(Mis)versioning as a quality assurance compromise in the development of numeracy curriculum in African languages

Abstract Along with literacy, numeracy is considered a critical skill that impacts on the success or failure of learners in the formative stages of the schooling system. In the context of the Language in Education Policy, which accords every learner in every public school the right to use the language of their choice in the process of being educated, the numeracy learning area should be taught and learnt in Sepedi. To operationalise this policy provision, curriculum policymakers generally subject learning materials available in English to a translation process and make them available in the various official African languages. This paper discusses the challenges encountered in translating numerical word expressions from English into Sepedi and offers, from a linguistic point of view, solutions to deal with the challenges encountered. Data were collected from existing Sepedi literature, and an analysis was conducted of how numerical word expressions are used and treated relative to how they were translated. To validate the literature’s authenticity in the use of the concepts under discussion, a survey was conducted amongst mature and home-language users of Sepedi. The findings show that there are contradictions in how plural forms of numerical word expressions are used by Sepedi language professionals, as is the case in other literature. This creates a problem for the teaching and assessment of these concepts in the foundation phase of the schooling system. Based on the available evidence, the paper makes an argument against the use of bo- when pluralising cardinal numbers in the context of numeracy. The paper concludes with a call for Umalusi to implement systems to quality-assure learning materials translated from English into African languages.


Introduction
Numeracy is one of the key skills that learners need to acquire early on to establish a sound foundation for better outcomes at all schooling levels. However, the data from national and international standardised tests in numeracy, such as the Annual National Assessments (ANA) administered between 2011 and 2014, and the Trends in International Mathematics and Science Study (TIMMS) spanning 24 years , provide evidence that South African learners perform sub-optimally relative to their counterparts elsewhere in the world (Howie 2005). Simultaneously, since the dawn of democracy in South Africa, much has been written about the factors involved in poor learner performance, including learners being educated and assessed in English, a language in which they are not competent (Heugh 1995;Alexander 2000;Setati 2002;Webb 2004;Madiba 2010). The most recent research conducted by Nunan and Shantone (2022) proves that many years after the dawn of democracy, not much progress has been made in bringing South African learners to a comparable level of achievement in both literacy and numeracy.
To underscore the importance of educating learners in a familiar language, several policies have been developed and refined over time. One such is the Language in Education Policy (LiEP) (Department of Education 1997), which makes provision for every learner in the South African public schooling system to receive education in the official language of their own choice. This lends expression to the provision made in the Constitution of South Africa (Republic of South Africa 1996) for learners to choose out of the 11 official languages the language that they wish to learn in. The provisions stem from the strong link already established through research between home language education and educational achievement, on the one hand, and the importance of establishing good foundations for better outcomes at all schooling levels, on the other hand (Howie, 2005 andSpaul, 2015).
The South African education authorities responded to these Constitutional and policy provisions by translating the Revised National Curriculum Statement (RNCS) (Department of Education 2002) and the subsequent Curriculum and Assessment Policy Statement (CAPS) (Department of Basic Education 2012) from English into the other ten official languages. The same approach is more often than not followed by publishers in translating the policy statements (the NCS and CAPS) into the actual learning and teaching support materials (LTSM). Publishing houses translate the LTSM, conceptualised in English, into African languages. The specific focus of this paper is a translation project initiated by one of the publishing houses in South Africa. The aim of this project has been to translate the series titled All-In-One Integrated Learning Programmes for the foundation phase (Grades 1 to 3). The series was translated from English to isiZulu, isiXhosa, Sepedi, Sesotho and Setswana. This integrated learning programme consists of three learning areas: life skills, literacy and numeracy. These learning areas are supplemented by a teacher's guide and a resource book for teachers. The work presented in this paper is based specifically on the numeracy learning area translated into Sepedi.
The translation or versioning practice persists despite research evidence pointing to its inappropriateness due to the linguistic and pedagogical differences between English and African languages (Koch 2009). One of the major challenges for curriculum designers and publishers alike, which is worth paying attention to urgently, is the determination of whether translated LTSM provide learners with an acceptable and similar level of quality learning. Umalusi, the Quality Council for General and Further Education and Training, is legislatively mandated to uphold standards and quality in the schooling system (from Grade R through to Grade 12), including quality assurance of intended and assessed curricula. Thus, it is Umalusi's role to quality-assure versioned or translated curricula to address the existing epistemic biases in educational materials translated into African languages.
The aforementioned background reveals that there is a lack of research focused on the use of or translations of numerical word expressions or cardinal numbers into African languages in general and particularly Sepedi. Taking this into account, the aim of this paper is to discuss conceptual and linguistic complexities that should be taken into account from a curriculum point of view when dealing with plurals of numerical word expressions to aid in understanding mathematical content adequately in whatever form. The research question addressed is: How should cardinal number plurals be formed in Sepedi in the context of the foundation phase numeracy curriculum?
While the research focuses on texts translated into Sepedi, the researcher expected that the findings would yield useful information to assist in improving the quality and standards of the texts translated or versioned into other African languages. The next section discusses the language situation that gives rise to the practice of translating or versioning of LTSM.

The South African education language policy context
Prior to 1994, Afrikaans and English dominated South Africa's education system as the two main official languages used in the process of learning and teaching. It was during that period that the study of English and Afrikaans as either first or second languages was compulsory for learners throughout the country (Umalusi 2012). In general, the use of indigenous African languages was limited to non-official settings. Since the coming into power of the democratic government, the linguistic situation has undergone an important reform. The linguistic reforms were set in motion by the Constitution of 1996, which declared that in addition to English and Afrikaans, the following nine indigenous languages are also official languages of the country: Sepedi, Sesotho, Setswana, Siswati, Tshivenda, Xitsonga, isiNdebele, isiXhosa, and isiZulu. In addition to directing the state to ensure that the status of these official languages is elevated and their use is advanced, the Constitution provides for all official languages to be treated equally (Republic of South Africa 1996).
Thus, the South African Constitution is firmly committed to equal treatment of all 11 official languages in all spheres. In fulfilling the obligations imposed by the Constitution in respect of assuring parity of esteem and equal treatment of all official languages, the then Department of Education (1997) introduced the Language in Education Policy to foster the principle of equality in the treatment of the 11 official languages for the purposes of teaching and assessment. The policy is explicit in terms of the right of every learner in every public school to use the language of their choice in the process of being educated. This includes receiving numeracy education in their preferred language.
In a similar vein, all official languages receive equal treatment in terms of their curriculum. A common core curriculum for all of South Africa's 11 official languages was designed and implemented. As it was conceptualised in English and 'versioned' into the other official languages, the home language curriculum is the 'same'. In addition to introducing 11 official languages as subjects and media of instruction in public schools, language standardisation policies were implemented to bring about the equivalence of different home-language examinations. This, then, is the brief general context. The paper now turns to the specific environment in which this study was undertaken.

Defining key concepts
The numeracy learning area makes extensive use of numerals of two types, i.e. ordinal and cardinal numbers. In order to lead a clear argument, these two key concepts should first be defined. For the purpose of this paper, cardinal numbers are defined as number words that are used to denote numerals. cardinal numbers differ from ordinal numbers in that the latter are used to show the order of things. The following sentences exemplify this difference.
(1) Ge o ntšha šupa mo go lesome go šala tharo. / When one subtracts seven from ten, the difference is three.
(2) Go na le dipukuntšu tše nne ka ofising ya moprofesara. Pukuntšu ya bone e ngwadilwe ka morago ga go gatišwa ga ya boraro. / There are four dictionaries in the professor's office. The fourth dictionary was compiled after the publication of the third one.
In Example (1), the number words šupa, tharo and lesome are used to denote the numbers being referred to. In Example (2), the words bone and boraro in the adjectival word groups ya bone and ya boraro, respectively, do not refer to any numeral. Instead, they are used to indicate the order in which the dictionaries were compiled. They are thus called ordinal numbers. All ordinal numbers, irrespective of the class of the noun which is qualified, take the prefix bo-. Now that the paper has distinguished between cardinal and ordinal numbers, what remains is to determine the word class of cardinal numbers.

