The Grandiose Post: How to be Successful in a College Math Course

Even if you are doing well, you may be able to do better. If you aren't meeting your own expectations, here's how to. The article below includes tips on how to study mathematics, how to approach problem-solving, how to study for and take tests, and when and how to get help.+

Study Skills

First, recognize the difference between active and passive study. 

You must be actively involved in managing the learning process, the math, and your study schedule.

• Take responsibility for studying, recognizing what you do and don't know, and knowing how to get your Instructor to help you with what you don't know.
• Attend class every session and take complete notes on how to do different types of problems. Instructors formulate test questions based on material and examples covered in class.
• Be an active participant in the classroom. If at all possible,work ahead. Try to work some of the problems before they are covered in class. (QR students: you need to be doing the classwork before coming to class. )That way you can go to class with a basis for what you do and don't understand about the new material. You can ask specific questions from other students, your instructor, or your SI. "Can you explain the difference between relative error and relative difference?" or "I lose track at this step." vs. "I don't get it." This is crucial. 
• You can help your classmates (which helps you solidify your skills!) with the stuff you do understand. This is why we work in groups. 
• Ask questions in class! If no one in your group knows how to do something, don't sit in frustrated confusion. Reach out and ask for help. There are probably other students in other groups wanting to know the answers to the same questions you have.
• If you have a few different concepts you're confused about, come to office hours, SI sessions, or the math center!Go to office hours prepared with specific questions, or questions about concepts. The math center is available to work through homework and ask questions if they come up. The SI sessions will already have math problems related to what is covered in the previous class. 
• Good study habits (i.e. 1. making a schedule for when you will complete assignments and work and 2. following it.) throughout the semester make it easier to study for tests.
• But how do I study for a test? Re-work problems from class. Don't just look at them, but actually cover up the answers and physically do the problems again. More about how to study for math here.

Studying Math is Different from Studying Other Subjects

• Math is learned by doing problems!!! Do the homework. Do the class work. Do the group work. The problems help you learn the formulas and techniques you need to know, as well as recognize the type of problem and what you need to do to solve it. 
• A word of warning: Each class builds on the previous ones, all semester long. You must keep up with the Instructor: do your best to attend class,but always do book work and connect assignments. Falling a class period behind puts you at a disadvantage, but falling behind completely (not doing outside-of-class work) is uh..yikes. 
• A word of encouragement: Each class builds on the previous ones, all semester long. You're always reviewing previous material as you do new material. Many of the ideas hang together. Identifying and learning the key concepts means you don't have to memorize as much.

College Math is Different from High School Math

A College math class meets less often and covers material at about twice the pace that a High School course does. You are expected to absorb new material much more quickly. Tests are probably spaced farther apart and so cover more material than before. The Instructor may not even check your homework.

• Take responsibility for keeping up with the homework. Make sure you find out how to do it.
• You probably need to spend more time studying per week - you do more of the learning outside of class than in High School. Remember: 8-12 hours. If this seems intimidating, I highly, highly, highly encourage you to read this post about making a study schedule.
• Tests may seem harder just because they cover more material. But! If you over-prepare, tests are not hard. Don't practice until you get it right: practice until you can't get it wrong.

  

  This is my #1 math tip of all time. 

Study Time

You may know a rule of thumb about math (and other) classes: at least 2 hours of study time per class hour. Please note that this 'study time' includes all time spent doing connect, group projects, class work, group work, etc. Start there, and see if you get the grades you want. I guarantee more time = better grades. 

• Take as much time as you need to do all the homework and to get complete understanding of the material.
• Form a study group.  (Or, you know, come to SI.) (Or both! 😮) Meet once or twice a week. You can also exchange phone numbers, and work on math over facetime. Go over problems you've had trouble with. Either someone else in the group will help you, or you will discover you're all stuck on the same problems. Then it's time to get help from your Instructor. A great place to start would be your table group- see when they are available and meet at panera, starbucks, the school library, or the community library (which often have study rooms available for groups!). Math is not only more fun, but more lucrative as a social exploit.  
• The more challenging the material, the more time you should spend on it. 

