Browsing by Author "Burgess, Timothy Angus"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Do games help the learning of probability? : a thesis presented in partial fulfilment of the requirements for the degree of Master of Educational Studies (Mathematics) at Massey University
    (Massey University, 1999) Burgess, Timothy Angus
    The value of using games to assist students' learning of probability concepts was investigated, primarily using qualitative methods. Games, although generally useful in mathematics for helping children learn, may not automatically be as useful in helping students develop normative probability concepts, particularly because of the nature of randomness. Sixteen students (Years 7 and 8) participated in the study. The students initially completed a written questionnaire which was designed to explore their understanding of probability. The students' misconceptions were categorized according to various types of probability reasoning. Two games were played by the students in groups of four, over two successive days; a game of chance on the first day, and a game of strategy and chance on the second. The game sessions, each lasting about 45 minutes, were audio-taped and video-taped. Group interviews were conducted during and following the playing of the games. The study found differences between students in their levels of involvement in and discussion about the games, and differences between the two types of games in the degree of interaction within groups, all of which influenced the games' effectiveness in developing probability learning by the students. There was evidence of inconsistencies in some students' probability reasoning and understanding. When the empirical results from the games conflicted with their ideas, the students were not necessarily aware of such conflict so consequently did not adjust their thinking. For the use of such games to maximize the opportunities for the students' learning of probability, some implications of the study for classroom teachers are suggested. Consequently the role of and knowledge and understanding of the teacher is critical to ensure effective learning of probability concepts by students.
  • Thumbnail Image
    Item
    Investigating the nature of teacher knowledge needed and used in teaching statistics : a thesis presented in partial fulfilment of the requirements for the degree of Doctorate in Education (Ed.D.) at Massey University, Palmerston North, New Zealand
    (Massey University, 2007) Burgess, Timothy Angus
    This thesis explores the knowledge needed for teaching statistics through investigations at the primary (elementary) school level. Statistics has a relatively short history in the primary school curriculum, compared with mathematics. Recent research in statistics education has prompted a worldwide move away from the teaching of statistical skills, towards a broader underpinning of statistical thinking and reasoning. New Zealand’s nationally mandated curriculum reflects this move. Consequently, little is known about the types of knowledge needed to teach statistics effectively. Ideas from two contemporary areas of research, namely teacher content knowledge in relation to mathematics, and statistical thinking, are incorporated into a new framework, for exploring knowledge for teaching statistics. The study’s methodological approach is based on Popper’s philosophy of realism, and the associated logic of learning approach for classroom research. Four primary teachers (in their second year of teaching) planned and taught a sequence of four or five lessons, which were videotaped. Following each lesson, a stimulated recall interview, using an edited video of the lesson, was conducted with the teacher. The video and interview recordings were analysed in relation to the teacher knowledge and statistical thinking framework. The results provide detailed descriptions of the components of teacher knowledge in relation to statistical thinking that are needed and used in the classroom. Included in the results are profiles of each teacher’s knowledge. These profiles describe ‘missed opportunities’, which were defined as classroom incidents in which teacher knowledge was needed but not used, and consequently resulted in the teachers not taking advantage of chances to enhance students’ learning. A number of significant themes were revealed, linked to knowledge for teaching statistics. The themes include: problems associated with teacher listening; the need for the teacher to be familiar with the data; students’ difficulties with various components of the statistical investigation cycle; and understanding variation and the development of inference. The study concludes that for effective teaching of statistics through investigations, it is necessary for teachers to have knowledge in each of four categories as related to each component of statistical thinking. If any aspect of knowledge is not available or not used, teachers will not enhance, and could disadvantage, students’ learning. Implications from the findings are considered for initial and on-going teacher education.