Cardinal numbers in the existing literature The word class of cardinal numbers
As regards the grammatical description of lemmas in a dictionary, Gouws and Prinsloo (2005: 124) state that 'Dictionaries are often consulted for the verification of the part of speech of the word represented by the lemma sign'. With regard to numerical word expressions, the question that is likely to confront the numeracy teacher or the lexicographer dealing with numerical word expressions as an onomasiological sub-field is: 'What is the grammatical status of cardinal numbers? In other words, do numerical word expressions have one or more than one part of speech function?' Just like certain word categories, cardinal numbers can have more than one part of speech function. They can be used either as adjectives or nouns. According to Louwrens (1994: 3), when fulfilling an adjectival function, the number word appears in a word group consisting of a qualificative particle and an adjective, as in the following example:
Here the adjective seswai, meaning 'eight', is preceded by the qualificative particle tše. In this context, the numeral seswai has been used as an adjective to describe the noun dikgomo, meaning 'cattle', with regard to number. In a different context, the numeral can be used to fulfil the function of a noun. For example:

Nouns
(4) Seswai ke nomoro ye e bopšago ka go hlakanya nne le nne ye nngwe. / Eight is the number you get when you add four to another four.
(5) Ge o ruta bana go bala dipalo, thoma ka tee o fihle ka lesome. / When you teach children to count, start with one up to ten.
What brings about the difference between the word seswai in (3) and that in (4) is the context in which they have been used. The words tee, meaning 'one', and lesome, meaning 'ten', in Example (5) above have the same part of speech function as seswai in (4). This is crucial information and such cases warrant careful treatment in a Sepedi dictionary. In two recent dictionaries, the Online Explanatory Northern Sotho Dictionary, which has now been taken off the internet due to logistcial constraints, and Sesotho sa Leboa Pukuntšu (Mojela et al. 2006), compiled by the same lexicographers working within the Sesotho sa Leboa National Lexicography Unit, one discovers that there are serious inconsistencies regarding the labelling of the parts of speech of numerical word expressions. Examples are shown in Table 1.
As can be noted, the dictionaries suggest that number names can perform up to five different parts-of-speech functions. Firstly, whereas the Online Explanatory Northern Sotho Dictionary treats all the number names, with the exception of tee, meaning 'one', as adjectives, the Sesotho sa Leboa Pukuntšu suggests that only pedi, tharo, tlhano, šupa and senyane are adjectives. Secondly, the online dictionary regards tee as an adverb, implying that tee can be used to modify the meaning of verbs. Thirdly, the bilingual dictionary indicates that tshela, meaning 'six', functions as a verb and neither as a noun nor an adjective. These are serious grammatical problems that lexicographers need to be aware of and address when compiling dictionaries. Adequate treatment of such problems is one of the crucial aspects leading to better dictionary articles.
So far, we have seen that numerical word expressions or cardinal numbers can perform more than two functions as parts of speech, one of which is nouns. The next question is: 'When used as nouns, how are numerical word expressions or cardinal numbers pluralised?' The aim of this paper is to investigate this, i.e., the proper method of forming cardinal number plurals in Sepedi. As space restrictions do not allow for the treatment of all the numerical word expressions, the presentation will focus only on the basic numbers, i.e., one (1) to ten (10).

