M.Ed. / High school mathematics learners often take mathematics education for granted. They study mathematics simply because it is included in the school curriculum, and thus required for them to pass so that they can obtain a school leaving qualification. They never really succeed in seeing and understanding the relevance of mathematics to their present and future lives. As a result, they fail to relate and apply classroom mathematics to the external environment. They fail to make mathematical connections that would enable them to be confident users of mathematics as an effective tool for solving problems, a means of communication and a way of supporting reasoning. This suggests that there may be some serious constraints associated with the teachers' instructional approaches, which hinder the learners' meaningful learning and understanding of the relevance of mathematics. Thus, there arises the need to examine the relationship between the teachers' instructional approaches and the learners' understanding of the relevance of mathematics. Such an examination may help to expose the strengths and limitations of the instructional approaches, so that the necessary adjustments can be made in the teaching practice to improve the learning of mathematics.

Please read the abstract (Summary) in the section 00front of this document / Thesis (PhD (Computer Aided Education))--University of Pretoria, 2007. / Humanities Education / PhD / Unrestricted

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This investigation emanates from the realization that Grade 3 children at schools in disadvantaged areas perform poorly in basic mathematics computations such as addition, subtraction, multiplication and division. The aim of the research was to establish the approaches teachers use when teaching mathematics computation. The qualitative approach, together with the research techniques commonly used with it, namely observation, interviews and document analysis was deemed appropriate for the investigation. The outcomes of the investigation revealed that the multilingual Grade 3 classes made it difficult to assist all children who experienced mathematics problems because teachers could not speak all the other languages that were not the language of learning (LoLT) of the school. Another obstacle that prohibited teachers from spending adequate time with children with mathematics problems was the time teachers were expected to spend on intervention programmes from the Department of Basic Education (DBE) aimed at improving schooling in general. Teachers could not make additional time that could afford children the opportunity of individual attention. With regard to the approach used for teaching mathematics, this study established that the teachers used the whole class teaching approach which is not a recommended approach because each child learns differently. It is recommended that teachers use a variety of teaching methods in order to accommodate all children and also encourage children to use concrete objects. It is also recommended that teachers involved in the SBSTs should consist only of members qualified in the subject and once these children are identified, remediation should take place promptly by their being enrolled (children) in the proposed programme. Finally, this study could benefit foundation Phase teachers in teaching mathematics based on the proposed strategy outlined after teachers’ challenges were identified. The outcome of the study could also be of value to the DBE, especially with curriculum designers. / Early Childhood Education and Development / D. Ed. (Early Childhood Education)

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"The fundamental aim of mathematics instruction is the teaching of problem solving. For the majority of people this means mathematics is a language with which they can express quantitative relationships. The meanings in this language must be understood; the language must be practiced and applied to life situations if mathematics is to serve its purpose in the school curriculum. To teach mathematics in this manner is a tremendous job. It requires a teacher not only with patience, understanding of the students, and an excellent mathematics background but also with a broader general background. He will need to be able to find varied functional relationships of mathematics to life and must have the skill to help the students understand these relationships, too. In summary, good mathematics instruction includes the proper proportions and the proper interweaving of meanings, drill, and applications at the appropriate level of the student"--Introduction. / "May, 1949." / Typescript. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science under Plan II." / Advisor: H. C. Trimble, Professor Directing Paper. / Includes bibliographical references (leaves 17-19).

This paper is a study of the general mathematics program in the secondary school. The purpose of this study is to help the inexperienced teacher plan his program of work for the year. The teacher will not find a definite program that he may follow step-by-step, but suggestions that will be of help in developing an effective program. / "August, 1950." / Typescript. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: H. A. Curtis, Professor Directing Paper. / Includes bibliographical references (leaf 22).

