Place value without number sense: Exploring the need for mental mathematical skills assessment within the Annual National Assessments

Mellony Graven

doi:10.4102/sajce.v3i2.45

Abstract

In this paper we examine the extent of the focus on number sense, enabled and accompanied by the development of efficient strategies for mental maths, in the foundation and intermediate phase. We do this through documentary analysis of the Curriculum and Assessment Policy Statements (CAPS) for these phases and the Annual National Assessments (ANAs). We argue that number sense and mental agility are critical for the development and understanding of algorithms and algebraic thinking introduced in the intermediate phase. However, we note from our work with learners, and broader evidence in the South African landscape, that counting-based strategies in the foundation phase are replaced in the intermediate phase with traditional algorithms. We share experiences in the form of vignettes to illuminate this problem. Whilst literature and the CAPS curriculum emphasise the important role of mental computation within number sense, we note that the ANAs do not include a “mental mathematics” component. This absence in assessment, where assessment often drives teaching, is problematic. We conclude with the suggestion that research be conducted into the viability/appropriateness of an orally administered mental mathematics assessment component in the ANAs as a way to establish a focus on number sense across the foundation and intermediate phases.

Highlights

In our work as the SA Numeracy Chairs at Rhodes and Wits University respectively and as doctoral and master’s research students in mathematics education across these institutions we collaborate with teachers and learners in over 25 primary schools in the broader Grahamstown and Johannesburg areas
In this paper we examine the extent of the focus on the development of number sense, enabled and accompanied by the development of efficient strategies for mental maths, in the foundation and intermediate phase
We do this through documentary analysis of the Curriculum and Assessment Policy Statements (CAPS) documents for these phases and the Annual National Assessments (ANAs)

Summary

Introduction

In our work as the SA Numeracy Chairs at Rhodes and Wits University respectively (first two authors) and as doctoral and master’s research students in mathematics education across these institutions (last two authors) we collaborate with teachers and learners in over 25 primary schools in the broader Grahamstown and Johannesburg areas. Across our experience of working with learners and teachers in the foundation and intermediate phase we have noted episodes which illuminate for us the critical problems relating to the absence of the development of number sense and mental agility. We share these as vignettes below that illustrate the problem in a way which national data in the form of extremely low average marks cannot. We can conclude that the majority of South African Grade 3 learners have not developed foundational number sense before entering the intermediate phase – which is premised on the notion of building on this foundational knowledge

Vignettes from the Eastern Cape and Gauteng

Examining the assessment of mental agility within the ANAs

Findings

Concluding remarks