Motivation Online

### Motivate: Problem Solving

In the previous section there were some general
tips in regards to homework sets as a whole. Here are some tips to help
you actually work the problems. Note that some of the ideas were
important enough that they are actually in both sections.

**Read the Problem.**

Read
the problem to get an idea of what you’re being asked to do. This
one of the biggest sources of point loss that I’ve seen in
grading. Too many students just skim the problem and assume they
know what’s going on and what they are being asked to do.

**Read the Problem Again.**

Now
that you know what you’re being asked to do, read the problem
again. This time around make note of what you are given and what
you need to find. Also make sure that you understand just
what you’re being asked to do.

**Clearly Note What You Are Asked to Find.**

Clearly write down somewhere what you’re being asked to find.

**Clearly Note What You Know.**

Clearly write down somewhere all the information you’ve been given.

**Draw a Diagram.**

If
appropriate draw a diagram and label what you know and what you
need to find. Often diagrams will suggest the solution technique,
so it’s a good idea to get into the habit of drawing them.

**Devise a Plan.**

Try
to figure out what you’re going to need to work the problem.
Identify formulas that may help you. See if there are any
intermediate steps/answers that will be needed in order to arrive
at the final answer.

**Work a Similar Problem.**

If
you can’t figure out how to work the problem find a similar
problem that is simpler. Work this then go back and compare what
you did in the simpler problem to the problem you’re asked to do.

**Work the Plan.**

Once you’ve got the plan, work it out to get the answer.

**Check Your Solution.**

Is
the answer in proper form? Does your answer make sense? If possible,
plug your answer back into the original problem as a check.

**Go Back Over the Problem.**

Once
you’re satisfied that you’ve got the correct answer go back over
the problem. Identify concepts/methods/formulas that were used for
the problem. Try to understand why these
concepts/methods/formulas were used on this problem. Look for
identifying characteristics that will help you identify this kind
of problem in the future.

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### Motivate: Doing Homework!

Note that this section contains some general tips
on making the most out of your homework. The next section contains tips
on actually working homework problems.

**Understand the Purpose of Homework.**

Mathematics is just not a subject that most people will instantly understand every single topic after hearing the instructors lecture. Most people need to work on some problems in order to really start to understand the topic. That is the point of the homework. It gives you a set of problems that will help you to understand the topics.

Remember that it almost always seems easier to watch an instructor doing problems on the board than it actually is. You won’t know if you truly understand the material and can do the problem if you don’t attempt the homework.

**Have The Actual Assignment.**

**Do the Assignment Promptly.**

**Be Organized.**

**Review.**

One of the biggest roadblocks in doing homework that I’ve seen in many students is that they completely ignore the notes and/or text. They look at a problem and if they can’t see how to do it they give up and go to the next problem. Often there will be a similar problem in the notes and/or text that can help you to get started!

**Read/Follow the Directions.**

**Be Neat.**

**Show All Work.**

**Check Your Work.**

### Motivate: Learn From Your Mistakes

**Review Homework.**

**Review Exams.**

**Understand the Error.**

**Get Help.**

**Rushed Errors.**

**Repeated Errors.**

**Keep a List of Errors.**

### Motivate: How To Study Mathematics

- Read what the instructor will be lecturing on before you go to class. Read slowly. Reading mathematics is not like reading a novel or even history. Speed reading techniques are not appropriate. Every word and symbol is important to the meaning. Do not skip the symbolic part of the text. This is often the most important part. If you do not understand a symbol, look in the glossary or in the earlier part of the text. Symbols are often explained when they are first introduced. If you still cannot find out what a symbol means, ASK! Read with a pencil in hand. Every time the author does a problem, do it on your own—either before or after you read his or her explanation. This makes sure you know what steps have been shown and, more importantly, which ones were omitted. If there is something you do not understand, try to formulate a question about it. Often if you can ask a specific question, you can answer it yourself. If you can’t answer it, you know what part of the instructor’s lecture requires your complete attention. Your question is ready if the lecture does not clear up your misunderstanding.

- Understand the concepts. Don’t be satisfied with vague ideas about how to work problems. Do the examples yourself, understand the concept illustrated, then try making up your own examples. Keep in mind that the questions on the exam may be very different from the example in the book.

- Practice. Be sure you understand the concepts before you practice. Then practice will help you remember and give you confidence in your mastery. Force yourself to remember the methods as you work problems; don’t look back in the book.

- Keep up with assignments (whether they are graded or not).The pace is much faster in college and keeping up to date with assignments helps you to better understand what is going on in class. Mathematics is not a spectator sport. The only way you can learn mathematics is by doing it. Following are some suggestions for getting the most out of the time you spend on homework.

