The first aim of this study was to identify important aspects of mathematical thinking, and to investigate the relationships between the different aspects of mathematical thinking and mathematics achievement. The second aim was to examine possible gender and school location (urban, suburban, and rural) differences related to aspects of mathematical thinking and mathematics achievement. Two assessments were developed that were suitable for students in the Year 11 scientific stream in Jordan. One test was for aspects of mathematical thinking and the other for mathematics achievement, the latter being consistent with typical school achievement tests for these students in Jordan. The researcher chose and developed items to test mathematical thinking and mathematics achievement from the Third International Mathematics and Science Study (TIMSS), the internet, research literature, specialist books in mathematics and his own experience. The data were collected in the 2003-2004 academic year from over 500 Year 11 scientific stream students (both male and female) at 20 randomly selected schools from six directorates in the Irbid Governorate, Jordan. In addition, 13 teachers were individually interviewed, and four groups of students were interviewed in focus groups to obtain information about their opinions and about different methods of thinking in mathematics. The teacher interviews were used to identify consistencies and inconsistencies between the test results and the respondents’ opinions of difficulty and importance. In addition, information was obtained about the classroom time teachers devoted to the different aspects of mathematical thinking and the teaching strategies they employed. Six aspects of mathematical thinking were identified by the study: Generalization, Induction, Deduction, Use of Symbols, Logical thinking and Mathematical proof. Mathematical proof was also the most difficult aspect, while Logical thinking was the least difficult. Female students had significantly higher mean scores than males on three of the six aspects of mathematical thinking and on the total test scores. Students attending suburban schools had significantly higher mean scores than students at urban and rural schools on four aspects, and on the total scores. Using multiple regression analysis, all six aspects were found to be important for mathematics achievement. Mathematical proof and Generalization were the most important aspects, Use of symbols and Logical thinking were next in importance, and Deduction and Induction were the least important aspects. Approximately 70 per cent of the variance in mathematics achievement was explained by the six aspects of mathematical thinking, gender, and school location. There was a high level of consistency between teacher opinions of the relative importance of aspects of mathematical thinking and the test results. However, there were some nconsistencies between the teacher opinions and test results with respect to relative difficulty levels of the six aspects. By clarifying the importance for mathematics achievement of the six aspects of mathematical thinking identified, this study has relevance for the teaching of mathematics to Year 11, scientific stream students in Jordan. / PhD Doctorate

Black students’ performance in mathematics on standardized examinations compared to White students is dismal; however, previous research has shown that there are highly effective high schools for Black students as defined by high levels of mathematics performance. Underachievement in upper-level high-school mathematics courses is a barrier for Black students’ access to many postsecondary education opportunities and contributes to an underrepresentation of Black students in the science, technology, engineering, and mathematics college majors and related careers. This dissertation examines the multilevel characteristics (student, teacher, department, and school factors) of high school mathematics programs as measured by Black students’ performance on standardized tests in 12th grade. The data for this study were taken from the Education Longitudinal Study (ELS) of 2002 from the National Center for Education Statistics of the U.S. Department of Education. Results indicated that the 12th grade achievement in mathematics of Black students is positively related to prior mathematics achievement, family SES, and the interaction between the teaching practices of mathematics teachers and students’ collective sense of safety. A surprising interaction effect indicated that in schools where there is collective sense about lack of safety and where students report low-quality mathematics teaching practices, Blacks are more likely to exhibit high student-achievement in mathematics than schools where the collective sense about safety is mixed (or where it is high) or where there is student consensus of good quality teaching practices.

