Worked examples
A common task in a lecture to 'work through an example' in order to show how to solve a particular kind of problem. The lecturer might write up a problem on the board and then show students how to solve it, step by step, perhaps asking questions at various points ('so, what should we do next?', 'how can we apply this rule at this step?' and so on). This type of worked example is often quite easy to turn into a sequence of multiple-choice questions. Just break the worked example up into a sequence of steps and think about what questions you can ask at each step. Then turn those questions into multiple-choice questions. In doing this, it is useful to think about common mistakes that you know from experience students often make. That will help you think of good incorrect options (also known as 'distractors') for the multiple-choice question.Here are some examples taken from a formal logic course. The problem to be solved is to decide whether a particular argument is valid or not. This is done by first translating the argument into a formal language and then applying a formal method (truth-tables or trees) to test the validity of the argument form. The following sequence of questions takes students step-by-step through this process.
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1. Translate the following argument into symbolic form: If the printer is unplugged or the ink cartridge is empty, the page will not print. The page did not print. Therefore the printer is not plugged in. p = the printer is plugged in c = the ink cartridge is empty g = the page was printed. A. (p v c) –> ~g, g |– ~p B. (p v ~c) –> ~g, g |– ~p C. (~p v c) –> ~g, ~g |– ~p D. (~p v c) –> g, ~g |– p |
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2. What truth values go in the missing spaces in the truth table for this argument? A. 1 B. 0 (~p v c) –> ~g, ~g |– ~p
3. The truth table shows that the argument is: A. Valid B. Invalid C. Impossible to tell. |
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4. Counter-examples to the validity of this argument are found on lines: A. 5 only B. 5 and 6 C. 1 and 3 D. 5 and 7
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The following PDF contains another example, this time using trees (tableaux) to work through a similar problem: