Cooperative learning has emerged to be a preferred teaching-learning model in South Africa since the inception of Curriculum 2005 (C2005) emphasising Outcomes-based education (OBE). However, the documented success rate of cooperative learning in mathematics was experienced in small group sizes (emanating h m small class size) of about five learners. This study, therefore, aims at affording mathematics teachers and learners of crowded classes an opportunity to effectively use cooperative learning, namely the Hour-glass model in mathematics lessons. The prevalence of crowded classes in the majority of South African schools seems to inhibit the effectiveness of cooperative learning in mathematics. The big cooperative group size of about eight learners in South African context results in very complex lines of communication between learners. The teacher spends more time trying to manage off-task behaviour of learners instead of engaging them in active participation in the learning of mathematics. The combined quantitative and qualitative research methods were used. For the former, the study orientation in mathematics (SOM) questionnaire and the mathematics academic achievement test were used to collect data with regard to the influence of the Hour-glass model on the learners' learning skills in mathematics, and on the mathematics academic achievement respectively. A specific true experimental design, namely, the Solomon Four-group design, was used because of a large sample size (n > 500), and its credited ability to control the sources of threats to internal validity. For the latter the lesson observation and interviews were conducted to collect information about the influence of the Hour-glass model on learners' social skills during cooperative learning in mathematics. The groups that received the treatment (i.e. Hour-glass model) achieved higher scores of practical significance in mathematics academic achievement test than the groups that did not receive the treatment The Hour-glass model also yielded positive social skills among learners during mathematics learning. The teachers who applied the Hour-glass model revealed that they coped easier with crowded mathematics classes when using cooperative small groups. However, the Hour-glass model did not significantly influence learners' learning skills in mathematics. Certain logistical and administrative limitations emerged with regard to the implementation of the Hour-glass model in the usual school setting. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2004.

The present study compares applications of continuous multidimensional item response theory (MIRT) models for their diagnostic potential. Typically, MIRT models have not been used for diagnosing the possession of skills or attributes by students, but several researchers have suggested that they can potentially be used for this purpose (e.g., Stout, 2007; Wainer, Vevea, Camacho, Reeve, Rosa, Nelson, Swygert, & Thissen, 2001). This study applies MIRT models to a standardized eighth grade mathematics achievement test that was constructed based on a hierarchically-structured blueprint consisting of standards, benchmarks, and indicators. Only the highest level, consisting of four standards, was used to define the dimensions. The confirmatory models were defined using the standards that had been scored for involvement in each item. For the current study, the exploratory MIRT (EMIRT) model was interpreted with respect to the dimensions. Then, the compensatory and confirmatory MIRT (CMIRT) models and the full information bifactor model were fitted. The interpretation of dimensions, empirical reliabilities of person estimates, and test- and item-fit were examined. Also, dimension and pattern probabilities were obtained for determining their diagnostic potential. Last, a noncompensatory MIRT model (MLTM-D; Embretson & Yang, 2011) and the DINA model (Haertel, 1989; Junker & Sijtsma, 2001) in use as diagnostic models were analyzed to compare pattern probabilities with the compensatory CMIRT model.

Cooperative learning has emerged to be a preferred teaching-learning model in South Africa since the inception of Curriculum 2005 (C2005) emphasising Outcomes-based education (OBE). However, the documented success rate of cooperative learning in mathematics was experienced in small group sizes (emanating h m small class size) of about five learners. This study, therefore, aims at affording mathematics teachers and learners of crowded classes an opportunity to effectively use cooperative learning, namely the Hour-glass model in mathematics lessons. The prevalence of crowded classes in the majority of South African schools seems to inhibit the effectiveness of cooperative learning in mathematics. The big cooperative group size of about eight learners in South African context results in very complex lines of communication between learners. The teacher spends more time trying to manage off-task behaviour of learners instead of engaging them in active participation in the learning of mathematics. The combined quantitative and qualitative research methods were used. For the former, the study orientation in mathematics (SOM) questionnaire and the mathematics academic achievement test were used to collect data with regard to the influence of the Hour-glass model on the learners' learning skills in mathematics, and on the mathematics academic achievement respectively. A specific true experimental design, namely, the Solomon Four-group design, was used because of a large sample size (n > 500), and its credited ability to control the sources of threats to internal validity. For the latter the lesson observation and interviews were conducted to collect information about the influence of the Hour-glass model on learners' social skills during cooperative learning in mathematics. The groups that received the treatment (i.e. Hour-glass model) achieved higher scores of practical significance in mathematics academic achievement test than the groups that did not receive the treatment The Hour-glass model also yielded positive social skills among learners during mathematics learning. The teachers who applied the Hour-glass model revealed that they coped easier with crowded mathematics classes when using cooperative small groups. However, the Hour-glass model did not significantly influence learners' learning skills in mathematics. Certain logistical and administrative limitations emerged with regard to the implementation of the Hour-glass model in the usual school setting. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2004.

