I am continually impressed by the link between seeing and understanding. This should not be surprising. How often have we had the experience of being told by a student (or colleague) that “I just don’t see it” after our failed attempts to explain a complex concept. If there is a relationship between seeing and understanding can we facilitate understanding by presenting the concept visually? This is not a novel idea but it is still one which often slips by me particularly in areas where I am facile (such as medical decision making).
Four times a year I lead a group third-year medical students through afternoon seminar on using test results in the diagnostic process. Although one could make this topic very broad, the focus of the seminar is essentially Bayes Theorem. There is plenty of evidence that this is a challenging topic for students in the health sciences (and practicing physicians). I certainly found it challenging when it was introduced to me in medical school. However, once mastered I had to wonder why students could not see how obvious Bayes Theorem is; it is only a simple mathematic transformation. When teaching Bayes Theorem it always seemed to take me multiple attempts at the computation and providing explanations until a few of the group grasped the concept of probability revision. Most would leave bewildered.
In frustration, I searched for a better approach- I thought my students should be able to experience the wonder of probability revision and not the pain of elementary mathematics. The search led to a wonderful report about simplifying bayesian inference by making it visual. (S Krauss, L Martignon, U Hoffrage. Simplifying Bayesian Inference. Conference on Model-Based Reasoning in Scientific Discovery, 1998. http://www.mpib-berlin.mpg.de/en/institut/dok/full/martignon/kssbimbri/kssbimbri.pdf) Students still are required to perform simple mathematical computations but the visual presentation of Bayes Theorem allows the students to see where they are in the process. Once completed students can easily go back and review the steps they took. This simple visual approach has turned afternoons of student frustration into afternoons of discovery where they come to “see” the importance of pre-test probability in interpreting a test result and “see” the importance of not only sensitivity but also specificity.
If you are facing a similar challenge in your teaching, I highly recommend that you take a look at this approach.