Additive Relations Word Problems in the South African Curriculum and Assessment Policy Standard at Foundation Phase

Abstract

Drawing on a literature review of classifications developed by each of Riley, Verschaffel and Carpenter and their respective research groups, a refined typology of additive relations word problems is proposed and then used as analytical tool to classify the additive relations word problems in South African Curriculum and Assessment Policy Standard (CAPS) for Foundation Phase. Inconsistencies and errors within the CAPS are exposed. Two different typologies are presented in the CAPS: first 'compare, combine and compare' and then 'change, compare and equalise' problem types are presented. For the latter typology 'join' and 'separate' actions are imposed onto static situations. Rather than referring to the 'whole-partpart' structure which is common across all problem types, a generalised 'start-change-result' structure is imposed. This is both incorrect (static situations do not have this structure) and inconsistent with the articulated distinction between take-away and difference models for subtraction expressed elsewhere in the CAPS. In light of this analysis it is recommended that adapted curriculum guidelines are developed and circulated to Foundation Phase teachers, teacher educators and curriculum advisors. The refined typology of additive relations word problems may be used to underpin professional development initiatives for Foundation Phase teachers, and for structuring the setting of the annual diagnostic assessments at this level.

Distribution of additive relation word problems in South African early grade Mathematics workbooks

“…The section ends by providing possible reasons for the problematic typologies used in the South African Foundation Phase CAPS. The problems with the typologies in CAPS were described by Roberts (2016a) and the possible reasons for these problematic formulations were uncovered when the early papers about word problem types were studied for this article.…”

“…In this article categories are named according to the labels used by Roberts (2016a). Roberts explains that the label 'change' is preferable to 'join/separate' because it emphasises the common action.…”

“…Although these subcategories are exemplified in the original typologies, they are not named. In some other typologies (such as the one used by Roberts [2016a]) only the 'compare more than' problems are exemplified. In the comprehensive typology developed in this article all the possible subcategories are included and named.…”

“…While other studies have adopted (or slightly adapted) an existing typology, this study describes alternative typologies and explains why they were not chosen. It also argues for the renaming of certain problem types (building on the work by Roberts [2016a]) and extends the chosen typology by including variations of certain problem types.…”

“…The renamed, extended and exemplified typology that is developed in this article provides not only an analysis tool for the current workbooks but also a practical reference tool for curriculum developers, workbook and textbook writers and teachers -both in South Africa and internationally -to make informed decisions about the types and spread of word problems offered to learners. In South Africa such a tool is valuable in the light of the problematic typologies uncovered by Roberts (2016a) in the South African Curriculum and Assessment Policy Standard (CAPS). It is also potentially valuable should the foundation phase Mathematics workbooks be reworked.…”