Problem Solving

Problem Solving (Homework and Tests)

• The higher the math class, the more types of problems: in earlier classes, problems often required just one step to find a solution. Increasingly, you will tackle problems which require several steps to solve them. Break these problems down into smaller pieces and solve each piece - divide and conquer!
• When you work problems on connect, write out complete solutions, as if you were taking a test. Don't just 'do it in your head.' Writing something down is 17x more effective than just reading it. If your answer is not right, rework the problem; try the guided solution, or phone a study buddy to see how they did it. If you can't get the answer, ask the instructor or SI after class, or come to

  
Gunkelman's office hours are
Monday 9:00 –10:00 AM and 12:00 –1:00 PM

Tuesday 9:00 –10:00 AM

Wednesday 9:30 –10:00 AM and 12:00 –1:00 PM

Thursday 9:00 –10:00 AM

Conti's office hours are:

Monday: 3 –4pm, 5 –5:30pm

Tuesday: 12 –1pm, 3 –4pm

Wednesday: 3 –4pm, 5 –5:30pm

Thursday: 12 –1pm

Friday: 12 -1:30pm

• Additional Hint: Both professors are highly skilled and extremely kind, so you can probably get away with going to the other professor if yours is not available.
• Another Hint: Screenshot the office hours for refrence. 

Tips on Problem Solving

• Apply Pólya's four-step process: (haven't I heard of that before somewhere?) 
  1. The first and most important step in solving a problem is to understand the problem, that is, identify exactly which quantity the problem is asking you to find or solve for (make sure you read the whole problem).
  2. Next you need to devise a plan, that is, identify which skills and techniques you have learned can be applied to solve the problem at hand.
  3. Carry out the plan.
  4. Look back: Does the answer you found seem reasonable? Also review the problem and method of solution so that you will be able to more easily recognize and solve a similar problem.
• Some problem-solving strategies: use one or more variables, complete a table, consider a special case, look for a pattern, guess and test, draw a picture or diagram, make a list, solve a simpler related problem, use reasoning, work backward, solve an equation, look for a formula, use coordinates.

"Word" Problems are Really "Applied" Problems

The term "word problem" has only negative connotations. It's better to think of them as "applied problems". These problems should be the most interesting ones to solve. Sometimes the "applied" problems don't appear very realistic, but that's usually because the corresponding real applied problems are too hard or complicated to solve at your current level. But at least you get an idea of how the math you are learning can help solve actual real-world problems.

Solving an Applied Problem

• First convert the problem into mathematics. This step is (usually) the most challenging part of an applied problem. If possible, start by listing out all the numerical information given in the problem. Rewriting the numbers make the problem less intimidating, and help you to organize your thoughts. Next, draw a picture. Label it with all the quantities mentioned in the problem. If a quantity in the problem is not a fixed number, name it by a variable. Identify the goal of the problem. Then complete the conversion of the problem into math, i.e., find equations which describe relationships among the variables, and describe the goal of the problem mathematically.
• Solve the math problem you have generated, using whatever skills and techniques you need (refer to the four-step process above).
• As a final step, you should convert the answer of your math problem back into words, so that you have now solved the original applied problem.

Studying for a Math Test

Everyday Study is a Big Part of Test Preparation

Good study habits throughout the semester make it easier to study for tests.

• Do the homework when it is assigned. Again, I must urge you to make a study plan in order to be sucessful in this endeavor. No more finishing connect at 11:59 pm, c'mon. 
• You cannot hope to cram 3 or 4 weeks worth of learning into a couple of days of study.
• On tests you have to solve problems; classwork problems and connect are the only way to get practice. (I mean, besides coming to SI sessions). As you do connect, write down problems and do them on paper, make lists of formulas and techniques to use later when you study for tests.
• Ask your Instructor or SI questions as they arise; don't wait until the day or two before a test. The questions you ask right before a test should be to clear up minor details, not explain major concepts. 

Studying for a Test

Start by going over each section, reviewing your notes and checking that you can still do the homework problems (actually work the problems again). Use the worked examples in the text and in your notes (you wrote down the connect problems, right?) - cover up the solutions and work the problems yourself. Check your work against the solutions given.

You're not ready yet! In the book, each problem appears at the end of the section in which you learned how do to that problem; on a test the problems from different sections are all together.

• Step back and ask yourself what kind of problems you have learned how to solve, what techniques of solution you have learned, and how to tell which techniques go with which problems.
• Try to explain out loud, in your own words, how each solution strategy is used (e.g. how to do a conversion, or how to find probability from odds). If you get confused during a test, you can mentally return to your verbal "capsule instructions". Check your verbal explanations with a friend during a study session (it's more fun than talking to yourself- but not by much).
• Put yourself in a test-like situation: mix together problems from different sections and create your own practice tests. You could use the applications from the end of each section to do this. 

Also:

• Start studying early. Several days to a week before the test (longer for the final), begin to allot time in your schedule to reviewing for the test. Another post details the 3-2-1 method as a way to do this
• Get lots of sleep the night before the test. Math tests are easier when you are mentally sharp.
• As Mrs.Gunkelman says, no caffiene & carbs. Eat a good breakfast. 

