Movements and patterns

In this subtheme, teacher responses that speak to the concept of geometric translations are presented. The findings from the interviews revealed ideas about movements in objects and patterns as ‘Translation concepts’ found in students’ out-of-school experiences. The following are results

Results from Teacher Interviews

Interviewer: (Q.6). What experiences of the learner do you consider relevant for incorporation in

teaching Translations?

Teacher A1: I use the notion of movement of objects to illustrate a translation. ... That is when an

object moves from one position to the other and that is an experience which students are familiar with... or I can talk about decorations or patterns they see on traditional objects that’s a translation when one shape gets repeated many times.

Teacher A2: With translations I simply apply the translation vector. I don’t have clear experiences

on this one related to learner experiences out there. That’s why we end up resorting to theory

Teacher B1: Usually in translation I just consider the movement of an object, like the movement

northwards ...so I just refer to movements from one place to another.

Teacher B2: As for translation I refer to it as a displacement. I will be trying to show students that

when we have an object on point A and it has been displaced to point B... and now that it is on point B students should see how the object has moved in terms of x-coordinate and y-coordinate.

Teacher C1: ok, translation i would talk about movement in a straight line in a particular

direction...and I mention that you have been translated nothing has changed... I have seen students actually enjoying that.

Teacher C2: I use the example of his (student) movement from home to school. That is a

translation.

Table 4.1 below summarises teachers’ responses on the Mathematics involving translations that are found in students’ out-of-school experiences. There were mixed responses from the participants particularly based on whether a participant did a teacher training course or not.

Table 4.1: Showing Teacher conception of out-of-school concepts related to a translation

Name of teacher School station type Out-of-school concept

Teacher A1 Mission boarding school - Movements of objects

- Patterns on traditional objects

Teacher A2 Mission boarding school - Nil

Teacher B1 Council run school - Movements of objects

Teacher B2 Council run school - Displacement of object

Teacher C1 Rural day secondary school

- Straight line movement

Teacher C2 Rural day secondary school

- Movement

The summary table above shows the different teacher responses to the interview question, item 6. The Mission boarding school is well resourced compared to the Council and rural day secondary schools in this study (see Section 3.1.1 in Chapter 3). Teacher A1 and Teacher A2 were both from a Mission boarding school (School A). Teacher A1, reported on aspects of object movements and patterns that appear on traditional objects as resembling typical translation concepts. Teacher A2, however, could not find a link between students’ out-of-school experiences with the translation concept. He referred to no experiences known to him that are related to translations.

In Table 3.1, which shows teachers’ demographic data, Teacher A1 holds a Teaching degree in Mathematics whilst Teacher A2 has no teaching qualification. In other words, Teacher A1 had been exposed to the pedagogy of teaching in his training, and hence was aware of the significance of building the linkage between the formal and informal mathematics, whilst Teacher A2 had not got a similar exposure. Shulman and Grossman (1988) clarify pedagogy as the science and art of

learning. Accordingly, pedagogy is the understanding in a field that are essential for teachers but may not be important for non-teachers (Teachers without training), like Teacher A2

.

The Council run school (School B) is located in a township area and is better resourced compared to the rural day school (School C) (see Section 3.1.1 in Chapter3). Teacher B1 and Teacher B2 both come from the Council run school (School B). Teacher B1 mentioned ‘the movements of objects’ as concepts of translation embedded in students’ out-of-school experiences, while Teacher B2 talked about a displacement of an object from one point to another. The two teachers literally referred to one and the same idea of the concept but teacher B1’s explanation was more grounded in the practical displacement than Teacher B2 who referred to the movement in terms of the cardinal points in a Cartesian plane.

Although both Teacher B1 and Teacher B2 hold degree qualifications (see Table 3.1) only Teacher B1 had a teaching qualification. This confirms again some difference in how a qualified and an unqualified teacher can view concepts in mathematics for teaching purposes. Shulman and Grossman (1988) argue about the importance of pedagogy within a teacher to be able to represent and model Mathematics ideas and concepts using objects and situations familiar to students.

Whilst all three schools studied in this research are rural bound, School C, a rural day secondary school is in the category of little or no resource support that could enhance students’ mastery of concepts (see Section 3.1.1). Both Teacher C1 and Teacher C2 were from the rural day secondary school. Teacher C1 and Teacher C2 gave more or less practical explanations of ‘movements’ as resembling translations (see Table 4.1). The two teachers both hold a minimum teacher’s qualification, a diploma teaching. In other words, Teacher C1 and Teacher C2 had examples of translations linked to student experiences they could use in the teaching and learning situation.

Of the six teachers, it emerges that only those who went through teacher training like Teacher A1 were more likely to see value in identifying and using examples for translation that are drawn from students’ out-of-school experiences. Thus, a teacher to be well equipped in terms of teaching and learning skills that value students’ out-of-school experiences in translation concepts they must have undergone some training in pedagogy.

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The study findings resonate well with results from the Centre of Development in Education (2010) study where it was found that an average mathematics teacher needs to be equipped with requisite

skills and concepts to be effective in a mathematics classroom. According to Mtetwa (2017) students in the traditional classes complain of failing to see meaningful connections of mathematics concepts and procedures with their life worlds. This suggests teaching and learning that is more robust and is directed at helping students relate their experiences with the topics in mathematics.