Mathematics is an increasingly important aspect of education because of its central role in technology. Learning mathematics at the elementary and middle school levels forms the basis for achievement in high school and college mathematics, and for the broad range of mathematical skills used in the workplace. Especially, the middle school years (e.g., Grade 6-Grade8) are crucial to success in mathematics because students must acquire the skills needed in higher levels of mathematics and complex reasoning ability based on the developmental perspectives on cognition (e.g., Piaget, Vygotsky). The purpose of the current study was to measure and interpret the mathematical achievement growth during the middle school years using some very recent advances (confirmatory multidimensional and longitudinal models) in item response theory. It was found that the relative strength of the content areas (mathematical standards and benchmarks) shifted somewhat across grades in defining mathematical achievement. The largest growth occurred from Grade 6 to Grade 7. The specific pattern of growth varied substantially by the socio-economic status of the student but few differences emerged by gender. The implications of the results for education and for developmental theories of cognitive complexity are discussed.

The purposes of the study were to (a) determine whether there was a significant difference in the mathematics achievement of students which may be attributed to any of the nine variations in trimester scheduling during the two-year period, and (b) to analyze the implications of trimester scheduling as they apply to teachers, counselors, and administrators in the middle school program. On the basis of careful treatment and analysis of data collected to ascertain the effect of time-lapse scheduling on mathematics achievement in arithmetic computation, arithmetic concepts, and arithmetic applications, the following conclusions, limited to the population studied, were drawn: 1. None of the nine time-lapse schedules had a significant differential effect on mathematics achievement. 2. The results of this study may be generalized to include the high, middle, and low achievement segments of the target population of students in all middle schools in the school district of this study. 3. Middle school administrators and counselors may schedule students into any convenient sequence of courses without fear of relative detrimental consequences to mathematics achievement. 4. Teachers need not be concerned that "learning loss" in mathematics due to different time-lapse schedules of the students will require different amounts of review prior to beginning work in a new trimester. 5. The Intensified Learning Plan is a viable program in mathematics in the school district's middle school plan of organization and scheduling.

The purpose of this study was to determine the effects of participation in a Computer-Assisted instructional program (CAI) on fourth grade student attitudes and achievement in reading and mathematics. This study, based on Campbell and Stanley's quasiexperimental design 10, utilized Diascriptive Reading software for the CAI mathematics group and Milliken Math Sequences software for the CAI mathematics group and was completed by 242 students. The time span between pretests and posttests was seven months. Iowa Tests of Basic Skills, Level 10, Form 7/8 was used for achievement testing and Estes Attitude Scale was used for attitude testing. Analysis of covariance was used to determine significance at the .05 level. The findings for this study were: 1. Reading Comprehension posttest scores were significantly higher for the control group than for the reading experimental group; 2. Reading Comprehension posttest scores were not significantly higher for boys than for girls within the reading experimental group; 3. Total math posttest scores were significantly higher for the mathematics experimental group than for the control group; 4. Concepts and Computation math subsets posttest scores were significantly higher for the mathematics experimental group than for the control group. There were no significant differences between the posttest scores of the two groups for the Math Problem Solving subset; 5. Total Math posttest scores were not significantly different for boys than for girls within the mathematics experimental group; 6. Attitude toward reading posttest scores were significantly higher for the reading experimental group than for the control group; 7. Attitude toward reading posttest scores were not significantly different for the boys than for girls within the reading experimental group; 8. Attitude toward mathematics posttest scores were significantly higher for the mathematics experimental group than for the control group; 9. Attitude toward mathematics posttest scores were significantly higher for girls than for boys within the mathematics experimental group.

