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Images and the Growth of Mathematical Understanding in Workplace Training
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during training they need to re-visit these existing understandings and images, make sense of them again in specific trades contexts, and modify and extend them and if necessary construct new understandings. We use elements of the Pirie-Kieren theory, specifically the notion of “images” to describe the way that John uses the mathematical concepts of multiplication and fractions within a pipe-fitting task. We highlight the potential limitations of his existing images for these concepts, at least in a form that is helpful in this context.
Methods and Data Sources
The larger study, currently underway, is made up of a series of case studies of
apprentices training towards qualification in various construction trades in British Columbia, Canada. The trainees and their instructor were observed and video-recorded over a number of sessions. The episode on which this paper focuses involved a small group of students in the shop working to calculate the length of a pipe component required for a threaded pipe and fitting assembly to be built to given specifications. This activity followed a formal lesson on this procedure in the classroom. The second author acted as a participant observer in this session and engaged with individual trainees as they worked on the task. The video recording of this episode was analysed using the Pirie-Kieren theory with a particular focus on identifying the mathematical images held, accessed, made, modified and worked with by John as he completed the task. It should be noted that the transcript offered below represents a very short extract from a number of hours of taping, and some of the comments and conclusions we offer draw on data beyond that presented here.
John and the pipefitting task
A drawing of the pipe assembly to be constructed is shown in figure one. The
students were assigned the task of constructing this assembly with a centre-to-centre measure (C-C) of ten inches. The values for the fitting allowance (A) and thread makeup (E) were provided elsewhere, and the length of cut pipe (P) had to calculated.
Figure One: Pipe assembly to be constructed by John using standard pipe fittings and a
cut piece of pipe.
The following episode begins at a workbench in the shop as John works to make sense of the calculations needed for this task. John:
Ok. So what I do now is, I know that it’s ten, what I’ve got to have total.
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| | Authors: Martin, Lyndon., LaCroix, Lionel. and Grecki, Sue. |
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during training they need to re-visit these existing understandings and images, make
sense of them again in specific trades contexts, and modify and extend them and if
necessary construct new understandings. We use elements of the Pirie-Kieren theory,
specifically the notion of “images” to describe the way that John uses the mathematical
concepts of multiplication and fractions within a pipe-fitting task. We highlight the
potential limitations of his existing images for these concepts, at least in a form that is
helpful in this context.
Methods and Data Sources
The larger study, currently underway, is made up of a series of case studies of
apprentices training towards qualification in various construction trades in British
Columbia, Canada. The trainees and their instructor were observed and video-recorded
over a number of sessions. The episode on which this paper focuses involved a small
group of students in the shop working to calculate the length of a pipe component
required for a threaded pipe and fitting assembly to be built to given specifications. This
activity followed a formal lesson on this procedure in the classroom. The second author
acted as a participant observer in this session and engaged with individual trainees as
they worked on the task. The video recording of this episode was analysed using the
Pirie-Kieren theory with a particular focus on identifying the mathematical images held,
accessed, made, modified and worked with by John as he completed the task. It should
be noted that the transcript offered below represents a very short extract from a number
of hours of taping, and some of the comments and conclusions we offer draw on data
beyond that presented here.
John and the pipefitting task
A drawing of the pipe assembly to be constructed is shown in figure one. The
students were assigned the task of constructing this assembly with a centre-to-centre
measure (C-C) of ten inches. The values for the fitting allowance (A) and thread makeup
(E) were provided elsewhere, and the length of cut pipe (P) had to calculated.
Figure One: Pipe assembly to be constructed by John using standard pipe fittings and a
cut piece of pipe.
The following episode begins at a workbench in the shop as John works to make sense of
the calculations needed for this task.
John:
Ok. So what I do now is, I know that it’s ten, what I’ve got to have total.
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