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A Simple Geometric Model Provides a Possible Quantitative Explanation of the Advantages of Immediate Feedback in Student Learning

Calculus is a known bottleneck for many students studying science and engineering. Various techniques have been developed to enhance the students’ success. A recent study [1] published in the Notices of American Mathematical Society showed that only one factor determines the success of a technique: the presence of immediate feedback. On average, students who receive immediate feedback learn twice faster than students who are taught in a more traditional way, with a serious feedback only once or twice a semester (after a test). The very fact that immediate feedback is helpful is not surprising: it helps the student clear misconceptions and avoid the wrong paths. However, the fact that different techniques involving feedback lead to practically the same learning speed-up is intriguing. To explain this speed-up, we provide a simplified first-order description of a learning process in simple geometric terms. We show that already in this first approximation, the geometric description leads to the observed two-fold speed-up in learning. 1 Immediate Feedback Improves Student Learning: Empirical Data Student understanding is extremely important. One of the main objectives of a course – whether it is calculus or physics or any other course – is to enable students to understand the main concepts of this course. Of course, it is also desirable that the students learn the corresponding methods and algorithms, but understanding is the primary goal. If a student does not remember