Thesis (Phd. (Education )) - Central University of Technology, Free State, 2015 / For learners to be effective computer applications users, they need three basic skills – computer literacy, computer fluency and intellectual and reasoning skills to apply computational techniques or computer applications to the problems and projects in a field. Computational thinking as addressed in the first literature chapter is the description and the promotion of new ways of thinking in an increasingly digital age. A computational thinker must constantly engage in technology advancements. Computational thinking is a way of solving problems and is a cognitive or a thinking process. To flourish in the world of work, computational thinking has to be a fundamental part of the way learners think and understand the world. It describes the mental activity in formulating a problem to allow a computational solution. The solution can be carried out by the learner or the computer or a combination of learner and computers. Problem-solving competency as addressed in the next literature chapter involves the ability to acquire and use new knowledge, or to use old knowledge in a new way to solve problems that are not routine. Problem-solving as a skill involves a range of processes that includes analysing, interpreting, reasoning, predicting, evaluating and reflecting. Learners need profound Computer Applications Technology (CAT) knowledge and a general reasoning ability as well as investigative strategies for solving ill-defined problems. To address the research questions, the researcher employed the QUAN-QUAL design in this study. In this study the quantitative method was used to gather data relating to the education of teachers, in-service training received and answers to certain computational thinking skills and problem-solving skills. It was also used to test the relationship between problem solving and computational thinking skills. A Likert-scale type questionnaire was completed by 150 CAT teachers. In addition, this study also employed the qualitative method with semi-structured interviews to gather data relating Abstract vi to problem solving and computational thinking skills. Eight CAT teachers were interviewed to ascertain the afore-mentioned. A pilot study was conducted with the aim to test the research approach and to identify potential problems that may affect the quality and validity of the results. The wording of some questions in the questionnaire was altered to ensure that the instrument measures what it is supposed to. Descriptive statistics in this study was used to describe the findings and the inferential statistics used to test the hypotheses and draw conclusions from the quantitative statistics. For qualitative data, thematic analysis was used to analyse the original data obtained from the semi-structured interviews. To promote critical thinking skills, teachers must engage learners in higher-order thinking. Findings show that teachers do not always use classroom practices that encourage critical thinking. It was encouraging that the majority of teachers do allow group work in the CAT classroom, as group work is an important facet in computational thinking and problem solving. The study culminates in a computational thinking and problem-solving toolkit developed by the researcher. This toolkit is intended primarily for facilitators (such as CAT subject advisors or CAT mentor teachers) to enable them to conduct workshops for fellow CAT teachers. By using this toolkit, teachers will gain an understanding of what computational thinking skills and problem-solving skills are and how to develop these skills in Grades 10 – 12 CAT learners.

This study investigated the effect of a blended-learning approach in the learning of problem-solving skills in a first-level distance education physics module. A problem-solving type of instruction with explicit teaching of a problem-solving strategy was implemented in the module, which was presented through correspondence, online using an in-house learning management system as well as two face-to- face discussion classes. The study used the ex post facto research design with stratified sampling to investigate the possible cause-effect relationship between the blended-learning approach and the problem-solving performance. The number of problems attempted, the mean frequency of using strategy in problem solving and the achievement marks of the three strata were compared using inferential statistics. The finding of the study indicated that the blended-learning approach had no statistically significant effect in the learning of problem-solving skills in a distance education module. / Educational Studies / M. Ed. (Open and Distance Learning)

