Authors: Caroline Long and Tim Dunne
This research explores approaches to the mathematics curriculum in the primary school in South Africa in order to understand why the mathematics standard is dropping; why learners are not grasping mathematical concepts easily; and where the ‘disconnect’ is between policy makers, educators and learners.
There are three approaches involved in constructing a curriculum; these can be applied separately or jointly. This paper discusses these three approaches, which are: the topics approach, the process (or operational) approach and the conceptual fields approach. These three approaches are summarised below:
|Topics approach||Process approach||Conceptual fields approach|
|· Evident in current CAPS curriculum in the week-by-week and hour-by-hour prescriptions.
· The rationale for this prescription is that our teachers are deemed not capable of interpreting an objectives-based curriculum, or of transforming these objectives into instructional units.
· Textbook writers provide the necessary details of the concepts for the teachers. This does not give the teacher leeway to interpret the curriculum in a beneficial manner for the learners.
· If strictly followed, then a level of proficiency will be achieved according to ANA.
· Concepts are taught in logical order, from easier to more advanced topics.
· Each topic is taught independently with no relevant connections.
· Invariant order and pace placed on teaching material does not take learners’ context into consideration.
|· Focus on problem-solving approach involving higher order thinking skills.
· If the lessons have been well constructed, with learners engaged with relevant problems this will propel their curiosity, exploration, and the discovery of new learning.
|· Integrates both topics and process approach.
· Focuses on the interrelationship between mathematical concepts so that concepts find meaning within a context.
· Enables a transition from one logical concept to the next and from concrete to abstract concepts.
· Requires the teachers to have a deep insight into mathematical concepts and foundations.
Each of the approaches is described in the paper, presenting both advantages and limitations. Secondly, the conceptual fields approach is illustrated (integrating the topics and process approach) in the planning of an exploratory instructional design. And thirdly, the five dimensions required for the understanding of a mathematical concept, are explained.
One of greatest challenges found was the lack of teachers’ mathematical knowledge, putting them at a disadvantage to engage completely with the necessary mathematical concepts to support learners understanding and needs. In addition, educators are currently following the set guidelines of the curriculum. If learners do not grasp a concept, there is no time for the teacher to revisit that concept, or the teacher does not have the skill set to rectify mathematical misconceptions. Following this, teachers need to effectively assess the learners’ knowledge; and assessment skills need to complement teaching resources.
The authors acknowledge that both the identification of topics and the presentation of progressively more complex topics are important, but advocate that it is the understanding of this progression that enables effective teaching.
A conceptual fields approach requires a deeper insight into the underpinning mathematical concepts, and also presents a route to mathematics proficiency through transforming implicit concepts-in-action to explicit and generalisable concepts.