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An algebraic thinking plays crucial and fundamental element of mathematical thinking for secondary students. An existing approach to build and to develop algebraic thinking is the problem solving strategy. This study describes algebraic thinking ability of students in solving number patterns’ problem. Six indicators of algebraic thinking were implemented, namely generalization, abstraction, analytical thinking, dynamic thinking, modelling and organization. The class 8^B was purposively chosen from high average score from other classes of SMPN 43 Surabaya, and all students of the class 8^B were given both mathematics ability and integer number patterns tests.

 

Twenty nine students were given mathematics ability and number patterns tests. Portfolio students from previous semester and the results’ tests were ranked into high, medium and low mathematics ability Three volunteer students with high, medium and low mathematics ability were respectively selected and interviewed based on the given tests. Each of these 3 students was interviewed by the researcher to gain further insight into their thinking. The given problem in algebraic thinking about integer problem.

 

1. The number of sequence are 3, 7, 10, 17, 27, 44, 54,….

Find the two next integer number of the sequence

2. Given a sequence , there are 1, 3, 6, 10, 15, 21, 28,…..

Find the two next number of the sequence

3.Given the first row have 9 red blocks, the second row thave 16 red blocks and the third row have 25 red blocks. How many red blocks that should have in the 8^th row?

 

Table 1 Result of the students in mathematics

 

Students ability

Number

High

2

Medium

15

Low

12

 

The result showed that 2 students with high mathematics ability, 15 students with medium mathematics ability and 12 students with low mathematics ability based on 29 students at class 8^B. Three volunteer students with high, medium and low mathematics ability respectively were interviewed based on their answer sheets.

 

The results emphasized that high ability student utilized their algebraic thinking based on the problem solving strategies, understand the problem, device a plan, carry out the plan and look back and satisfied all algebraic thinking indicators such as generalization, abstraction, analytic thinking, dynamic thinking, modeling and organization The medium ability student implemented algebraic thinking except in writing the problem solving strategies of algebraic thinking’s indicators and utilized their algebraic thinking in generalization, abstraction, modeling, and dynamic thinking but still can explain the problem solving strategy that they used. However, the low ability student was not able to address at least two indicators of  algebraic thinking, such as generalization and modeling but can write the problem strategy. This study suggests to the mathematics teachers for gradually developing algebraic thinking and reasoning by demonstrating more variously problem solving examples in the class, for instance by implementing such either discovery-inquiry method or problem-based method in mathematics’ teaching and learning

 

Algebraic thinking, mathematics ability, integer problem, problem-based method