- Understand the purpose of homework. Homework in mathematics classes is assigned to help you understand certain concepts and to help you build certain skills. Homework is not assigned to you because it is important to get the right answers. Your instructor already knows the answers.

- Try to understand the process, not the specific problem. Classify problems in the assignment by problem type. Although this is often done for you by the directions, it is not always. Do each assigned problem and then check it in the back of the book. Try to figure out why you missed the ones you did instead of just working toward the answer. A similar problem may be on a test or quiz.

- Mark homework problems you still do not understand and get help with them before the next class. The next lecture may build on a concept or skill you did not understand in the homework. When you do get help, make notes on what you learned, so that you can study them for the test.

- Before closing the book, look back over the assignment and try to explain to yourself what the assignment was about, what each kind of problem was asking, how you got the answers and what the answers tell you. This process will help you understand the material and will help you discover what you don’t understand.

- Keep your homework in a convenient and neat notebook so that you will be able to find questions or difficulties you have quickly and easily. This will also provide an invaluable study guide for tests.

- Ask questions. Do not hesitate to ask questions. Ask your instructor for help after you have tried to pull class notes and textbook explanations together for review and still don’t understand. Write down specific problems so you have them ready; don’t be vague and say you just don’t understand.

- Don’t hesitate. Get help right away. Tutoring and help sessions are available. The longer you wait before getting help, the harder it will be to get caught up. Most of the time when you feel lost, it is just one concept that you are missing, so get help quickly. One missed concept in a math class will make the rest of your math career a hardship. Don’t feel embarrassed to ask questions and get help; even the best mathematicians have felt completely lost at some point.

### Motivate: General Tips for Studying Mathematics

These are some
general tips that where either important enough to single out or just
didn’t seem to fit into any of the other sections.

**Go To Class.**

Remember that math is cumulative. If you don’t go to class you will miss important material that will be used in later sections and/or important announcements.

**Get to Class On Time.**

**Listen During Class.**

**Take Good Notes.**

Note as well that this seems to contradict the previous tip. It is often hard to both listen and take a good set of notes. This is something that one often only gains with practice. You need to be able to listen while you are writing down the important parts of the lecture.

If you find that are having trouble both listening and taking good notes then you might consider bringing in a tape recorder and record the lecture.

Note however that prior to doing this you should first speak with your instructor. There are a few instructors out there in the world that do not like to have their lectures recorded.

**Ask Questions.**

**Listen When Others Ask Questions.**

**Review Notes After Class.**

**Make a Set of Index Cards.**

**Learn The (Proper) Notation.**

**Get Into A Study Group.**

**Note Due Dates.**

**Budget Adequate Time For Studying/Homework.**

**Do Homework After Each Class.**

**Do Homework Without Notes and Book.**

**Do More Homework.**

**Practice, Practice, Practice.**

**Persevere.**

**Keep Old Homework and Exams.**

**Don’t Forget Your Textbook.**

**Seek Help If You Need It.**

**Have the Proper Attitude.**

### Motivate: How To Study Mathematics 2

Before I get into the tips for how to study math
let me first say that everyone studies differently and there is no one
right way to study for a math class. There are a lot of tips in this
document and there is a pretty good chance that you will not agree with
all of them or find that you can’t do all of them due to time
constraints. There is nothing wrong with that. We all study
differently and all that anyone can ask of us is that we do the best
that we can. It is my intent with these tips to help you do the best
that you can given the time that you’ve got to work with.

Now, I figure that there are two groups of
people here reading this document, those that are happy with their
grade, but are interested in what I’ve got to say and those that are not
happy with their grade and want some ideas on how to improve. Here are
a couple of quick comments for each of these groups.

If you have a study routine that you are
happy with and you are getting the grade you want from your math class
you may find this an interesting read. There is, of course, no reason
to change your study habits if you’ve been successful with them in the
past. However, you might benefit from a comparison of your study habits
to the tips presented here.

If you are not happy with your grade in
your math class and you are looking for ways to improve your grade there
are a couple of general comments that I need to get out of the way
before proceeding with the tips. Most people who are doing poorly in a
math class fall into three main categories.

The first category consists of the largest
group of students and these are students that just do not have good
study habits and/or don’t really understand how to study for a math
class. Students in this category should find these tips helpful and
while you may not be able to follow all of them hopefully you will be
able to follow enough of them to improve your study skills.

The next category is the people who spend
hours each day studying and still don’t do well. Most of the people in
this category suffer from inefficient study habits and hopefully this
set of notes will help you to study more efficiently and not waste
time.

