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The questions we construct sometimes involve the intersection of two or even three different question types, e.g., Guiding and Factual Questions, Probing and Guiding Questions, Probing and Factual Questions and Probing, Guiding and Factual Questions.
| 1 | Probing Question |
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The questions provided assist students to explain which of the problem solving strategies used is the most correct. |
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| 2 | Factual Questions |
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The questions provided assist students in clarifying or extending an understanding of the properties of the definite integral, e.g., 1. the value of a definite integral remains unchanged if its variable is replaced by any other symbol, 2. by the interchange in the limits of the definite integral, the sign of the integral is changed, 3. By decomposing the integration interval, the additive integral is formed. |
| 3 | Guiding Questions |
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The questions provided assist students in clarifying or extending an understanding (misunderstanding) of the properties of the definite integral for the given function, e.g., rational functions; provide the next step in a procedure and demonstrate types of well-known integration formulae the students should use. |
| 4 | Guiding and Factual Questions |
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The questions provided assist students in justifying the properties of the definite integrals, e.g., the facts of Question 1, Question 2 and Question 3; applying it to a current problem to verify the definite integral for symmetric functions, periodic functions and even/odd functions in a step-by-step manner based on a set of specific integration techniques such as integration by substitution. |
| 5 | Probing and Guiding Questions |
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The questions provided assist students in verifying the property of the definite integral in a step-by-step manner and matching all information in a correct sequential order by recalling important prior knowledge of mathematical results such as knowledge of Question 1 and Question 2 and Part II of the Fundamental Theorem of Calculus. |
| 6 | Probing and Factual Questions |
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The questions provided assist students in elaborating on their thinking for finding the definite integral of the given problem value in a procedural manner and giving a reason why the answer is obtained based on the expected prior knowledge. |
| 7 | Probing, Guiding and Factual Questions |
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The questions provided assist students in verifying the definite integral of the given problem value in a step-by-step manner and matching all information in a correct sequential order by recalling important prior knowledge of mathematical results such as the property of a period function and giving a reason why the answer is obtained. |
Schedule of final examination is:
The Calculus Project Teams, Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong.