Scaffolding using writing tasks

Throughout the data collection period, it was clear that learners encountered challenges when implementing the writing tasks in mathematics lessons. Scaffolding was necessary to address these challenges so that learners were able to use writing tasks in mathematics in Grade 3. In chapter 2, scaffolding was described as the learning activities the teacher or more knowledgeable other (MKO) uses to develop knowledge (Siyepu, 2013:5). In this study, scaffolding occurred in the following ways. Scaffolding was provided through the implementation of writing tasks as a means of breaking up a problem into manageable parts. Peer interaction and collaboration were other forms of scaffolding. Learners were prompted during observation when they solved mathematical problems. Written and verbal feedback were also given to enhance the learners’ ability to solve problems.

The writing tasks themselves were used as a form of scaffolding which helped to support and develop learners’ ability to solve mathematical problems (Daniels 2001:108). Writing tasks created opportunities for learners to construct and apply mathematical knowledge. The mathematical problems learners solved during this study were linked to the mathematical knowledge they were expected to develop as part of the CAPS Mathematics curriculum prescribed for Grade 3. The problems used learners’ number learning within the sphere of addition, subtraction, multiplication and division. By solving these problems, learners made connections with these mathematical concepts. For example, the third problem learners

of counting in fours and/or the related multiplication table (Figure 5.16). Learners’ development of mathematical knowledge was scaffolded through this problem. This was the case with other mathematical problems as well as other writing tasks in this study. Burns’s (1995a) methodology of using writing in mathematics was introduced and implemented as a tool to scaffold learners’ understanding and support learners when they solve mathematical problems.

Figure 5.16 Learner 5 (A) Writing – Problem 3

When learners solved the mathematical problems, they were sometimes provided with more manageable steps to find a solution. The problem was broken up into parts so that learners solved one part first before moving on to the next part. Doing so simplified the learners’ role in order to solve the problem (Daniels, 2001:107). Below is an excerpt from the field notes taken during research which describes the scaffolding given when learners solved the first problem during the writing intervention. The problem for the average ability group reads as follows:

32 birds land on the bird table. There are now 71 birds there. How many birds were already on the table?

While moving around the group I realised that the learners did not understand that there were 71 birds in total and they had to find the initial amount. I needed to break down the problem by drawing it on the board and guiding them with prompts and questions to understand that the solution could not be more than 71.

Figure 5.17 Learner 4 (A) Writing-Problem 1 Figure 5.18 Learner 5 (A) Writing-Problem 1

The examples above (Figure 5.17 and Figure 5.18) show how learners from the average ability group were able to solve the problem after scaffolding had occurred. These learners erased the work they had done before scaffolding so no comparison is possible between their strategies before and after discussion. Seeing learners’ attempts at various strategies would have helped me to better understand the decisions they made to try alternate strategies. These strategies show that Learner 4 and Learner 5 understood the context of the problem and were able to solve it according to the addition/subtraction problem type. Learner 4 used addition and explained that counting was used to arrive at the solution. Learner 5 used his knowledge of place value to decompose 71 into tens and ones. He explained how he subtracted 32 when he crossed out tens and ones. He displayed knowledge of subtracting through the decade when he crossed out ten and changed it to 9.

The group of average ability learners needed a visual representation of the problem coupled with verbal prompts to understand the context of the problem. Polya (1957:110) explains that relevant elements from formerly acquired mathematical knowledge should be used to solve the present problem. Learners solved similar addition/subtraction problem types in previous mathematics lessons that required them to find the missing addend. By using a visual presentation, it was possible to relate previous problems and mathematical ideas.

Scaffolding occurred in this study through prompts given to learners while they solved mathematical problems (Sperry Smith, 2013:10). One occasion where prompts were required was when learners solved the fifth problem of the writing intervention. As shown in

problem. But, he did not go beyond drawing these tallies in order to solve the problem. Written feedback was provided in order for him to continue working on this problem the following day. He was uncertain of the feedback given so further scaffolding was necessary. While he was explaining his strategy, his tallies were circled into groups of three by the researcher as a means of scaffolding his understanding of the context of the problem. He was asked what this circling represented. Learner 7 (BA) was able to use the circled tallies to clarify that one group represented one tricycle with three wheels.

When learners engaged in the writing tasks in the lessons, different forms of scaffolding took place to develop learners’ understanding of the writing tasks as well as their mathematical knowledge. Scaffolding and prompts were not provided during the pre-test and post-test because this could have negated their purpose which was to determine whether the writing tasks supported learners’ mathematical problem-solving abilities.

Based on these findings, it is evident the use of writing in mathematics could be a means of providing scaffolding to overcome some of the difficulties learners encounter when implementing writing tasks. Writing tasks, verbal prompts and the teacher/researcher’s written feedback may scaffold learners’ conceptual understanding when they engage with mathematical problems.