algebra, statistics and logic  : Introduction   
   

The assessments included eleven tasks which investigated students understandings, processes and skills in the areas of mathematics called algebra and statistics. Algebra involves patterns and relationship in mathematics in the real world, the use of symbols, notation and graphs and diagrams to represent mathematical relationships and ideas, and the use of algebraic expressions for solving problems. Statistics is concerned with the collection, organisation and analysis of data, the estimation of probabilities and use of probabilities for prediction.

One task was identical for both year 4 and year 8. Six tasks had overlapping versions for year 4 and year 8 students, with some parts common to both levels. Two tasks were attempted by year 8 students only, and two by year 4 only. Five of eleven tasks have been selected as link tasks to be used again in the year 2001, and therefore are not described in detail here. The other tasks are released tasks for which full details are given.

The chapter presents the assessment tasks in the following order:

  • The released tasks attempted by both year 4 and year 8 students;
  • The released tasks attempted separately by year 4 and year 8 students;
  • The five tasks which will be used as link tasks.

Results show that year 8 students were clearly more capable than year 4 students in recognising and maintaining algebraic patterns and relationships, but like year 4 students, struggled when fractional components had to be considered. A high percentage of year 4 students could see patterns and relationships that did not require too much calculation or understanding of underlying processes. Surprisingly, only half of year 4 students correctly used basic symbols of <, =, > to show relationships between numbers. In a team task involving problem solving and logical thinking, there was little difference between year 4 and year 8 in co-operative strategy development. However, a larger percentage of year 8 teams were more skilful in checking and refining their answers. On task components common to both year levels, on average about 30 percent more year 8 students than year 4 students achieved success.