Students often ask for these types of examples with answers, believing that they are doing well if they can match a problem to an example. Unfortunately, this often does not work and often makes the students less likely to continue studying. In order to make this type of learning more effective, the following tips can help. Make sure you understand the main idea behind the question before answering it:
Do not make the student work through the problem alone. Assign the responsibility to the student that will help them answer the problems much easier. For instance, if the problem requires the student to solve for x, then the student should answer that without looking at any other papers on the table. They should then pass the problem to the person who has the equation for x, so that the student does not have to look up anything else in the book. Using a calculator is fine when the student is solving for x, but using a more generic calculator that can handle all the different cases will make the problem much easier to solve.
Practice the example questions that you give students so that they do not have to spend too much time trying to answer them. For each class that you teach, it is likely that there will be at least a few examples that will test the skills of your students. Spend just five to ten minutes giving this example to each student so that they get comfortable with how to solve for an answer.
When your student is having trouble with one of their examples, do not only give an easy answer. Tell them that they can find more examples online. This is a way for you to get them thinking in a different way and to spark some creative thinking. After all, many students get into trouble by getting stuck working on one problem, regardless of how easy it may be.
You may want to let your student see the problem again. Let them re-read the question and try to find an answer for it. Even though finding the answer may be hard, they may find that they can eliminate a number of answers that they were not considering before. It can be difficult for students to completely eliminate a complicated question from their mind, but it can be much easier to find an answer by changing the way that they think about the problem.
Another important thing is to encourage your student’s use of calculators throughout the class. It can be tempting for many students to just let their calculators are used as if they are doing nothing at all. However, this can be counterproductive. If you ask your student to do a problem, but then they use their calculator instead of working it out, you may be encouraging them to do as much work as possible and not really work at all. If you want them to be successful in their coursework, make sure that they understand the usefulness of their calculator. After all, it is not something that they will be able to get rid of very easily.
Calculus examples are a great way for you to help your students learn how to solve problems. In order to do this, though, you need to encourage them to work at it. This may mean that they have to come up with their own solutions or it may mean that they need to check out an example. Either way, though, this will allow them to work on problems in a way that will make them much easier to solve.
