Discovering the Hidden Value of Math
By Heather Shanks
“Mathematics is food for the brain,” says math professor Dr. Arthur Benjamin. “It helps you think precisely, decisively, and creatively and helps you look at the world from multiple perspectives . . . . [It’s] a new way to experience beauty—in the form of a surprising pattern or an elegant logical argument.”1 A powerful description, but what if your family struggles with math? How do you teach math in a way that helps your children catch that vision?
THE MYTH: YOU WILL USE THIS IN REAL LIFE
I recently spoke with a mom who often pleads with her kids to study math, telling them they will need it later in life. Her mathematically frustrated offspring are skeptical. She wonders why so many children say: “I don’t need to learn this. I am not going to be an engineer anyway, so why bother?” My response was: “Their young minds can’t find a tangible, long-term benefit. Short-term fun and ease is much more appealing.” For that same reason, the “you’ll use this someday” argument can be exhausting and ineffective. It may even sabotage your efforts if your children recognize it as a lukewarm truth.
Before my Inbox fills up with flaming emails, let me elaborate. I took Advanced Placement Calculus in high school, college-level Math Theory, and graduate-level Statistics. As an adult, I have many responsibilities, yet I use almost none of that knowledge now. I am not atypical. On a daily basis, most people primarily use the four basic functions of math: addition, subtraction, multiplication, and division. Even at work, most professionals are not steeped in algebraic equations daily. Computers do the heavy lifting, and kids know that. Using their future prospects as motivation for completing their algebra assignment doesn’t convince them. You need to help your children override here-and-now thinking, but how?
THE REAL SECRET OF MATH
In his insightful book, The Equation for Excellence: How to Make Your Child Excel in Math, Arvin Vohra reveals a simple, yet powerful, concept that most people overlook. In a nutshell, he points out that you don’t do math because you are smart; you do math because it makes you smarter.2 Mathematical thinking builds the brain, just like weight-training builds the muscles. Mental discipline and clear thinking are required to master mathematical concepts. Both will make your children better at whatever they love. The best part is, whether they love art, Bible study, building, logic, or debate, their brains are being better equipped in the here and now.
Math is about making connections and seeing patterns. The concrete and abstract thinking required by math builds the brain’s muscles, which in turn prepares you for other academic pursuits. The study of math is actually a springboard to increasing overall intelligence!
We all know that Leonardo da Vinci was a gifted artist. What most people don’t realize is that he was also a brilliant mathematician. Da Vinci used the concept of “connessione,” or connectedness, to create notebooks filled with ideas, formulas, and theories that were very advanced for his time.3 The secret recipe to math appreciation involves the internal motivation to increase intelligence rather than the external motivation of using it someday. Instead of telling your kids that they will need geometry if they decide to become an engineer, tell them that math will make them a better fill-in-the-blank (artist, football player, writer) right now.
HOW MATH BUILDS THE BRAIN
How does math do this? Math trains the brain to see connections and builds the neural pathways that make the brain stronger for all other things. These pathways serve as building blocks for myriad interests and subjects by:
• Creating the basis for systemic thinking.
• Developing the ability to analyze and solve problems.
• Stretching the mind to work on unfamiliar tasks with confidence.
• Developing the sequencing skills critical to arriving at accurate results or logical conclusions.
• Promoting caution and care in thinking by deciphering complex math problems to arrive at an accurate answer.
• Learning through the trial and error to integrate different principles to arrive at a logical conclusion.
These are cognitive resources that your child can draw on right away, regardless of his future career plans.
YOUR NOT-SO-SECRET WEAPON
What are the tools for developing those cognitive resources? The Math Toolbox offers an overall picture of a comprehensive math program. One piece of that toolbox is drill. Much maligned over recent decades, drill is still very relevant to a solid education. In the name of fun, math educators have overlooked the value of fundamentals. As Susan Wise-Bauer wisely pointed out in The Well-Trained Mind, rote memorization has been ridiculed and looked on as a “lower-order” math skill, as though it were inferior somehow to higher-order math skills.4
The real fun in math comes from mastery, but mastery cannot happen without first mastering the fundamentals, or the facts of math. Why? Your brain has two basic memory types: working and long-term. Your working memory has approximately seven active “slots” available for solving problems, depending on the complexity of the information involved.5 Working memory slots are critical to higher-order processes, such as multi-step algebra problems. If you have been diligent with drill, the brain’s working memory slots are free for analysis, because the fundamentals are safely tucked into long-term memory. If basic math facts haven’t been committed to long-term memory, the mind is occupied with formulas rather than analysis.
