A cognitive model of year five pupils’ algebraic thinking / Piriya Somasundram

This study was carried out to investigate cognitive constructs that could contribute to year five pupils' algebraic thinking and to reveal the web of connection between these constructs. In this study, proposed cognitive constructs are number sense, operation sense, symbol sense and pattern sense. The dependent variable was year five pupils' algebraic thinking. This study applied descriptive research method to for data collection and analysis. Seven hundred and twenty year five pupils from a district of Malacca took part in this study. The samples comprised both female and male pupils from rural and urban schools. Data were collected using two instruments, assessment of number, operation, symbol and pattern senses (ANOSPS) and algebraic thinking diagnosis assessment (ATDA). ANOSPS comprised 15 multiple choice mathematical questions, while ATDA comprised 17 short answer mathematical questions. The data were analysed using structural equation model (SEM) to derive a model which could predict year five pupils’ algebraic thinking. Hence, researcher adopted partial least square-structural equation model (PLS-SEM) method to carry out the evaluation process. Four direct effect relationships were hypothesized from independent variables to dependent variables. Moderating effect of gender and location were also tested. A two-stage approach was employed which involved the evaluation of measurement model followed by an evaluation of the structural model. Findings of this study revealed that number sense, operation sense, symbol sense and pattern sense significantly influence year five pupils' algebraic thinking. This indicated the proposed independent variables play crucial role in the development of algebraic thinking in primary school. The findings also indicated there is no difference in algebraic thinking performance between female and male year five pupils. However, the algebraic thinking performance of urban school of year five pupils was better than rural school year five pupils. In addition, this study also revealed, symbol sense and pattern sense play mediator role between independent variables and year five pupils’ algebraic thinking. Lastly, the findings showed, gender doesn’t moderate all of the hypothesized four direct relationships. Location does moderate two of the hypothesized direct relationships. The direct effect size of operation sense on rural school year five pupils’ algebraic thinking is significantly higher than the urban school year five pupils. Followed by this, the direct effect size of symbol sense on rural school year five pupils’ algebraic thinking is also significantly higher than the urban school year five pupils. Findings of this study provided evidence that number sense, operation sense, symbol sense and pattern sense are important constructs in the development of algebraic thinking in primary school level. It also provided an awareness on what is algebraic thinking in primary school level and how the number sense, operation sense, symbol sense and pattern sense are intervened together. Algebraic thinking of primary school pupils can be enhanced by appropriate healthy classroom discussions while teaching arithmetic. Making sense of numbers, underlying properties of arithmetic, generalisation, and conceptual meaning of equal sign should be given more priority compared to getting a correct solutio