If I have 7 oranges in one hand and 9 oranges in the other hand, what do I have? (See the end of the post for the answer.
I spent 45 stimulating minutes at the third and fourth grade family math night yesterday. A group of families from both grades gathered together to play math games and to talk about math with their children and with Rose Reilly, lower school math coordinator, and with lower school principal and assistant principal, Namita Tolia and Dawn Wheatley.
Our family played a few games, the simplicity of which allowed us to practice and explore some important math concepts and skills. As we played, I observed my son employing a variety of strategies as he addressed the problems presented, sometime doing work in his head, sometimes on paper, sometimes using strategies different than I would have expected (or chosen) and sometimes using the more standard American algorithms. (I say American as I am told that there are other countries where the arithmetic algorithms are quiet different.) He seemed to have a plan as to when to choose a certain strategy or skill and, while I was impatient for him to just “line up the numbers,” when I allowed him to get there on his own, he got he right answer or knew when he was wrong, retooled and then “got it.”
Stepping back from my more personal experience, as I watch students move through our math program, I see them retaining this problem solving ability as they develop facility with the more standard algorithms, those that many of us learned in our math classes some number of decades ago. We see students move into the middle school and high school confident and able, eager to continue to learn math and to move quickly to acquire new skills. In the high school we have seen a growing group of our students, some who are from our middle school and some who join LREI in ninth grade, participating with confidence and agility in accelerated math classes.
Back to the third grade. I find myself, as a parent, wanting my child to learn the more standard ways of solving problems, even when I can admit to myself that for many, many people—smart successful people—learning the algorithm first and practicing it without application, without discovery, without truly understanding the mathematics behind it did not allow us to employ it at will, to move with agility between strategies, to know when our answers were wrong. Our goal is have children understand the mathematics, to have a deeper sense of why an algorithm works, when and where it works and then to bring in the arithmetic that allows for more automaticity.
A final thought on this. I know that learning these skills leads to success in the older grades, in a range of subject areas and experiences. I am fully on board with teaching the more intellectually challenging mathematics first, I am committed to this yet, as my child has to choose a method and truly think about the problems rather than simply solving a series of arithmetic puzzles, I can become frustrated (“Can’t he please do it the way I did it?”) and also want to see it be easier for him. When I can pull away, I get to “easier not being better” and the old ways not always being more successful (Thank you, Elisabeth Irwin) and I can allow myself to watch him struggle and know that eventually it will all be okay. Better than okay, finding your own way, a lack of initial routinization, creates a sense of mastery, of resilience and of self-confidence. All good things.
Ans a final thought. Thank you to those who accepted my invitation to share a cup of coffee and a discussion about New Year’s resolutions. While we happily strayed from the topic, we had a nice conversation. I invite all to gather for a conversation on Monday, February 4th at 8:45a.m. in the Sixth Avenue cafeteria with an initial focus, referencing the above, of thinking about the ways in which we interact with our children as they are struggling, when they might be unsettled and when they are involved in situations that might have made us uncomfortable. I encourage you to read an excerpt from an excellent book, The Parents We Mean To Be by Richard Weissbourd. You can read an excerpt and hear an interview with the author at: http://www.npr.org/templates/story/story.php?storyId=102831737. Please join us.
Answer: Big hands.