published_or_final_version / Education / Doctoral / Doctor of Education

While professional developers have been encouraging teachers to plan for discourse around problem solving tasks as a way to orchestrate mathematically productive discourse (Stein, Engle, Smith, & Hughes, 2008; Stein, Smith, Henningsen, & Silver, 2009) no research has been conducted explicitly examining the relationship between the plans that teachers make for orchestrating discourse around problem solving tasks and the outcomes of implementation of those plans. This research study is intended to open the door to research on planning for discourse around problem solving tasks. This research study analyzes how 12 middle school mathematics teachers participating in the Mathematics Problem Solving Model professional development research program implemented lesson plans that they wrote in preparation for whole-class discussions around cognitively demanding problem solving tasks. The lesson plans consisted of the selection and sequencing of student solutions to be presented to the class along with identification of the mathematical ideas to be highlighted in the student solutions and questions that would help to make the mathematics salient. The data used for this study were teachers' lesson plans and the audio-recordings of the whole-class discussions implemented by the teachers. My research question for this study was: How do teachers' written plans for orchestrating mathematical discourse around problem solving tasks influence the opportunities teachers create for students to reason mathematically? To address this research question, I analyzed the data in three different ways. First, I measured fidelity to the literal lesson by comparing what was planned in the ISAs to what was actually took place in the implemented debriefs. That is, I analyzed the extent to which the teachers were implementing the basic steps in their lesson (i.e. sharing the student work they identified, addressing the ideas to highlight and the planned questions). Second, I analyzed the teachers' fidelity to the intended lesson by comparing the number of high-press questions in the lesson plans (that is, questions that create opportunities for the students to reason mathematically) to the number of high-press questions in the implemented discussion. I compared these two sets of data using a linear regression analysis and t-tests. Finally, I conducted a qualitative analysis, using grounded theory, of a subset of four teachers from the study. I examined the improvisational moves of the teachers as they addressed the questions they had planned, building a theory of how the different ways that teachers implemented their planned questions affected the opportunities for their students to reason mathematically around those planned questions. My findings showed that it was typical for the teachers to implement most of the steps of their lesson plans faithfully, but that there was not a statistically significant correlation between the number of high-press questions they planned and the number of high-press questions they asked during the whole-class discussions, indicating that there were other factors that were influencing the frequency with which the teachers were asked these questions that prompted their students to reason mathematically. I hypothesize that these factors include, but are not limited to, the norms in the classrooms, teachers' knowledge about teaching mathematics, and teachers' beliefs about mathematics. Nevertheless, my findings did show that in the portions of the whole-class discussions where the teachers had planned at least one high-press question, they, on average, asked more high-press questions than when they did not plan to ask any. Finally, I identified four different ways that teachers address their planned questions which impacted the opportunities for students to reason mathematically. Teachers addressed their questions as drop-in (they asked the question and then moved on as soon as a response was elicited), embedded (the ideas in the question were addressed by a student without being prompted), telling (the teacher told the students the `response' to the question without providing an opportunity for the students to attempt to answer the question themselves) and sustained focus (the teacher sustained the focus on the question by asking the students follow-up questions).

This study investigated the effect of a blended-learning approach in the learning of problem-solving skills in a first-level distance education physics module. A problem-solving type of instruction with explicit teaching of a problem-solving strategy was implemented in the module, which was presented through correspondence, online using an in-house learning management system as well as two face-to- face discussion classes. The study used the ex post facto research design with stratified sampling to investigate the possible cause-effect relationship between the blended-learning approach and the problem-solving performance. The number of problems attempted, the mean frequency of using strategy in problem solving and the achievement marks of the three strata were compared using inferential statistics. The finding of the study indicated that the blended-learning approach had no statistically significant effect in the learning of problem-solving skills in a distance education module. / Educational Studies / M. Ed. (Open and Distance Learning)

This project is a study to determine if a group of middle school students can improve their problem solving ability by means of curriculum of nonroutine problems that was presented over a six month period.

