https://orcid.org/0000-0001-9756-6622
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ABSTRACT
The comparison of different languages in terms of specific mathematical ideas can provide insights into the nature of mathematics and into the learning and teaching of mathematics in both languages. This paper uses a typological perspective to contrast the language of comparison of isiXhosa and English, specifically when comparing countable quantities and numbers. Four canonical early grade mathematics texts in South Africa, written in English and translated into isiXhosa, were used as a source and were compared using interlinear morphemic glossing. An analysis of the texts exemplifies differences between isiXhosa and English. For example, in isiXhosa the word ngaphezulu can mean both “more” and “above”. This can cause a conflict when using representations such as the standard hundred chart where bigger numbers appear below smaller numbers. These and other findings may be of interest to instructional designers, teacher educators, and teachers of early grade mathematics in both isiXhosa and English.
Acknowledgements
This study would not have been possible without the insights of many isiXhosa speaking colleagues and friends, in particular: Amanda Zazini, Sindiswa Mtati, Ms Yekwa, Mrs Didi, Nobuntu Mazeka, Zinyaswa Zuma, Bambelihle Nkwentsha, Zola Wababa, Zikhona Gqibani, Nolutsha Parafini, Mashiya Pithi, Sinovuyo Mcunukelwa, Bulelwa Galada, Bomikazi Njoloza, Silondiwe Madikizela and Hlumela Mkabile.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 isiXhosa is one of four Nguni languages spoken in South Africa, the others being isiZulu, isiNdebele and siSwati. isiXhosa is spoken by more than 8 million South Africans (of a total of 57 million). As a Bantu language, isiXhosa has many linguistic features that differ substantially from the linguistic features of English and other Indo-European languages.
2 Modality refers to linguistic devices that indicate the degree to which an observation is possible, probable, likely, certain, permitted, or prohibited. For example “Sive must be home” and “Sive might be home” have different modal meanings.
3 See Comrie, Haspelmath, and Bickel (Citation2008) for the Leipzig glossing rules used widely in linguistics
4 IsiXhosa is an agglutinative language and words are made up of many morphemes.
5 In linguistics the > sign signals that two letters have combined and are replaced by one new letter.
6 The prefix kuna- is made up of the locative prefix ku- and the connective prefix na- and should technically be glossed as ku-na “by-with”. However, for the purposes of this paper kuna- will be glossed as “compared.to”.
7 The alternative forms of ku- are kwi-, kwii-, and koo-
8 nga- is the instrumentative prefix used to describe an instrument e.g. She wrote in the sand by means of (with) her finger.
9 A locative adverb is a type of adverb that refers to a location or to a combination of a location and a relation to that location
10 The alternative forms of kuna- are kune-, kunee-, kuno- and kunoo-
11 The alternative forms of kwa- are kwe-, kwee-, ko-, koo-
12 We distinguish between “reach a target” problems which involve one set and “equalise” problems which involve two sets. While the early work on additive relation word problems included equalise problems (see Carpenter and Moser (Citation1983) as well as Riley, Greeno, and Heller (Citation1983)), later work generally excludes this category. See Mostert (Citation2019a) for a more detailed discussion about equalise problems.