The formation of cardinal number plurals in Sepedi
It is common knowledge that in Sepedi, noun plurals 'are formed by replacing the singular prefix with the corresponding plural prefix' (Van Wyk et al. 1992: 7), as in: This is the generally accepted way of forming noun plurals in Sepedi. The introductory section of this paper mentioned that numeracy is one of the learning areas that curriculum implementers normally translate from English into African languages, including Sepedi. For example, NB Publishers' series called All-In-One Integrated Learning Programmes authored by Meij and Sullivan (2003) has been translated into various African languages for use in the foundation phase (Grades 1 to 3). In the English version of the numeracy learning area, one finds, amongst others, instructions such as the following: (7) Write 3 rows of 2s with different colours.
(8) Count in 5s and join the dots.
Because the numbers 2 and 5 are expressed in figures, to translate the whole sentences, translators need to go through several steps. Firstly, they should substitute the figures 2 and 5 with numerical word expressions: (9) Write 3 rows of twos with different colours.
(10) Count in fives and join the dots.
Secondly, they need to provide translation equivalents for the bolded words in singular: Finally, the translator can apply the rules of grammar to pluralise pedi and tlhano. As suggested by Van Wyk et al. (1992: 7), the translator would replace the singular prefix with the corresponding plural prefix. To someone who is knowledgeable of grammatical conventions, this seems to be a straightforward task. However, as both pedi and tlhano do not display any class prefixes, at this stage, the poor translator does not succeed in forming plurals. It seems that this type of exercise is a difficult one. This was confirmed during an interview in which one interview respondent remarked as follows: 'I would like to see the findings, this wasn't [an] easy task'.
To perform this task successfully, one must know that when functioning as nouns, all the Sepedi numerals from one to nine belong to class 9. 'The class prefix of this class is always a nasal… which is deleted after it has caused sound strengthening' (Lombard et al. 1985: 44). But not everyone has this intuitive knowledge, as we will demonstrate later in this paper. After consulting with one another, the translation team members realised that their assumptions led them astray, as they could not agree on the plural prefix for the number names. The team then decided to look up those words in the existing Sepedi dictionaries in the hope that they would provide guidance on how the plurals should be formed.

The treatment of cardinal numbers in existing Sepedi dictionaries
Unfortunately, as far as cardinal number plurals are concerned, a systematic trawl through existing Sepedi bilingual and monolingual dictionaries did not reveal anything substantial. Amongst the dictionaries consulted are Hartshorne et al. (1984), Kriel (1976), Kriel (1983); Kriel et al. (1989), Kriel et al. (1997), , Prinsloo et al. (1997) and Ziervogel and Mokgokong (1988). The available dictionaries treat only the singular forms (with no indication of class or gender), suggesting that cardinal number plurals do not exist. Even in the Northern Sotho Terminology and Orthography No. 4. (Departmental Northern Sotho Language Board 1988), which claims that "Terms included in this list, are intended in the first place for use in the primary school and have mainly been taken from syllabuses from the various subjects of the primary school. Terms that were required after the introduction of the new syllabuses and the "new approach" accompanying them, were also incorporated as far as possible (e.g. for Mathematics and General Science), one will look in vain for number plurals.
Depending on the context within which they occur, cardinal numbers may be used as adjectives and again as nouns. In the following examples the words bahlano and mabedi are adjectives appearing in word groups consisting of a qualificative particle, prefix and stem.
(13) Maloko a lesome a AFRILEX ga se a tsošološa boleloko bja ona mo ngwageng wo. / Ten members of AFRILEX have not renewed their membership this year.
In Example (12), ba is the qualificative particle, the prefix of bahlano is ba-, and -hlano is the stem. In Example (13), the qualificative particle is a, le-is the prefix, and the stem is -some. It is for this reason that most grammarians classify the number words as adjectives in Sepedi. In terms of a different context, however, number words can be used as nouns, as in: (14) Tlhano ke nomoro ye e hwetšwago ge go hlakanywa tharo le pedi. / Five is the sum of three and two.
(15) Ge o ruta bana go bala dipalo, thoma ka tee o fihle ka lesome. / When you teach children to count, start with one to ten.
In the context of these two sentences, the number words tlhano, tee and lesome function as nouns because they refer to numerals. And, in turn, they can be grouped into noun classes. This immediately implies that these cardinal numbers have both a singular and a plural form, although a cursory glance at them might lead one to conclude that number plurals do not exist in Sepedi. It is, therefore, not surprising that existing Sepedi dictionaries do not provide the necessary data for a sound treatment of cardinal number plurals. To put it differently, they do not include class information for every singular number to tell the user implicitly how the plural should be formed. The fact is that, in general, language plurals of numbers do not appear to be frequently used. At the same time, however, a review of mathematical sources reveals that cardinal number plurals do exist, as those materials, especially those used in the foundation phase, do make use of them.

