Research in Engineering Education Symposium 2011 - rees2009

Universidad Politécnica de Madrid (UPM) Página 302 de 957
developed based on the findings of the previous two studies, and were aimed at revealing
the variation in students’ understanding. Results reported here are based on data collected
from all three studies, as they each help decipher part of the “outcome space”. Guided by
Variation Theory, our analysis aimed to identify the different ways students viewed the
role of the scale in representing different objects and how they explained the structure of
the scales. We also place special emphasis on characterizing students’ conceptions in such
a way that contrasts between them would reveal the aspects of variation that distinguish
them.
Findings
Eight categories of conception were identified, which describe a hierarchy of successively
more sophisticated understanding with category eight being the most sophisticated (See
Table 1). These conceptions also belong to four super-ordinate categories � Fragmented,
Linear, Proportional, and Logarithmic. According to Variation Theory, each category is
distinguished from the next one on one aspect of variation. The aspects of variation are
inclusive, which means that the awareness of an aspect that separates conception
categories that are further along in the progression implies the awareness of the aspects
that differentiate any of the less sophisticated categories. The progression is thus defined
by the increased complexity of students’ awareness of the aspects of variation students are
aware of, the more sophisticated their conception is.
Category one and two represent conceptions of scale that are fragmented in nature, which
describes the view that objects belonging to different “worlds” (i.e. the macro-, micro-, and
nano-world) are too different to be represented on a continuous scale; in other words,
they each need their own separate scale. What sets these two categories apart is the aspect
of variation “Integrated of numbers”, which refers to whether any numerical
measurements of object sizes are integrated with the scale of choice. The category one
conception places objects on the scale qualitatively (i.e., the sun is far away from the atom,
because it is much bigger), but does not use any numerical systems to quantify the
ordering.
Categories three and four both reflect the belief that a scale based on absolute size
differences (i.e. by using subtraction) is most appropriate for representing objects of
widely varying sizes as those given in our studies. They are qualitatively different from the
fragmented conceptions, because they demonstrate the awareness of “Continuum”, the
key understanding that a scale is a continuum that can representd both very small and
very bi objects regardless of which “world” they belong to. The aspect of variation “Log
scale awareness” highlights the difference between category three and four, i.e., category
four is more advanced because it indicates the attempt to incorporate some features or
components of the logarithmic scale in scale construction.
Categories five and six represent proportion-based understanding of scale, which means
that the appropriate scale for objects differing much in size should be based on the objects’
relative size differences (i.e., by using division). The aspect of variation “Proportion”
clearly specifies this feature, as it differs from the linear conceptions that are based on
Proceedings of Research in Engineering Education Symposium 2011
Madrid, 4 th - 7 th October 2011