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The following study utilizes data from the High School and Beyond Study in order to predict mathematics achievement using both student characteristics and school level characteristics. Utilizing Hierarchical Linear Modeling, this study extends the body of literature by exploring how race, socio-economic status, and gender, as well as the percentage of minority students in a school, whether or not the school is Catholic, the proportion of students in the academic track, and the mean socioeconomic status of the school all affect mathematics achievement. Through this methodology, it was possible to see the direct effects of both student level and school level variables on achievement, as well as the cross-level interaction of all of these variables. Findings suggest that there are discrepancies in how different types of students achieve, as well as how those students achieve in varying contexts. Many of the variables were statistically significant in their effect on mathematics achievement. Implications for this research are discussed and considerations for future research are presented.

The following study utilizes data from the High School and Beyond Study in order to predict mathematics achievement using both student characteristics and school level characteristics. Utilizing Hierarchical Linear Modeling, this study extends the body of literature by exploring how race, socio-economic status, and gender, as well as the percentage of minority students in a school, whether or not the school is Catholic, the proportion of students in the academic track, and the mean socioeconomic status of the school all affect mathematics achievement. Through this methodology, it was possible to see the direct effects of both student level and school level variables on achievement, as well as the cross-level interaction of all of these variables. Findings suggest that there are discrepancies in how different types of students achieve, as well as how those students achieve in varying contexts. Many of the variables were statistically significant in their effect on mathematics achievement. Implications for this research are discussed and considerations for future research are presented.

Thesis (M.S.) -- Central Connecticut State University, 2005. / Thesis advisors: Philip Halloran and Timothy Craine. "... in partial fulfillment of the requirements for the degree of Master of Science in Mathematics." Includes bibliographical references (leaves 42-44). Also available via the World Wide Web.

archives@tulane.edu / 1 / Emily A. Lewis

In this qualitative action research study, five lower-achieving freshman prealgebra students in a rural high school were interviewed about mathematics anxiety. The subjects ranged in age from 13 to 15 years and included three boys and two girls, of which one was Hispanic, one was African-American, and three were Caucasian. These students had tested below the fourth-grade level in mathematics during their eighth-grade year and were placed in special pre-algebra classes, which met for 30 additional minutes each day and progressed with more depth, but at a slower pace. The researcher employed personal interviews to answer the research question: How do students describe and cope with mathematics anxiety? The researcher utilized the constant comparative method to analyze data and developed the following seven categories: setting and background information; self-image; mathematics difficulties; success in mathematics; support for learning; teacher support; and coping techniques, which was the context of the students’ anxiety. While they have encountered some success in mathematics, the descriptions of support from family and student friends, along with teacher support, explain how these students’ cope with the anxiety. When the students talked positively about mathematics, they discussed activities that made mathematics fun or enjoyable. However, these participants also spoke of negative mathematics experiences as early as the first grade. A poor self-image, as it relates to a student’s mathematical knowledge, affects current learning. Past negative perceptions appeared to contribute to their defeat. The findings coincided with previous research that mathematics anxiety is negatively related to mathematics achievement. Students reported gains from hands-on activities, facilitative teaching, teacher encouragement, additional assessments, and goal settings, but interview data suggested they had mostly given up on getting much better in mathematics, because they thought they were not going to succeed. They stopped trying and giving up was their way of coping.

The purpose of this study has two phases. In the first phase, a model that explains students&rsquo / mathematics achievement in TIMSS-R will be proposed. In the second phase, the proposed model will be evaluated to interpret the similarities and differences across three culturally and linguistically different countries / Turkey, the Netherlands, and Italy. This study will basically combine students&rsquo / answers on TIMSS-R Students Questionnaire items with their mathematics achievement scores obtained from TIMSS-R Mathematics Achievement Test. In order to achieve this, items in the student questionnaire will be grouped under latent variables and then the related models will be established. Thirty-seven items selected from the TIMSS-R Student Questionnaire were analyzed using principle component factor analysis for each country. The results indicated seven interpretable dimensions. Based on the results&rsquo / of factor analysis of Turkey, the latent variables were generated by selecting the observed variables with highest loadings. These latent variables were / out-of-school activities, socioeconomic status, importance given to math, math classroom iv climate, perception of failure, teacher-centered and student-centered activities. The proposed mathematics achievement model was tested by structural equation modeling for each country separately with the sample of 4772, 2728, and 2781 eighth grade students in Turkey, the Netherlands, and Italy, respectively. In all of the countries perception of failure was the strongest factor explaining the mathematics achievement of the eighth grade students. The other two important factors explaining mathematics achievement were socioeconomic status and student-centered activities for Turkey and Italy / out-of-school activities and importance given to math for the Netherlands. The results indicated that Turkey and Italy have more similar results when compared with the Netherlands. Different than the other countries in Turkey instructional activities formed two separate dimensions such as / teacher-centered and student-centered instructional activities. Since this finding emphasized the important role of teacher in the Turkish education system, it was suggested that more importance should be given to the teacher education.