The final category is those people who
simply aren’t spending enough time studying. Students are in this
category for a variety of reasons. Some students have job and/or family
commitments that prevent them from spending the time needed to be
successful in a math class. To be honest there isn’t a whole lot that I
can do for you if that is your case other than hopefully you will
become a more efficient in your studies after you are through reading
this. The vast majority of the students in this category unfortunately,
don’t realize that they are in this category. Many don’t realize how
much time you need to spend on studying in order to be successful in a
math class. Hopefully reading this document will help you to realize
that you do need to study more. Many simply aren’t willing to make the
time to study as there are other things in their lives that are more
important to them. While that is a decision that you will have to make,
realize that eventually you will have to take the time if you want to
pass your math course.

Now, with all of that out of the way let’s
get into the tips. I’ve tried to break down the hints and advice here
into specific areas such as general study tips, doing homework,,
studying for exams,

*etc.*However, there are three broad, general areas that all of these tips will fall into.**Math is Not a Spectator Sport**

You cannot learn mathematics by just going to class and watching the instructor lecture and work problems. In order to learn mathematics you must be actively involved in the learning process. You’ve got to attend class and pay attention while in class. You’ve got to take a good set of notes. You’ve got to work homework problems, even if the instructor doesn’t assign any. You’ve got to study on a regular schedule, not just the night before exams. In other words you need to be involved in the learning process.

The reality is that most people really need to work to pass a math class, and in general they need to work harder at math classes than they do with their other classes. If all that you’re willing to do is spend a couple of hours studying before each exam then you will find that passing most math classes will be very difficult.

If you aren’t willing to be actively involved in the process of learning mathematics, both inside and outside of the class room, then you will have trouble passing any math class.

**Work to Understand the Principles**

You can pass a history class by simply memorizing a set of dates, names and events. You will find, however, that in order to pass a math class you will need to do more than just memorize a set of formulas. While there is certainly a fair amount of memorization of formulas in a math class you need to do more. You need to understand how to USE the formulas and that is often far different from just memorizing them.

Some formulas have restrictions on them that you need to know in order to correctly use them. For instance, in order to use the quadratic formula you must have the quadratic in standard form first. You need to remember this or you will often get the wrong answer!

Other formulas are very general and require you to identify the parts in the problem that correspond to parts in the formula. If you don’t understand how the formula works and the principle behind it, it can often be very difficult to use the formula. For example, in a calculus course it’s not terribly difficult to memorize the formula for integration by parts for integrals. However, if you don’t understand how to actually use the formula and identify the appropriate parts of the integral you will find the memorized formula worthless.

**Mathematics is Cumulative**

You’ve always got to remember that mathematics courses are cumulative. Almost everything you do in a math class will depend on subjects that you’ve previously learned. This goes beyond just knowing the previous sections in your current class to needing to remember material from previous classes.

You will find a college algebra class to be very difficult without the knowledge that you learned in your high school algebra class. You can’t do a calculus class without first taking (and understanding) an Algebra and a Trigonometry class.

So, with these three main ideas in mind
let’s proceed with some more specific tips to studying for a math
class. Note as well that several of the tips show up in multiple
sections since they are either super important tips or simply can fall
under several general topics.

### Motivate: Taking Notes

Here are a couple of tips for taking notes in the class.

**Listen in Class.**

Do not just write down what you see on the board. No instructor is going to write down every word they say and sometimes the important ideas won’t get written down.

**Write Down Explanatory Remarks.**

**Note Important Formulas/Concepts.**

**Question Your Instructor.**

**Note Topics You Don’t Understand.**

**Review/Edit Your Notes.**

**Review Regularly.**

### Motivate: Studying for Examinations

Here are some tips on studying for exams.

**Start on Day One.**

You should always be studying for the next exam. Do a little each day, or at the very least start studying 2-3 days before the exam. Do NOT start studying the night before the exam. Cramming, while a time honored college tradition, just doesn’t work as well as spending time each day studying, especially with a math class.

**Get a Good Nights Sleep.**

Get a good nights sleep the night before the exam. It is important to be well rested and mentally sharp when you take the exam.

**Make a List of Important Concepts/Formulas.**

Review your notes and make a concise list of important concepts and formulas. Make sure you know these formulas and more importantly how to use them!

**Rework Homework Problems.**

Do not just read over the homework problems. Actually rework them. Writing down the steps will help you to remember them. Make sure that you try to do the problems without looking at the solutions.

**Rework Book/Notes Examples.**

Cover up the solutions to book or note examples and try to rework them. When looking for problems from the book don’t forget that most books have a review section at the end of each chapter that usually contains more problems.

**Look for Identifying Characteristics in Problems.**

While doing your homework you knew which section it came out of. This provided some clues as to the solution process. During an exam you won’t have this to help you. So, while reviewing your homework look for identifying characteristics that will give you clues on how to identify that kind of problem.

**Take a Practice Exam.**

Find some problems and treat them a practice test. Give yourself a time limit and don’t use your notes or book.

Source: http://mathematics-module.blogspot.com/

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