Cardinal number plurals in existing Sepedi literature
The literature review has shown that Gleimius et al. (1979) and Fletcher and Moloise (1974) are the only authors who have treated plurals for Sepedi cardinal numbers in their work. The analysis of these sources shows, however, that there are two conflicting methods used in the formation of cardinal number plurals. As far as the first method is concerned, the prefix bo-(of noun class 2a) is added to a number word to denote plurality. Consider the following examples: (16) Na ke botharo ba bakae ka mo go 18? (Gleimius et al. 1979 (18), one can clearly see that the plurals of most numbers end up in two different classes. However, notwithstanding the fact that both bo-and di-are used to express plurality in the Sepedi cardinal numbers (0 to 9), the type of plurality expressed differs in each case (cf. Van Wyk 1987). The question that arises from this is: 'Which plural prefix should be used consistently in treating cardinal numbers in Sepedi?' I will return to this question later in this paper. Seeing that translators, existing dictionaries and literary works do not offer a suitable solution to the problem, the next logical step was to do a survey among Sepedi language practitioners.

Research question
This paper employs a qualitative method in addressing the research question: 'How should cardinal number plurals be formed in Sepedi in the context of the foundation phase numeracy curriculum?' In answering the research question, a questionnaire was designed and administered to a selection of participants. The profile of the participants is described below.

Instrument
The instrument used in retrieving information from the participants regarding cardinal number plurals was a two-page questionnaire comprising two sections. The first section explicitly dealt with the plurals of numbers. To be more specific, a table with three columns was designed. All the singulars for the numbers were written in the first column, and the second and third columns were reserved for the participants to indicate the plurals for these numbers. In the second part of the questionnaire, the participants were asked a few general questions about their background. In order to ensure answers that were as honest as possible, the questionnaire was completed anonymously.
Furthermore, to determine alignment between participants' responses and the concrete use of the language in real texts (language authenticity), the Pretoria Sepedi Corpus (PSC) (SADiLaR 2018), which at the time of this study contained approximately six million words, was queried. The value of the corpus queries lies in the fact that they indicate the plural with the highest frequency of use or the most frequently used numeral in Sepedi.

Participants
The questionnaire, prepared in Sepedi, was distributed to a sample of 20 seasoned language worker participants. The sample was small because it was decided to limit the survey to people working in the Sepedi language environment. In other words, people who work with the language every single day. The participants included lexicographers, translators and terminologists. The respondents are not only language professionals but also mother-tongue speakers. Of the 20 respondents, 8 were males and 12 were females. As regards age, it is interesting to note that all of the participants are mature language users, as shown in Table 2.

Data analysis
Data were analysed by way of thematic content analysis. The themes arising from the collected data were clustered under the four broad headings of (a) suggestions for the plural of tee, (b) pluralisation of numerals from pedi to tlhano, (c) pluralisation of numerals from tshela to senyane, and (d) the suggested plural for lesome. The fifth and final theme is based on the frequency of occurrence of the pluralised numerals in the Sepedi corpus.
The next section presents the results emanating from the analysis of the responses of the participants.