A good example of the power of drill is the highly successful Asian math system. One Asian program many homeschoolers are familiar with is Singapore Math (www.singaporemath.com/Homeschool_s/60.htm). Although I often hear complaints that Singapore is short on drill, that assessment isn’t quite accurate. Drill is an integral part of the Asian math system. In the Asian world, drill is part of everyday life, and the Singapore program assumes this. The concept is very logical but not intuitive to the American mind. The key to countering this is to drill with our students in the way that Asian parents and teachers routinely drill with their students.
WHAT NOT TO DO
Some popular education theories and methods can sabotage math-based brain development. Here are some tips that can help you avoid some of the most common traps:
• Bits and Pieces Math. The ever-debated Chicago Math (ucsmp.uchicago.edu/secondary/overview) has been a washout in many school systems because some educators leave out the drill. Experiential programs can be quite valuable. However, when vital components are eliminated, they become thin and weak. Make sure you use all four components of a comprehensive program, as illustrated in the Math Toolbox.
• Quick Math. Classroom teachers are often overwhelmed by the challenge of teaching many students who represent many different levels of knowledge and maturity. Consequently, they often try to just get through the material as quickly as possible. For the brain to be stretched, though, it needs time to ponder and mull. Homeschooling gives us the flexibility to put in the necessary time for thorough learning. Don’t shy away from letting kids take time to struggle with problems.
• The Math Silo. Look at most math texts and you will find math instruction with very little math background. Yet, the history of the subject and its great minds are very pertinent to the experience of learning math. By looking at the lives of great mathematicians, students can personalize the subject. As they learn about the progression of math, they realize how different theories developed.
Don’t be intimidated by some of the more scientific concepts I have presented. The big takeaway here can be summed up in the following statement by Vohra: “You are not just making him [your child] better at math; you are making him better at thinking.”2 That statement reflects my personal math philosophy, and I encourage you to adopt it as yours.
Math builds skills in concrete reasoning, spatial reasoning, and logical reasoning. It sharpens the mind and helps eliminate fuzzy thinking, equipping your children with tools to defend their worldview and make smart choices. Guide your children to see math as a gift from our Maker to equip us to better understand His world.
I also recommend that you read The Equation for Excellence. Written in clear, easy language, Vohra’s refreshing explanations give parents concrete information about how to teach math, as well as how to motivate your children to appreciate math. If you have older children, check out The Teaching Company’s Joy of Mathematics course. (I suggest waiting for it to go on sale, which usually happens at least once each year.) Get inspired about math instead of getting weighed down by it. This book is also a terrific resource for students.
FINAL WORDS OF ENCOURAGEMENT
It doesn’t take the IQ of a genius to harness the brain-building power of math. Perseverance is more important than raw talent. Brains have both a natural aptitude and a capacity for growth; they aren’t limited to one or the other. The next time you want to encourage your children in their math studies, teach them to see that math is not a burden but rather is a tool that will help them excel—right now.
Heather Shanks, aka Professor Mom, is an author and researcher specializing in best practices in academic curriculum, character education, and learning styles. The Professor Mom website (www.professormom.net), is an education planning ministry for moms, providing low-or no-cost resources and coaching to help families create an authentic home education. Heather enjoys living and homeschooling in the Midwest with her husband, Professor Dad, and their two sons.
1. www.teach12.com/ttcx/coursedesclong2.aspx?cid=1411, The Teaching Company—Joy of Mathematics Course Description, accessed Jan. 25, 2010.
2. Vohra, Arvin, The Equation for Excellence: How to Make Your Child Excel at Math, Roland Media Distribution, 2007, italics added for emphasis.
3. Gelb, Michael J, How to Think Like Leonardo da Vinci: Seven Steps to Genius Every Day, Random House, Inc., 1998.
4. Wise-Bauer, Susan and Jessie Wise, The Well-Trained Mind: A Guide to Classical Education at Home, W. W. Norton & Company, 2009.
5. Vohra, Arvin, The Equation for Excellence: How to Make Your Child Excel at Math, Roland Media Distribution, 2007.
Copyright 2010. Originally appeared in The Old Schoolhouse Magazine, Spring 2010. Used with permission. Visit them at theoldschoolhouse.com. For all your homeschool curriculum needs visit the Schoolhouse Store.
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