Quantitative Techniques is traditionally a subject with a poor pass rate at Walter Sisulu University. In search of a turnaround strategy, the purpose of this study was to determine the level of problem-solving proficiency of Quantitative Techniques students, which is suspected to influence achievement in this subject. A descriptive survey design was used in this research. Second-year ND (Marketing) students (128) took part in the study. A questionnaire and a written test were used to collect data. A profile of participants’ problem-solving was determined. Their weaknesses and strengths in problem-solving were investigated. The problem-solving proficiency of participants with regards to the biographical variables of Gender, Age, Mathematics background and whether they took Data Handling training at school or not were explored. A model, based on Polya’s four stages of problem-solving, was used to measure the students’ level of problem-solving proficiency, which was 59,16%. Findings suggest that the students achieved highest in understanding a problem (72,29%) and making a plan to solve the problem (73,77%). They are weakest at interpreting their results (29,38%). MANOVA results showed no statistical significance for the biographical variables. The univariate results suggest that age, Data Handling training at school and Gender could affect problem-solving proficiency. Since the findings of this study indicate a strong relationship between participants’ problem-solving proficiency and their actual achievement, some intervention is recommended. An intervention could be in the form of a section on problem-solving in the course, supplemental instruction or an introductory course. Course and curriculum content should be revised to address students’ proficiency in problem-solving. / Mathematical Sciences / M. A. (Statistics Education)

Quantitative Techniques is traditionally a subject with a poor pass rate at Walter Sisulu University. In search of a turnaround strategy, the purpose of this study was to determine the level of problem-solving proficiency of Quantitative Techniques students, which is suspected to influence achievement in this subject. A descriptive survey design was used in this research. Second-year ND (Marketing) students (128) took part in the study. A questionnaire and a written test were used to collect data. A profile of participants’ problem-solving was determined. Their weaknesses and strengths in problem-solving were investigated. The problem-solving proficiency of participants with regards to the biographical variables of Gender, Age, Mathematics background and whether they took Data Handling training at school or not were explored. A model, based on Polya’s four stages of problem-solving, was used to measure the students’ level of problem-solving proficiency, which was 59,16%. Findings suggest that the students achieved highest in understanding a problem (72,29%) and making a plan to solve the problem (73,77%). They are weakest at interpreting their results (29,38%). MANOVA results showed no statistical significance for the biographical variables. The univariate results suggest that age, Data Handling training at school and Gender could affect problem-solving proficiency. Since the findings of this study indicate a strong relationship between participants’ problem-solving proficiency and their actual achievement, some intervention is recommended. An intervention could be in the form of a section on problem-solving in the course, supplemental instruction or an introductory course. Course and curriculum content should be revised to address students’ proficiency in problem-solving. / Mathematical Sciences / M. A. (Statistics Education)

University of Macau / Faculty of Education

The aim of this study was to explore the effects of a problem-solving heuristic instructional method on Grade 6 learners’ achievements in algebra. Two main theories inspired the design of this teaching method, namely the modelling and modelling perspective, and action, process, object, schema (APOS) theory. Modelling and modelling perspectives guided the development of modelling-eliciting activities used in the teaching method and the APOS theory guided the sequence of activities used to develop Grade 6 learners’ conceptions in algebra. The impact of the problem-solving heuristic instructional method was investigated with 198 Grade 6 learners from four different primary schools in the Zululand district of Kwazulu-Natal that were conveniently sampled. A mixed-method approach was used in this study and a hypothesis was formulated to investigate the effects of the teaching method on the learners’ achievements in algebra. The qualitative component consisted of a pre-intervention class observation of mathematics lessons of all four mathematics educators in the schools used for this study. The design and implementation of the problem-solving heuristic instructional method and the quantitative component employed non-equivalent control group design with pre-test and post-test measure. The main instruments for data collection were an observation schedule to document sequence of events in the classroom during the class observation, a standardized achievement test in algebra used to measure effects of the problem-solving heuristic instructional method and modelling-eliciting activities used as a medium of interaction between learners and the researcher during the implementation of the problem-solving heuristic instructional method. Findings from the class observation indicated all four schools made use of comparable traditional methods of instruction. The implementation of the problem-solving instructional method gave insights into how a problem-solving heuristic instructional method can be developed and used in Grade 6 algebra lessons, and the factors that could influence learners’ conceptual development in algebra. The findings from the quantitative component supported the initial hypothesis that improved scores in algebra are achieved through participation in the problem-solving heuristic instructional method. Quantitative data was analysed using the t-test, analysis of covariance, Johnson-Neyman (J-N) technique and the effect size. / Mathematics Education / D. Phil. (Mathematics Education)