Twenty-sixth International Conference on Learning

Abstract

We shall concentrate on an integrated college course in algebra and trigonometry. In order to allay anxieties, the first few minutes of every session are devoted to a review of topics already covered. Contrary to the way mathematics was taught in the past, no time is allotted for writing calculations on the blackboard while the students arduously take notes. A board however should be used to draw interconnections between mathematical disciplines. Following the presentation of a new principle automatically transmitted to smartphones or laptop computers brought to the classroom, the remaining time is spent on an open exchange of student reactions, teacher criticisms, and further clarifications. Teacher-student interaction — one speaks and others listen —can lead to improvements in comprehension. Even at the elementary level, the learner must possess some ability for choosing a strategy before working on details. To prove the square root of two is irrational, a feasible approach involves proof by contradiction, definitions of rational and even numbers, and a mathematical valid substitution of variable, all of which when applied implies an apparent contradiction. Only with repeated readings of theory and extensive practice of reviewing solutions of similar problems at home can this skill be acquired. No time is allotted for writing calculations on the blackboard while the students take notes. Following presentation of a new principle of algebra or trigonometry, transmitted to smartphones or laptop computers brought to the classroom, time is spent on an open exchange of student reactions, teacher criticisms, and further clarifications.