PUPILS' PROCESSES OF THINKING: LEARNING TO SOLVE ALGEBRAIC PROBLEMS IN ENGLAND AND THAILAND

simplifying algebraic problems. The findings are drawn from an algebra test given to 103 English pupils and 186 Thai pupils. This paper focuses on one of the six themes explored during the study. The simplification theme has been split into level one: simplify one variable, level two: simplify two variables, level three: simplify two variables with brackets, and level four: simplify two variables of second order with brackets. The pupils’ processes in simplification were categorised from their written responses. English and Thai pupils used the same processes to simplify the level one question. The differences were increased when they faced the harder items. The main difficulties were dealing with negative signs and multiplying out the brackets. OVERVIEW Basic education in England is organised on the basis of four Key Stages: Key Stage 1 caters for pupils aged 5-7 (Year 1-2), Key Stage 2 for pupils aged 7-11 (Year 3-6), Key Stage 3 for pupils aged 11-14 (Year 7-9), and Key Stage 4 for pupils aged 14-16 (Year 10-11). In Thailand, it is comprised 6 years for primary education (Primary 16, aged 6-12), 3 years for lower secondary education (Secondary 1-3, aged 12-15), 3 years for upper secondary education (Secondary 4-6, aged 15-18). The design of the test was based on the algebra contents in the National Numeracy Strategy: Framework for teaching mathematics year 7, 8, and 9 in England and on the mathematics curriculum for the lower secondary level in Thailand. The test seeks to illustrate pupils’ processes of thinking for each item at different levels of difficulties. There are 6 themes altogether, patterns/sequences, simplification, substitution, equations, functions/graphs, and word problems. Within each theme, there are 4 levels of difficulty ranging from the easiest level to the most difficult one. The second theme of the test, simplification, is the process of adding and subtracting like terms in an expression. Like terms are those having exactly the same letters and exponents. They may differ only in their coefficients. This theme was tested using four questions, designed to observe the pupils’ processes of thinking as they manipulated the like terms in different forms of expression. The questions are shown below: