry out a process, give a mathematical explanation, and express misconception and errors. Four kinds of teacher responses to these struggles were identified as situated along a continuum: telling, directed guidance, probing guidance, and affordance. The outcomes of the student‐teacher interactions that resolved the students’ struggles were categorized as: productive, productive at a lower level, or unproductive. These categories were based on how the interactions maintained the cognitive level of the implemented task, addressed the externalized student struggle, and built on student thinking. Findings provide evidence that there are aspects of student‐teacher interactions that appear to be productive for student learning of mathematics. The struggle‐response framework developed in the study can be used to further examine the phenomenon of student struggle from initiation, interaction, to its resolution, and measure learning outcomes of students who experience struggle to make sense of mathematics. / text

This thesis is about the process of becoming, or not becoming, a primary school mathematics teacher. The aim is to understand and describe the professional identity development of novice primary school mathematics teachers from the perspective of the novice teachers themselves. The study is a case study with an ethnographic direction where seven novice teachers have been followed from their graduation and two years onwards. The ethnographic direction has been used to make visible the whole process of identity development, both the individual and the social part. The empirical material in the study consists of self-recordings made by the respondents, observations and interviews. The empirical material is analysed in two different but co-operating ways. First a conceptual framework was developed and used as a lens. Second, methods inspired by grounded theory are used. The purpose of using them both is to retain the perspective of the respondents as far as possible. At the time of graduation the respondents are members in a community of reform mathematics teaching and they want to reform mathematics teaching in schools. In their visions they strive away from their own experiences of mathematics in school and practice periods. Four cases are presented closely in the thesis as they show four various routes into, and out of, the teaching profession. These four cases make visible that the respondents’ patterns of participation regarding teaching mathematics changes when they become members in new communities of practice with mathematics teaching as part of the shared repertoire. But, the four cases also make visible that the existence of such communities of practice seems to be rare and that the respondents’ different working conditions limit their possibilities of becoming members in those that exist. During the time span of this study, the respondents hardly receive any feedback for their performance as mathematics teachers. Even if they teach mathematics they don´t teach it as they would like to and they don´t think of themselves as mathematics teachers. Two years after graduation none of the respondents has developed a professional identity as primary school mathematics teacher. A primary school teacher in Sweden is a teacher of many subjects but they are the first teachers to teach our school children mathematics. For the respondents to develop a sense of themselves as a kind of primary school mathematics teacher, mathematics teaching has to become part of their teacher identities. For this to become possible, mathematics must become a part of their image of a primary school teacher as an image of a primary school mathematics teacher. Furthermore memberships in communities of practice with mathematics in the shared repertoire must be accessible, both during teacher education and after graduation. Then professional identity development as a primary school teacher would include becoming and being a teacher of mathematics.

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.