Abstract
The continuous research on mathematical attainment is a part of the International Project on Mathematical Attainment (IPMA) in which such countries as Brazil, Czech Republic, England, Hungary, Holland, Ireland, Japan, Poland, Russia, Singapore and USA are participated. The aim of this project is to monitor the mathematical progress of children from the first year of compulsory schooling throughout primary school and to study the various factors which affect that progress, with the ultimate aim of making recommendations at an international level for good practice in the teaching and learning of mathematics. In Japan, the total of eight different public primary schools have agreed to participate in the project. We asked all two-cohort children and their classroom teachers from these schools to be involved and to take mathematical attainment tests for six years. At the present we have carried out three tests, i.e. Test 1, Test 2 and Test 3 to the about 500 children of first cohort for two years. The purpose of this paper is to analyze the data of these tests, to investigate children's progress of mathematical attainment and to present a way of seeing the fixity of mathematical attainment in order to find out some suggestions for improving the teaching and learning of mathematics at these primary schools. First, according to the percentage of correct answer to each test item, we made such categories as high [H], medium [M] and low [L] attained items. We found out there were five different types of [H→H ], [M→H], [L→H], [L→M] and [L→L] based on the progress of each test item from Test 1 to Test 2 or from Test 2 to Test 3. For example, the type of [H→H] means that for those test items in this type children had done well at the first test and did so at the second test a year later. The type of [L→H] means that for those test items in this type children had not done well at the first test and became to be well at the second test a year later. It reflects a positive effectiveness of the teaching and learning of mathematics for one year. Using these types, we found out that the teaching and learning of mathematics at the first grade was more effective than that one at the second grade in these schools. Second, we defined the fixity of mathematical attainment such that for three tests if a child's changing pattern of correct (1) or incorrect (0) on an item is [1→1→1] or [0→1→1] then the child's mathematical attainment on the item is fixed. We found out that four items in Test 1 were insufficiently fixed among children and suggested that more efforts should be made in the teaching and learning of mathematics related these items.