Comparing the mathematics performance of American students to their counterparts in other countries has been a common theme in recent literature, with conclusions generally finding that American students are falling far behind. One response to this problem may involve research which has shown a modest positive correlation between student interest and achievement in math (Koller, Baumert, & Schnabel, 2001; Schiefele, Krapp, & Winteler, 1992). Being able to identify students with high levels of interest in math may allow educators to provide advanced instruction to such students. Current measures of student interest in mathematics are lacking in that they often are not based on any one theory, they do not cover all characteristics of individual interest, and are based on a self-report format. Therefore, the goal of this thesis was to develop a teacher identification form of student interest in mathematics to add to the literature a psychometrically sound measure of student interest in math which is assessed by classroom teachers instead of the students themselves. The teacher identification form was developed based on the characteristics of individual interest as defined by Hidi and Renninger’s (2006) Four-Phase Model of Interest Development. To determine reliability and validity of the form, second through sixth grade math teachers in six elementary schools in Warren County, KY completed the form both in a pilot study and also later as part of an identification process for students to receive advanced math instruction. For the purposes of data analysis, results were separated by grade. Reliability estimates for the form, as indicated by Cronbach’s alpha, were found to be .934 for third grade, .925 for fourth grade, and .901 for fifth grade. The overall Cronbach’s alpha for grades two through five was .926. These high reliability coefficients indicate high consistency among the items. Validity of the identification form was established by correlating results with the Iowa Tests of Basic Skills (ITBS) math section, a standardized assessment taken by all students in the six schools. Correlations between teacher identification rating composites and ITBS math scores were as follows: .379 for third grade, .417 for fourth grade, and .460 for fifth grade. The sixth grade data set was incomplete, and thus that correlation for was .300. Each individual item on the identification form and the grade composite scores all correlated with ITBS math scores significantly at the .01 level, indicating sufficient validity of the form. An important observation about the results is that the highest validity coefficients as well as the narrowest range of correlations were found for fifth grade data. The next highest correlations were found for fourth grade, and the lowest correlations and widest range of correlations were found for third grade data. The possibility that this pattern of results may be due to better developed individual interests of older students or that students’ individual interests are more easily identified by their teachers in higher grades is discussed.

There is a growing interest in studying the influence of parental involvement on student achievement, as well as factors that influence parents' choices in being involved in their children's education. This study examined the relationships among socioeconomic status, parental involvement, and students' mathematics achievement in Jordan and the United States. It also investigated the reasons that motivate parental involvement in both Jordan and the United States. For data collection, a four-section instrument was distributed to parents/guardians of students in grades four, five, and six from Jordan and the United States in order to collect demographic information, socioeconomic status, parental involvement levels, mathematics achievement, and qualitative data about the nature of parental involvement and parents' reasons for being involved in their children's mathematical education. The study revealed no relationship between socioeconomic status and parental involvement in Jordan. In the United States, however, the study revealed a positive relationship between socio-economic status and parental involvement at home; only parents' education level had a statistically significant relationship with parental involvement at school. The study further revealed a positive relationship between parental involvement at home (PIH) and students' mathematics achievement (SMA) in both Jordan and the United States. Also, a positive relationship between parental involvement at school (PISC) and students' mathematics achievement (SMA) was observed in the Jordan sample. However, no relationship between PISC and SMA was found in the United States sample. Also, the findings revealed a positive correlation between SES and SMA for the United States sample. However, in the Jordan sample, a positive relationship existed between family income and SMA, and parents' education level and SMA, while no relationship was found between parents' employment status and SMA. Furthermore, the findings revealed a significant difference only between the correlation coefficients of PIH and SMA between Jordan and the United States. The findings of the qualitative data analysis did not particularly support the quantitative findings, but they did provide a clear understanding of parents' diverse reasons for why they chose to be involved in their children's education, such as social and economic gains for their children. It also showed what parents believed affected or influenced their ability or choices with regard to being involved in their children's education. In light of the findings, a number of recommendations were given for further research and practice, specifically with regard to curriculum development and the design of parent-school communication programs.

