The aim of Hardman's exploratory case study was to understand how teacher "B", a 38 year old male was using computers to teach Mathematics to thirty 13 year old learners in a rural school. Teacher "B" had a 4 year diploma, and never specialised in Mathematics. He had to rely on Maths Methodology which formed part of his initial training. People considers him as a Maths specialist, and he teaches Grade 6 and 7 Mathematics. There are enough computers in the classroom, and he was expected to use the computer as a tool.
Lessons were videotaped, and the transcriptions of these videotapes were transcribed for use in the research study. Although the teacher had only 2 hours training in the use of computers, interviews were conducted with him before lessons (Hardman: 2005).
Results of the research were reported in two sections:
- Interview data: aimed at how the teacher uses the computer in the classroom.
- Actual practice: what objects the teacher acts on in different contexts, and if the computer has led to a shift in pedagogical practice across different contexts.
Contradictions are tracked by by focusing on "how" the teacher talks about computer use in the Mathematics classroom. The teacher is driven by OBE and favours group work as a tool to act on as object of his lesson. He was concentrating on fractions, because he felt that the knowledge will be useful to the learners. The teacher is keen to finish the curriculum quickly (Hardman: 2005).
Object /division of labour contradiction
This teacher unfortunately has to face one of the biggest contradictions, which surfaces from South Africa's move from a transmission based pedagogy to a more progressive Outcomes Based Educational setting. This contradiction is happening in the classroom, and that is the choice between group work and being able to reach all children while encouraging the development of creative autonomous learners (Hardman: 2005).
Tool / division of labour contradiction
The division of labour opened up new possibilities for student-centered pedagogy. The use of the computer in the classroom, and the fact that the teacher could not assist, created opportunity for students to become teachers of other students.
Tool / object contradiction
The object of this lesson for the teacher was to teach mathematics to learners. He wanted them to understand fractions using the computer. The teacher sees the computer as a tool for higher order, instead of seeing it as a tool for developing a very important cognitive skill of drill and practice. For this teacher, there is a contradiction between the tool and the object. There is also a contradiction where the teacher sees the computer as a low level tool, instead of a higher level tool (Hardman: 2005).
Rules / Subject contradictions
With the use of the computers the teacher creates rules for the use of the computer, which makes access to the computer unattractive to learners. The teacher feels threatened by the lack of knowledge when using the computer.The teacher feels that the learners will see him as stupid. The learners should actually learn to experiment with it. There is actually a contradiction between the Department's policy and the the teacher's creativity to ensure that teachers do not regard him as ignorant (Hardman: 2005).
For the teacher is the way the learners respond to the use of the computer. He sees it as a carrot which is dangled in front of them,. The contradictions around how the computer is used as a tool, and and the computer as a tool for investigations, impacted on the activity system. This lead to a contradiction between the teacher's need to teach mathematics and the use of the computer as a device of investigation, drill and practice (Hardman: 2005).
Tools, objects, division of labour, community and rules
The teacher and the learners share a common object - and that is for the teacher to teach and the learners to learn. The object informs us about the labour in the classroom. The teacher determines the mathematical meaning in the class and the learners as students, or at the most basic, reproducers of text (Hardman: 2005).
The most important toll used by the teacher is language. The teacher lacks computer skills, and this threat is overcome by instituting classroom rules. The teacher is restricting the learners by pacing, sequencing and selection of content studied. The object of the lesson becomes the technical skill to act on the computer. The teacher uses material, language and non-verbal actions as tools to act on within the traditional classroom. In the computer lab the teacher becomes more formal, and rely on language to explain mathematical content. He also uses language to control discipline in the class (Hardman: 2005).
As soon as the lessons are taking place in the lab, the teacher's language become exclusive especially with the use of language. The computer becomes the object of the lesson, and the understanding of mathematics drops into the background. When the computer is used as a tool, it is used to act on a lower level cognitive skills such as drill and practice (Hardman: 2005).
With the introduction of the computer into mathematics, a number of contradictions were experienced in the classroom. One of the most important contradictions is between the use of the computer as instrument for recall and practice, and is therefore used as an instrument for exploration (Hardman: 2005).
The need to use the computer as a tool required of the teacher to rethink the teaching and learning in the classroom, causing contradictions between the use of the computer as a tool for drill and practice, or as a creative tool to promote an understanding for mathematics (Hardman: 2005).
Hardman, J. 2005. An exploratory case study of computer use in a primary school mathematics classroom: New technology, new pedagogy? University of Cape Town. Perspectives in Education, Volume 23(4). December 2005.