There are surveys carried out repeatedly on the same set of units. In connection with such research, we are talking about the dependent samples. The aim and the contribution of this diploma thesis is a summary of available methods for analyzing data from dependent samples for both continuous and discrete variables. The Czech literature has been devoted to this topic only marginally. The theoretical part is divided into two main parts for two waves and for more waves of exploration, which are further divided according to the type of reference variable. The third part is devoted to the application of the theoretical information in a market research.

The purpose of this study was to explore solution strategies that can enhance the achievement of low-performing Grade 12 learners in the following mathematical aspects: finding the general term of a quadratic sequence, factorising third degree polynomials, determining the centre and radius of a circle, and calculating the angle between two lines. A convenience sample of twenty-five low-performing Grade 12 learners from a secondary school in Capricorn District of Limpopo Province participated in the study which adopted a repeated-measures research design. Learners were exposed to multiple solution strategies and data were collected using achievement tests. Findings indicated significant differences in learners‟ average scores due to the solution strategies used. In determining the general term of a quadratic sequence, learners‟ scores were significantly higher when they used formula and the table method than with the method of residues and solving simultaneous equations. Synthetic division made learners to achieve better scores than long division and equating coefficients in factorising third degree polynomials. The use of formulae to find the centre and radius of a circle made learners to have better achievement scores than completing the square. In calculating the angle between two lines learners‟ scores were better using formula and the cosine rule than using theorems. It was concluded that exposing low-performing Grade 12 learners to multiple solution strategies would enhance their achievement in the mathematical aspects explored in the study. Some of the solution strategies that made learners to achieve better results were not in the prescribed mathematics textbooks. The study therefore recommends that mathematics teaching should not be textbook-driven and that low-performing Grade 12 learners should not be regarded as beyond redemption. / Mathematics Education / M.Sc. (Mathematics, Science and Technology Education)

The purpose of this study was to explore solution strategies that can enhance the achievement of low-performing Grade 12 learners in the following mathematical aspects: finding the general term of a quadratic sequence, factorising third degree polynomials, determining the centre and radius of a circle, and calculating the angle between two lines. A convenience sample of twenty-five low-performing Grade 12 learners from a secondary school in Capricorn District of Limpopo Province participated in the study which adopted a repeated-measures research design. Learners were exposed to multiple solution strategies and data were collected using achievement tests. Findings indicated significant differences in learners‟ average scores due to the solution strategies used. In determining the general term of a quadratic sequence, learners‟ scores were significantly higher when they used formula and the table method than with the method of residues and solving simultaneous equations. Synthetic division made learners to achieve better scores than long division and equating coefficients in factorising third degree polynomials. The use of formulae to find the centre and radius of a circle made learners to have better achievement scores than completing the square. In calculating the angle between two lines learners‟ scores were better using formula and the cosine rule than using theorems. It was concluded that exposing low-performing Grade 12 learners to multiple solution strategies would enhance their achievement in the mathematical aspects explored in the study. Some of the solution strategies that made learners to achieve better results were not in the prescribed mathematics textbooks. The study therefore recommends that mathematics teaching should not be textbook-driven and that low-performing Grade 12 learners should not be regarded as beyond redemption. / Mathematics Education / M.Sc. (Mathematics, Science and Technology Education)

The gap that exists between English language learners and English speaking students’ achievement in mathematics continues to grow. Moreover, students are now required to show evidence of their mathematics knowledge through writing in standardized assessments and class assignments. The purpose of this study was to analyze students’ writing in mathematics and the metacognitive behaviors they portrayed through their writing as they solved mathematics problems. The instruments included a pretest, two biweekly tests, and a posttest. The writing instruction encompassed students learning to solve problems by using Polya’s four phases of problem solving which was completed in 12 sessions over a period of 6 weeks. Garofalo and Lester’s framework which renamed Polya’s phases into orientation, organization, execution, and verification, was used to look at the metacognitive behaviors students used. The participants included 67 students enrolled in four third grade classes, who were English language learners and English speakers. This research followed a quasi-experimental design, with a treatment group and a control group. A one-way repeated ANOVA was used to analyze the data. The findings showed no significant difference between the mathematics achievement scores of treatment and control. However, growth trends in achievement scores revealed that the treatment group scores were increasing faster than the control group scores across the four tests during the 6-week study. Moreover, significant differences were found between the treatment and the control groups when the problem solving with metacognitive behaviors scores were analyzed. Descriptive statistics showed the frequency of occurrence of each of the problem solving phases increased steadily across the four tests for the students in the treatment group. During the posttest, 100% of treatment group students wrote about metacognitive behaviors they used during the orientation and organization phases, 91.4% wrote about their metacognition for executing the solution, and 80% wrote about the verification process they followed. These findings are useful to education professionals who are interested in creating programs for teaching mathematics at the elementary level that include effective problem solving practices. This evidence-based method may be adopted in school districts with large populations of ELLs in order to assist these students when solving problems in mathematics.