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The questions we construct sometimes involve Walsh and Satters's ten question types: Essential Questions, Hook Questions, Diagnostic Questions, Questions to Check for Student Understanding, Probing Questions, Inference Questions, Interpretation Questions, Transfer Questions, Predictive Questions, and Reflective Questions.
| 1 | Essential Question | Integrates facts around a main idea or concept | The first question engages students in thinking at the conceptual level and assists students in constructing schemata that assist in knowledge transfer in the applications of the definition of a continuity function. |
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| 2 | Hook Question | Is intentionally designed to spark student curiosity or interest | The second question and the fourth question provided allow students to answer and become involved with content using a coach approach, e.g., fill in all missing pieces in a correct sequential order by typing specific numbers, even if they know little about finding the limiting value of a continuous function. |
| 3 | Diagnostic Question | Is often formed by teachers drawing on their experiences if teaching a concept to previous groups of students - forming questions around concepts and/or skills with which prior classes have had difficulty | The third question and the fifth question provided allow students to activate prior knowledge of the definition of a continuity to enable determination of the correctness/ incorrectness of these concepts, connect new content to existing knowledge for finding the limit value of a continuous function, or to engage in learning activities through plotting the figures using Geogebra, which rectify misconceptions by finding a list of correct solution orders. |
| 4 | Question to Check for Student Understanding | If planned, teachers design it as a formative assessment question to generate information that they can use to inform their next instructional move and that students can use to modify their learning strategies | The sixth question provided allows students to correct misunderstandings of the definition of a discontinuous function or fill in voids by providing additional instruction for finding the length of the jump. Geogebra provides an interactive mechanism for student self‐assessment and allows them to check their findings. |
| 5 | Probing Question | Focuses on the part of the student response that was incorrect, incomplete, or unclear | The seventh question provided assists students in clarifying or extending an understanding (or misunderstanding) of the points of discontinuity of the given function and helps to scaffold student thinking in a step-by-step solution approach, understanding its solution via the graphical visualization, and learning in a logical manner. |
| 6 | Inference Question | Requires students to use evidence to draw a tentative conclusion | The eighth and thirteenth questions provided encourage students to find evidence on the continuity of the product/sum of absolute functions and of a composite function, analyze these newly formed composite functions, and make determinations about the continuity of these new functions, e.g., fill in missing information for obtaining these limiting values. |
| 7 | Interpretation Question | Asks students to personally evaluate content under study | The ninth question provided allows students to form a final judgement for choosing the correct theorem for a given set of solid calculations after gathering all relevant/given information. |
| 8 | Transfer Question | Requires students to apply information in a novel setting | The tenth question provided allows students to determine the differentiability of the function and builds student confidence and self‐efficacy through the opponent’s participation in interactive discussion. Students are required to check their opponent’s answers. Students will see in which part they made incorrect answers and then they are able to redo the same problem. |
| 9 | Predictive Question | Engages students in “if‐then” thinking | The eleventh, twelfth and fifteenth questions provided allow students to determine the value of the differentiability of the function based on the if-then condition and guide students in cause‐and‐effect thinking. |
| 10 | Reflective Question | Asks students to assess their personal relationship to the content they are studying | The fourteenth question provided allows students to find the function that satisfies a few function properties and its differentiability and facilitates student self‐regulation and self assessment, where these steps are: 1. Students are required to check their opponent’s answers. 2. Students will see in which part they made incorrect answers and then they are able to redo the same problem or work out a follow up problem that we recommend. |
Schedule of final examination is:
The Calculus Project Teams, Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong.