Abstract
Background: Teaching using manipulatives is emphasised, especially in the early grades, to help learners conceptualise operations on whole numbers. Therefore, teachers’ competencies in using manipulatives is the key in helping learners master these basic operation skills.Aim: Drawing from the literature on using manipulatives to improve learners’ performance in mathematics, this study recounts foundation phase pre-service teachers’ conception of using manipulatives to enhance their competencies and reasoning skills to model the solution in number operations.Setting: Data presented here was collected from 31 participants. These pre-service teachers either passed mathematics or mathematical literacy with 40% at the grade 12 level.Methods: Data was collected from participants’ written work (e.g. classroom tasks, homework, tests and examinations) and during class discussions. Interviews were conducted with some students. We analysed their conception guided by the APOS theory, namely, Action-Process- Object-Schema.Results: We observed improvement in the conception of using manipulatives among pre-service teachers. In the first semester, most students display action conception of using manipulatives to either represent or model a solution. However, in the second semester, most students either display process or object conception as explained in the genetic decomposition. We attributed the improvement to change of instruction in the second semester as we taught in accordance with the APOS theory.Conclusion: It is evident that there are a number of contributing factors to pre-service teachers’ conception of mathematical concepts, and teacher educators need to pay particular attention to these to help pre-service teachers master the concepts they would teach at school.
Highlights
This article focusses on analysing foundation phase pre-service mathematics teachers’ evolution of their conception of using manipulatives in number operations
In the quest to answer our perennial question about preservice teachers’ conception of using manipulatives and exploring the contributing factors that enable or hinder their conception, we concluded that student conception of using manipulatives to represent whole numbers and model solution in addition and subtraction of whole numbers gradually evolved
This we observed as we saw from the above data in semester 2 that many students showed the interiorisation of action into a process and further encapsulating process into objects, showing conceptualisation of the concept
Summary
This article focusses on analysing foundation phase pre-service mathematics teachers’ evolution of their conception of using manipulatives in number operations. In his article entitled ‘What it means to understand mathematics’, Usiskin (2015:19) argues that for a person to have a full understanding of mathematical concepts, one needs to be well versed with skills and algorithms associated with the concept, uses and applications of the concept, representations and metaphors, and the history of the concept. These dimensions are important for concept development, they cannot be developed all at once because as much as they are interrelated they are independent of each other (Usiskin 2015). Teachers’ competencies in using manipulatives is the key in helping learners master these basic operation skills
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