The Process And Types Of Difficulties In Constructing Concept Image Of Graph Function That Involve Derivative Order Through Graphing Calculator Usage
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Date
2016-06
Authors
Raja Maamor Shah, Raja Lailatul Zuraida
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Abstract
The purpose of this research is to study the process students experienced, the type of difficulties encountered and the forms of combination of representatives that have always been used when using graphing calculator in constructing concept image of derivative order that relates to graph function towards minimum point, maximum point, increasing function, decreasing function, concave up and concave down. Research sampling is made up of six (6) second semester students under the Bachelor of Science in Mathematics with Education Program. This research uses qualitative approach which involves unstructured interview. A flow chart the process of constructing concept image, the type of difficulties encountered and the form of combination of representatives that have always been used by every participant for each term has been developed. Research found that the activities that occur in the process of constructing the concept image of minimum point, maximum point, increasing function, decreasing function, concave up and concave down that involves derivative order using graphing calculator starts with drawing a suitable graph function, determining the minimum and maximum points position or the shape/section of increasing, decreasing, concave up and concave down, relating the term with derivative(s) order and determining the relation between the term and derivative(s) order. To determine the minimum and maximum points position or the shape/section of increasing, decreasing, concave up and concave down, participants apply the concept definition that do not involve derivative order. The sequence of
these four activities is same for each of the terms and for each participant. The relation obtained was compared to the concept definition that involves derivative order. None of the participants manage to construct correctly the concept image of minimum point, maximum point, increasing function, decreasing function, concave up and concave down that associate with the concept definition involving derivative order. Among the major types of difficulties encountered in constructing the concept image that associate with concept definition that involves derivative order are such that participants cannot interpret the slope, the second derivative and the changes of the slopes into mathematical symbols and the relation that they did for one term is the construction of concept image of other term. The forms of combination of representatives that has been used in constructing the six terms concept image that involve derivative order are the graphical and symbolic representations. Participants used symbolic representation to check and verify the relation between the term and first derivative obtained by using graphical representation is the same. To relate the term with second derivative, participants used symbolic representation.
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The type of difficulties encountered and the forms of combination of representatives , that have always been used when using graphing calculator in constructing concept image