Teaching and Learning 'Rate of Change'' (Slope) in Senior Secondary Schools in Australia

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Analysing understanding is an essay which will discuss the researched issue of Teaching and Learning of ’rate of change (slope)’ in Senior Secondary Schools in Australia. Students require a contextual knowledge of slope “so that they come to see slope as a graphical representation of the relationship between two quantities’ (Center for Algebraic Thinking (CAT), 2014). Without the multiple understandings required to master ‘rate of change’ and algebra many students are ill equipped to go on to levels of higher mathematics. It is necessary to engage students at level where they utilise the skills of enquiry, collaboration, hypothesis, deductive reasoning, and experimentation in real-world examples so that misconceptions are be identified for remedial purposes. The use of Information Communication Technologies (ICT) can greatly assist teachers in providing differentiated learning environments to provide maximum learning outcomes for the diverse student population.
Skemp (1976/2006) defines relational understanding and instrumental understanding and argues the need teachers to adopt relational understanding methods to their teaching practices. Instrumental understanding is simply a remembering of steps or algorithms in a process, which produces correct answers. Relational understanding requires students to gain knowledge, which adds to their schema of the topic being studied, and thereby enables them to apply the correct processes to solve a problem even when confronted with new situations.
The specific curriculum topic that this essay will concentrate on is ‘rate of change’. One problem, not peculiar to mathematics, is that terminology can be confusing to students unless they are schooled in the interpretation of words which are i...

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....) Retrieved from http://www.kaputcenter.umassd.edu/projects/simcalc/
Skemp, R. (2006). Relational understanding and instrumental understanding. Mathematics Teaching in the Middle School, 12 (2), 88-95. (Originally published in Mathematics Teaching, 77, 20-26, 1976)
Stump, S. L. (2001). High school precalculus students' understanding of slope as measure. School Science and Mathematics, 101(2), 81-89. Retrieved from http://ezproxy.utas.edu.au/login?url=http://search.proquest.com/docview/195206492?accountid=14245
Swan, M. (2009). Improving learning in mathematics. [audio podcast]. Retrieved from https://mymediaservice.utas.edu.au:8443/ess/echo/presentation/a7cee02d-a875-4f39-bf08-2373bb104428/media.mp3
Walter, J. G. & Gerson, H. (2007). Teachers’ personal agency: Making sense of slope through additive structures. Educational Studies in Mathematics, 65(2) pp. 203-233

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