5.3 Mapping Social Factors that Inform Students’ Perceptions and Conceptions of Mathematics - 90
5.3.4 Teacher’s perceptions of mathematics
The significance of the teacher’s perceptions in influencing students’ conceptions and perceptions of mathematics lies in the element of co-creation of meaning in classroom practice. That is, the process of teaching and learning entails the sharing of meaning between the student and teacher which therefore renders the teacher’s conceptions important to understand as they are expressed in the teaching and learning process. The students claim that in teaching, the teachers play out their own perceptions of mathematics which tends to be contagious and in some instances counter their efforts. This is quoted as follows:
Student 1: “In fact I don’t remember anyone struggling with mathematics at primary school, everybody did it - we were told it was important, have to know how to add just like you know how to read”
Student 9: “Maths teachers give the impression that maths is hard thus kids give up before they even fail. They should make students perceive it like it is any other subject”
Student 10: “It is like they knew that maths is hard so they had come to make it easy for us”
Student 2: “Teachers are dreadful. I was not comfortable, I felt scared to ask and it seemed everyone else around me understood it and so I accepted my fate that this is not for me”
Student 4: “The mathematics class brought me anxiety and I felt I knew nothing”
The students shared the sentiment that the teachers endorsed a sense of an elevated status for mathematics from the rest of the subjects and that it is only accessible to a few students not all of them. The students claim that teachers expressed this by being hard on them as if to confirm that mathematics is hard. This suggests that teachers legitimise society’s stereotype
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about mathematics being hard, which makes for continuity in the negative collective consciousness about mathematics between classroom and out-of-classroom environments.
Where mathematics was treated as any other subject, the students admitted to having enjoyed and passed it. As Konings et al (2005:649) point out in the literature, “teachers perceive the learning environment through the lenses of their own conceptions, and will act and react accordingly”. This must be viewed in light of the fact that the teachers themselves are a product of the same society that lacks the mathematics habitus but had happened to crack the mathematics code either through exposure to a culture that is rich in the mathematics disposition or by applying themselves and mastering the tricks of the game through trial and error or by other means. It can therefore be said that, in teaching, teachers transmit the schemes of knowledge that make up their habitus. By virtue of the teachers being products of the same society that acculturates their students, they tend to anticipate stumbling blocks in their teaching and judge their students’ behaviour based on their schemes of knowledge about the subject as informed by their own experiences. This endorses Bourdieu’s (1990:86) claim that “an individual’s habitus is an active residue of his or her past that functions in the present to shape his/her perceptions”.
i) Corporal punishment
The students singled out some of the teachers’ actions that are perceived or conceived to have been as a result of the perceptions and conceptions teachers hold about mathematics. The students argued that a teacher’s perceptions are expressed through actions such as
‘dreadfulness’ and some disciplinary practices such as corporal punishment. This confirms the assertion that teachers act out the schemas of knowledge that inform their own experiences with mathematics during teaching. As noted in the literature, Naong (2007:284) argues that teachers claim that “they did not experience any harmful effects when corporal punishment was administered to them as students and they see no reason why they should not administer it to their learners as well”. Corporal punishment is thus a translation of the schemes of knowledge to a physical language about what counts as a corrective measure in mathematics learning. It could also be a way for teachers to vent their frustration about anticipated mathematics outcomes. This according to the students deterred most of them from liking mathematics, let alone pursuing it, as it was an uncomfortable situation to be in.
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Ability grouping was also identified as an unfavourable practice in mathematics classrooms that students perceived and conceived would have a negative outcome to mathematics learning. Only two students attested to having been subjected to this practice but it is a notable factor as it was claimed by the students to have influenced their perception and conception of mathematics. One is quoted as saying:
Student 1: “Undergrad social science students were mixed with pure science students for a mathematics class and science students were better mathematicians than we were. I felt out of place and felt I was not intelligent enough to contribute and grasp it. I was unable to cope and looking for an excuse and I was rescued by the split to do maths for social sciences”
The mixing of science and social science students is a rare arrangement and was a Malawian experience. However, the underlying idea that the study explores is the mixing of students with distinctly varying mathematics comprehension levels. It has been described as over- selection by Lamont et al (1988:158 in quoting Bourdieu 1974). The author notes that this is where “individuals with less valuable cultural resources are subjected to the same type of selection as those who are culturally privileged and have to perform equally well despite their cultural handicap, which in fact means they are asked to perform more than others”. The mixing of the social science students in student 1’s response was thus a form of over- selection.
These sentiments were shared by student 2 as follows:
Student 2: “Students who were poor in mathematics had their own class. It was discriminatory. We felt we were kids with special needs”
Notably, student 2 was a foreign student who had done her high school in RSA. The practice of ability grouping referred to here was in high school in a RSA school. This contributes to students’ negative conception and perception of mathematics in that “naturally humans act to portray a desired identity” (Lamont et al 1988:158). It is evident from the two submissions that ability grouping is a social and physical environment that imposed an undesired identity, particularly for those students that were placed in low achieving classes as deconstructed from their submissions. The element of imposition of identity lies in the fact that they had no
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choice in how they wanted to present themselves particularly those that were affirmed as less able or ‘students with special needs’. As student 1 asserts... we were mixed.... which implies that it was not their doing nor was it a matter of choice. “It is in human nature to avoid scenarios that invite unwelcome self-definitions, and seek out and actively create situations that provide the kind of image they want to be associated with and desire” (Lamont and Lareau, 1988:158). This explains why the students perceived mathematics as not for them and thus were looking for an excuse not to do it, as confessed in their responses.
Students’ self-elimination or self-exclusion has been identified as a normal reaction as Konings (2005: 653) argues that when humans find themselves in specific social settings that they do not feel at ease in or when they confront cultural norms that they are not familiar with, according to. This assertion has been confirmed by the students as follows:
Student 6: “We were advised that in a test, we should not be stuck on the question that we are struggling with but move to those that we feel we can do. I did that with one test, kept moving through the sums until I got to the end. It was then that I decided that it’s not for me and that some people are good at it and some are not……..and I am not”
Student 12: “In form 3 I started to spend longer time trying to solve mathematical problems yet others take shorter time. After a few attempts I still could not get it and I thought this is just not for me”
The students’ self-perceptions about mathematics have been summed up by student 4 who submitted that:
“When you spectacularly fail, it is an indication that you belong somewhere else”
From these submissions, the perceptions of students’ ability mediated the relationship between perceptions of mathematics and mathematics outcomes in that students tended to eliminate themselves from participating in mathematics as an activity that they were not successful in and to adjust their aspirations to their perceived chances of success. The responses attest to the fact that the students’ attempts to pass mathematics did not yield the desired results and thus adjusted their aspirations to alternative avenues where they had a chance of success.
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5.3.5 Perceived Usefulness of Mathematics to Post Graduate Social Science Students