Background: Workbooks were introduced by the South African Department of Basic Education (DBE) in 2011. Although the workbooks were designed as supplementary materials, in some schools they are used as the sole teaching text. Therefore, an analysis of the content coverage of the workbooks is warranted. This article provides such an analysis in terms of additive relation word problems.Aim: This article aims firstly to expound on the existing literature to propose a comprehensive additive relation word problem typology and secondly to analyse the prevalence of particular word problem types in the foundation phase Mathematics workbooks.Setting: This research was conducted in South Africa, focusing on additive relation word problems in foundation phase Mathematics workbooks.Methods: A comprehensive typology of additive relation word problem types was developed based on typologies used in previous studies. All the additive relation word problems in the 2017 Grades 1–3 foundation phase Mathematics workbooks were categorised according to this typology.Results: In total there were 61 single-step additive relation word problems with numerical answers across the three grades. This is a small number in comparison to other countries. There was also an uneven distribution of problem types, with more problems in the easier subcategories and fewer or no problems in the more difficult subcategories.Conclusion: This article provides evidence for the need to revise the word problems in the DBE workbooks. It also provides a theoretical framework to use in the revision of the workbooks and in any supplementary teaching material developed for teachers.
to English, such isiXhosa, one of South Africa's nine official African languages.This study contributes to the limited research on early grade word problems in languages other than English by examining compare type word problems in isiXhosa. The study offers a sub-typology for compare type (difference unknown) problems, both in English and in isiXhosa. The relative difficulty of the problems in the isiXhosa sub-typology is then empirically tested using data collected from an adapted early grade mathematics assessment (EGMA).The following two research questions are answered in this study:• Are certain types of isiXhosa compare type problem easier for learners to solve than others? • If so, is the relative difficulty influenced by:ß the formulation of the comparative question ß the problem situation?
Theoretical and methodological perspectivesThis article is informed by theoretical perspectives and methodological tools from linguistics that have proved helpful for research into the way different languages express mathematical concepts, as proposed in a recent paper by Edmonds-Wathen (2019). This article also draws on theoretical perspectives from variation theory, a general theory of learning largely developed by Marton and Booth (1997) and later extended by Watson and Mason (2005) in relation to mathematics learning.Edmonds-Wathen (2019) proposes using a typological framing for research on the diversity of mathematical expression in different languages and using interlinear morphemic glossing to present examples in different languages. These perspectives and methodologies are particularly pertinent for studies done by a researcher not fluent in the language that is being studied. Edmonds-Wathen points out that linguists often work with languages that they are unfamiliar with, either by working with translated texts or by working closely with bilingual speakers. She argues that mathematics education researchers can, and do, work in similar ways, with this study being a case in point. This study was undertaken by an English speaker with an emergent understanding of isiXhosa. The researcher worked very closely with a number of isiXhosa speakers to deepen her understanding of isiXhosa, particularly in relation to compare type problems.
A number of post-colonial countries in Africa have introduced home language instruction for the initial years of schooling. This policy is particularly challenging in mathematics, as there is a paucity of research on how the linguistic features of African languages might be leveraged for the teaching and learning of mathematics. This paper examines the linguistic features of certain African languages, pertaining to number names, by describing five linguistic features of one particular African language, isiXhosa. The five features are: syntactical category, transparency, regularity, length of words and differences between spoken and written language. Different early-grade mathematics texts in English and isiXhosa are compared to explore the implications of these features for the learning and teaching of mathematics. The study concludes that there are both constraints and affordances of learning number names in isiXhosa and other related African languages and suggests how the affordances might be leveraged and the constraints mitigated.
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