Relative difficulty of early grade compare type word problems: Learning from the case of isiXhosa

Ingrid E Mostert

doi:10.4102/pythagoras.v41i1.538

Abstract

Word problems form an important part of the early grade mathematics curriculum in South Africa. Studies have shown that the relative difficulty of word problems differ: learners are more likely to solve certain types of word problems than others, with compare type problems being the most difficult. In order to help early grade learners understand and solve compare problems, it is important to understand the relative difficulty of different types of compare type problems and the factors that contribute to their relative difficulty. While these factors have been studied in English, less research has attended to word problems in other languages, such as isiXhosa. In this study a typology of isiXhosa compare type (difference unknown) word problem was set up. The typology included two dimensions, namely the problem situation and the comparative question. The relative difficulties of specific word problems from this typology were compared by analysing the results from an early grade mathematics assessment administered to two cohorts of Grade 1–3 isiXhosa learners in five rural Eastern Cape schools. The analysis showed that in isiXhosa, as in English, some compare type problems are easier to solve than others. Problems with ‘matching’ situations are easier to solve than problems with ‘no matching’ situations. Problems with alternatively formulated comparative questions, specifically those using - shota or kangakanani , are easier to solve than those using a more classic formulation. This study highlights the importance of understanding the ways in which African languages express mathematical ideas in order to identify and leverage affordances for teaching and learning mathematics.

Highlights

Word problems are a central, yet hard-to-teach, aspect of early grade mathematics
Even though there is not a big difference between the facility score of these two questions, the chisquared test (p = 0.006 < 0.05) confirms that the difference in facility score is significant. These results raise a number of points regarding the relative difficulty of isiXhosa compare type problems in early grade mathematics, some of which are relevant for English
While the ‘standard’ formulation of compare problems is difficult, this and other studies have shown that certain formulations of compare type problems are easier for learners to understand and to solve, both in English and in isiXhosa

Summary

Introduction

Word problems are a central, yet hard-to-teach, aspect of early grade mathematics. For example, in South Africa word problems have been identified as a recurring weakness in the South African Annual National Assessments (ANAs) (Department of Basic Education, 2012, 2014, 2015). Sepeng, 2013), there has been little research into early grade word problems in African languages. How many more bananas does Sbu have than Sive?’ While there has been some research into early grade word problems in South Africa Petersen, McAuliffe, & Vermeulen, 2017), and some research into word problems and African languages in higher grades This is problematic as more than 75% of learners are taught mathematics in an indigenous African language in the first four years of formal schooling (Spaull, 2016)

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Discussion

Conclusion