Number strategies of Grade 2 learners: learning from performance on the learning framework in number test and the Grade 1 annual national assessments - Weitz, Maria S. (My University, 2013)
Several commentators describe the low performance of South African students in mathematics as ‗a crisis‘. In the Foundation Phase specifically, there is evidence of a lack of shift from concrete counting-based strategies to more abstract calculation-based strategies (Ensor et al., 2009; Schollar, 2009). Concrete counting-based strategies refer to actions where the learner cannot find the answer to a mathematical problem without using concrete objects. In contrast, abstract calculation-based strategies involve strategies where the child does not need concrete objects to find the answer, but can instead use mental calculations in which numbers have been transformed into abstract objects upon which operations can then be carried out. Ensor et al argue that the poor mathematical results in South Africa are the result of inefficient moves made by learners from counting to calculating. In their study, many students failed to move their thinking sufficiently forward from concrete counting actions to abstract thinking. The focus of this study is to investigate a sample of Grade 2 learners‘ strategies on tasks drawn from the Learning Framework in Number (LFIN) test and responses on number related questions in the Annual National Assessment tests (ANA). I use the Learning Framework in Number to describe the stage of learners in their shift from concrete to a more abstract way of thinking about number. The theory of reification refers to the turning of processes into objects, and in this research, the origin of an abstract object in reification is explored. I also aim to understand the kinds of information I can get from children‘s grasp of early number strategies, by looking at the responses of learners on the ANA and LFIN tests. My research question is: What do the two tests (ANA and LFIN) tell us about the strategies on early number used by a sample of Grade 2 learners in a township school in Gauteng? The two critical questions that follow from this are:  How does learner performance on number problems compare across the two tests?  What evidence in relation to concrete/abstract strategies is evident in the responses of learners in the two tests? My findings showed that the learners in the school that I investigated still relied a great deal on concrete counting methods to answer questions. In spite of this, the mean ANA mark were much higher than the LFIN mean. The low number range of the ANA test, (1-34 for most of the number related questions), made it possible for the learners to use concrete counting (fingers or tallies) to answer the questions. The relatively low LFIN mark range indicated that children had difficulties in moving to more abstract ways of working with number. The implications of the reliance on concrete counting is potential difficulties when the learners move into higher grades where the number range is much higher, making the use of concrete methods time consuming and error prone.
A Research Report submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements of the degree of Master of Science. October 2012, Johannesburg.
Keywords: Numeracy - Juvenile literature.; Numeracy - Problems, exercises, etc. - Juvenile literature.