I wasn't very good at school math when I was little. I took a long time to memorize my times tables and hated the endless pages of questions. I remember vividly the first time I did well on a math task at school. My grade six teacher had a star chart for students who did well in math. A gold star for a perfect score and a silver star if you made only one mistake. I yearned for a star.
One day, while sitting over yet another page of very boring multiplication problems (I think they were double digit by double digit), I suddenly realized that the math in front of me was a battle ground. It was odds versus evens, and the odds were the bad guys. I eagerly took my pencil in hand and worked away at each problem to see who would win. When I finished, I took my paper up to be marked and received a perfect score! What made this day memorable was my teacher's response. My teacher looked at me with great suspicion and took out not a gold, but a silver star. The unfairness of that moment is probably why I still remember that episode.
On the other hand, what is important about that day is that the odds versus evens battle stuck with me. I began to notice patterns. I began to see that an odd number multiplied by an even number or an even number multiplied by an even number will always result in an even product, but that odd by odd multiplication will always resulted in an odd answer. Interesting - right?
My parents were never big on homework. They worked full time and were tired at the end of their day. I don't think they had the energy to fight us over homework, but they also felt that we had a right to play. I am so thankful for that. One kind of play, though, was really fundamental to my love of math today.
My dad used to sit at the table with us and we would have fun math talks. We would talk about why some numbers were squares and how fractions worked. I knew about square numbers before I ever heard of multiplication - and I understood how they worked because my dad shared his love of math with us. We never sat around memorizing times tables or doing addition problems, but we talked about math all the time. Thank you Dad!!!
Even in high school, I wasn't a brilliant math student. When a concept interested me, I did really well, but I was no good at the boring stuff. In grade ten we had to write an international math test. That was fun! I remember enjoying all of the challenges and getting really stuck on a problem about trapezoids. I'd never heard of one and after finishing, went back to that page and read the question over and over again, trying to figure out what a trapezoid was.
Some time later, my math teacher came to me with a strange, puzzled expression on his face. He told me that I had received the top score in my class on that test. Mind you, my class had about 20 kids in it, but some of them were incredible math whizzes who could calculate at lightening speed. I thought that was pretty cool, but it didn't really affect my ability to do well in class.
I didn't go on to do much math in university. I took one wonderful statistics course that really made me think about the nature of data. I also took the math for teachers course and worked with some friends who struggled in that course. They didn't have a Dad who made math fun and for them the concepts that we learned that year were a big challenge. For me, they were exciting and I learned a lot by helping my friends understand the big ideas.
I still didn't think that much about math until one day during teacher training, a young woman said to me, "Wow! You want to teach grade 7? I couldn't even do the math." In that instant, I had a shiver of recognition. This woman was in teacher training and, after having graduated from a BC school, obtained a bachelor's degree, and completed the teacher's math course, she did not feel capable of doing grade 7 math, let alone teaching it. We as a school system were doing something fundamentally wrong. I began to seriously question our skills and drills approach to teaching math.
Since then, math has been a huge focus of my own teaching program and research shows that there is little place for skills and drills in developing a numerate society. I don't mean to say that it's not helpful to know your math facts. Of course it is, but there is so much more to it and those math facts help with fluency, but not much with comprehension.
When we teach reading, we teach a skill called decoding which allows children to learn to read the words. We also teach a skill called comprehension that allows children to think about what the words, sentences, paragraphs, and stories mean. Most children can learn to decode quite easily and can read a mile a minute. Many of those children understand very little of what they read. They don't know that their brains are supposed to be engaged while reading, and so, we teach them.
The same holds true for mathematics. Most children can learn to add, subtract, multiply, and divide. These are skills that can be done by rote. Unfortunately, many of those who ace those skills have no idea what's really happening to the quantities they are working with. For this reason, how we teach math in BC is undergoing a fundamental and profound shift. We are moving away, finally, from skill and drills and towards a much more comprehensive understanding of mathematics. This is something to be really excited about, but I understand how frustrating it can be for parents.
What I do much of the time in math class leaves my students' heads reeling. I don't intend for them to fully understand each and every concept, but to learn to play with math much as my father played with me. I want them to begin to see the beauty in math and to look for patterns and relationships between numbers. I want them to see that they are dealing with not just number, but quantity. I want them to be able to do math in their heads and to be able to stop and think about how they just got that answer. I want them not only to be good at arithmetic, but to be numerate. Most of all, I want to make sure that each child has an opportunity to work in his or her zone of proximal development.
If you look back at my post on the zone of proximal development, you will see that much of your math time in school was probably spent in your zone of actual development doing skills and drills on math you had already mastered. Or... if you were one of the unlucky ones, the math lesson went on ahead of you, leaving you feeling like a fool and the math was entirely outside of your zone. Neither of those feels good and the only children who benefit are those smack dab in the middle.
I want my students to feel challenged, but not overwhelmed. I want them to feel like all this stuff is starting to make sense and that they're good at it, but not that it is either too easy or too hard. This is, quite frankly, and exhausting daily dance that I do with my students. There is a huge range of understanding and ability in any classroom and meeting all of those needs requires a great deal of thought and energy. I wouldn't have it any other way though. Each child deserves to become a mathematician in their own right and at their own level.
As you will see in this weekend's blog posts, if I were to send home the work that we do in class, you would be confused and so would your child. That would be extremely counterproductive.
On the other hand, there is something you can do. Look together for patterns, discuss numbers and how amazing they are. Read the blog and talk about the math we do, but don't worry if your child cannot explain it. It's not yet in their zone of actual development, so they probably won't be able to articulate well what we are doing. Begin to see the mathematics of your world as beautiful and so too will your child.
If you're looking for a good math read, Leonard Mlodinow's book,
The Drunkard's Walk, (not about a drunkard, but an expression) is a fabulous read that requires no mathematical background. The book is about the nature of randomness and is a lot of fun to read or listen to and will give you a starting place for thinking about mathematical relationships in a new way.
Jake
Sir Sloth-a-lot
Parrot (as yet unnamed)
