Of course, given the initial velocity and launching angles, the answer to this question can be determined by calculating the time required for each cannonball to reach its target, but with a little thought, the answer can also be determined using only logic.

Students individually try to solve the question for about two or three minutes. Their responses are recorded using clickers.

I use software called 'Beyond Question,' which was provided with my clickers, to see when all students have answered and how many students have selected each response. With these figures at hand, two options are possible after the results are announced:

1. One can use peer tutoring. Students are asked to find a partner who has answered differently from themselves and try to justify their answer to the other student. This method works well, and students participate enthusiastically; however, the teacher cannot follow all the discussions, at best listening to those going on nearby. Once the discussion is over, students modify their responses if they've changed their minds.
2. One can also have a class discussion and ask for a volunteer to openly explain the logic behind their reasoning in order to convince others. Five or six students can try to convince class members that their answer is correct and that the others are wrong. Throughout these discussions, students are at liberty to change their vote, and the teacher can instantly see the effect, positive or negligible, of each discussion on student opinion. Using this approach, the teacher can provide additional information, if required, when a particular student explanation is correct but not fully developed or explain why another response is incorrect. The problem with this tactic is that it is usually the same students who answer while others remain more or less passive.

It is not always necessary to have a discussion. If more than 80% of the class responded correctly, a rapid explanation for those in the minority will suffice before moving on. If practically no one got the right choice, on can provide futher information in the form of hints or directly ask those who did succeed to explain their reasoning. Occasionally, a student will tell you their answer is the result of a guess, but sometimes a very sophisticated correct explanation will emerge.

Obviously, student interest cannot be maintained without grades linked to the understanding of basic concepts. On my exams, fifteen theoretical questions appear, counting for two points each. Students are aware that this type of question will be on the test and try hard to understand the reasoning that led to the correct response. If you want to see examples of theory questions (in French) used in the exams, they are available for the three Physics courses on the site - La physique à Mérici.

Have you done something similar in your courses on theory in Physics or in another subject? Share your ideas and comments with Profweb readers by using our Reader Response Feature.

In case you were wondering, it is Cannonball B that arrives first at its target!