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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 Questions |
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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 basic integration formulae for the given function, e.g., polynomials, exponential and logarithmic functions, trigonometric functions and rational functions; provide the next step in a procedure and demonstrate the kinds of integration techniques or types of well-known integral formulae that students should use. |
| 3 | Guiding Questions |
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The questions provided assist students in clarifying or extending an understanding (misunderstanding) of basic integration formulae for the given integrand, e.g., rational functions; provide the next step in a procedure and demonstrate the integration by substitution, the integration by parts, and the integration by partial fractions. |
| 4 | Guiding and Factual Questions |
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The questions provided assist students in justifying the properties of basic integration formulae for the given function (e.g., rational functions, exponential functions, trigonometric functions, and algebraic functions), using prior knowledge (e.g., rationalization, simplification, cancellation, factorization, substitution rule, completing the square, partial fractions), and applying it to a current problem for finding the integral in a step-by-step manner based on a set of specific well-known integration results and mathematical formulae. |
| 5 | Probing and Guiding Questions |
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The questions provided assist students in verifying the integral result 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 a trigonometric identity/inequality or the property of inverse functions. |
| 6 | Probing and Factual Questions |
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The questions provided assist students in elaborating on their thinking for finding the correct integral in a step-by-step manner and giving a reason why the answer is obtained. |
| 7 | Probing, Guiding and Factual Questions |
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The questions provided assist students in verifying the integral results 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 trigonometric identities/the power series of exponential and logarithmic/trigonometric functions/the inverse matrix method/a well-known integration formulae 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.