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The purpose of this study was to examine the effect of training in self-regulated learning strategies on math anxiety and mathematics achievement among preservice teachers. The self-regulated learning strategies examined included personal time management, how to read your mathematics textbook for understanding, organizational skills, mathematics test taking and preparation, and the use of estimation in solving mathematics problems. Preservice elementary teachers with these improved learning skills may in turn become more successful teachers of mathematics. The effect of training in self-regulated learning as a treatment for math anxiety is not well established. However, self-regulated learning has been associated with improved mathematics and science problem solving (De Corte, Verschaffel, & Op't Eynde, 2000; Taylor & Corrigan, 2005; Zan, 2000). Increased use of self-regulated learning strategies has also been associated with a reduction in test anxiety (Hofer & Yu, 2003; Pintrich, 2000; Zeidner, 1998). Therefore, training in self-regulated learning strategies has the potential to reduce math anxiety among preservice elementary teachers. Elementary education majors in a course in mathematics concepts were given training in self-regulated learning strategies. A control group of similar students received the same classroom instruction by the same college professor. The professor did not participate in the training sessions that were led by this researcher. Both treatment and control groups were given pretests and posttests: the Abbreviated Mathematics Anxiety Scale - to measure math anxiety, the Motivated Strategies for Learning Questionnaire - to measure use of self-regulated learning strategies, and a Mathematics Achievement Test - to measure changes in content knowledge. The analyses used t-tests and correlations to compare the participants' pretest and posttest scores on the three scales. The use of self-regulated learning strategies was not shown to reduce math anxiety or improve achievement among the elementary education majors in this study. This result may have been due to various limitations, such as insufficient time for applying and following up on the training and an inability to fully embed the training into the course content. Future research should investigate if, given the proper conditions, self-regulated learning strategies will reduce math anxiety and improve the learning of mathematics concepts, leading to more effective mathematics teaching in the elementary classrooms. / CITE/Mathematics and Science Education

The hypothesis that a structured, sequenced, approach to mathematics learning, based on the application of learnt facts, decreases mathematics anxiety and increases mathematics achievement is tested. A literature study and an empirical investigation were conducted with respect to the relationships between maths anxiety, maths achievement and teaching methods. A qualitative research design which focussed on the cross-case analysis of different case studies was used. The qualitative case study involves multiple methods such as interviews, observations and a pretest, posttest design. It analyses and compares the effects of the Kuman method, used as the intervention programme, on maths anxiety and maths achievement of an experimental group and a control group. The results of this research indicate that learners on the intervention programme who showed a decrease in anxiety, showed an increase in achievement. This has implications for the teaching methods used in South Africa. / Teacher Education / M. Ed. (Specialisation in Guidance and Counselling)

The primary purpose of this study was to determine if the implementation of an intervention involving teachers' use of children's literature, related storybook manipulatives, and a scaffolding (LMS) approach to learning would improve preschool children's mathematics test scores. Additionally, the LMS approach was examined to determine whether teachers' perceptions of their effectiveness in mathematics instruction changed from the beginning to the end of the study. The subjects of the study included 60 preschool-aged children and six teachers from two child care centers. The preschool teachers participated in either a control or experimental condition (the LMS approach) in their daily mathematics instruction with their preschool children. The researcher tested the children using the Test of Early Mathematics Ability and an abbreviated version of the Stanford-Binet Intelligence Scale. The study was based on two main research questions. The first question asked if there was a difference in the Test of Early Mathematics Ability total posttest scores between children in the literature-manipulatives-scaffolding intervention group and children in the control group after assuring equivalency of the two groups. The second question addressed if preschool teachers believed they were more effective in their mathematics instruction after implementing the LMS approach with young children. The answer to the first research question was that there was no statistically significant difference in the Test of Early Mathematics Ability total posttest scores between children in the literature-manipulatives-scaffolding group and children in the control group. However, the answer to the second question was that preschool teachers believed they were more effective in their mathematics instruction after implementing the LMS approach with young children. Recommendations for future research on early childhood mathematics include the investigation of preschool children's ability, achievement, and interest in mathematics; teachers' use of mathematics scaffolding techniques; and longitudinal mathematics interventions beginning during the preschool years.

School leaders are expected to make decisions that improve student mathematics achievement. However, one difficulty for school leaders has been the limited amount of research concerning content-specific (e.g., mathematics) school leadership and its effects on student achievement. School leaders do not make decisions in isolation; rather, they make decisions as part of a complex adaptive system (CAS), as proposed by complexity theory. The purpose of this study was to explore the role the school leader plays in students’ mathematics achievement through the lens of complexity theory. The researcher collected survey data from K-12 school leaders and conducted focus group interviews to answer the research questions. The researcher found a significant regression equation predicting the school-wide average SAGE mathematics proficiency scores based on several characteristics of the school leader and student demographics. Distinctive patterns emerged in the decisions and actions made by school leaders based on school-wide SAGE mathematics proficiency. Results suggest that the school leaders’ first role in promoting higher student mathematics achievement is to directly and indirectly facilitate a shared vision of mathematics education between stakeholders in the CAS. The school leader’s second role is to actively work to recruit and retain the highest quality teachers possible.