What is it?
One of the first questions I tried to answer as an instructor was “where do I draw the line between ‘the student has some gaps in their understanding of the material’ and ‘the student has not done the prerequisite material in order to succeed in this class’. After some self reflection I came up with the “State Diagram of Knowledge”.
Credit: https://github.com/FenixFeather/cs173-flowchart/blob/master/173-flowchart-work.svg
This FSM/DFA represents what the student’s current state of knowledge is. Every student starts off in the “NULL” state. In this state you know nothing about the concepts being taught. Well knowing nothing is kind of a lie, but I will get into that later. A student that wants to learn will start off in the NULL state and try to transition to the “I got this!” state. In the early stages of learning students go to lecture and do the prerequisite readings. Each of these actions act as a transition function that will enable the student to progress to a state where they have done all the prerequisite studying before moving onto activities that are designed for them to apply their understanding. Once you have done all the prerequisite studying (labeled “L+R” for having went to lecture and done the reading in my example), then the you have to participate in a very important activity; self reflection. Self reflection is one of the many ways to turn passive learning to active learning. After self reflection you will be able to determine whether you are “lost”, “confused”, or “Got this!”. Take note of the dotted line in the diagram. Notice what is on the right of the line, but not on the left; Office Hours. I call this line the “line of Good Faith Attempt”. This is where I draw the line between a student having holes in their understanding and just not having done the prerequisite material. It is only until a student reaches this line of good faith attempt that I think an instructor is needed. An instructor’s job is to take a “lost” student and nudge them to the “confused” state and finally to the “I GOT THIS!” state. Sometimes when I do my job really well I can take a “lost” student and jump them to the “I GOT THIS” state. However it is not my job to orate the class notes to the student. It is not my job to work out countless practice questions that are already in the textbook. It is not my job to write out every definition that has already been painstakingly typeset for a pdf file.
I also want to clarify that a “lost” student is by no means equivalent to a “NULL” student. A “lost” student has went to every lecture and read all the notes. This student has all the surface level knowledge down already. They know every definition that is needed to solve the problems at hand. They have seen every example problem worked out in detail. What they haven’t done yet is piece all the knowledge together and understand how all the definitions and facts relate to each other. They can’t apply the tools they have crafted yet and that is exactly where you come into the picture. When a “NULL” student comes to office hours before a homework assignment is due what is really happening is that they want you to somehow “bypass” all the time needed to go to lectures and read the notes. They view you as the person who is able to tell them exactly what they need to know to solve the problem at hand and nothing more. But there is no substitution to hard work. Office hours are merely meant to complement the lectures and readings. Office hours are NOT designed to substitute hours of lectures and readings. Just think about it. If everything a student needed to know to succeed in your class could be relayed in a 15 minute office hour session, then why are you bothering spending hours every week lecturing and having them spend hours reading notes?
Finally I want to address what I meant in the beginning when I said that it’s a lie to say that a NULL student knows absolutely nothing. Lets take a look at the “Got this!” state one more time. Notice that it is circled twice meaning that is an accepting/end state. This where you hope every one of your students end up. What I want you to think about is “what arrow leads into the NULL state?”. You can argue that the “NULL” state is the start state of this FSM and that it acts as a source and the “Got this!” state acts as the sink of this graph. However I like to think that every “Got this!” state has an arrow leading out of it into another “NULL” state. That’s right! Every “Got this” state serves as a prerequisite to another learning objective. The “Got this” state for pre-calculus has an arrow leading to the “NULL” state of calculus. I say that this is the FSM of knowledge, but the illustration on this page is merely a very zoomed in version of the very complex network knowledge is. Knowledge is actually many state diagrams of knowledge linked up with potentially many “Got this!” states funneling into a more grand “NULL” state.
Discussion
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Email: bschong2@illinois.edu