Findings
Theme 1: Suggestions for the plural of tee (one) I deal first with tee, meaning 'one', since it is the numeral with the fewest suggested plural prefixes. In terms of corpus queries, tee is one of the most frequently used numerals in Sepedi, as it has 5 207 occurrences in the PSC, which stand at approximately six million words (SADiLaR 2018). In other words, tee belongs to the top 100 most frequently used words in Sepedi.
The information presented in Figure 1 shows the distribution of the participants' preferences in terms of the plural prefixes for tee. This graphic presentation shows that the respondents suggested four different plural prefixes: bo+, di+, ma+ and ba+. Of these four, bo+ and di+ are the most preferred plural prefixes. This does not come as a surprise because, in the context of the responses, both ma+ and ba+ function as adjectival prefixes. Thus, they are not truly plural prefixes. Regarding bo+, Figure 1 shows that it was preferred by 45% of the participants, while 40% suggested that di+ should be used in pluralising tee. We now move on to deal with the next thematic area.

Theme 2: Pluralisation of numerals from pedi (two) to tlhano (five)
As shown in Table 3, even though we are dealing with up to five or six possible plurals for one form of the singular, the intuition of the average mother-tongue speaker indicates that the most preferred strategy to pluralise numerals from pedi (two) to tlhano (five) is to prefix these numbers with bo+ (as in bo+nne = bonne). The second-most preferred strategy is to prefix di+ (as in di+nne = dinne), followed by the strategy to prefix with ma+ (as in ma+hlano = mahlano).
Here, it is interesting to note that the results for bo+ are similar to those for di+. In other words, the participants see no semantic difference between the use of bo+ and di+ as prefixes to turn a numeral in singular into a plural form. The implication of this is that either bo+ or di+ can be used at the beginning of a singular numerical word expression to form a plural.
I will now focus on the participants' suggestions on how to pluralise tshela, šupa, seswai and senyane, that is, the numbers six to nine.

Theme 3: Suggestions for the plural of tshela (six) to senyane (nine)
As is the case with the numbers from pedi (two) to tlhano (five), the opinions of the respondents are that either bo+ or di+ can be used at the beginning of a singular numerical word expression to form a plural for any numeral from tshela (six) through to senyane (nine), as shown in Table 4.  As in the case of pedi (two) through to tlhano (five), the same pattern of suggestions is evident here. By way of example, in turning the numerals into plurals, tshela (six) becomes botshela when using bo+, the most preferred option, or ditshela when one uses di+. The same applies to senyane (nine), as it becomes either bosenyane or dinyane. So, it can be concluded that from pedi (two) to senyane (nine), the preferred prefixes are bo+ and di+. Figure 2 compares the preferences of the respondents with regard to the three prefixes bo+, di+ and ma+ for the first nine numerals. The graph shows that for pedi (two), tharo (three), nne (four) and tlhano (five), bo+ and di+ can be used interchangeably because the overlap is substantial. From tshela (six) to senyane (nine), there is an almost 50:50 split between preference for bo+ and di+. Regarding the prefix ma+, only a minority suggested its use as the plural prefix for numerals.

Theme 4: The suggested plural for lesome (ten)
This fourth theme presents the opinions of the participants in terms of which prefix to use when turning lesome (ten) into a plural. This is juxtaposed with the occurrences of the numeral in plural in the corpus.   The second column of the table represents the frequency of occurrence of the word lesome (ten), while the third shows its plural forms in the corpus. Columns five and six show the participants' preferred options.
As can be noted in Table 5, few participants tried to force the prefix di+ onto lesome. A total of 8, or 40%, of the mother-tongue speakers opt for masome as the first option and another 40% as the second option. It is clear from the fieldwork that this noun belongs to class ma-for the plural. The responses are in line with the concrete use of the language in real texts, as the results of corpus queries indicate that masome is the plural with the highest frequency of use. This brings me to the final theme, which is not based on the responses of the participants, but rather on the frequency of the occurrence of the numerals in the corpus.

