Using errors and misconceptions as a resource to teach functions to grade 11 learners - Malahlela, Moloko Victor (My University, 2017)
This research report focussed on the teaching of the function concept directed at the errors the learners make as well as the misconceptions which could be associated with those errors. The study was conducted at a secondary school in Johannesburg, South Africa. This was a qualitative error analysis study which also had a form of interventional or remedial teaching. The research was driven by the following research questions: (1) What errors and misconceptions do grade 11 learners show on functions?, (2) What learning affordances and constraints can be created if teaching is directed at learners’ errors and misconceptions? and, (3) To what extent can the learners’ achievement on the topic functions be boosted if teaching is directed at learners’ errors and misconceptions? The study used a purposive sample of six grade 11 mathematics learners from a group of 34 learners. To answer these questions, I structured the study to encompass numerous phases of data collection using different instruments. Firstly, I constructed a test instrument and used it on this group of grade 11 learners. These learners had been taught functions earlier in the year, so the test was diagnostic to measure the cognitive levels of the learner on the concept and also to establish the errors made and misconceptions they carried onto the section from other sections or picked up from the function concept. The study was mainly based on the constructivism theory of learning and teaching, but also had other theories to link to it such at the socio-cultural theory, the APOS (actions, process, object and schema) theory, the concept image and concept definition as well as the variation theory. The errors I picked up from the pre-test I classified and analysed using the conceptual framework grounded on the abovementioned theories. It was this analysis which enabled me to structure the desired intervention program together with the teacher after which I conducted a post-test with the subjects. Other forms of data collection such as the interview and observation were employed during the study. I used the interview to get clarity from the learners’ pre-test questions responses, whilst the observation I used during the intervention lessons the teacher had with the learners. Indeed the findings were that, while there was a substantial improvement on learner performance on the post-test, it appeared clearly that cognitive levels of the learners on the function concept had been enhanced. This improvement of performance was a result of the teaching that was directed at the errors, which also interprets to having created a favourable environment which could be interpreted as learning affordances to boost the learners’ understanding of the function concept.
A research report submitted to the Wits School of Education and the Faculty of Science, University of the Witwatersrand in partial fulfilment of the requirements for the degree of Master of Science by combination of coursework and research. Johannesburg, 5 June 2017
Keywords: Mathematics--Study and teaching; Functions; Education, Secondary--Research; Constructivism (education)--South Africa--Johannesburg