Estimation in Tongan schools

Abstract

In recent years, estimation has become increasingly prominent in the mathematics curriculum statements and recommendations in western countries including the United States, United Kingdom, Australia, and New Zealand. Tonga, too, has produced a draft syllabus on mathematics in which estimation has a prominent place (Tonga Ministry of Education, 1992a). Much of the research on estimation has been conducted in the United States, and a small number of studies in the United Kingdom, Japan, Australia and New Zealand. In Tonga, research on mathematics education is almost non-existent and no research on estimation has been conducted in Tongan classrooms. A belief that estimation is one of the most useful mathematical skill both in the classroom and everyday life, together with a concern about the lack of research data on this important topic determined the focus of the present study. The study reported in this thesis involved a review of estimation in both formal and informal learning in Tonga, a review of the research literature on estimation and research in three secondary and two primary schools in Tonga. This study was designed to investigate estimation in Tongan schools by focussing on students’ measurement and computational estimation skills and strategies, and to explore ways of teaching these topics. A small sample of 18 form three (i.e. 13-15 year olds) and 12 class six (i.e. 10-11 year olds) students from three secondary and two primary schools in Tonga took part in this study. These students were interviewed before and after taking part in an instructional unit on measurement estimation activities. In addition, the computational estimation ideas of the 12 primary students were explored through individual interviews before and after an instructional unit on computational estimation strategies. Students’ ideas and strategies identified from the first individual interview data were used to design an instructional unit on measurement and computational estimation. Thus a study of measurement estimation of both primary and secondary students preceded that of computational estimation of primary school students. Furthermore, a questionnaire was used to collect data on teachers’ views regarding estimation. In particular, the present study investigated the following: i) What estimation strategies are used by Tongan students in measurement and computation? How have the students constructed these strategies? How effective are the students’ estimation strategies? ii) What other mathematical skills and/or concepts do students need in order to become proficient estimators? iii) What are the mathematics teachers’ views regarding estimation? What estimation strategies are currently taught and encouraged by mathematics teachers in Tongan classrooms? iv) How can students’ existing ideas about estimation be utilised to develop teaching strategies which will further develop this mathematical process? The interview data showed that students’ existing ideas of standard measures formed the basis for their strategies for estimating measures of length. On the other hand, ideas and benchmarks developed in everyday life experiences were the basis of the strategies for estimating the measures of weight and capacity. The data also showed that class six students relied on ‘conventional algorithms’ to solve computational estimation tasks suggesting a lack of appropriate and effective computational estimation strategies. The data showed that the instructional unit on computational estimation strategies helped students shift from the reliance on ‘conventional algorithm’ to the use of appropriate estimation strategies, particularly the ‘rounding procedure’. Data also showed that many experiences with a variety of benchmarks and standard measures, making comparisons and judging relative sizes of objects, and reflections on their estimates helped students develop appropriate measurement estimation skills and strategies. Even though teachers viewed estimation as useful, it was not a major part of their pre-service and in-service training and as well as current classroom practices. The needs for specific preservice and in-service programme on estimation activities were identified by the teachers. The thesis argues that measurement estimation tasks provide the means by which students’ variety of ideas and experiences (both in and out of school) could be used in the mathematics classroom. By their very nature estimation tasks require the use of a variety of procedures, answers and assessment procedures. Reflection on their answers and strategies allow students to ascertain the reasonableness of their ideas. Both teachers and students need to be involved in making decisions regarding acceptable ranges for the answers and the criterion to be used for the assessment of estimates. These should encourage students to become more actively involved in their mathematics learning. Estimation has the potential to provide much needed variety in the Tonga mathematics classroom. This thesis ends with a discussion of the implications of the main results for learning, teaching, resource and curriculum development, assessment and future research.