1. Iterations of translations from German to four South African languages in a mathematics competence test Iterations of translations from German to four South African languages in a mathematics competence test Elizabeth Henning & Lara Ragpot

2. VYGOTSKIAN LENS - LANGUAGE  External speech becomes internal speech (thinking)  Words are thus semiotic tools that do not actually form, but that facilitate concept formation  Words become placeholders during conceptual change (Carey, 2009)  Words are agents for assembling information to form concepts (Spelke, 2012)

3. Elizabeth Spelke  “(n)atural language plays a pivotal role in the development of abstract numerical and geometric concepts and does so by serving as the primary medium for combining information productively across distinct systems of core knowledge” (Spelke, 2012: 312)  “Once a speaker has learned the terms of a language and the rules by which those terms combine, she can represent the meanings of all grammatical combinations of those terms without further learning. The compositional semantics of natural languages allows speakers to know the meanings of new wholes from the meanings of their parts” (Spelke, 2003: 307)

4. Stanislas Dehaene (2011:263) argues for the  “universality of the number sense and its presence in any human culture, however isolated and educationally deprived” and that  “(p)rogess on the conceptual scale of arithmetic depends on the mastery of a toolkit of mathematical inventions. The language of numerals is just one of the cultural tools...”

5. Some issues to consider with an interview format test Language serves as combinatory agent in assembling knowledge to form concepts once children learn through language and other symbols (Spelke, 2012; Carey, 2009) Thus young children lodge much of their early understanding of maths (in the forming of concepts) in their use of language. Tests that assess their knowledge in oral interview format is thus not free of the effects of language, although, after many iterations, such a test could come close to a reliable translation.

6. So what? We have some evidence from the research on 3000 children that language effect can be minimised (if not completely neutralised) to ensure unidimensionality of the instrument used to test mathematics competence.

7. SOUTH AFRICA: Language - some background 11 Officials languages Marko test translated into 4 languages English home language & English first additional language split? Progression of translation process Test is now in its14 th iteration in the translation process Various people contributed to the translation process

8. Some of the results, pertaining to number words. Number names as activity: In isiZulu “shiya” means to “leave behind or abandon.” Thus, for example, “ yisishiyagalombili” means you leave two behind. This gives an indication of moving on with the new quantity. It gives a clear image of partitioning and pre-empts an understanding of part and whole while the learner is still at the counting level. Number names as ‘to be’: Some counting names pre-curse cardinality. Number names as concrete notions Number names that presuppose finger counting

9. Item 5 English “What number is between 5 and 7? Supposed to be a level 2 question. SeSotho children struggled with this SeSotho“Ke palo efe e tlang mahareng a hlano (5) le supa (7)?” Direct English translation “On the outsides (poles) of five and seven what number is in the middle?” Raises question from a level 2 to a level 4 question

10. DIFFERENCES Item 29 “What number is one smaller than 5?” “Lyiphi inombolo engaphansi ngo-1 ku-5?” (isiZulu) Directly translated the isiZulu says: “What do you get when you take 1 away from 5” “Ke palo efe e nyane ho hlano (5) ka nngwe?” (seSotho) Directly translated the seSotho says: “What do you get when you have 5 and you take away 1” Originally this item is on level 5 – because of the translation the answer is already evident in the question Takes the level of the question back on the number line – which is level 2/3

11. DIFFERENCE Item 30 English: “What number is one bigger than 7?” isiZulu: “Lyiphi inombolo engaphezulu ngo-1 ku- 7?” Directly translated the isiZulu says: “What do you get when you add 1 to 7” Sesotho“Ke palo efe e kgolo ho supa ka nngwe?”(Sesotho) Directly translated the Sesotho says: “What do you get when you add 1 more to 7” Originally this item is on level 3 – because of translation, it takes the level of the question to level 2

12. Items 36 and 37 Results for item 36 was comparable in all four of the languages Item 37 was problematic for Afrikaans, isiZulu and Sesotho Why? Translation – difference between 36 and 37

13. ITEM 36: Here are 4 stars, and behind the clouds are hiding another three stars. How many stars are there all together?

14. ITEMS 50 and 51: F RUIT English: “Can you divide the fruit (10) for Bongani and Naledi so that both have the same? Put the fruit by Bongani and Naledi.” Meaning of ‘fruit’ is too general isiZulu translation – the isiZulu word for ‘fruit’ is ‘lezithelo’ which can mean ‘fruit’ or it can mean ‘stuff’ (things) seSotho: “Na o ka arolela Bongani le Naledi ditholwana ka ho lekana? Beha ditholwana pela Bongane le pela Naledi.” seSotho children struggled as they were confused by the word ‘fruit’, as fruit in seSotho ‘ditholwana’ and this can mean fruit as in food or fruit as in ‘consequence/outcome’ ‘Arolela’: - ‘give a part of, divide unfairly”

15. THANK YOU BAIE DANKIE KE A LEBOHA NGIYABONGA