Using a case study approach, this investigation focused on the nature of the relationship between computer related expenditures and student achievement in mathematics, with consideration given to the mediating factors influencing the relationship. Some of these factors included the types of computers and software being used, the objectives of computer instruction, teacher preparation in the use of the computer as an instructional tool, the amount of time individual students had access to a computer during the school year, and the socioeconomic status of pupils. Two of the twenty-five largest school districts in Texas were selected as the subjects for this study. Numerical data were collected from existing documents including general ledgers, bid tabulations, test score tables, and records showing the numbers of students participating in the free and reduced price lunch programs. Specific information regarding the implementations of the instructional programs was gathered through observations and 2 interviews with principals/ teachers, and students in four— teen junior high schools in each of the two school district. The districts exhibited more differences than similarities in the approaches to using computers for instruction in mathematics. One district, for about two hundred dollars per student, purchased a prepared, copyrighted, and patented program consisting of mini-computers and sixteen terminal remote labs used exclusively for the remediation of students two or more years behind in achievement in mathematics. The other district purchased microcomputers at a cost of about ten dollars per student and introduced a three to six weeks unit on computer programming into the eighth grade mathematics curriculum. Although neither district demonstrated clear patterns of increased achievement, tendencies did emerge which would suggest some linkage between concentration of the program and achievement. Other factors emerging from the fortythree taped interviews indicated that achievement test scores of students should not be the only measure of the worth of the computer-assisted instructional programs used in these school districts.

This study aims to find out the relationship between Working Memory Capacity and Verbal and Mathematical Achievement. The participants were 60 students at Hacettepe University School of Foreign Languages Department of Basic English. For measuring working memory capacity, one simple (Digit Span Task) and one complex (Reading Span Task) were used. Verbal achievement of the participants was measured both in their native language (Turkish) and their foreign language (English). For measuring their native language achievement, the participants&rsquo / Turkish scores in Y&uuml / ksek&ouml / gretime Ge&ccedil / is Sinavi 2010 (Transition to Higher Education Examination) / and for measuring their foreign language achievement, the participants&rsquo / scores in Hacettepe University School of Foreign Languages Department of Basic English Elementary Groups Achievement Exams I and II were used. For measuring their mathematical achievement, the participants&rsquo / Mathematic scores in Y&uuml / ksek&ouml / gretime Ge&ccedil / is Sinavi 2010 (Transition to Higher Education Examination) were used. The data was analyzed using a statistical package program (SPSS Version 18.0). The data analysis results revealed that there is a relationship between working memory capacity and verbal and mathematical achievements of the participants. It was tentatively concluded that, as the working memory capacity of the participants increase, so might their achievement in verbal and mathematical subjects. This result was discussed in terms of its implications, which may be that, if working memory capacity could be improved / the cognitive processes which the working memory is responsible for might also improve.

This research project, which was modeled on the constructivist theory of acquiring knowledge, and on recent recommendations regarding classroom instruction, investigated the impact of problem-based teaching and learning (PBTL) on the performance of high school mathematics learners. The effect of an intervention programme on an experimental group of students was compared with a control group by assessing their mathematical knowledge and skills; their procedural proficiency and conceptual development on varied mathematical contents; their skills in managing and controlling learning; and their views towards their learning programmes. The results obtained indicated that the experimental group indicated a higher conceptual understanding, an improved use of procedures, a higher level of managing and controlling learning, and positive views towards the programme and interest in the fundamentals of learning mathematics. An analysis of the data obtained by the on-progress instruments employed for the experimental group also indicated improved quality of participation and reflective thinking practices. / Educational Studies / M. Ed. (With specialisation in Mathematics Education)

Some learners in South Africa perform poorly in school, especially in Mathematics. In 2010 the Department of Basic Education announced their concern regarding the pass rate. The National Education Department circulated a report in 2008 on some Grade 3 and Grade 6 learners who took part in a research project and only achieved level one and two in literacy (vocabulary), as well as numeracy (Mathematics). Several factors contribute to this shocking situation, such as the absence of the use of meta-cognitive strategies, number strategies, as well as language strategies. The prime goal of this study was to investigate the use of meta-cognitive strategies and Mathematical vocabulary during problem solving by Grade 7 learners. Three primary schools were invited to participate in the qualitative investigation. From these schools three top achievers (one per school) and three under-achievers (one per school) were invited to participate in the quantitative investigation. The study includes the results of the quantitative aspects of the investigation. Learners had to answer questions about predictions, achievements, control, as well as evaluation during the quantitative investigation. During this process, most of the learners predicted that they would do well and evaluated that they did well, but their marks for the questions about their achievements and control were in fact different. It is important to inform Mathematics teachers and learners about meta-cognitive strategies and Mathematical vocabulary, and the influence it can have on the learners’ achievements, as well as the positive effect during the learning of Mathematics. / MEd (Mathematics Education), North-West University, Potchefstroom Campus, 2014

