Math is the science of patterns. Mathematicians study patterns and relationships. They use a system of structured logic to analyze these relationships which are then often described using one or more of the languages of mathematics. At its core, math is pure logic.
As I’ve taught these young women to plan and cook meals, maintain a house, assemble furniture, hem pants, repair a car, and plant gardens, I’ve realized that they all share a common background that contributed to their lack of life skills. While their families focused on academic and professional achievement, their mothers never taught them to be self-sufficient, problem solving, independent thinkers. They have book-learning, transcripts, degrees, and job skills, but they haven’t learned how to apply these skills outside of their fields of study. They have not learned how to teach themselves new skills.
I see many of my younger students heading in this direction. Their parents rush them from one activity to another as they focus on their academic achievement. They make sure that they get every advantage to get the best grades and highest test scores. Somehow they assume that life skills like time management, organization, responsibility, and problem solving will magically appear with age. It won’t.
While people are often impressed by the stories of the ‘super geniuses’ that I’ve worked with who started college at ages 9, 10 or 11, it’s my daughter who provides the road map that I use to design our programs. It’s not just that she can bake a perfect loaf of sour dough bread, install a laminate floor, negotiate leases, sew the most comfortable PJs, create all our advertising, manage our website, explain the neurobiology of giftedness, diagram sentences, and conjugate Latin verbs. It’s that she taught herself how to do all those things. She took the initiative to read books, articles and research journals, consult with experts, experiment, evaluate results, and continue to pursue a topic until she was satisfied that she understood it. It’s her lack of fear of the unknown -- her confidence that she can learn anything -- that makes her my pride and joy.
This is what I want for my students. I don’t just want to teach them math. I want to teach them how to overcome their fear of the unknown. I want them to gain confidence that they can learn anything.
Some of this I can accomplish in the classroom. I do this by not just focusing on how to solve a particular problem but by training them to practice problem solving techniques. Why does this problem look so scary? Can you identify the worst part of it? Can you think about a way to address just this one issue? Take things one step at a time. Break down big problems into smaller parts. Don’t skip steps. These are all things I say over and over to my students as we work through different types of problems to develop different math skills. With my older students I also talk to them about applying these techniques to other areas of their life.
Sometimes well-meaning parents make this task difficult. Some assume that if they can’t understand the homework, then it must be too hard for their child. Others who are more confident in their math skills often provide ‘too much big help.’ Whether they argue that their child shouldn’t be expected to complete such difficult assignments, make excuses for incomplete or sloppy work, or walk them through assignments that they are supposed to complete on their own, they are all sending their children the same message. They are giving them votes of non-confidence. They are saying “I don’t expect you to be a self-sufficient, problem solving, independent thinker.”
Parents don’t intentionally plan to send this negative message or sabotage their child’s personal growth. As mothers, it's in our nature to protect our children from the unknown -- to shield or children from the "big, bad adult world," -- to maintain their innocence for as long as possible. But we must not forget that we can continue to do all of these things whilst still allowing for personal growth. Parenting, like all other facets of life, is about balance -- balancing "easy" with challenging -- balancing praise with discipline -- balancing fun with necessary -- balancing freedom with restrictions.
Our successes are only as great as our failures. The road to success is paved with cobblestones, roadblocks, and accidents. Yet, it is this journey that creates a truly successful individual empowered to take on the world.
I frequently use current events in math class. This is our latest endeavor!
What is Logic?
In the United States, formal training in logic is often limited to writing formal proofs in high school geometry classes. Yet, logic can easily be introduced to younger students through fun games and puzzles.
The first time I saw him, he reminded me so much of Q. The way he rolled his head back when he was thinking. His lack of eye contact when speaking. His abnormally precise language, his obsession with numbers, especially very large numbers resulting from doubling, irrational numbers and those resulting from functions unknown to any mathematician other than himself. I played with him the way I’ve played with countless other children I’ve met like this. I created patterns and let him expand on the series. I invented functions using made up notation to see what he would do with them. His mother, anxious that he would make a good impression, encouraged him to look at me and answer my questions. “Wait” I hush her, almost in a whisper. “He’s thinking.”
Before each math class, I check and restock all the supplies my students will need: wide ruled paper, colored pencils, crayons, and pens. Pens? Not Pencils? Yes, pens not pencils – black and purple pens to be precise.
I know this is unconventional but there’s a method to my madness. Think about it: Why do we use pencils for math? Normally this question is met with a blank stare since the use of pencils for math is so universal that most have never considered questioning this convention. The obvious answer, of course, is to erase our mistakes but, why do we want to erase our mistakes when we know that we learn from our mistakes?