SECCIÓN TRANSVERSAL

The indicator used as an analysis factor was the extent to which the teachers were able to embrace students’ out-of-school experiences in the teaching of Transformation Geometry. In this part lessons conducted by teacher A1, B1 & C1 were evaluated as shown in the ensuing discussion.

The researcher first of all looked at whether the teachers used meaningful contexts in introducing their lessons. Teacher A1 used the context of catapult to talk about stretch and teacher B1 introduced by recapping on previously covered topics whilst Teacher C1 introduced by asking students to give a bit of account about how the mirror operates. Teacher C1, when teaching rotation, had instances where a connection was sought between mathematics concepts and students experiences out-of-school, for instance where the teacher asked for examples that depict a rotation.

Teacher C1: Can you tell me examples in real life where a rotation can still occur apart from the

clock and wheel?

Learners responded by citing examples they have had experiences with. This, according to Freudenthal (1991), is critical in the teaching and learning of mathematics concepts. Of the three teachers Teacher A1 used a meaningful context that exposes the notion of a stretch. In teacher B1’s however there was no meaningful context used. Teacher C1 used a meaningful context where he was talking about what happens when one looks into a mirror.

Secondly, the researcher looked at integration of the topic with other topics and in all three topics taught there was some evident of the reference to other relevant units for example teacher C2 referred to symmetry in elaborating about reflections.

Thirdly, the researcher looked at whether the nature of problems given to students invited learners to discuss their solutions critically. At School A and School C the two teachers used group work and that provided room for students to be highly interactive during the tasks. There was evidence of participation in some demanding exercise.

Finally, were the problems guiding students to use their informal methods or strategies instead of directly using the formal ones. Elements of this principle were only prevalent in teacher A1’s lesson, where students were asked questions like: what determines the extent of the stretch. Lessons

for Teacher B1 and Teacher C1 did not prove any prevalence of the principle. At School B the Teacher B1 used a clear exposition which limited students’ chances to debate, argue and discuss.

Thus, of the three teachers Teacher A1 was more inclined to a lesson that incorporates RME elements. In other words, the observed lessons at School B and C demonstrated a situation where the teaching of concepts was very deductive. The philosophy behind RME theory is that students must be given the opportunity to reinvent Mathematics. In other words, students would need a chance to follow the footsteps of the inventor.

The notion of mathematising is important as it familiarises students with a mathematical approach to everyday life situations. That is, it offers possibilities and limitations of knowing when a mathematical approach is appropriate and when it is not (Fauzan, 2002). Such approaches develop in learners, strategies based on their own experiences and informal knowledge and invite them to solve the problems (motivational factor) (Freudenthal, 1991).

However, in general Teacher B1 and Teacher C1‘s approaches in teaching Transformation Geometry were rather far from contributing to students’ mastery of concepts as they valued mastery of procedures. This is a setback to success in transformation geometry. The idea of approaches that are more learner-centred is a directive from policy documents (the National syllabus) rather than from teachers’ own beliefs (Stols, Ono & Rogan, 2015). According to Ersoy and Duatepe (2003) the Transformation topic in Geometry is rather enjoyable for children and bears some features that can promote their creative thinking. For example, a rug pattern which is repetitive, shifted, or rotated, will help them to become aware of the geometry around them.

According to Freudenthal (1991), Mathematics must be connected to reality and also regarded as a human activity. Only at School A were students accorded a chance to view Transformation Geometry in a real world of experience. From the findings it can be concluded that Teacher A1 used an approach in teaching Transformation Geometry based on some key elements of RME as shown above. According to the second learning principle of RME, Gravemeijer (1994) advocates for a broad attention to be given to visual models, model situations (in this case the catapult) that arise from problem solving activities because it will help students move through various levels of abstraction. In the RME Model, the statement ‘mathematics must be connected to reality’ means that Mathematics must be close to learners and must be relevant to everyday life situations. At

derive them from the reality by means of adequate contexts and in an informal manner (Purpura, Baroody & Lonigan, 2013). This encouraged stimulation of learners’ understanding of Transformation Geometry.

Learners increase understanding when taught how the concepts acquired can be used outside classroom. Contexts used should be meaningful to students. Without the ability of teachers to support learning by simplifying concepts via effective use of students’ world experiences, Africa's education efforts will stagnate and eventually retrogress (Wachira, 2014)

Challenges cited above have a negative effect on learner comprehension of transformation geometry as experienced by mathematics teachers. Usually, teaching transformation geometry is limited to informing students what is meant by a particular transformation, how it is used to transform a shape (Jones, 2002). This kind of approach does not encourage students to make logical connections and explain their reasoning.