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whether or not they were doing the work correctly. Fiona also helped those learners who were slow by cutting for them while the learners had to paste. Therefore Fiona was interacting with her learners while scaffolding the instruction to learners. She only moved on to the next step when all the learners had understood what she was teaching. Fiona provided individual assistance during each lesson.
Fiona’s class size contributed to the way she taught, because it was small. She had 20 learners in her classroom. Thus providing individual attention to the learners was not a challenge to her.
Moreover, Fiona had all the resources she needed for her data handling lessons, and her learners also had everything they needed for their learning, including the necessary pens, coloured pens, glue and scissors.
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when recitation is used as a method of teaching. Learners memorise and forget easily. The researcher witnessed this during lesson observations. Learners were reciting numbers every day, but still could not remember this information in the following lesson. They would struggle, for example, with the 3 times table.
When the researcher observed the participants teaching data handling, memorisation was the dominant instructional strategy. This traditional method of teaching does not provide learners with an opportunity to share ideas about the data handling topic presented (Mahalingam, Schaefer & Morlimo, 2008). Thus, this method deprives learners of the collaborative learning which promotes critical thinking. Traditional strategies generally encourage learners to memorise facts rather than to develop conceptual understanding (Birgin, 2011).
Nevertheless, memorising the mathematical equations and concepts is not important, but what is imperative is to capture the satisfaction produced by comprehending the reason things happen (Riveros, 2012). This is part of critical thinking. Memorisation is in contrast with social constructivism, because social constructivist teachers believe that learners have to be guided properly to be able to formulate answers on their own (Solso, 2009). In other words, learners do not need memorisation to master mathematical skills. Memorisation does not promote discovery or collaborative learning (NCTM, 2013).
In addition, memorisation does not promote critical thinking and communication (Towler, 2014).
Out of eight participants, two did not use the memorisation instructional strategy. When asked the reason for not using, for example, the repetition method, Felicity stated as follows:
… I do not ask learners to repeat anything in class because I want them to learn to listen to an individual when talking … If they know that something is going to be repeated they will not listen …
Felicity was emphasising the importance of the listening skill in the classroom, because if learners lack this skill they may experience a problem in their learning. Other teachers had a different opinion about using the memorisation instructional strategy, for example Betty’s comment was the following:
… we want them to be able to count and to recall numbers ... we get so interested when we see them being able to count. You can also see those people who cannot count and also those who cannot count can learn by hearing others and join them … it stays in their heads when they repeat. We do it for those who do not listen in class. So when you make them repeat you want them to understand what you are saying. They can repeat even more than two times so that they will understand …
Betty believes that learners will be able to understand what is taught when they memorise mathematical concepts. In other words, she was of the opinion that coaching learners is the effective way of teaching and assists learners to grasp what is taught. Jabu also believed that memorisation is effective when teaching data handling: “… so it is better to make them repeat so
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that even the one who did not understand while I was explaining will do …”. Jabu believed that memorisation assists learners that do not understand when she explains. In other words, she used memorisation to accommodate all of the learners.
According to Gordon and Nicholas (2005), learners who learn by memorising, when asked leading questions, show a lack of understanding to accompany that learning. Therefore most of the time learners repeat and reproduce what they learn not because they understand, and at a later stage they might forget or may not be able explain around those facts or concepts.
Most of the participants (6 out of 8) were asking learners to memorise facts rather than understanding them or allowing learners to find ways of understanding data handling concepts on their own. Peter (2012) states that mathematics teachers can develop learners’ critical thinking skills by assessment strategies that challenge learners intellectually rather than memory recall.
Therefore the issue of memorisation has been a barrier to thinking and reflection in the classroom (Vassall-Fall, 2008).
Cai and Wang (2010) conducted a study that investigated Chinese and American teachers’
beliefs concerning effective mathematics teaching. The Chinese and American teachers believed that there are two kinds of memorising: memorisation after understanding and memorising before understanding. According to the findings, the teachers from these two countries recommended memorisation after understanding. The reason they gave was that memorising after understanding assists learners in retaining knowledge, and that knowledge could be applied efficiently to solve problems. Therefore the Chinese and American teachers were not against memorisation, but felt that memorising is effective if it is done for retaining after understanding is gained.
What the researcher realised in the participating schools is that teachers asked learners to memorise before understanding, because the participants used the memorisation strategy first before employing other instructional strategies. However, Schollar (2008) and Taylor (2008) argue that the loss of the importance of memorisation, and the initiative of discovery learning and that learners cannot be wrong are the origin of much learner underachievement.
Therefore, there are many different ideas on the notion of memorisation as an instruction during the teaching and learning process. Some researchers view memorising facts as effective and others not. However, drawing the two ideas together – using memorisation together with other instructional strategies – could be of benefit to the learners.
It is important to check the learning goal before employing the instructional strategy when teaching (Ermeling et al., 2015). A good instructional strategy for one learning goal might not be effective for another (Sapon-Shevin, 2013; Emerling, et al., 2015). Thus, the participants used different instructional strategies to teach data handling. The participants needed to plan or to have objectives to use certain instructional strategies when teaching, so that they would teach according to the desired learning goals. For example, if the learning goal was for the learners to
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know numbers, then they could ask them to recite number tables. Repeating facts and memorising throughout the lesson may not contribute to learners’ understanding of data handling concepts or content.