The purpose of this study was to determine: * what the influence of attitude is on the mathematical achievement of the standerd 8 pupil, * which factors contribute mainly to the attitude of the standard 8 pupil towards mathematics. The literature study defined the concept "attitude" as widely as possible. The relationship between attitude and academic achievement was discussed and special reference was given to mathematics achievement. In the literature study factors which can influence mathematical achievement were also discussed. Special reference was given to: * cognitive and non-cognitive factors, * factors referring to the parents, * factors referring to the school situation, * the influence of the peer group and friends, * other factors which can be related to achievement in mathematics. An empirical investigation was undertaken by means of a self developed attitude scale to determine to which extent attitude towards mathematics can influence achievement in this subject. I.Q. counts and percentages were available from report cards. The most important findings from this study were that attitude influences mathematical achievement to a large extent. Further findings proved that attitudes towards mathematics are influenced largely by the student's previous mathematical achievements, as well as the gender group to which the learner belongs. These findings underline the important role of the teacher, as well as the supportive role of the parents in creating a positive attitude towards Mathematics. The achievement of the learner can be improved by motivation and support. This will result in a more positive attitude towards mathematics and will consequently widen the career choices of the learner. / Thesis (MEd (Voorligting))--PU vir CHO, 1996

The purpose of this study was to determine: * what the influence of attitude is on the mathematical achievement of the standerd 8 pupil, * which factors contribute mainly to the attitude of the standard 8 pupil towards mathematics. The literature study defined the concept "attitude" as widely as possible. The relationship between attitude and academic achievement was discussed and special reference was given to mathematics achievement. In the literature study factors which can influence mathematical achievement were also discussed. Special reference was given to: * cognitive and non-cognitive factors, * factors referring to the parents, * factors referring to the school situation, * the influence of the peer group and friends, * other factors which can be related to achievement in mathematics. An empirical investigation was undertaken by means of a self developed attitude scale to determine to which extent attitude towards mathematics can influence achievement in this subject. I.Q. counts and percentages were available from report cards. The most important findings from this study were that attitude influences mathematical achievement to a large extent. Further findings proved that attitudes towards mathematics are influenced largely by the student's previous mathematical achievements, as well as the gender group to which the learner belongs. These findings underline the important role of the teacher, as well as the supportive role of the parents in creating a positive attitude towards Mathematics. The achievement of the learner can be improved by motivation and support. This will result in a more positive attitude towards mathematics and will consequently widen the career choices of the learner. / Thesis (MEd (Voorligting))--PU vir CHO, 1996

The purpose of the study was to investigate the effects of discovery and application based instruction (DABI) on students&rsquo / mathematics achievement and also to explore opinions of students toward DABI. The research was conducted by 118 ninth grade students from Etimesgut Anatolian High School, in Ankara, during the spring semester of 2001-2002 academic year. During the study, experimental groups received DABI and control groups received Traditionally Based Instruction (TBI). The treatment was completed in three weeks. Mathematics Achievement Test (MAT) and Logarithm Achievement Test (LAT) were administered as pre and posttest respectively. In addition, a questionnaire, Students&rsquo / Views and Attitudes About DABI (SVA) and interviews were administered to determine students&rsquo / views and attitudes toward DABI. Analysis of Covariance (ANCOVA), independent sample t-test and descriptive statistics were used for testing the hypothesis of the study. No significant difference was found between LAT mean scores of students taught with DABI and traditionally based instruction when MAT test scores were controlled. In addition, neither students&rsquo / field of study nor gender was a significant factor for LAT scores. Students&rsquo / gender was not a significant factor for SVA scores. However, there was significant effect of math grades and field selections of students on SVA scores.

