The goal of this paper is to evaluate commonly held criticisms of the practice of ability tracking in high school mathematics. To do so, I employ data from the National Education Longitudinal Study of 1988 and follow-ups to model classroom selection and education production. This paper will focus only on the causes and effects of tracking on students who were tracked as low-ability in eighth grade. From this, we can see how many students, if any, switched out of the low-ability track by tenth grade and how various switches have affected their test scores in mathematics. I find that students exercise mobility between ability-tracks as late as tenth grade and that ability-track placement is largely determined by test scores. In addition, I find evidence that there would be minimal, if any, test score improvement among low-ability students if they were all moved to a class of heterogeneous ability. / Master of Science

The integration of discrete mathematics into the secondary school curriculum (grades 7-12) is an important consideration because the mathematical area is dynamic and interesting, providing students the development of mathematical thinking. Also, it provides for teachers the opportunity to develop innovative mathematics instruction. Since the publication of the document Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989), it has been difficult to determine how many schools have integrated discrete mathematics as a separate or as an integrated course in the school mathematics curriculum. Moreover, the mathematics education research community has, for the most part, not focused on teachers' perceptions about teaching and learning discrete mathematics as an area of investigation. Because of the lack of research in this area, the researcher investigated preservice secondary mathematics teachers' perceptions about discrete mathematics and their reactions to the integration of discrete mathematics into the school curriculum. The researcher purposely selected four preservice secondary teachers who were enrolled in a mathematics course in the fall of 2005. Various data sources were used to get a deep understanding of each participant, including selected coursework, an online survey, and interviews. Results indicated that these preservice teachers perceive discrete mathematics as meaningful to students, as it emphasizes processes such as problem solving and mathematical thinking, and it provides opportunities to use innovative instruction. Because of this, the preservice teachers believe that discrete mathematics should be integrated in the school mathematics curriculum. In addition, several factors that affect the integration of discrete mathematics in the school were identified. These factors are the state curriculum and testing, the historical emphasis of algebra and calculus in the school curriculum, the National Council of Teachers of Mathematics (1989, 2000) Standards documents' views of discrete mathematics, teachers' views of discrete mathematics, the lack of knowledge of discrete mathematics, and the lack of materials and guidelines for teaching discrete mathematics. / Ph. D.

Thesis (M.Ed.)--University of Hong Kong, 1980. / Includes bibliographical references (leaf 171-176). Also available in print.

The general performance of learners in mathematics in most secondary schools in South Africa is not encouraging. Statistics reveal that there is a general poor performance in mathematics and related science subjects especially in those schools located in previously disadvantaged communities. There is just a need for appropriate interventions of the significance of mathematics in present society which is now characterised by high information and technology thrust. The objective of the study was to investigate the impact of the tutorial intervention programme on the performance of a grade eleven mathematics class with a view to improving the mathematics performance of these grade 11 learners. The selection of the action research based method was premised on the idea that it would help the researcher to improve his tutoring practice as well as contributing to better learner performance. Data was collected through the use of qualitative research methods. These involved observation, the utilisation of focus group discussions of learners, and in-depth interviews with randomly selected learners and other mathematics colleagues. A careful mix of learners of different learning abilities was made so that high performers would assist those whose performance was lower. In each group of five at least two high performers were included. Findings of the study point to the effectiveness of the tutorial process, justifying its adoption on a long term basis. In general, it can be concluded that the tutoring strategies used by the researcher had a positive effect on the knowledge retention of the learners. This conclusion was arrived at from an observation of improved test results over time, the learners' views in the questionnaires as well as those of peer observers. / Magister Educationis - MEd

The purpose of this study was to learn about the underlying factors that might help to explain differences in performance and engagement among middle school girls in mathematics. The study employed a qualitative approach to observe and listen directly to the voices of middle school girls and their parents and math teacher as they reflected on their experiences and thoughts about the girls‟ performance in and long-term goals related to mathematics. My goal was to hear what forces were working in and around the girls that might lead them to engagement or disengagement with mathematics. Through the use of journals, interviews, and classroom observations, I collected data on six adolescent girls attending a middle school in a small New England city. The data collected were viewed through several lenses including the triads created by parent-student-teacher and the triads of “high-performing” and “low-performing” girls. Six themes emerged: factoring in the algebra class; finding seats; relating to the teacher; social networking and engagement; untangling performance and engagement; and structuring class. These themes helped to explain some of the differences between the girls‟ performance in and engagement with mathematics. In addition, they suggested that the concept of engagement was contextual and somewhat elusive. The study raised questions about where engagement was taking place (in school or out, in math or another class), whether it was a solitary endeavor or a social creation, and the complex relationship between engagement and performance. Further longitudinal work with girls and young women as they progress through school will be important to the understanding of how, why and when girls engage or disengage from the study of mathematics.

