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

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 countingbased 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.

What mathematics knowledge for teaching is used by a Grade 2 teacher when teaching counting

“…While research has established that mathematics is poorly performed in South Africa allegedly because most teachers lack adequate content and pedagogy, it has also been noted that the trajectory of poor performance begins at FP because of poorly developed number sense (Graven 2016;Graven et al 2013;Hoadley 2012;Schollar 2008). Graven (2016) argues that learners exit FP with inefficient arithmetic strategies and as a result fail to cope with the arithmetic demands of the higher grades.…”

“…Number sense develops as mathematical knowledge in children. Graven et al (2013) propose that number sense is more than just the ability to count, name, identify and write numbers. Rather, they argue that number sense includes having a sense of what numbers are, understanding their relationship to one another, being able to perform mental math calculations efficiently and effectively, and being able to use numbers in real-world situations.…”

The Assessment Purpose Triangle: Balancing the Purposes of Educational Assessment

“…Not surprisingly, shortly after these events, the government announced a decision to participate in fewer international comparative studies, claiming that this was to allow the interventions that were put in place to take full effect (Human Science Research Council, 2006). South Africa's annual national assessments (ANAs) were implemented as an alternative accountability measure in 2011 (Graven et al, 2013) by the new Department of Basic Education. These standardized national assessments examine languages, mathematics, literacy, and numeracy from Grades 1 to 9 (6-16 years) (Department of Basic Education, 2017).…”

Resisting the desire for the unambiguous: productive gaps in researcher, teacher and student interpretations of a number story task

“…The Department of Basic Education's (DBE) Annual National Assessments (ANA), consistently point to poor mathematics results with only 3% of learners achieving 50% or more in the last written ANAs in 2014 (DBE, 2014). Widespread evidence of an absence of number sense in FP learners is a critical concern not sufficiently addressed (Graven et al, 2013). A focus on producing (and awarding marks for) 'the right' answer irrespective of whether methods used are efficient or appropriate masks the challenges of the lack of Foundation Phase (FP: Grade R-3 ages 5-9) competences.…”