It seems as if there is a continued problem with mathematical performances nationally. The rate, at which FET (Further Education and Training) phase learner s discontinue Mathematics as a result of poor mathematical performances, is of great concern. This research study determined how academic self-confidence could have an influence on learners’ abilities to perform in Mathematics. The literature review confirmed that there could be a link between academic self-confidence and mathematical performance. Consequently, the researcher wanted to establish if the same could be found at a school where the emphasis is very much on mathematical achievement. The school is based in Northern Johannesburg (D10) in Gauteng, South Africa. By applying an explanatory mixed method approach (quantitative, followed by qualitative methods), the researcher identified a clear link between this school’s learners’ abilities to perform in Mathematics and their academic self-confidence. Amongst others, positive links were also identified between the learner s’ comprehension of Mathematics, their problem- solving skills as well as educator assistance, which in turn influence their academic self - confidence and consequently al so their performance s. A cycle of mathematical influences was identified that demonstrated that the influence i s not only working one way, but that a cycle forms; academic self-confidence influences the learner’s ability to perform in mathematics and mathematical performance s al so influence academic self - confidence, causing a continuous cycle of influence. / MEd (Learner Support), North-West University, Vaal Triangle Campus, 2013

在統計學上，我們常使用皮爾森相關係數(Pearson’s Correlation Coefficient)來表達兩變數間線性關係的強度，同時也表達出關係之方向。傳統之相關係數所處理的資料都是明確的實數值，但是當資料是模糊數時，並不適合使用傳統的方法來計算模糊相關係數。而本研究探討區間模糊樣本資料值求得模糊相關係數，首先將區間型模糊資料分為離散型和連續型，提出區間模糊相關係數定義，並提出廣義誤差公式，將相關係數作合理的調整，使所求的出相關係數更加精確。在第三章我們以影響數學成就評量的因素，作實證研究分析，得出合理的分析。而此相關係數定義和廣義誤差公式也能應用在兩資料值為實數或其中一筆資料值為實數的情況，可以解釋更多在實務上所發生的相關現象。 / In the statistic research, we usually express the magnitude of linear relation between two variables by means of Pearson’s Correlation Coefficient, which is also used to convey the direction of such relation. Traditionally, correlation coefficient deals with data which consist of specific real numbers. But when the data are composed of fuzzy numbers, it is not feasible to use this traditional approach to figure out the fuzzy correlation coefficient. The present study investigates the fuzzy samples of interval data to find out the fuzzy correlation coefficient. First, we categorize the fuzzy interval data into two types: discrete and continuous. Second, we define fuzzy correlation with interval data and propose broad formulas of error in order to adjust the coefficient more reasonably and deal with it more accurately. In Chapter Three, we conduct empirical research by the factor which affects the evaluation of mathematical achievement to acquire reasonable analysis. By doing so, broad definition of coefficient and formulas of error can also be applied to the conditions of either both values of the data are real number or one value of the data is real number, and can explain more related practical phenomenon.

It seems as if there is a continued problem with mathematical performances nationally. The rate, at which FET (Further Education and Training) phase learner s discontinue Mathematics as a result of poor mathematical performances, is of great concern. This research study determined how academic self-confidence could have an influence on learners’ abilities to perform in Mathematics. The literature review confirmed that there could be a link between academic self-confidence and mathematical performance. Consequently, the researcher wanted to establish if the same could be found at a school where the emphasis is very much on mathematical achievement. The school is based in Northern Johannesburg (D10) in Gauteng, South Africa. By applying an explanatory mixed method approach (quantitative, followed by qualitative methods), the researcher identified a clear link between this school’s learners’ abilities to perform in Mathematics and their academic self-confidence. Amongst others, positive links were also identified between the learner s’ comprehension of Mathematics, their problem- solving skills as well as educator assistance, which in turn influence their academic self - confidence and consequently al so their performance s. A cycle of mathematical influences was identified that demonstrated that the influence i s not only working one way, but that a cycle forms; academic self-confidence influences the learner’s ability to perform in mathematics and mathematical performance s al so influence academic self - confidence, causing a continuous cycle of influence. / MEd (Learner Support), North-West University, Vaal Triangle Campus, 2013