Notes on Success in Learning Mathematics - Based on Years of Talking to Successful Students
There is a great deal of independent work required to be successful in this or any college course, and part of the college experience is helping you become an active, independent learner. The approach to this course may be significantly different from courses you have taken in the past, particularly if you are coming into the course directly from high school. Much less time is spent on review and drill. More time is spent on explaining, exploring and discussing the concepts, and modeling problem solving. The review and drill component of the course is essential, but must occur mostly outside of the classroom.
The rule of thumb for success in any college course is that you should be spending at least 2 hours working outside of class for every hour in class. This translates into at least 6 hours of outside work for a 3-credit class, and 8 hours for a 4-credit class. Below, I have listed some Simple Keys to Success as well as some more extensive "truisms" that will help you maximize your learning.
Simple Keys to Success
Practice, practice and practice some more!! Discuss questions with your classmates or a math lab tutor. Set up time most days to at least do a couple of exercises.
Work with math exercises and material on a regular and consistent basis to learn the material presented in class. If you had trouble with a particular idea, continue to work with it regularly to ensure that the material "sticks" with you! Make time most days to try some homework, review your notes, or read material in your book. The more consistently you think about mathematics, the more likely it is that you will truly come to understand the intricacies of the subject.
Work with ideas SOON after class. Brain research shows that if you don't review ideas soon after hearing them, then the effectiveness of the lesson diminishes rapidly! Even just reviewing the notes, and thinking back through the material presented in class can have a profound effect on how well you process the ideas.
Actively work to learn the language of mathematics, so that you can articulate your questions and your process of solution.
Mark your questions clearly so that you can ask them at the beginning of the next class. Let sticky notes become your new best friend!
Use the resources available! That includes asking me questions, talking to classmates, using the math lab, and reading the book.
Give math the time it takes! Devote enough time outside of class to reading, practicing, reviewing notes and becoming proficient with the technology. (The standard college rule of thumb is 2 hours of work outside of class for every hour in class.)
GETTING TO KNOW OTHER STUDENTS IN CLASS CAN HAVE A VERY POSITIVE IMPACT ON YOUR WORK
While it is essential to understand that learning material and making it your own requires significant individual work, you MAY also find it helpful to spend some time working with others. This gives you the opportunity to discuss ideas, utilize the terminology, see things from another perspective, and develop essential communication skills. Mathematics is a language, and as such, you must both write and speak the language to fully master the material. It can also be helpful to make connection with others who may be having the same frustrations, or who can help make things "click". No matter what your experiences have been in the past, I assure you that there will be at least one other student in the class who can communicate about mathematics in a way that suits your own style. As you become more and more willing to open up and share ideas and thoughts, you will find that the material becomes more interesting and engaging. This helps make all the work this course takes seem worthwhile.
If you are out for any reason, it is your responsibility to find out about and make up any work that you miss. Having someone from class who you can call, text or email will be a big help in this regard.
DOING WELL IN MATH REQUIRES CONSISTENT EFFORT
You are much better off doing your work regularly in small blocks, as opposed to trying to "catch up over the weekend". You may be amazed how much headway you can make by even spending 20 minutes concentrating on a few problems. Oftentimes, large blocks of intense work are less effective than several smaller blocks, particularly when you are dealing with detail oriented material that can be quite complex in nature.
When you get a homework assignment, begin it immediately. If you do the work in small blocks, rather than trying to do the entire assignment in one sitting, you will find you can do a much better job, and be far less overwhelmed by the assignment. If one problem causes you trouble, try to document where your questions begin, and move on to work on another problem.
Learning from mistakes made is a very powerful tool in any math course. Setting up a system of tracking problem areas, seeking appropriate input, and reconciling any misunderstandings is absolutely essential for your success. Begin devising a system right away. Delaying this could mean that you will not successfully complete the course. It is very difficult to make up lost ground in a college course.
