Exploring multiplicative reasoning with grade four learners through structured problem solving

[摘要] South Africa’s performance in mathematics education is ranked amongst the world’s worst.This performance is not only alarming at an international level, but also nationally. AnnualNational Assessments (ANA) conducted by the Department of Education have showed thatthe level of mathematics across the foundation and intermediate phase is poor with apronounced dip in performance at a Grade 4 level (Department of Basic Education, 2014).Multiplication and division are common challenging areas that contribute to this poorperformance. This is concerning as mathematics is globally recognised as a key competencefor providing access to higher education and developing a country’s society and economy.My study, aimed at exploring multiplicative reasoning with Grade 4 learners throughstructured problem solving, is focused on the learning of multiplication and division withinthe context of an intervention concentrated on developing learners’ ability to modelmultiplicative situations. Shifts in the use of models were investigated following a smallscaleintervention in which different modelling approaches (particularly ratio modelling)were introduced and developed. A control group was used to determine the usefulness of theintervention. Questions which I sought to answer were: (a) what kinds of multiplicativereasoning (models) are Grade 4 learners using prior to intervention, (b) what changes, if any, are seenin overall performance, across the intervention and control group, in the post-test, and, (c) what kindsof differences in model use were associated with the shifts in performance?The main dataset comprised of 61 pre- and post-test scripts across three Grade 4 classes in aformer Model C school in a Johannesburg district. A sample of 15 interviews were alsoconducted across the classes. Document analysis and transcription notes were used to analysedata with a Realistic Mathematics Education (RME) framework informing my analysis.Findings from my study reveal that prior to intervention, Grade 4 learners presented limitedmultiplicative models which were predominantly confined to traditional algorithms. After thesmall-scale intervention, learners used a broader range of models with an emerging take up ofratio models. The success rate associated with the models presented by learners alsoimproved. Limited and/or no changes in model use and their respective success rates wereseen in the control group suggesting that the intervention program was useful. These findingssuggest that, as a future recommendation, it would be worthwhile to investigate the outcomesof running a similar intervention in less privileged settings.

[发布机构] University of the Witwatersrand