Part 3: Three learner stories emerging from across the data sources

All club sessions from May 2012 to May 2013 were video recorded and transcribed. However detailed analysis of all the transcripts is beyond the scope of this thesis. Instead transcripts were read and sections were coded for where aspects of learner dispositions in terms of the indicators given in the tables above were evident for the three case study learners. For each learner, critical incidents within all club sessions were also examined to further illuminate possible disposition patterns.

Then, in line with my chosen methodology of using learner stories as one of the main methods of characterizing dispositions and analysis (Carr & Claxton, 2002; Sfard & Prusak, 2005; Heyd-Metzuyanim & Sfard, 2012) I developed and present 3 learner stories compiled in large part from:

1) The Wright et al (2006) interview assessment Instrument results for each learner 2) Analysis of all the videos of the club sessions with these three learners plus illustrative

critical incidents in these sessions of each learner.

3) The Productive Disposition Instrument interviews of the three learners (the above stories are included here where relevant)

5.4.1 Saki’s Story

Saki began the club in May 2012 with extremely weak mathematics skills and a complete dependence on the concrete and a failure to see patterns. We are yet to see evidence of him sense - making as a key aspect of his mathematical working in club sessions and throughout the data collection process no data collected showed evidence of this aspect of a productive disposition for Saki.

In the timed procedural fluency assessment (i.e. the doing of operations (See Table 7 for data and Appendix B for the instruments): add and subtract numbers up to 10; doubling e.g. 5,13,15,16 etc., and add & subtract 10 to a number Saki showed some improvement in scores over the year. Thus in the first timed test in 2012 Saki managed only 2 out of the 153 possible sums (only 1.3%) while in 2013 he managed 7 out of the 153 sums (i.e. almost 4.5%). While his doubling score remained constant his addition and subtraction up to 10 and of 10 to a number improved.

In the Wright et al.’s (2006) instrument interview conducted by the facilitator in May 2012 (see Appendix D for an example of a filled in interview schedule), he lost track when counting backwards and could not read 1025, and he had no idea of a ½ or a ¼. With regard to his dependence on the concrete, he also adhered to 1-to-1 counting as indicated in Wright et al. (2006) interviews. While he attended all club sessions and also worked to answering questions, most of all in the homework books (showing the most resilience and steady effort among the three in respect of the homework), it has been hard to shift him forward to conceptual thinking and seeing patterns rather than 1 to 1 concrete finger counting. For example: saying to him 10 + 2; 10 + 3; 10 + 4 and pushing him to see the pattern (of say just adding one more in each case) rather than looking at and counting on his fingers. His attention struggled to focus on seeing the pattern. Thus he would count on his fingers starting at 1. More recently (May 2013) the facilitator noted more progress with seeing patterns although he still struggles to see and use the abstract patterns (personal interaction).

The recorded club sessions showed Saki as confident in his homework book-work which he showed the facilitator at the start of sessions. There is evidence that his reasoning to support this view of himself as being strong at maths, is that he sees the mere doing of maths as making him clever, thus for example in the interviews he says in response to why he likes maths? , “because it will make me clever” coupled with his pattern of ‘steady effort’ in doing quantities of homework well above the

class average. He sees his ongoing participation in the club and ability to do the concrete way as what being good at maths is. He does not envisage what is needed in order to see mathematics as

sensible, useful, and doable (elements of productive disposition). Though in regard to doable, he

exhibits a strong measure of steady effort in his homework book and in class.

Saki had advanced since May 2012 in the degree to which he could articulate in words his opinions and feeling about mathematics. Thus in May 2012 in responding to questions posed in the SANC Productive Disposition Instrument interviews: (e.g. What is maths? Tell me about Mpho in the classroom? Tell me about Sam in the classroom? Etc.) Saki could only provide limited explanations often only one-word answers, but by mid-2013 he has elaborated more on each question, using examples of maths objects in his explanations. (See Table 4). For example, Saki response to Maths is….. in May 2012 all he says is: “(Die beste!) It is the best!” By May 2013 responding to the same question he says: “(goed om the leer want did help)…..is good to learn because it helps… (om goed

in die class is wil leer) ….it is good to learn in the class……..(ons doen wiskunde tel, plus, minus, as gelye, skryf nommers)…..we learn maths [to] count, to add, to minus, divide, write numbers. …

(klub lekker want jy tel jou same)…...the club is nice because you count your sums.” (SANC Productive Disposition Instrument, May 2013 – Saki)

In the club sessions he chose to remain quiet (even when probed and encouraged) possibly to cover himself from embarrassing himself in providing wrong answers unless he is helped and pushed to think and answer. He appears very shy and answers very quietly – even winning the Bingo game (a maths activity) he beamed but would not shout out ‘Bingo’ as a norm even with prompting (and tickling from the facilitator. He is yet to see sense making as a key aspect of maths and the facilitator is still working towards this. Of interest the i-pads worked well to allow his progress as this did not require group participation or discussion/ keeping up with other learners and reduced distraction. Similarly the club facilitator found in her last session that making him and others close their eyes when she demonstrated for example the pattern of ‘the 10 times table’ or ‘the pattern of the 11 times table’ seemed to work well to enable Saki’s focus. Thus the removal of the social noise that seemed to affect Saki helped his focus on patterns.

Below I provide two narrative vignettes of Saki based on two transcribed extracts of critical incidents related to Saki’s participation in maths club sessions. This vignette illuminates his shyness even when he has won mathematically:

Vignettes of Saki