Now that you know a little about brains, let’s see what that information implies.
Prof. Bob has a point. An example. Students take a statistics course in the fall semester, learning about t tests, correlation, and other data-ish things. The next semester, a professor says to a class,
“The correlation coefficient is -0.82, with an alpha of less than 0.001. What does that tell you? Anyone? Anyone?”
Silence. (Cue cricket sounds.) Think the class scene in Ferris Bueller’s Day Off.
What’s going on? Putting aside shyness, there are several explanations:
- The students never learned about correlation.
- The students did learn, but have forgotten.
- The students know, but don’t know that they know.
Brains, connections, input, and stuff
Here’s a brain:
You can think of the dots as neurons, or concepts (abstracted from patterns of activation across neurons). For our purposes, we’ll call them concepts.
The concepts are connected to each other. Trigger one, and it will activate connected concepts, depending on the number and strength of the connections.
The boxes are inputs, like “see a cat wearing a birthday hat,” or “hear ‘Smoot–Hawley Tariff Act.’” Different inputs trigger different concepts. For example, Smoot-Hawley triggers a memory of soul crushing boredom.
A math course
A student – let’s call her Joann – takes a math course. It’s a typical university intro math course, with too many topics crammed into too little time (OK, that’s a value judgement). The textbook presents context-free math. There isn’t much attempt to link it to the practical world. The exercises give equations, rather than describing situations.
Math isn’t Joann’s thing. She does the best she can, learning some facts, and some procedures, without understanding them in depth. Her brain looks like this at the end of the semester:
The math concepts are isolated, with limited connections to other concepts. The cues that trigger the math concepts tend to be context specific. That is, for this student in this course, cues like “linear equation” and “problem from chapter 5” only make sense in MATH 101 brain space.
Joann moves on
Joann takes her math final. She get a C in the course. That’s all she needs to pass. Sigh of relief.
Cues like “linear equation” vanish from Joann’s life. Here’s her brain now:
The MATH 101 concepts aren’t activated. Their cues were context specific, and Joann isn’t in the MATH 101 context anymore. She can go weeks without hearing “linear equation.” Further, the MATH 101 concepts aren’t connected strongly to non-MATH 101 concepts. When a cue activates a non-MATH 101 concept, the activation is unlikely to spread to the MATH 101 concepts.
What happens to weakly connected concepts that aren’t triggered? Joann fuhgeddsaboudsem.
Given what we learned about brains, Joann’s forgetting is predictable. It isn’t an aberration.
We could replace the current version of MATH 101 with a Cycourse designed to help students build deeper connections. We’ll talk about that when we get to Cycourse design. Spoiler: fewer concepts, more applied exercises, and learning how to think about problem solving (metacognition) with the help of patterns and big ideas.