New Zealand's National Education Monitoring Project commenced in 1993, with the task of assessing and reporting on the achievement of New Zealand primary school children in all areas of the school curriculum. Children are assessed at two class levels: Year 4 (halfway through primary education) and Year 8 (at the end of primary education). Different curriculum areas and skills are assessed each year, over a four year cycle. The main goal of national monitoring is to provide detailed information about what children can do so that patterns of performance can be recognised, successes celebrated, and desirable changes to educational practices and resources identified and implemented.

Each year, small random samples of children are selected nationally, then assessed in their own schools by teachers specially seconded and trained for this work. Task instructions are given orally by teachers, through video presentations, or in writing. Many of the assessment tasks involve the children in the use of equipment and supplies. Their responses are presented orally, by demonstration, in writing, or through submission of other physical products. Many of the responses are recorded on videotape for subsequent analysis.

In 1997, the third year that national monitoring was implemented, three areas were assessed: mathematics, social studies, and information skills. This report presents details and results of the assessments of mathematics.

The framework for mathematics identified five areas of knowledge (number, measurement, geometry, algebra, and statistics), linked to five major processes and skills. The importance of attitudes and motivation was also highlighted. The chapter structure in this report rearranges the knowledge areas a little, separating tasks involving money from other tasks in the number and measurement areas, and placing the algebra and statistics tasks in one chapter.

Information about the students' performance on number tasks (excluding money tasks) is presented in Chapter 3. Year 8 students were substantially more successful than year 4 students on the task components which both year levels attempted. On average, about 35 percent more year 8 students than year 4 students succeeded. Most students knew their basic addition facts well, and did quite well on tasks involving the addition of two, three and four digit numbers, but multiplication facts were much less consistently known. Subtraction involving adjustment (renaming) proved too difficult for most year 4 students and for a substantial proportion of year 8 students, while year 8 students had quite limited success with tasks involving division, fractions and decimals. It is intriguing to note that on most tasks involving reasonably complex computations, it was common to find 60 or more different answers from the approximately 450 students attempting the task at a given year level! Students at both levels did much better when using calculators than when calculating mentally or with paper and pencil.

Chapter 4 presents results for tasks involving money. On task components common to both year levels, on average about 40 percent more year 8 students than year 4 students were successful. A high percentage of year 8 students and a moderate percentage of year 4 students gave accurate answers when using real money to answer questions concerned with counting value, calculating and giving the right change. Paper and pencil computation tasks followed a similar pattern, but with success rates lower. Less than half of the 8 students were successful with most of the tasks in which they were asked to calculate the monetary values of percentage discounts on priced items.

Chapter 5 presents results for tasks involving measurement of length, area, volume, weight (mass), time and temperature. On tasks common to both year levels, on average about 30 percent more year 8 students than year 4 students achieved success. Students achieved higher levels of success in making measurements than in estimating measurements. Where task components involved computation or linking two steps to achieve a desired result, success rates were markedly lower than where direct measurements or single step processes were sufficient.

Information about the students' performance on geometry tasks is presented in Chapter 6. On task components common to both year levels, on average about 30 percent more year 8 students than year 4 students were successful. Students at both levels generally had more difficulty with tasks involving three dimensional objects and relationships than with those involving plane geometry.

Chapter 7 presents results for tasks in the areas of algebra, statistics and logic. On task components common to both levels, on average about 30 percent more year 8 students than year 4 students were successful. The ability of year 4 students to maintain sequences and patterns declined sharply when larger numbers or more complex patterns were used. A similar decline was evident for year 8 students when fractions were used. Surprisingly, only half of year 4 students correctly used the basic symbols <, =, and > to show relationships between numbers.

Results from the mathematics survey are presented in Chapter 8. The survey sought information from students about their curriculum preferences and perceptions of their own achievement. Among twelve school subjects, mathematics was the third most popular at both year levels, behind art and physical education. Enthusiasm for doing mathematics, in and out of school, declined markedly from year 4 to year 8, but similar declines have been observed in national monitoring surveys in several other curriculum areas. About half of the students at both year levels said they wanted to keep learning mathematics when they grew up. Somewhat surprisingly, 28 percent of year 4 students and 41 percent of year 8 students said that they "didn't know" how good their teacher thought they were at mathematics.

Chapter 9 reports the results of analyses which compared the performance of different demographic subgroups. School size, school type (full primary or intermediate), community size or geographic zone did not seem to be important factors influencing mathematics achievement. At both year levels, girls performed as well or better than boys on every task except one, and also displayed more positive attitudes to doing mathematics in their own time. Year 4 Mäori students were noticeably more positive about mathematics than their non-Mäori counterparts, but non-Mäori students outperformed Mäori students on more than two thirds of the tasks at both year levels. Similarly disturbing results were obtained for the comparisons involving school socio-economic index and the proportion of Mäori students in schools. The results for schools with more than 5 percent Pacific Island students are particularly interesting: at year 4 level students attending these schools did worse on two thirds of the tasks, but at year 8 level they did worse on only one eighth of the tasks. A similar pattern has been reported in other NEMP reports.