Spatial thinking processes employed by primary school students engaged in mathematical problem solving

This thesis describes changes in the spatial thinking of Year 2 and Year 4 students who participated in a six-week long spatio-mathematical program. The main investigation, which contained quantitative and qualitative components, was designed to answer questions which were identified in a comprehensive review of pertinent literatures dealing with (a) young children's development of spatial concepts and skills, (b) how students solve problems and learn in different types of classrooms, and (c) the special roles of visual imagery, equipment, and classroom discourse in spatial problem solving. The quantitative investigation into the effects of a two-dimensional spatial program used a matched-group experimental design. Parallel forms of a specially developed spatio-mathematical group test were administered on three occasions—before, immediately after, and six to eight weeks after the spatial program. The test contained items requiring spatial thinking about two-dimensional space and other items requiring transfer to thinking about three-dimensional space. The results of the experimental group were compared with those of a ‘control’ group who were involved in number problem-solving activities. The investigation took into account gender and year at school. In addition, the effects of different classroom organisations on spatial thinking were investigated~one group worked mainly individually and the other group in small cooperative groups. The study found that improvements in scores on the delayed posttest of two-dimensional spatial thinking by students who were engaged in the spatial learning experiences were statistically significantly greater than those of the control group when pretest scores were used as covariates. Gender was the only variable to show an effect on the three-dimensional delayed posttest. The study also attempted to explain how improvements in, spatial thinking occurred. The qualitative component of the study involved students in different contexts. Students were video-taped as they worked, and much observational and interview data were obtained and analysed to develop categories which were described and inter-related in a model of children's responsiveness to spatial problem-solving experiences. The model and the details of children's thinking were related to literatures on visual imagery, selective attention, representation, and concept construction.

Meanings of the terms, problem and problem solving across the school curriculum

Many teachers at all levels of education find it hard to articulate what the terms problem and problem solving mean. This study was designed to explore the meanings of these concepts held by people involved in education.

Tasks and pedagogies that facilitate mathematical problem solving

This is a report from one aspect of a project seeking to identify teacher actions that support mathematical problem solving. The project developed a planning and teaching model that describes the type of classroom tasks that can facilitate mathematical problem solving, the sequencing of the tasks, the nature of teaching heterogeneous groups, ways of dfferentiating tasks, and particular pedagogies. We report here one teacher's implementation of the
model using a unit of work that he planned and taught. The report provides important insights into the implementation of the theoretically founded model and the responses of students. We found that the model can be used for planning and teaching and for encouraging problem solving. The model has a positive effect on the learning of most students. Specific teachers actions were identified in order to address the needs of the students we are most
keen to support, those experiencing dfficulties.

Beyond Simon’s means-ends analysis : natural creativity and the unanswered ‘why’ in the design of intelligent systems for problem-solving

Goal-directed problem solving as originally advocated by Herbert Simon’s means-ends analysis model has primarily shaped the course of design research on artificially intelligent systems for problem-solving. We contend that there is a definite disregard of a key phase within the overall design process that in fact logically precedes the actual problem solving phase. While systems designers have traditionally been obsessed with goal-directed problem solving, the basic determinants of the ultimate desired goal state still remain to be fully understood or categorically defined. We propose a rational framework built on a set of logically interconnected conjectures to specifically recognize this neglected phase in the overall design process of intelligent systems for practical problem-solving applications.

Sex differences in achievement in year 12 mathematics and non-routine problem solving

In 1991 all Victorian year 12 students undertook the new Victorian Certificate of Education Mathematics Study designed by the Victorian Curriculum and Assessment Board. This paper presents the results of a study into sex difference in achievement in the new VCE Mathematics study in Victoria. An important goal of the study designers was to encourage more equal participation in senior secondary mathematics by females and males and to include assessment of mathematical skills previously not assessed in a year 12 course in Victoria. These new tasks could conceivably change the degree and direction of sex difference in achievement in senior secondary mathematics.

Associations between confidence, persistence, and optimism : illuminating optimistic problem solving activity

As part of video-stimulated post-lesson student interview studies of problem solving activity, Williams (2005, 2011) found successful problem solvers were optimistic. This study interrogates data from three students from a broader study: the role of optimism in collaborative problem solving and how to build it. The research question that focuses this study is “What associations exist between confidence, persistence, and optimism?” The question is explored both theoretically and empirically for the purpose of increasing understanding of the nature of optimistic problem solving activity by linking it to more familiar constructs. Students were progressively selected to further the interrogatory process. It was found that confidence and persistence did not necessarily occur together, and when they did, activity associated with these two characteristics was not sufficient for optimistic problem solving activity to occur. Perseverance was also required.

Toward a holistic theory of strategic problem solving

To date, many of the models and theories that seek to explain problem solving and decision making, have tended to adopt an overly reductionist view of the processes involved. As a consequence, most theories and models have proved unsuitable in providing managers with a practical explanation of the dynamics that underpin problem solving. A substantial part of a manager’s time is taken up with problem solving and decision making issues. The question of whether managers possess the necessary problem solving skills, or have access to “tools”, which can be used to manage different types of problems, has become an issue of some importance for managers and organisations alike. This paper seeks to contribute to the current literature on problem solving and decision making, by presenting a conceptual model of problem solving, which is intended to assist managers in developing a more holistic framework for managing problem solving issues.