Taking a Math Test

Test-Taking Strategy Matters

Just as it is important to think about how you spend your study time (in addition to actually doing the studying), it is important to think about what strategies you will use when you take a test (in addition to actually doing the problems on the test). Good test-taking strategy can make a big difference to your grade!

Taking a Test

• First look over the entire test. You'll get a sense of its length. Try to identify those problems you definitely know how to do right away, and those you expect to have to think about.
• Do the problems in the order that suits you! Start with the problems that you know for sure you can do. This builds confidence and means you don't miss any sure points just because you run out of time. Then try the problems you think you can figure out; then finally try the ones you are least sure about.
• Time is of the essence - work as quickly and continuously as you can while still writing legibly and showing all your work. If you get stuck on a problem, move on to another one - you can come back later.
• Work by the clock. On a 50 minute, 100 point test, you have about 5 minutes for a 10 point question. Starting with the easy questions will probably put you ahead of the clock. When you work on a harder problem, spend the allotted time (e.g., 5 minutes) on that question, and if you have not almost finished it, go on to another problem. Do not spend 20 minutes on a problem which will yield few or no points (when there are other problems still to try- definitely do this at the end, use ALL your time.).
• Show all your work: make it as easy as possible for the Instructor to see how much you do know. Try to write a well-reasoned solution. If your answer is incorrect, the Instructor will assign partial credit based on the work you show. USE YOUR UNITS.
• Don't waste time erasing! Just draw a line through the work you want ignored and move on. Not only does erasing waste precious time, but you may discover later that you erased something useful (and/or maybe worth partial credit if you cannot complete the problem). Please, please, please don't leave problems blank. A wrong answer counts against you in the same way leaving a problem blank does. Try your best, and get partial credit or even a pity point. 
• In a multiple-step problem, outline the steps before actually working the problem.
• Don't give up on a several-part problem just because you can't do the first part. Attempt the other part(s) - if the actual solution depends on the first part, at least explain how you would do it.
• Make sure you read the questions carefully, and do all parts of each problem.
• Verify your answers - does each answer make sense given the context of the problem?
• If you finish early, check every problem (that means rework everything from scratch).

Getting Assistance

When

Get help as soon as you need it. Don't wait until a test is near. The new material builds on the previous sections, so anything you don't understand now will make future material difficult to understand.

Use the Resources You Have Available

• Ask questions in class. You get help and stay actively involved in the class.
• Visit the Instructor's Office Hours. Instructors like to see students who want to help themselves.
• Come to SI Sessions: we work together on problems covered in the previous class session.
• Ask friends, members of your study group, or anyone else who can help. The classmate who explains something to you learns just as much as you do, for he/she must think carefully about how to explain the particular concept or solution in a clear way. So don't be reluctant to ask a classmate.
• Go to the Math Center or make a free tutoring appointment on campus.
• All students need help at some point, so be sure to get the help you need.

Asking Questions

Don't be afraid to ask questions. Any question is better than no question at all (at least your Instructor/tutor/SI will know you are confused). But a good question will allow your helper to quickly identify exactly whatyou don't understand.

• Not too helpful comment: "I don't understand this section." The best you can expect in reply to such a remark is a brief review of the section, and this will likely overlook the particular thing(s) which you don't understand.
• Good comment: "I don't understand why f(x + h) doesn't equal f(x) + f(h)." This is a very specific remark that will get a very specific response and hopefully clear up your difficulty.
• Good question: "How can you tell the difference between the equation of a circle and the equation of a line?"
• Okay question: "How do you do #17?"
• Better question: "Can you show me how to set up #17?" (the Instructor can let you try to finish the problem on your own), or "This is how I tried to do #17. What went wrong?" The focus of attention is on your thought process.
• Right after you get help with a problem, work another similar problem by yourself.

You Control the Help You Get

Helpers should be coaches, not crutches. They should encourage you, give you hints as you need them, and sometimes show you how to do problems. But they should not, nor be expected to, actually do the work you need to do. They are there to help you figure out how to learn math for yourself.

• When you go to office hours, your study group, or a tutor, have a specific list of questions prepared in advance. 
• Again, I prepare SI sessions with questions, but I can attempt to leave time at the end if you have a specific question. Normally, I will have planned to go over a problem like yours. I have defitinely worked it in if its from the previous class period. 
• Do not allow yourself to become dependent on a tutor. The tutor cannot take the exams for you. You must take care to be the one in control of tutoring sessions.
• You must recognize that sometimes you do need some coaching to help you through, and it is up to you to seek out that coaching.

Ok. Now, think to yourself, (better yet- write down) what's my plan? What are 3 things mentioned in this article I will try?

You can always talk to me after class (or during class for math lit students) if you want a 1-on-1 math chat . We can look at your situation and analyze what you can do in order to be successful.