As mathematical modeling gains popularity in K-12 classrooms, it is important to define what this entails for both students and teachers. The following study reviews various definitions of mathematical modeling and how these definitions are relevant for middle grades (5-9) teachers. Following a professional development workshop on mathematical modeling, four middle school teachers expressed their views about teaching mathematics through modeling tasks. This study documents the teachers' perceptions of what it means to model with mathematics, which tasks are most appropriate for their students, and why this is important in each of their classrooms. Although the teachers varied in their views depending on the context and circumstances surrounding each modeling task, they agreed that mathematical modeling helps students build critical thinking skills and provides an opportunity to align mathematics concepts with engaging, realistic phenomena.

Response to Intervention (RTI) has primarily been used as an early intervention in the elementary grades to improve the reading of all students; however, in recent years, mathematics has been added to the program and this addition has not been systematically evaluated. Guided by Deno's problem-solving model, the purpose of this qualitative case study was to gain insight on how middle school mathematics teachers use the problem-solving process to design interventions for struggling students and to understand the strategies they used to implement the plan. The research questions addressed how the problem-solving method is used when creating and implementing interventions, as well as the impact of the intervention on student achievement. The first phase of data collection was a focus group interview with 6 middle school RTI teachers. A convenience sample of participants described how the problem-solving method was used in planning the RTI process. The focus group interview was recorded, transcribed, and coded to find common themes among the responses. Data regarding the RTI implementation, as well as associated instructional strategies, benefits, and challenges were discussed. The second phase of data collection came from mean mathematics state test data from a cohort group of middle school students in 2012, 2013, and 2014. Scores were compared to determine if there was an increase in the percentage of students who scored at levels 3-4, as well as a decrease in the level 1 and 2 scores. Inconsistent data on the state test did not support the findings of the focus group. Social change can be achieved through this RTI mathematics study by providing teachers with instructional strategies that cultivate the growth of academic confidence and achievement of all students in the general education classroom.

This study examined the different types of mathematical errors exhibited by primary level pupils in Brunei when working with fractions. In addition, the study examined pupils' attitudes towards the learning of fractions and investigated if there were gender differences among Bruneian pupils' performances with fractions and with their attitudes towards fractions. The study was longitudinal in nature and its two phases involved a single cohort of Primary 5 pupils followed through a full year period in four government-funded primary schools in Brunei Darussalam. Pupils' mathematical errors were assessed by means of researcher-developed paper-and-pencil tests, while pupils' attitudes towards the learning of fractions were measured by means of an adapted version of attitude questionnaire that has been used previously with Bruneian pupils. Guided by six research questions, a number of statistical analyses were carried out to ensure the validity and reliability of the instruments used. These included piloting and revising the instruments, the use of Cronbach's alpha with the items in the attitude questionnaire, and the calculation of the Pearson Product Correlation Coefficient between scales of the questionnaire. The data was analysed by calculating the percentages and means of occurrences of each type of error. Paired and independent sample t-tests were carried out in order to investigate gender differences in pupils' errors and the impact of further instruction on fraction at the P6 level, while the GLM test was administered in order to investigate if there were significant change in pupils' attitudes towards fractions from the pre- to the posttests. Qualitative information obtained through pupils' interviews, field notes and lesson observations was used to support the quantitative data. / The study revealed that though pupils' achievement in the post-test improved, their performances on fraction work remained generally unsatisfactory. Many pupils in the study continued to have difficulty with the basic operations on fractions and resorted to the use of keyword strategies in dealing with word problems. Despite the pupils' unsatisfactory performance in the diagnostic tests, they generally held very positive attitudes towards the learning of fractions. No significant gender differences were observed either in pupils' performance in working with fractions tasks nor with their attitudes towards the learning of fractions. The findings of this study also highlight a number of issues for mathematics teachers to consider when dealing with fractions, and the findings also have implications for the quality of the instructional activities provided by the teachers, for the impact of language transfer in the medium of instruction - that is, from Bahasa Melayu to English at the pupils' Primary 4 level- and for the quality of the teacher training program in Brunei.

