An exploratory study of the difficulties with simple arithmetic word problems among primary school academically low achievers

Abstract

All teachers encounter children with different abilities. It is a constant challenge and teachers do their best to identify the poor performers and understand the reasons for their poor performance. But when a whole class is poor in a particular subject, it raises the question why. The purpose of my study was to examine the reasons why a whole body of students at primary level found difficulty in learning mathematics. I wanted to understand whether it was a lack of conceptual knowledge or procedural knowledge – or both; to see how they coped with simple problems (‘find the sum’, ‘missing addend’ and ‘guessing game’), and, when they found these problems a challenge, what were the hurdles to their understanding.

I studied a group of students at a particular school. I was aware that they all had difficulties in understanding mathematics. In all, I interviewed 27 students (one-to-one or in pairs) and also observed them in a classroom context to identify common difficulties. I selected four students (who had exhibited difficulties which were common to all 27 students) for further interviews. I wanted to investigate common difficulties in greater depth and to identify any other difficulties that were either peculiar to one or other of those four students, or which might reasonably be also attributed to the other 23 students.

In the case of my students, they seem to lack both conceptual and procedural knowledge. Even where they had some procedural knowledge, I identified failures in that knowledge. Examples include insufficient flexibility, failure to use counting on, failure to translate a word problem into a proper number sentence, being able to write a number sentence but unable to operate it, being unable to count by grouping and regrouping, and moving to the use of number sentences when they were not properly equipped to understand them.

Although good procedural skills could help in increasing conceptual knowledge, the students showed a marked lack of understanding of part-whole relationship. An understanding of part-whole relationship is fundamental to the understanding of mathematics and, in my view, is one of the first steps so that children can then become adept at learning using procedural knowledge. This lack of conceptual knowledge seems certainly to have hindered the students from gaining procedural knowledge – and, in turn, this lack of procedural knowledge has hindered their gaining of conceptual knowledge.

Lack of conceptual knowledge or procedural knowledge can easily be overlooked unless the teacher is able to observe carefully where the student is going wrong and questioning why that should be so. In the busy classroom with a curriculum to get through and more than several students to teach, it is unsurprising that teachers might easily overlook the reason why a child is having a problem with mathematics. It is understandable that a teacher might jump to the wrong conclusion – perhaps assuming that a child cannot solve the problem because they have worked it incorrectly rather than that the issue is much more fundamental – the child has not made sense of the problem at all.

The message for teachers, I respectfully submit, has to be that, when faced with students who are performing badly in mathematics, it is vital to ascertain the reason. Is it a conceptual or a procedural issue? Where exactly is the student going wrong? What is the very root of the problem? Only when we get to the very root of the problem can we devise an effective teaching strategy to put it right.