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Images and the Growth of Mathematical Understanding in Workplace Training
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understand the mathematics that is captured by this tool is essential for a worker. Whilst we acknowledge that such understandings are not likely to be made explicit during every task, the possession of a powerful and flexible set of mathematical images related to this offers something to fold back to, should memory fail, or the need arise to work in a new context. Certainly for John, being able to connect multiplication by two with the image of placing the two equal lengths of pipe together, and of then understanding how this can be represented on a measuring tape could have been a valuable experience, as would be the exploration of fractional units on the tape.
We contend that in the apprenticeship training classroom there is a need to re-visit
concepts such as addition, multiplication, fractions etc. and to go beyond learning merely how to operate on and with numbers. In particular, there would seem to be a need to explore the existing understandings that trainees bring with them, to consider the appropriateness of these images for vocational related tasks, and to occasion the construction of new images as needed, drawing upon the use of common workplace tools and resources as appropriate.
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The research reported in this paper is supported by the Social Science and Humanities Research Council
of Canada, (SSHRC) through Grants #831-2002-0005 and #501-2002-0002. We would also like to thank United Association of Journeymen of the Plumbing and Pipefitting Industry Trade School, Local 170, Delta, BC for their assistance with this project.
References: Folinsbee, S. (1995). Workplace Basics in the 1990s: Critical Issues and Promising
Practices. In W.F. Spikes (Ed.), Workplace Learning (pp.3-14). San Francisco: Josey-Bass Inc.
Millroy, W.L. (1992). An Ethnographic Study of the Mathematical Ideas of a Group of
Carpenters. NCTM Monograph Number 5. Reston: National Council of Teachers of Mathematics.
Nicholson, B. (1998). Math Works! In M.E. Belfiore (Ed.), Chronicling the Learning
Curve: Workplace Education Instructors Share their Stories (pp.1-8). Don Mills, ON: ABC Canada.
Noss, R., Hoyles, C. & Pozzi, S. (2000). Working Knowledge: Mathematics in Use. In
A. Bessot & D. Ridgway (Eds.), Education for Mathematics in the Workplace.(pp.17-36). Dordrecht: Kluwer Academic Publishers.
Pirie, S., & Kieren, T. (1994). Growth in mathematical understanding: How can we
characterise it and how can we represent it? Educational Studies in Mathematics, 26 (2-3), 165-190.
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| | Authors: Martin, Lyndon., LaCroix, Lionel. and Grecki, Sue. |
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understand the mathematics that is captured by this tool is essential for a worker. Whilst
we acknowledge that such understandings are not likely to be made explicit during every
task, the possession of a powerful and flexible set of mathematical images related to this
offers something to fold back to, should memory fail, or the need arise to work in a new
context. Certainly for John, being able to connect multiplication by two with the image of
placing the two equal lengths of pipe together, and of then understanding how this can be
represented on a measuring tape could have been a valuable experience, as would be the
exploration of fractional units on the tape.
We contend that in the apprenticeship training classroom there is a need to re-visit
concepts such as addition, multiplication, fractions etc. and to go beyond learning merely
how to operate on and with numbers. In particular, there would seem to be a need to
explore the existing understandings that trainees bring with them, to consider the
appropriateness of these images for vocational related tasks, and to occasion the
construction of new images as needed, drawing upon the use of common workplace tools
and resources as appropriate.
1
The research reported in this paper is supported by the Social Science and Humanities Research Council
of Canada, (SSHRC) through Grants #831-2002-0005 and #501-2002-0002. We would also like to thank
United Association of Journeymen of the Plumbing and Pipefitting Industry Trade School, Local 170,
Delta, BC for their assistance with this project.
References:
Folinsbee, S. (1995). Workplace Basics in the 1990s: Critical Issues and Promising
Practices. In W.F. Spikes (Ed.), Workplace Learning (pp.3-14). San Francisco:
Josey-Bass Inc.
Millroy, W.L. (1992). An Ethnographic Study of the Mathematical Ideas of a Group of
Carpenters. NCTM Monograph Number 5. Reston: National Council of Teachers of
Mathematics.
Nicholson, B. (1998). Math Works! In M.E. Belfiore (Ed.), Chronicling the Learning
Curve: Workplace Education Instructors Share their Stories (pp.1-8). Don Mills,
ON: ABC Canada.
Noss, R., Hoyles, C. & Pozzi, S. (2000). Working Knowledge: Mathematics in Use. In
A. Bessot & D. Ridgway (Eds.), Education for Mathematics in the Workplace.
(pp.17-36). Dordrecht: Kluwer Academic Publishers.
Pirie, S., & Kieren, T. (1994). Growth in mathematical understanding: How can we
characterise it and how can we represent it? Educational Studies in Mathematics, 26
(2-3), 165-190.
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