It seems that more than any other subject, math evokes feelings of stress, aversion, anxiety, and maybe even fear in all but the math enthusiasts. I have even seen adults with advanced science degrees shudder at the sight of equations. Some people do naturally understand math well, but that does not mean everyone else is doomed to a bad relationship with the subject. When a student does not have a solid connection to a subject, learning feels like work and exams become sources of stress. The goal of this blog is to give students a few tools that they can use to try to build a connection to the subject of mathematics that will also make studying more effective.
Students have certainly heard their teachers tell them to study smarter not harder. The following are some tried and tested tools to help students study smarter. Not all these tools will work for each student. Students should be encouraged to try and test which tools they enjoy (yes, enjoy). If students enjoy the process of learning, demonstrating mastery of the material (such as on an exam) will come naturally. While these tools were specifically developed in mathematics classes and based on the experience of mathematics students, with some creativity, they could work for any subject.
With all that said, the rest of this post is written for the student.
Education is the passport to the future, for tomorrow belongs to those who prepare for it today.
― Malcolm X
The Communicator
You may have noticed that many word problems in mathematics textbooks end with the sentence “Explain your reasoning.” You may be thinking that if the problem is already solved and the steps are written out, why would you need to explain?
It turns out that the reason you are asked to explain by your textbook, your teachers, and your tutors is not to give you extra work, but because explaining (either by writing out an explanation or saying it out loud) really helps the learning process, and there are scientific studies to support this. You may have heard the saying that the best way to learn is to teach. Indeed, this is a great study technique to ensure you are learning and understanding the concepts. You may ask yourself, “If I am just a student, who should I teach?” The answer is anyone who is patient enough to listen.
If you learned how to find the area and circumference of a circle in school today, ask a family member if you can try to teach it to them after dinner tonight. You may find that in the process of explaining a concept, you get stuck. Remember where you got stuck, and ask your teacher, tutor, or a classmate the next day at school. You will find that if you understand concepts well enough to explain them to someone else without getting stuck or confused, it will be much easier to do the problems, even the hard ones!
Does your ‘student’ have to know math to listen to your explanation? Absolutely not! The point of the exercise is to have you explain a concept out loud from start to finish in a logical manner. If you know you missed a step or are unsure about a concept and your ‘student’ or listener did not notice, make sure you ask for help. If your ‘student’ or listener does know some math, have them ask you questions at the end of your explanation. The questions you cannot answer point to details you need to go back and review.
The Competitor
Perhaps you can complete your homework but you get stuck or unsure about problems once you are taking a test. One of the best ways to prepare for a test (once you have studied and know the material well enough to practice) is to make your own math test.
Pretend you are the teacher in your math class. You may have noticed certain patterns in the way your teacher gives exams and teaches the material. (For example, in class and for homework, you have to solve problems, but on exams, you have to explain your reasoning and write out short answers.) Use your observations as you pretend to be the teacher. Now, go through the material being tested, and make an exam. You can pick out problems from your textbook or another textbook. You can also modify problems from class, homework, or practice tests. If you are doing this solo, wait a day, and then take your exam. This is a great way to get practice and understand the big picture topics you are learning. If you are preparing for an exam early, make 2 or 3 short tests and try to beat your best score.
The Enthusiast
Maybe you love reading, history, art, music, or sports, but math just never makes any sense. Because you never feel that you really understand the concepts, working out the problems is confusing and laborious. The beautiful thing about math is that it is everywhere, in literature, history, art, music, sports, and anything else you can think of. These connections are sometimes not fully utilized in the classroom for learning purposes, but it does not mean you cannot find them yourself or with the help of a teacher, tutor, friend, or parent.
I once had a student who was having trouble understanding parabolas. He is an avid tennis competitor, so we examined parabolas as tennis ball trajectories. He was able to visualize the problem he was solving, understand how it relates to a sport that he loves and plays several hours a day, and the rest was just easy algebra. Not sure how the topic you are studying today in math class relates to your passion? Google it, go to the library, ask your parents and teachers. Find out! Students who can see and understand how a mathematical concept is applied in the real world often gain a better understanding of the concept, have an easier time with word problems, and ace the parts of the test that ask you to explain your reasoning.
The Artist
You understand concepts and can solve most problems, but those word problems that utilize multiple steps and concepts leave you confused. How do you use both a concept from algebra and another one from geometry to solve a problem? Start by drawing a diagram. Label it with all the information you have available. Then think about the tools that you have learned. The steps to a solution may begin to emerge, kind of like when you are putting together a jigsaw puzzle. Drawing diagrams is a great way to study as well. It helps you make connections among different concepts and problem types. Drawing out a flowchart of all the concepts learned in a chapter or diagram of a general problem set up with variations helps you remember long term, sometimes better than looking at a chart in a book.