One of the most interesting new approaches to learning is set forth in the book Mindset: The New Psychology of Success by Carol Dweck, professor of psychology at Stanford. In it she advances the theory that there are two different mindsets that determine how people view their ability to improve. Those with a fixed mindset believe that they were born with a certain level of intelligence and talent and that there isn’t anything that they can do to change that — their challenge in life is learning to maximize the results of using what they have. You are either smart or you’re not — you’re either good at math or you’re not. The other approach is what she calls a growth mindset. People with a growth mindset believe the brain, like other parts of the body, can be strengthened and trained by using the correct procedures. Fortunately, educating people about how the brain works can help someone with a fixed mindset change their outlook and adopt a growth mentality. The effect can be quite liberating. Helping people to understand that they can have a positive effect on their performance encourages them to put in the required time and effort to develop the necessary skills.
How to value your success with the subject
Dweck encourages parents and educators to praise students based on their effort rather than on their innate ability. Students who perform well on a test should be told “You did very well. What strategies did you use to study for this exam?” as opposed to “You did very well on that exam. You are so smart”. Students need to be taught how to study and encouraged to realize that for many people repeated practice is the key to success. Practicing math is actually a way of improving the brain’s ability to perform certain functions, just like practicing the violin improves one’s ability to play in a symphony orchestra.
In Outliers: The Story of Success, Malcolm Gladwell attempts to identify the cultural values that contribute to the success of Asian students in the study of mathematics. Gladwell focuses his attention of the parallels between the characteristics required to cultivate rice as it has been done in East Asian countries for thousands of years and the characteristics exhibited by math students raised in East Asian cultures – patience, persistence and painstaking effort. In support of these, he cites a study by Earling Boe, an educational researcher at the University of Pennsylvania. Boe examined the results of the TIMSS test, the international test that is used to compare the educational achievement of different countries. As part of the data collection, students are asked to fill out a long questionnaire prior to taking the assessment. It is so long, in fact, that many students leave answers blank. What Boe discovered was that if you compare the questionnaire rankings with the math rankings, they are identical. In other words, countries whose students are willing to sit still and concentrate long enough to fill out a seemingly endless questionnaire are the same countries whose students score highest on the math test.
This correlates with the research of Stevenson and Lee into the influence of culture on academic success. They have determined that in countries such as Taiwan and Japan, parents place more emphasis on effort rather than one’s innate intellectual ability in school success. Moreover, parents in these countries tend to set higher expectations and standards for their children. In turn, students spend more time on homework and value homework more than American children. (Stevenson, H.W., & Lee, S. (1990). Contexts of achievement: A study of American, Chinese, and Japanese children. Monographs of the Society for Research in Child Development, 55, 1-119).
If you suffer from math anxiety, you can make some changes yourself that will reduce stress and improve performance. Stop focusing on the grade and concentrate on developing a deeper understanding of the material. For most people, time and hard work are the keys to mastery.
Ask your instructor for suggestions as to how you can structure study time to be more efficient.
Make flash cards with a problem on one side and a method of attack on the other. Frequently just having the first step is enough to help you remember how to solve the problem.
Try to devote some time each day to working on math. Seven evenly spaced half-hour sessions are much more effective than a 3 ½ hour marathon study session.
Take notes and put into your own words how to tackle problems — pretend you are preparing lecture notes to tutor a friend. Frequently the act of verbalizing what it is you are doing and why will make it easier for you to remember.
Look for patterns. Many students who are weak in math mistakenly think of it as a collection of thousands of unrelated formulas. Math is very logical and systematic. If you can see the pattern then it is easier to see the relationship among different problems.
Take charge of your own learning. Take practice tests to diagnose your own weaknesses and work to remedy them. If your book doesn’t provide practice tests, make them yourself. Put problems that you feel are representative of what you have learned in a section on flash cards with the answers on the reverse side. Shuffle the deck and deal yourself your own personal practice test.
Explore the vast array of resources that are available online. Just because you are taking an online class it doesn’t mean that you can’t sit through a math lecture and take notes if that’s the way you like to learn. Just Google the topic and look for videos. YouTube has an abundance of math videos as does the Khan Academy. There are also lots of sites that demonstrate how to work problems — many have applets that allow you to manipulate the numbers and explore the results of changing different elements.
Do not stay up late studying for a math test. Math isn’t about remembering isolated facts. It’s about seeing patterns and remembering concepts and how to apply them. For your brain to perform those types of functions, it needs a good night’s sleep.
Eat berries on the morning of a test — especially those that are dark blue or black in color. You’re counting on your brain to come to your rescue, you may as well give it the fuel it needs for peak performance!
The bottom line is that for most people learning math is simply a question of putting forth a lot of time and effort. The good news is that the more you practice, the better you get at it. Some people even find that they can get to the point where it’s more like the Sunday Puzzler and they can actually relax and enjoy it!
By Caroline Richards
Assistant Professor, Mathematics at American Public University