Imagine a Solution
Imagine you are a student studying some particular topic. You may be using a textbook, computer based material, or a web site. Suppose that material is not appropriate for you at your current level of expertise. Now, imagine that you could click a button or enter a code number in a program and choose from a list of alternate material that is all specifically written for the exact topic you are studying. If you are studying the integral of the sine function, then all of these explanations only cover the integral of the sine function. No more, no less. Each of those alternate explanations, whether they are text or multimedia, would be ranked according to difficulty level and the amount of prerequisite knowledge required to understand them easily. If none of these explanations help you, you can then review the list of prerequisites for this topic and discover that your proficiency in some of these prerequisite topics is lacking. “That’s why I couldn’t get it!” you tell yourself. So you simply click a button and go straight to the appropriate material to study each of those prerequisite topics. Once you have achieved an appropriate level of understanding in each of these other topics, you return to the original topic and find you can now grasp it easily.
Now you can move on to the next topic in your detailed syllabus or lesson plan. This time you check the prerequisites first to save yourself even more time. Suppose you meet all the prerequisites for the next topic but still can’t understand it. You have read all the different explanations available and it just isn’t sinking in. What if you could then click another button and instantly search the web for all the web pages that contain information only about this exact topic. The search links take you directly to the specific paragraph within the page that discusses your specific topic because they are encoded with the same topic ID used to identify the topic you are studying. And you don’t waste a single second sifting through unrelated material. Unfortunately, all of it was too advanced for you so now you decide you need to ask someone else for help. But what if you didn’t have to wait till the end of the week or even tomorrow to get your question answered. What if you could post your question — using any media you desired — some place where thousands of educators and students all over the world would see it and likely respond within minutes? Isn’t that better than Googling till you are blue in the face?
Once you fully understand the topic, you decide you could have written a better explanation than any of the ones available. So you write up your version of the explanation and post it. People discuss it for a while and perhaps suggest improvements. Then, when you think it is ready, you submit it for vetting. This is when thousands of certified educators get a chance to examine your explanation for accuracy. If any errors are spotted then you get a chance to revise your explanation. By the time you are finished you really know this topic like the back of your hand. It will probably stick with you forever. After several certified educators sign off on your explanation you get your chance at immortality by having your explanation added to the vast library of knowledge for others to learn from. Your explanation will now appear when anyone else in the world clicks that button to look for alternative explanations. Who knows, if yours is good enough it may even be the first many see when they first look at that topic.
Now it is time to do your homework. Your instructor has created an electronic list of the specific problems he wants you to do. Depending on the subject matter and the way the professor prefers to grade papers, you may enter your answers in the computer or write them down. If you have trouble with a problem you can do the exact same thing that you did when you were studying the topic in the first place. You can check to make sure you understand all the prerequisites well enough to complete the problem without struggling too much. If you just simply can’t get it, you can even look at hints or even a complete solution to the problem. Your professor knows this, which is why he only considers the problems to be practice. If he wants to make sure you really have to do the work then he can choose from a special pool of problems that have no solutions posted. But he knows this is a moving target because new solutions to problems are being posted every day. What the professor does know is that he has explained to you how difficult it will be to get a good grade on the test if you haven’t worked through these problems yourself. The great thing about using the DEMML™ system is that you actually can work through the problems yourself because of all the thorough solutions available complete with multiple explanations for each one. Your professor is not too very concerned about the homework because he knows it will all come out in the test. That is why homework only counts for a very small part of your grade. Naturally, some of your professors remain old school and make up their own problems for you to do or pull them from old textbooks.
Several weeks have gone by since you first studied some of the topics that will be on the upcoming test. But you are confident you will do well. Your computer has been regularly asking you questions about all the material you have studied, to keep it fresh in your mind. Each question has been just a little bit different — thanks to the huge library of questions and problems available — so you know you understand the concepts and know the material rather than just memorizing the answers to a few questions on a few flashcards. You walk into the test and easily ace it. Not because the questions are easy or even because you have seen them before. But because all of the questions are well worded and are at the exact difficulty level promised by your professor. You notice your professor seems less stressed than last year. Perhaps this is because he didn’t have to stay up all night creating multiple versions of the same darn test. He easily created all these versions of the test by simply selecting from that same vast library of question and problems. All he had to do is set his software to filter the available questions based on the electronic syllabus he created before the course even started. That syllabus told the software exactly how difficult the questions should be and which topics should be covered. All he needed to do is pick the questions he liked best and print out the tests. He didn’t need to worry about students memorizing answers to problems they had seen before because there are so many questions for the software to choose from that no one could possibly memorize even a small portion of them.
After your course is over you do not worry about forgetting material you may need for future courses. You have already downloaded the electronic syllabuses for all your future classes. The prerequisites listed in those syllabuses tell your computer exactly which topics to make sure you don’t forget. So your computer occasionally asks you questions about just those topics. This doesn’t bother you too much because it only goes back to a topic when it predicts you are likely to start forgetting the material. By combining recent research into how the brain decides what to remember along with your personal history of ability to remember this material — your “forgetting curve” — the computer can bring things up with just the right frequency. Not so often that you get tired of seeing it, but just often enough so that you don’t forget it. As time goes on, the material is so set in your brain that the computer only needs to bring it up once a year or so just to make sure. And you barely even need to work at remembering it.