The purpose of the study was to predict mathematics achievement with self-confidence in mathematics, actual work effort in mathematics, and perceived importance of work effort in mathematics, and to investigate the gender differences with respect to those variables. The study was conducted in Ankara, Turkey with 157 eight-grade students (87 boys, 70 girls) from a private school. The following measuring instruments were used: (1) Confidence in Learning Mathematics Scale, (2) Effort as a Mediator of Mathematical Ability Scale, (3) Homeworks and Mathematics Achievement Tests. The validity and reliability of the measuring instruments were tested by the researcher. The data of this study were analyzed by using Stepwise Multiple Regression Analysis and Multivariate Analysis of Variance (MANOVA). The results of the study indicated that (1) the combined effect of three predictor variables (Self-confidence, actual work effort, and perceived Importance of work effort) on students&rsquo / mathematics achievement was significant (R2adj=0.543). Girls&rsquo / mathematics achievement was significantly (R2adj=0.531) affected by three predictor variables (Self-confidence, actual work effort, and perceived importance of work effort). Whereas for boys, two variables (Self-confidence and actual work effort) were the predictors which had a significant combined effect on mathematics achievement (R2adj=0.539). (2) There was no statistically significant mean difference between girls and boys with respect to self-confidence, actual work effort, perceived importance of work effort and mathematics achievement.

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)

xvi, 136 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / An examination of evidence-based practices for mathematics reveals that a solid grasp of key algebraic topics is essential for successful transition from concrete to abstract reasoning in mathematics. In addition, experts indicate a need to emphasize formative assessment to allow results to inform instruction. To address the dearth of technically adequate assessments designed to support data based decision making in algebra, this study examined (a) the validity of algebra and mixed computation curriculum-based measurement for predicting mid-year general math and algebra outcomes in 8th grade (b) growth rates for algebra and mixed computation CBM in the fall of 8th grade, (c) whether slope is a significant predictor of general math and algebra outcomes after controlling for initial skill, and (d) whether growth rates differ for pre-algebra and algebra students. Participants were 198 eighth grade pre-algebra ( n = 70) and algebra (n = 128) students from three middle schools in the Pacific Northwest. Results indicate moderate relationships between fall performance on mixed computation and algebra CBM and winter SAT-10 and algebra performance and significant growth across the fall. Growth was not found to predict general math and algebra outcomes after controlling for initial skill. Future studies should examine (a) growth rates over an extended period of time with a larger sample of classrooms, (b) instructional variables that may impact growth across classrooms, and (c) the impact on student performance when data gleaned from the mixed computation and algebra CBM are used to support data based decision making in middle school algebra and pre-algebra classrooms. / Committee in charge: Roland Good, Chairperson, Special Education and Clinical Sciences; Elizabeth Ham, Member, Special Education and Clinical Sciences; Leanne Ketterlin Geller, Member, Educational Methodology, Policy, and Leadership; Christopher Phillips, Outside Member, Mathematics

abstract: The primary purpose of this study is to examine the effect of knowledge for teaching mathematics and teaching practice on student mathematics achievement growth. Thirty two teachers and 299 fourth grade students in three elementary schools from one school district in urban area participated in the study. Most of them are Hispanic in origin and about forty percent is English Language Learners (ELLs). The two level Hierarchical Linear Model (HLM) was used to investigate repeated measures of teaching practice measured by Classroom Assessment Scoring System (CLASS) instrument. Also, linear regression and a multiple regression to examine the relationship between teacher knowledge measured by Learning for Mathematics Teaching (LMT) and Developing Mathematical Ideas (DMI) items and teaching practice were employed. In addition, a three level HLM was employed to analyze repeated measures of student mathematics achievement measured by Arizona Assessment Consortium (AzAC) instruments. Results showed that overall teaching practice did not change weekly although teachers' emotional support for their students improved by week. Furthermore, a statistically significant relationship between teacher knowledge and teaching practice was not found. In terms of student learning, ELLs have significantly lower initial status in mathematics achievement than non-ELLs, as were growth rates for these two groups. Lastly, teaching practice significantly predicted students' monthly mathematics achievement growth but teacher knowledge did not. The findings suggest that school systems and education policy makers need to provide teachers with the chance to reflect on their teaching and change it within themselves in order to better support student mathematics learning. / Dissertation/Thesis / Ph.D. Curriculum and Instruction 2012