The purpose of this research was to examine the possible associations between the perceived classroom environment of high school students, the level of mathematics anxiety that they possess, and their attitudes towards mathematics. This marks the first time that these three fields of research have been simultaneously combined. Data were gathered from 745 high school mathematics students in 34 classes in high schools in the Southern California area using three instruments: the What is Happening In this Class? (WIHIC) learning environment survey created by Fraser, McRobbie, and Fisher (1996), an updated version of Plake and Parker's (1982) Revised Mathematics Anxiety Ratings Scale WRS), and a mathematics version of selected scales from Fraser's (1981) Test of Science-Related Attitudes (TOSRA). This revised attitude instrument was called the Test of Mathematics-Related Attitudes (TOMRA). Using statistical methods, the three instruments were checked for internal consistency reliability, factor structure, and discriminant validity. The RMARS and WIHIC were both found to exhibit good reliability and factorial validity in mathematics classrooms in Southern California, while the TOMRA yielded two scales of the four a priori scales, Enjoyment of Mathematics Lessons and Normality of Mathematicians, which met reliability and factorial validity standards. Within-class gender differences were analysed using paired t-tests combined with a modified Bonferroni procedure and effect sizes. Between- student gender difference were investigated using MANOVA. Simple correlation and multiple regression analyses were performed to identify possible associations between the learning environment and anxiety/attitudes scales. Qualitative data were collected from interviews and inductive analysis was performed in order to refute or corroborate the quantitative findings. / Significant within-class gender differences were found in four areas of the learning environment (Student Cohesiveness, Task Orientation, Cooperation, and Equity), but no gender differences in attitudes were found. All four learning environment areas were perceived in a more favourable light by females than by males. Individual gender differences were similar, with a significant difference also being found in Teacher Support, as well as both types of mathematics anxiety, namely, Learning Mathematics Anxiety and Mathematics Evaluation Anxiety. In order to carefully identify the relationships between the classroom learning environment and mathematics anxiety, analyses were conducted for both factors of mathematics anxiety. While no association between the learning environment and Mathematics Evaluation Anxiety was found, there were significant associations between Learning Mathematics Anxiety and three areas of the learning environment: Student Cohesiveness, Task Orientation, and Investigation. Significant associations between the Normality of Mathematicians attitude scale and the learning environment scales Equity and Involvement were identified, while three areas of the learning environment (Investigation, Task Orientation, and Cooperation) had a significant relationship with Enjoyment of Mathematics Lessons. Qualitative data analyses confirmed relationships between anxiety, attitudes, and classroom learning environments. The data also suggest that the structure of the mathematical content is linked with the level of anxiety that high school students feel.

Syftet med min studie är att belysa elevers uppfattningar om vad det innebär att ha matematik. Delar av studien ägnas åt att lyfta fram uppfattningar som elever i behov av särskilt stöd, d.v.s. elever med åtgärdsprogram, har. Åtta elever intervjuades i en fenomenografisk studie om vad de lägger i begreppet "att ha matematik". Studien visar att det finns en uppfattning att det individuella arbetet är grunden för att ha matematik och att kommunikation mellan elever ses som ett avsteg från matematiken. Det kvantitativa formella matematikarbetet med läroboken betonas av eleverna. Men samtidigt finns också en uppfattning att matematik kan has i samlärande. När eleverna hjälper varandra utvecklas lärandet hos alla förutsatt att det finns ett matematiskt tänkande enligt denna uppfattning. Det finns också en uppfattning om att det existerar ett visst samband mellan den informella vardagsmatematiken och den formella skolmatematiken. Men utanför matematiklektionerna upplevs matematiken finnas endast när eleverna rent påtagligt räknar och mäter. De intervjuade eleverna med åtgärdsprogram i matematik tenderar ha en uppfattning som starkare betonar att matematik has individuellt i läroboken, helst utan hjälp och ofta med fokus på algoritmer. Att räcka upp handen för att söka hjälp och att samarbeta tycks därför för dessa elever inte vara eftersträvansvärt. Den informella och den formella matematiken uppfattas ha få beröringspunkter. Utanför läroboken finns inte så mycket matematik enligt intervjuade elever med åtgärdsprogram. Risken är att det gemensamma matematikarbete som framhålles i Lpo94 av eleverna inte uppfattas som matematiklärande. Eleverna kan därmed missa de lärtillfällen som bygger på lärande i kommunikation. Att endast arbete i läroboken räknas som att ha matematik torde inte underlätta för elever i behov av särskilt stöd att förstå matematikens roll i vardagen. Så ska vi med dessa elever arbeta vidare med deras formella lärande i läroboken eller ska vi i stället börja arbeta för att eleverna ska förstå kopplingen mellan den informella och den formella matematiken för att öka den matematiska förståelsen?