Reports and surveys by the U.S. government and international organizations have repeatedly acknowledged the achievement problem in math in K-12 regardless of various efforts (e.g., by the U.S. Department of Education) to diminish it. To address the problem in math achievement in K-12, teachers, scholars, and the U.S. government have developed various materials and intervention tools. As a potential platform to address the problem in math achievement, video games generate a large variety of perspectives on their value. Along with the debate on the game's inherent good or bad features, there is also a debate on the effectiveness of video games as a learning tool. Regarding these debates and the ambiguous results on video games as learning tools, Greitemeyer and Mügge (2014) postulated that games can provide both positive and negative impacts according to their content (i.e., violent and pro-social games). However, recent literature investigating the use of video games in varied learning contexts shows that the learning effectiveness of games is still inconclusive. A potential reason is that video games mostly facilitate implicit qualitative understanding. Video games consist of rich interactive experiences that help to foster understanding of qualitative relationships in gameplay more than quantitative proficiency that is required in the formal school system (Clark et al. 2011; Squire, Barnett, Grant, & Higginbotham, 2004). Another reason is that educational game designers have paid little attention to designing and developing learning supports in educational games. Therefore, the current study aims to address a comprehensive question -- How does an educational game, through the use of learning supports, promote the application of acquired qualitative understanding to math problem solving in formal educational contexts? A promising method to address the aforementioned problem is to externalize cognitive and metacognitive processes (Lajoie, 2009). Externalizing Problem Representation (EPR) refers to a cognitive behavior in which a learner constructs her own representations overtly (Cox, 1999). The processes of EPR are to re-order information in problem solving, to clarify ambiguous parts of the problem, and to modify and enact mental representations including mental animations and images. EPR helps to make missing and implicit information or representations explicit. There are several synonyms of Externalizing Problem Representation (EPR), such as external representation (Zhang, 1997), externalized cognition (Cox & Brna, 1995), and re-representation (Ainsworth & Th Loizou, 2003). From the semiotics perspective, EPR can be categorized into two forms by its sign: Iconic and symbolic. Although the potential benefits of externalizing problem representation was claimed in prior research, little attention was paid to investigating the design of EPR in video games. Compared to the studies of mental problem representation, few empirical studies on external representation have been conducted. Hence, it is warranted to examine the efficacy of learning support that promotes externalizing problem representation in two formats (i.e., iconic and symbolic) in the video-game-based learning setting. In light of this, the purpose of this study is to investigate whether EPR-promoting scaffolds (in iconic vs. symbolic formats) enhance qualitative understanding and quantitative proficiency in ratios and proportional relationships in a learning game context. Specifically, the learning game will request players to respond to either iconic or symbolic learning probes that help to externalize the mental representations of the math problems in the game. In this study, quantitative proficiency refers to the problem solving proficiency in both game and formal education context. The current study involves two levels of task complexity (i.e., low complexity vs. high complexity) as a moderating variable. The study addresses the following research questions: 1. Will iconic learning probes promoting EPR enhance qualitative understanding and quantitative proficiency in ratios and proportional reasoning, with the task complexity controlled in the educational game? 2. Will symbolic learning probes promoting EPR enhance qualitative understanding and quantitative proficiency in ratios and proportional reasoning, with task complexity controlled in the educational game? 3. Will iconic learning probes promoting EPR, in comparison to symbolic learning probes promoting EPR, be more effective in enhancing qualitative understanding and quantitative proficiency in ratio and proportional reasoning, with task complexity controlled in the educational game? To accomplish the purpose of this study, learning probes that prompt learners to externalize their internal problem representation were developed in two different formats, iconic and symbolic, based on Mayer's math problem representation model. In the experiment, forty-five participants in this study processed either iconic or symbolic learning probes during their gameplay. Finally, qualitative understanding and quantitative proficiency were measured three times: before this study, after playing the shipping container episode with a low complexity task, and after playing the shipping container episode with a high complexity task. Regarding Research Question 1, the result of repeated-measures ANOVA indicates that, for participants in the Iconic Learning Probe (ILP) group, the difference in qualitative understanding between the pretest, posttest, and posttest 2 was not statistically significant whereas the difference in quantitative proficiency between the pretest, posttest 1, and posttest 2 was statistically significant. Regarding Research Question 2, the result of repeated-measures ANOVA indicates that, for participants in the Symbolic Learning Probe (SLP) group, the difference in qualitative understanding between the pretest, posttest 1, and posttest 2 was statistically significant whereas the difference in quantitative understanding between the pretest, posttest 1, and posttest 2 was not statistically significant. Regarding Research Question 3, since there was a significant interaction between the times of measurement and the types of EPR in regard to both qualitative understanding and quantitative proficiency, pairwise comparisons using the Bonferroni method were drawn. There were significant differences in participants' qualitative understanding between ILP and SLP groups in posttest 1 and posttest 2 whereas there was no significant difference in participants' qualitative understanding between ILP and SLP groups in the pretest. Regarding the quantitative proficiency, there were significant differences in participants' quantitative proficiency between ILP and SLP groups in posttest 1 whereas there was no significant difference in participants' quantitative proficiency between ILP and SLP groups in the pretest and posttest 2. In the final chapter, I discussed major research findings of this study based on the theoretical research reviewed in Chapter 2. Then I described the implications of this study and suggestions for future study. / A Dissertation submitted to the Department of Educational Psychology and Learning Systems in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2016. / January 12, 2016. / Includes bibliographical references. / Fengfeng Ke, Professor Directing Dissertation; Gordon Erlebacher, University Representative; Valerie Shute, Committee Member; Vanessa Dennen, Committee Member.

