UWI - Mona
Mathematics is an area that is widely known and studied. It is the foundationof many subject areas and is a subject that equips one with skills and knowledge suitable for the real world. Mathematics is defined as a reasoning activity that involves observing, representing and Investigating relationships in the social and physical world, or between mathematical Concepts themselves (BOS NSW, 2002). The Britannica Online (Academic Edition) also defines mathematics as a science that deals with logical reasoning and quantitative calculation, its development involves an increasing degree of idealization and abstraction of its subject matter. Mathematics consists fundamentally of concepts, which are abstract generalised ideas. Mathematics therefore is the application of physical and mental operation to concepts. Mathematics as a subject can be learnt two basic ways. Its understanding can either be procedural (understanding the process) or conceptual (understanding the concept). Teaching of mathematics should therefore be focused on the development of conceptual understanding as this involves seeing the connections between concepts and procedures, and being able to apply mathematical principles in a variety of contexts.
Adding It Up defines conceptual understanding as "the comprehension of mathematical concepts, operations, and relations," (p.141). It is the first of The Five Strands of Mathematical Proficiency. It is an integrated and functional grasp of the mathematical ideas(as indicated by the NRC, 2001)and means that an individual has ‘sufficient understanding to work intelligently and productively with the concept and continue to make progress’(Devlin, 2007), while enabling them tolearn new ideas by connecting those ideas to what they already know. Conceptual understanding is referred to commonly as conceptual knowledge (Anderson,...