I make it a particular point for first-semester college students to teach them how to learn effectively. I do something similar for second-semester students especially if most of them were not in my class the previous semester. For a precalculus class, I may stress the points below throughout the semester. For a Calculus II class, I adapt myself according to their performance. I should note that when I say I teach them to learn effectively, I recognize that it took me a long time to learn how to learn and it might take most of my students a few years, too.
I have several things I try to tell them at opportune times. When possible, I tell it through a story. It helps to have an interesting roommate in college, or to have made mistakes yourself when you were a college student. I usually say such things at the beginning of class, and limit it to one thing per class. Some of the things I say are appropriate for everyone and some moreso for a student who is struggling with something. In the latter case, I might say those things only in person. It's good to have a balance of positive and negative examples. Positive seems better, but sometimes a warning example is the best you can do, especially if a few students might might recognize themselves in the story.
The important thing is to give advice when the students are receptive to it. Sometimes a student will ask something in class that is a perfect lead-in to one of the points. A few of the topics are meant to prepare the students for advice. For instance the "work versus effort" discussion and the biology of learning below establish terms for discussion I can use throughout the course. One of the times you will have their greatest attention is the day you hand back the first test. (For that reason, I think it is good to have an early test, around three weeks into the term, while there is still time for the student to adjust.) It is important that I have the terms in place before I have that conversation.
Since I am trying to get them to change their habits, it takes a lot more than just telling them what to do and what not to do. It helps to get them to recognize that their habits need improvement. It also takes a lot of reinforcement.
Below, I have put the words I say to the class or student in quotes, more or less as I might say it. Occasionally discussion or comments will appear outside the quotes.
- Work versus effort. "In physics, work is the product of the component of force applied in the direction of motion. For instance, when you move a heavy object, the work done is proportional to the distance the object is raised. If you carry a 100 lb. object across the quad, it takes a lot of effort, but you do no work if the object is not raised. Learning takes work and effort. You want to raise the level of your understanding standing. You want as much as possible your efforts to be efficient and result in work accomplished." Not all my students know physics, so this needs a brief explanation such as I wrote above. I usually tell this a week or two into the term and well before the first test. Then I remind them right after the first test before they get the scores back. "If you find that your performance wasn't as good as you wanted, you might consider how effective your study habits have been. What you did, did it get the work done? If you have questions or concerns, come see me. I know lots of good strategies for studying and can help you."
- Learning takes work. "Learning alters the neural networks in the brain, and the alteration takes energy. It really does take work in the sense of physics." This might be what I say the day after the work versus effort story.
- How learning happens. "When a neural network is formed, it is connected to other networks, other knowledge. There is a process of forgetting that naturally occurs in which the new network becomes less likely to be activated unless it is used. The more it is used the more easily it is activated. More networks form around it as our understanding deepens. One of the more powerful ways to reinforce this new knowledge is when it is used to create motor activity." Some teachers are creative and make up dances or other physical activity. "Writing out the solution to a problem is motor activity. So is illustrating the solution with a graph."
- Practice. "The primary way to learn mathematics is to practice solving problems." I tell them several times. I can connect it to the description of how learning happens above when appropriate. "Once you learn how to solve a problem, practice solving problems the way you will be tested -- without resources, writing complete solutions. When you don't need to look things up, you will know that you know how to do it."
- Recall. "The effort to recall reinforces knowledge and makes it easier to recall it. Trying to recall it in different situations helps, too. You can trying recalling things on the way to the cafeteria, say the derivative rules," or how to solve a type of problem, or a proof, etc., according to what's appropriate to the course.
- Memorization. "A carpenter does not plan to build a house by saying that whenever a hammer is needed, he or she can run down to the community center and rent one. If you're going to build solutions to problems, you have to have the appropriate tools at hand. You'll have to decide what needs to be memorized -- I'll give you hints when I think something is important. In mathematics it is much less than, say, in foreign language or some science courses. The best way to do it is in short, frequent, intensive intervals; then less and less frequently. Pick two times each day some hours apart and practice, with flash cards if you like, for fifteen minutes."
- Memory and understanding. "Memory is unreliable, at least my recall of facts is. It is easy to switch the facts around, get a minus sign wrong, and so forth. There are a couple things you can do to help. If you understanding why, then that can be used to check. Another is to learn a way to check." (For instance, for the sign of the derivatives of sine and cosine, in the first quadrant, the sine is increasing and the cosine is decreasing.)
- Repetition. "Sometimes it is more important to repeat a problem than to work a new one." When a student has struggled to work through a problem, I say, "Now what I would like you to do is later tonight or perhaps tomorrow, work the problem again and see if you have learned how to do it."
- Knowing that you have learned. In response to when a student says, "I don't know why I did poorly": "Did you work the review problems alone and unaided by the textbook and your notes?"
- Being prepared for the test. (1) "What do you think is the most important thing to do to be prepared for the test?" (Wait for their answers. You'll get an insight into some of your students, and generally you find out they know half the things you would tell them -- at least, they know what to say.) My answer: "To show up. You're not prepared to take the test if you're not there." Then I work back from that to the things it implies, such as getting a good night's sleep, etc. (2) "Be prepared to take the test the day before it is offered. If you wake up and, nightmare!, the test was that day, you should be able to do a good job. If for some reason there is something you still have trouble with, then you have another day to figure it out."
- Help each other. "Forming habits is easier when your friends are doing it, too. And learning, especially learning difficult material, is easier when your friends are doing it, too."
- Learning how versus learning to study. It is relatively easy to learn the words of the answer to the question, "How should you study?" It is harder to learn to make it part of one's habitual practice.
- Positive attitude. It is particularly important that the teacher have faith that the students can do it. Students can sense sincerity. Forming or breaking habits is difficult and the student will have to do it for himself or herself. It took me until junior (3rd) year of college to feel that I had formed good habits and knew how to learn effectively. I tell that to my students. I emphasize that they need to be patient with themselves and they will improve. If they continue improving, they will become excellent.
I started thinking about these things several years ago, when a good student, one who had won a scholarship, came to me and said she was surprised by the questions on the test and they were not what she expected. I said, "Well, let's look at the test. Maybe I made a mistake." So we went through the test and quickly summarized what each problem was about. Then I said, "Now, let's look at the syllabus." It corresponded exactly with the test. She said, "Wait! It's that's simple?!" It made me start paying closer attention to what the students do not know about going to college/university. Last fall, another student, even more highly qualified, earned a D on the first test in Calculus II and came to me for advice. On the next test, he made only one minor error. When I returned the test, he exclaimed out loud, "Oh my gosh! Studying pays off." My colleagues often have a "Well, duh" response, but to me it shows just what the teacher needs to do.
Finally, let me recommend again the physics-based description work versus effort. Such gimmicks often have varied success in the hands of a variety of people, but this one has been effective for me. I do not get far fewer complaints about how hard the student tried; rather, they say, "I put in a lot of effort, but I still did bad. What can I do to improve?" First, I think that is where their attention should be. And second, asking for help is so much more pleasant, both for me and for them.
Helping people change their behavior requires patience. I know the above helps some -- I would say most of my students this year -- and would help all. There are always students struggling with personal issues. A few have said it helped with the rest of their college career.