This dissertation presents findings from a study investigating of the effects of a middle-school intervention, using the "Skill-Builders" curriculum, on participating students' attitudes, self-efficacy, achievement, self-regulated learning, and classroom learning behaviors in mathematics. The main research questions were 1) will a nine week school-counselor-led intervention using the "Skill-Builders" curriculum have a significant effect on the outcome variables of interest, and 2) will the effects be different for females than for males. A repeated measures ANOVA was used to test for differences between conditions and between sexes on all outcome measures. Results from the study demonstrated statistically significant post-intervention differences between students in the experimental and control conditions on their attitudes toward math learning, self-efficacy, achievement, and self-regulated learning behaviors, and the gains made by students in the experimental condition were maintained at follow-up. Students in the control condition showed no changes or declined on measures of attitudes, achievement, self-efficacy, and self-regulated learning behaviors at post-test and follow-up. Results also indicated a significant interaction for sex and condition, which suggests that the intervention had different effects for the participating females than the males. Implications of the findings, within the theoretical framework of the study and within the context of school counseling outcome research, are discussed.

This study compared the estimates of reliability made using one, two, three, four, five, and unlimited consecutive failures as ceiling rules in scoring a mathematics achievement test which is part of the Iowa Tests of Basic Skill (ITBS), Form 8. There were 700 students randomly selected from a population (N=2640) of students enrolled in the eight grades in a large urban school district in the southwestern United States. These 700 students were randomly divided into seven subgroups so that each subgroup had 100 students. The responses of all those students to three subtests of the mathematics achievement battery, which included mathematical concepts (44 items), problem solving (32 items), and computation (45 items), were analyzed to obtain the item difficulties and a total score for each student. The items in each subtest then were rearranged based on the item difficulties from the highest to the lowest value. In each subgroup, the method using one, two, three, four, five, and unlimited consecutive failures as the ceiling rules were applied to score the individual responses. The total score for each individual was the sum of the correct responses prior to the point described by the ceiling rule. The correct responses after the ceiling rule were not part of the total score. The estimate of reliability in each method was computed by alpha coefficient of the SPSS-X. The results of this study indicated that the estimate of reliability using two, three, four, and five consecutive failures as the ceiling rules were an improvement over the methods using one and unlimited consecutive failures.

Mathematical modeling is a thinking process that applies various sets of cognitive attributes – one component of intellectual resources (i.e., cognitive resources). Students are able to develop cognitive attributes when they engage in mathematical modeling activities. Furthermore, using many of the cognitive attributes developed during the mathematical modeling process, students solve mathematics problems, for example, in assessments. Examining students’ mastery of these cognitive attributes, we can investigate relationships between students’ cognitive development through mathematical modeling practices in classrooms and their performance on mathematics assessments. The purpose of this research is to quantitatively and empirically investigate the relationships between students’ development of mathematics cognitive attributes and their achievement. For the current study, we selected the four cognitive attributes representing different stages of the mathematical modeling practices – select, analyze, compute, and represent. The generalized DINA (deterministic inputs, noisy “and” gate) is applied to generate students’ mastery profiles of the cognitive attributes from their responses to test items. Using students’ mastery profiles as datasets, three secondary analysis studies are conducted with linear regression analysis and multivariate approach to repeated measure ANOVA. The findings show that development of the four cognitive attributes in mathematical modeling is positively related to mathematics achievement. In addition, students, who developed select and compute throughout 4th to 8th grades, scored higher in mathematics assessment with large degrees of effects. The findings suggest important implications to teachers: Students need to have opportunities develop a wide range of cognitive attributes of mathematical modeling, which would result in higher achievement. Teachers need to have instructional emphases on different stages of mathematical modeling depending on grade levels: students’ representing a solution at elementary-school levels; and analyzing a problem situation and selecting strategies at middle-school levels. The study also suggests teachers shift an instructional emphasis from learning mathematics contents to high-order thinking like mathematical modeling to accomplish higher mathematics achievement.