Requisitos básicos para que la batería de filtros sea

M ore than 75% o f the w hole cohort comes w ithin this age range. Thus, I claim they are a sam ple o f “typical cases” (Lincoln and G uba, 1985, p. 200)

T able 5.1: T en participants interview ed in T ier 2

Participants in T ier 2

G ender COSC grade P articipant In T ier 3

B eatrice Fem ale Pass

M osha Fem ale Pass

N om sa Fem ale Pass ❖

Sebu F em ale Pass

_ j ❖

Tseli Fem ale Pass ❖

Litha M ale Credit ❖

M otati Female Credit

Thandi Fem ale Credit ❖

M able Fem ale Fail

M inah Fem ale Fail

A n alysin g P articip an ts’ R esponses

It w as established in C hapter 4 that m an y student teachers considered

m athem atics as a ‘challenging venture’ that dem ands effort and critical thinking from learners. B ecause this perception o f m athem atics em erged as a th em e w ith the greatest w eight in C h ap ter 4, it was im portant to consider this perception w hen analysing the transcripts. It w as again observed in C hapter 4 that students expect the m athem atics courses offered at the college to equip them w ith skills that w ill enable them to ‘develop a n understanding o f m athem atics’ and T eam how pupils le am m athem atics

easily’. These ideas that were m entioned by th e m ajority o f participants in T ier 1 are useful in looking at the extent to w hich they influence stu den ts’ thin kin g as they talk about the answ ers they gave to tasks in Section 2 o f th e survey instrum ent. In order for m e to perform detailed analysis I choose to focus on each o f th e ten students as a particular case b y studying one transcript at a tim e so that all ten transcripts can be reported thoroughly and a com posite picture drawn.

B e a tric e ’s C ase

A t th e beginning o f this project in Tier 1, B eatrice w as tw enty-six years old. B eatrice is a w om an from Leribe district. The record o f h er perfo rm an ce in school m athem atics show s that she has achieved a relatively good grade in m athem atics in national exam inations. For instance, in Standard 7 exam ination she obtained a first class (1st class) in m athem atics, in Form C she obtained a sym bol C, and in Form E she obtained a pass. From an analysis o f B eatrice’s w ork on Section 2 o f the survey instrum ent (tasks) I realise that it is only task 1(a) that is incom plete; and all other tasks are correct. D uring the interview , B eatrice w as asked to give com m ents on her w ork on tasks 1(a), 6, and 7, and she was further asked about representations she could u se in h er class w hen on teaching practice.

T he follow ing excerpt presents the conversation I had w ith B eatrice w ith regard to task 1(a):

B eatrice: I really d id n ’t know w hat to do in th is problem , but I th in k i f I could use like ... w hen I look at it closely now I think I can have w ays o f struggling w ith it.

B eatrice: I f I can say this is a sort o f ... w hat these pictures ... I rem em ber I did som ething like this in m athem atics lectures ... as a sort o f a num ber array. H aving been taught how to use the num ber array I th ink I can tackle this problem now.

Researcher: A lright, w hat w ould be the answ er? Beatrice: C an I please w ork it out?

Researcher: O K ...

Beatrice: M y first num ber is 17 and w e subtracted 5 from it. W hat I w ill do is ju s t to shade these pictures differently and get m y num ber. {Initially B eatrice h a d sh ad ed ju s t 12 counters). I ’ll shade this one {referring to 17), as I have already shaded it in this w ay and this one {referring to 5) w ould ju st m ark the process on it and get th e answ er ...

A ccording to the excerpt above, B eatrice had encountered som e problem s w hen solving this task in T ier 1 because she could n o t recognise the relevance o f the diagram accom panying the task. She also om itted to w rite d ow n th e answ er (12). H ow ever, at th e tim e o f interview B eatrice w as w ell able to m ake connections betw een the tw o representations. This is because as she puts it, she “did som ething like this in m athem atics lectures” .

B eatrice w as then asked to com m ent on task 6, w h ich involved m oney to be spent on buying exercise books. In T ier 1, B eatrice had provided th e follow ing textual explanation:

Figure 5.1: Beatrice’s response to Task 6

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This explanation ties well w ith w hat she said during th e interview . U nlike m ost o f her peers w ho solved this problem w ith repeated subtraction o r addition, B eatrice recognised it as division w ith a grouping structure. She suggests “sm all stones” as counters that w ould be used to represent m oney for learners in buying books. T hese could be used as an enactive representation o f th e problem . It is interesting that w hile B eatrice suggests this representation for item 6 she did not recognise th e iconic array in item 1 as counters that could b e used to represent the operations. P erhaps th e static nature o f the diagram s presented in tasks 1(a) and (b) w as n o t helpful to her thinking, since she did n o t recognise the co u nting properties o f the tw o representations as com m on or possible for both.

W hen w orking ou t the solution to Task 7, B eatrice gave a detailed account in th e form o f a text th at enabled her to obtain th e correct answ er (36). T h e follow ing extract presents B eatrice’s work:

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Figure 5.2: Beatrice’s response to Task 7

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