Here are a few interesting ideas shared during the first set of talks about teaching with clickers at the Joint Mathematics Meetings earlier today. (This post’s title inspired by the following books seen at the exhibits: Calculus Gems, Mathematical Diamonds, More Mathematical Morsels, and Biscuits of Number Theory.)
Kathryn Ernie (University of Wisconsin-River Falls) shared ways that she and her colleagues use clickers in their college algebra courses. One use that she mentioned was to warm students up before “traditional” in-class quizzes. By asking students a clicker question or two, then discussing those questions prior to a graded quiz, the students are able to approach the quiz with a little more confidence.
Ben Galluzzo (Shippensburg University) also talked about graded quizzes. However, in his case, clicker questions aren’t warm-ups for the quiz; the clicker questions are the quiz. Clickers allow Ben to turn his quizzes into learning experiences for his students. After each quiz question, he discusses the question with the class before moving on to the next question. This can work particularly well when he has more than one quiz question of the same type. Students who miss the first one can learn from the discussion of that question and apply what they’ve learned to the subsequent question. Students like this because they appreciate the chance to redeem themselves.
Aprillya Lanz (Virginia Military Institute) mentioned that teaching with clickers help students stay awake and engaged during class. This is particularly important for her since many of her students are freshmen (“rats” as they’re called at VMI) who are required to participate in all kinds of strenuous physical activities, particularly on Sunday nights. This can make for some very sleepy students in Monday morning classes.
Daniel Joseph (also VMI) described a problem that those who teach calculus often see: His calculus students often struggle because of pre-calculus misconceptions. They can’t tackle the calculus because they get tripped up by algebra and other pre-calc topics. He described several methods he’s tried to combat this, but he finds that the students’ over-confidence trips keeps these methods from working. The students say they “know” all the pre-calculus material because they’ve studied it in the past. Daniel appreciates how clickers provide his students with frequent evidence that they don’t know it as well as they think they do.
Daniel shared one approach to attacking this problem–using clicker questions in a pre-semester pre-calculus course for incoming freshmen. He’s interested in hearing ideas for hitting this issue, with or without clickers, in the calculus course itself. Any ideas?
(By the way, Daniel used the phrase “attack this problem” at least five times in his presentation. Given that he teaches at a military institute, I figured that was language that comes naturally to him. Thus my use of the verbs tackle, combat, attack, and hit above!)