Please guard against spending a lot of time "spinning your wheels". Instead create an effective system of marking areas of concern or confusion, and seek input as soon as possible. Always realize that you should find that questions, and even some areas of confusion do occur regularly. This is indicative of material at the appropriate level of challenge. If everything was easy, you would not be expanding those brain cells!
You may often find that if you leave the material alone for a while, insights or ideas may come to you. Your brain is amazing, and can often sift through material even if you are not consciously thinking about it.
Because of demands from other courses and other commitments, it may be challenging to keep up with the work load all the time. However, try to do some work regularly - even if that means just reading through and completing your notes, or filling in some description for an exercise done in class. It is best if you make sure you build in some time each day to at least attempt some of the practice exercises. Setting up a "Work Plan" for each day can help you start the semester off right for all of your courses. Keeping the material current in your mind will help you maximize what you learn during class time, and allows for the opportunity to have lots of little details "click" into place.
WHAT WORKED IN THE PAST MAY NEED TO BE EXPANDED AND TWEAKED NOW
Techniques or approaches you used in the past to learn material are not guaranteed to be enough now. As you work through a progression of courses, the level of the material usually requires that you expand and adapt your approaches to learning. Most students do find that as the complexity of the material increases, it helps significantly to talk to others, use the math lab, or make use of my office hours. I strongly recommend that you work to establish an effective routine of work and study early in the semester. It will help you navigate your way more smoothly through the course.
Keep an open mind. Things may seem much different to you than courses you completed in the past, but recognize that by the end of the semester, you will have become a more powerful, independent learner. This is indeed part of what college is all about! This is the very thing that employers look for and value in their employees!
Always remember that learning is active, and being an effective learner means that you are willing to continuously monitor and tweak your approach! Do not allow yourself to get locked into a mindset that does not allow for new approaches. But....keep in mind that change is often uncomfortable. If you are being asked to do something you have not done in the past, you may initially be resistant. Do not allow this initial resistance to prevent you from accepting the challenge of something new.
Keep in mind that if I ask you to do something, or require a particular component in the course, there is a well thought out reason for it! I work continuously to refine my teaching, and what I offer to you is the result of much careful thought and input from former students who told me what worked for them. You always grow as a learner when you are truly open to trying new things!
THERE ARE APPROACHES THAT HELP ENSURE SUCCESS!
Immediately begin reading the text - book, and using the supplemental material to become proficient with the technology. Although I cover as much material as I can in class, you are responsible for filling in some of the details for the material in any section. It is therefore essential that you read your text book for each section we cover.
Consider reaching out to at least one or two other people in the course who you feel comfortable talking to about the material. This, more than any other action, will help you deal effectively with taking a demanding course, particularly as the semester progresses.
Immediately begin seeking help to resolve problem areas. Much of this help must be sought outside of the classroom. Do not get caught up in thinking that all of your questions can be answered in our class time together each week! There is much ground to cover during that time, and although I do my very best to answer as many questions as I can in class, you must work on seeing the connection between what is covered in class and what you are asked to do. Oftentimes, I will cover a concept or skill by answering one question that actually applies to several other questions that you may have had difficulty with. Keep this in mind so that you try to see how the exercises I do review relate to other similar exercises.
Keep in mind that if you are experiencing difficulty, undoubtedly there are other students in the same boat. Though many people think they are alone in their confusion and frustration, rarely is that the case! Make the commitment to yourself to talk to me either in class, or outside the class if you are experiencing difficulty.
Remember, you must be active in your own learning, but I am happy to help you along your learning path.
I ask that you commit to putting the necessary time and effort into the course. When I know you are trying hard, I am always willing to give you the guidance and help you need to make it over the hurdles. Remember, your grade for the course is reflective of whether or not you have demonstrated mastery of the material.
Please try to see me as someone who can help you learn rather than as your nemesis. I cannot know how to most effectively help you unless you communicate with me. While I will maintain a high standard for the course, I am always happy to help you develop the means to be successful. Let's work together!
Material created by J. Halsey - Updated Spring 2013 - This material should not be used without permission of J. Halsey.
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