Theme 5: Frequency of occurrence of the plural forms in the corpus
It has already been stated that the corpus is a valuable resource that indicates the plural form with the highest frequency of use in real-life situations. The PCS frequencies for the plurals of the cardinal numbers from tee (one) through to senyane (nine) have been summarised in Table 6.
In the first column in the table above, we present the numerals, while the second column shows the frequencies for each numeral in singular. The third and fourth columns indicate the frequencies for each corresponding plural. As far as the plurals are concerned, one notes that the corpus contains relatively few occurrences. Although the frequencies for botee (meaning ones) and bošupa (meaning sevens) are indeed telling, one must also carefully consider the context to see whether they are truly plurals of the numbers. The analysis of the occurrence of each numeral with the prefix bo+ in the corpus shows that the numbers that take bo-as a prefix do not always refer to plurals.

Discussion
The paper argues that in the formation of plurals in the context of the foundation phase numeracy curriculum, the prefix di+ should be used instead of bo+. The foregoing examples show the semantic differences that exist between the plurality expressed by the prefix bo+ and that indicated by di+. As the prefix, ma+ does not receive much support from the results of the survey. Therefore, it need not be considered in the context of the search for the plurals of cardinal numbers.  There are three reasons why this paper argues against the use of bo-as a plural prefix for cardinal numbers. Firstly, an important difference between bo+ and di+ lies in the meaning expressed by each of them. When commenting on the use of bo+ as a plural marker, Van Wyk (1987: 35)

maintains that
Bo-is frequently used as a marker of respect or status without implying plurality, a fact which seems to have been overlooked by all authors of Northern Sotho except Nokaneng (n.d.: 35).
That bo-does not express distributive plurality is a fact supported by Taljard (2001). With reference to days of the week, Taljard writes that there is a distinct semantic difference between the plurality expressed by bo+ and di+: The prefix bo+ is often used to indicate associative plurality. Usually, ordinary plurals express distributive plurality, thus monna 'one man', but banna 'many men'. When one uses bo+ it can indicate the same kind of plurality, but it can also indicate associative plurality. Thus, botate can mean either 'fathers' in the sense of one, two, three, four fathers (e.g. These kids all have different fathers), but it can also mean 'father and company' i.e. other people who are associated with him on the basis of certain shared semantic features (e.g. father and his brothers, father and the other members of the kgoro, etc.). The prefix bo+ very often expresses associative plurality when used together with adverbs... Secondly, as seen in the foregoing examples, the prefix bo+ is often used with adjectives, in which case it is followed by an adjectival stem. Thirdly, it has been shown that numerical word expressions have undergone sound strengthening. They are, therefore, class 9 nouns. Furthermore, according to Van Wyk et al. (1992: 7), 'Plural forms of nouns in class 9 are formed by placing the plural prefix di+ to the left of the entire singular form'. Thus, it is necessary to end this section by re-emphasising the point that di+, and not bo+, should be used consistently when pluralising cardinal numbers in the Sepedi versions of the numeracy learning material.

Conclusion
This paper has discussed conceptual and linguistic challenges that are encountered in versioning or translating cardinal numbers into African languages in curricula conceptualised in English. Based on the research evidence gathered, together with the associated corpus queries, the specific argument of the paper is that in the formation of plurals of numerical word expressions in Sepedi, the prefix di+ should be used as opposed to bo+ in the context of the foundation phase numeracy curriculum. This is because the associative plurality expressed by the latter differs semantically from the distributive plurality that is expressed by di+.
To ensure adequate understanding of mathematical content in whatever form, there is a need for versioned or translated mathematical curricula to be responsive to the character of African languages. Clearly, Umalusi, the body that is legislatively mandated to, inter alia, perform quality assurance of school curricula from Grade R through to Grade 12, should subject the versioned or translated materials to rigorous quality assurance processes to address the existing epistemological biases, especially in the formative years of the schooling system. This forms an integral part of the enhancement of the quality of general and further education and training. Otherwise, it will always be difficult, if not impossible, to realise the Constitutional commitment of equal treatment for all official languages. Similarly, the provision made by the Language in Education Policy for every learner to receive education in their preferred language will remain a moving target. At the same time, this should provide the stimulus for research, reflection and debate, which make the next iteration of the curriculum possible.