Submittedto the Faculty of Arts in partial fulfilment of the requirements for the degree of Master of Arts in Clinical Psychology in the Department of Psychology at the University of Zululand, South Africa, 1993. / In this study difficulties relating to mathematics problem solving were linked to the way people see themselves as problem solvers. Following this line of reasoning, Mathematics anxiety is viewed as a product of the student's distorted perception of his/her ability to do mathematics. It was further argued that negative beliefs about oneself were at the root of poor performance in mathematics problem solving. A cognitive restructuring method designed to change such distorted perceptions, and a subsequent change of behaviour was explored. On the basis of the promising results of this study, a recommendation is made that students with mathematics anxiety should be identified early and advised to seek psychological help before they lose hope completely.

The sixth grade teachers at Mooberry School in Hillsboro, Oregon were not pleased with the way they were teaching math. The students, grouped by ability, had a poor self-concept about math and felt “locked into” one class. During the summer of 1973, these teachers considered ways to change their math instruction. Reading was done to determine the most promising practice in math education in the United States. A successful approach to learning appeared to be individualized instruction, as is discussed in this paper. Many different individualized programs were studied, grouped into eleven general categories, and described in detail. The Mooberry sixth grade teachers adopted none of these programs, but instead developed a rotating system of math instruction. The teachers prepared for this rotating system by developing a sequence of math skills, to span the sixth graders through the year. Each teacher was responsible for individualizing instruction in two or three units of the sequence. The writer developed units in division, plotting coordinates on a grid, graphing and geometry. This rotating system of math instruction is individualized in that the students work at their own pace through the sequence of skills. The students move from concept to concept, and thus from teacher to teacher, gaining competence in as much of the cycle as they can master during the school year. The writer has described her approach to the units she covers in the cycle. The textbook has been eliminated and task cards have been developed. Student booklets, answer books, a grade book and a report card have been designed. A typical math class and steps of the cycle are described in the paper. The program has been used during the 1973-74 and 1974-75 school years. The teachers looked for evidence of success to indicate whether to continue their program in the same manner. Informal notes were kept on the work habits, skills and attitudes of the students. A formal questionnaire was given to the student by the Educational Development Center at the end of the 1973-74 school year. The students indicated, through multiple choice questions, that they felt positive towards math instruction, that they deserved and were capable of good grades in math, and that they rated math as their favorite class. A narrative questionnaire was given to the writer's homeroom at the end of the 1974-75 school year. Those students wrote positive comments about the math system and again indicated how pleased they felt about their math abilities. Metro math test scores for 1974-75, by the Metropolitan Area Program Board, give the reader a background on the type of student in the Mooberry attendance area. These students were above regional and national norms. The principal of the school, Mr. Ron Stewart, wrote his evaluation of the program, which is included in the paper. Questions have been raised about the program and have been listed for the reader. The teachers who developed the program hope, as more questions are raised and answered, that the rotating math program can change to meet the needs of the students, school and community. The sixth grade teachers at Mooberry School feel pleased that they were able to develop a rotating system of math instruction for their students. Both the informal and formal data indicate that the program is enjoyable for the students, helps students develop self-confidence in math education and helps the students gain competence in math skills and concepts.