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The questions we construct sometimes involve Mason's question types: Specializing, Generalizing, Conjecturing and Convincing.
| 1 | Specializing | Trying special cases by looking at examples | The first three questions provided allow students to master the procedures for finding the derivative of a function using the first principle of differentiation. Our aim is to let students review the conceptual aspects of differentiation through learning by doing using comparing, sorting and organizing questioning types. |
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| 2 | Generalizing | Looking for patterns and relationships | Questions four through six are provided to allow students to find the derivatives of composite functions, i.e., functions that involve rational functions, absolute functions and trigonometric functions. Our aim is to first let students verify the calculation steps and reach a final answer and then select the correct differentiation rules and techniques and delete irrelevant information using completing, deleting and correcting questioning types. |
| 3 | Conjecturing | Predicting relationships and outcomes | Questions seven and eight provide students the chance to not only make use of implicit differentiation for finding the derivative of a function but also trace all the calculation steps through learning by doing. Our aim here is to let students do the same calculation steps for different problem settings and select a correct answer using both changing and varying questioning types. To help them understand the nature of the questions, students are asked to solve this problem from back to front and obtain the final answer by making one of two choices for every step of the calculation using reversing and altering questioning types. |
| 4 | Convincing | Finding and communicating reasons why something is true | The ninth and tenth questions provided allow students to master the procedures of finding the second derivative of a function involving with inverse function. These questions guide students to look for reasons why the results can appear and convince the other students about their finding using the results obtained. Using explaining, justifying, verifying and refuting questioning types, our aim is to have students first solve the problem and then mark their opponent’s answers (reciprocal marking). Students will see in which part they made incorrect answers and then work on a follow up question that we recommend. |
Schedule of final examination is:
The Calculus Project Teams, Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong.