I was dismayed to read in the Washington Post article of May 20, 2013 “Montgomery math grades, test scores aren’t adding up,” about the persistently low scores on standardized math tests for the past five years in Montgomery County, Maryland, high schools. Montgomery County is the top ranked public school system in the number one nationally ranked state at providing K -12 public education for the past five years. If this is the best we can do in education, how bad is the worst? What is wrong?
Many factors were cited in the article for causes of this problem, but there was no consensus of opinion. One factor was not mentioned, which was critical in my own education a generation ago: how math is introduced early in the education process. It is important to show math’s connection to everyday experience because math is fundamentally important to life and learning? Math has been said to be the common language of the universe, and so, can be taught and learned in the abstract. But the application of math in the everyday world requires context to have meaning. Why isn’t this connection made early and reinforced to make math more relevant and exciting throughout the education process?
Solving problems in context and solving them abstractly are different thought processes. Math is easier to learn first in the context of familiar specifics (1 apple + 3 apples = 4 apples), and then transitioned to abstract form, 1 + 3 = 4. Algebra is about equalities. Balancing the two people on a see saw is the same as balancing two sides of an equation on an equals mark (with pluses, minuses, divides and multipliers, as needed). This dance between context and abstract in learning continues to the highest levels of learning and problem solving. Context-based math problems tend to test deep learning more than abstract-based math problems, which reinforce rote rule-based learning. Both are needed, but the first is more accessible and interesting to most people.
I have a PhD in physics and learned math both ways in high school but not until a life-changing event happened to me. I was a below average student as a sophomore in high school until I took the dreaded Algebra II class taught by Ms. Elizabeth Furr in a small Virginia town. Every year Ms. Furr would give a difficult extra credit problem to solve during the winter holiday period that no one was usually able to solve. Usually it was based on a familiar context which would yield an answer that was something familiar. I had been getting Cs and Ds during the year because I was not a good test taker. I would try to figure things out during tests from context rather than learn the rote short cuts to get answers quickly. I never had enough time to finish. After a winter holiday when I was 15, we all turned in our attempts at solving Ms. Furr’s assigned problem. She surprised me by announcing angrily that only one person got the right answer that year, me. The answer after all the math was done spelled out MERRY CHRISTMAS. At the end of class, she asked me to stay.
She looked me in the eye and simply said, “Learning and getting good grades are not the same; but you have to do both. Learning is for you, grades are for me and the world because I am required to grade your learning with tests. These grades are important because they help determine your future opportunities in the world. True learning will help you be successful with opportunities that good grades make possible. You are a very smart person (a nice surprise to me) but you have to figure out how to do both learning and test-taking well. To truly learn requires that you question, analyze, reflect, connect, consider context, and understand. Fundamental learning like that will stay with you for life. Keep doing that, and give me “A work” on tests and we will both be happy.” Thanks to Ms. Furr, I developed a life-time love of learning that continues to this day and has broadened to include the study of how society learns, and changes from what it has learned.
As I reflected on this pivotal experience many decades ago, I wondered if an early introduction to why math is fundamentally important in all aspects of life would generate a more open student mind set towards math. Math is not just for future scientists and engineers, but is connected to ALL of everyday life; not to learn the power of its basic principles and tools is to be at a disadvantage for the rest of your life.
Math, and by inference the logic it is built upon, has created the underlying fabric of modern life, including: laws for equably governing our society, language grammar and syntax for writing, business for creating jobs and wealth, apps for managing our personal finances, rules for playing and analyzing sports, notes and designs for creating music and art, navigation tools and technology for adventures near and far, being able to communicate with 7 billion people over the Internet, and building dumb and smart machines that multiply our muscle and brain power to work for us.
All of this is because our human brains are pattern seeking and pattern creating organs, and the patterns we seek and create in each of life’s activities are mathematical in architecture and function. The better we understand math the better we can recognize, create and improve the patterns that matter most to us. With virtual reality coming up on us fast, math may be the new cool course to take.
Math is connected to life!