Options
Pattern generalisation in mathematics : primary four pupils’ success rates and strategies
Author
Choo, Michelle Bee Lang
Supervisor
Chua, Boon Liang
Abstract
Generalisation refers to the process of identifying and extending commonalities across cases, and expressing the relationship underpinning the commonalities with a functional rule. It is an important component of mathematical activity, permeating many topics in mathematics. Many researchers regard generalisation as the heart of mathematics because generalising is a fundamental and crucial skill central to mathematics learning. However, many pupils, both at the primary and secondary levels, struggle to learn and understand pattern generalisation.
Pattern generalisation tasks are a common feature in the Singapore primary and secondary mathematics textbooks. A typical task displays the first few terms of a pattern and asks pupils to find a particular term, the position of a particular term, and an expression for the functional term. Results of the Trends in International Mathematics and Science Study (TIMSS) conducted both in years 2007 and 2011 show that Singapore primary school pupils performed well in tasks asking for the next term but not in tasks requiring an expression for the general term. The generalising strategies used by the pupils to obtain their answers were also not analysed. The present study set out to investigate Primary Four pupils’ pattern generalisation in linear figural tasks. Specifically, it examines the pupils’ success rates and their generalising strategies to find (a) terms that are near and far from the last given term in the task, (b) the figure numbers when given the terms, and (c) the functional rule.
A mixed methods research design involving both quantitative and qualitative approaches was adopted for the present study. A 75-minute paper-and-pencil test, called FUN-PATS comprising three tasks, was administered to 57 Primary Four pupils (34 boys and 23 girls) and followed by video recorded one-to-one interviews with nine pupils. Pupils’ responses in the FUN-PATS test were carefully coded and the interviews were thoroughly transcribed.
The research study has produced the following eight key findings: (1) The success rates of the Primary Four pupils decreased as the tasks became progressively more difficult. (2) Majority of the pupils was successful in finding the near term in the three pattern generalisation tasks. A sizable number of pupils succeeded in finding the far terms. (3) Rule construction was not highly successful across all three tasks. (4) No more than two-thirds of the pupils were able to find the figure numbers in the three tasks. (5) Functional Numerical and Recursive were the two most popular generalising strategies used. (6) The Functional Numerical strategy was predominantly used for rule construction. (7) Undoing and Recursive were the most commonly used strategies to find the figure number of the three tasks. (8) Majority of the successful P4 pupils in rule construction were High Ability pupils. Findings from the present study were then used to propose implications for teaching and learning, as well as recommendations for further study.
Pattern generalisation tasks are a common feature in the Singapore primary and secondary mathematics textbooks. A typical task displays the first few terms of a pattern and asks pupils to find a particular term, the position of a particular term, and an expression for the functional term. Results of the Trends in International Mathematics and Science Study (TIMSS) conducted both in years 2007 and 2011 show that Singapore primary school pupils performed well in tasks asking for the next term but not in tasks requiring an expression for the general term. The generalising strategies used by the pupils to obtain their answers were also not analysed. The present study set out to investigate Primary Four pupils’ pattern generalisation in linear figural tasks. Specifically, it examines the pupils’ success rates and their generalising strategies to find (a) terms that are near and far from the last given term in the task, (b) the figure numbers when given the terms, and (c) the functional rule.
A mixed methods research design involving both quantitative and qualitative approaches was adopted for the present study. A 75-minute paper-and-pencil test, called FUN-PATS comprising three tasks, was administered to 57 Primary Four pupils (34 boys and 23 girls) and followed by video recorded one-to-one interviews with nine pupils. Pupils’ responses in the FUN-PATS test were carefully coded and the interviews were thoroughly transcribed.
The research study has produced the following eight key findings: (1) The success rates of the Primary Four pupils decreased as the tasks became progressively more difficult. (2) Majority of the pupils was successful in finding the near term in the three pattern generalisation tasks. A sizable number of pupils succeeded in finding the far terms. (3) Rule construction was not highly successful across all three tasks. (4) No more than two-thirds of the pupils were able to find the figure numbers in the three tasks. (5) Functional Numerical and Recursive were the two most popular generalising strategies used. (6) The Functional Numerical strategy was predominantly used for rule construction. (7) Undoing and Recursive were the most commonly used strategies to find the figure number of the three tasks. (8) Majority of the successful P4 pupils in rule construction were High Ability pupils. Findings from the present study were then used to propose implications for teaching and learning, as well as recommendations for further study.
Date Issued
2016
Call Number
QA11.2 Cho
Date Submitted
2016