One of the reasons I am so much enjoying N.'s developing numeracy is my own traumatic experience of math in first grade. It would not be an overstatement to say that my experience of math instruction in school scarred me for life; because of this I am especially drawn to Holt's account and thrilled with N.'s experience of math so far.
When I was six years old and in first grade, we had to take timed tests of addition and subtraction problems. We were supposed to complete a sheet of problems in a certain amount of time without error. If we did that successfully, we moved up to a test to be completed in a shorter time, and then another and another, each test to be completed in a shorter time than the last. The point was to drill math facts so that you could eventually do them automatically without thinking. I couldn't progress beyond the tests with the longest time allowed. I understood how to add and subtract and I could do it correctly, but not quickly. My parents were concerned, so they had me practice the timed tests at home. I still vividly recall my father's desk in the dining room where I sat to take the tests, the florescent glow of avocado green desk lamp, the menacing red numbers of the digital desk clock.
Timed math tests constituted my first experience failing at something in school. And I definitely felt like a failure. It was humiliating to see my friends moving up through the test levels while I had to take the longest timed test again and again. I hated practicing the tests at home. I felt anxious about my parents' concern because I knew that doing well in school was important, and I wanted to do well. Describing it here, I find it hard to believe these little tests ended up looming so large in my life, but in some ways I never really got over my inability to succeed on those tests. I developed a phobia about timed tests more generally to the extent that my mom had to ask my teachers throughout elementary school not to announce the time remaining on the yearly California Achievement Tests; I was afraid I would freeze up and not complete the test if I heard how much time I had left.
The consequence of my first grade timed math tests was that I thought I wasn't good at math, and I thought this all the way through high school, even though what I wasn't good at at the earliest stage simply was doing math quickly. I also had a very difficult time memorizing the multiplication tables, even though I had a very good memory for words. I think now that in addition to the anxiety I had already developed about math thanks to the first grade timed tests, I struggled with the multiplication tables because I hadn't really internalized the relationships of numbers to each other. The times tables were content-less to me, a series of meaningless numbers. My favorite experience of math came outside of school, in a book my mom bought me called The I Hate Mathematics Book which presents mathematical concepts in real-world contexts (I still remember the pages on permutations and combinations of ice cream flavors).
Despite have an analytical and logical turn of mind, and good spatial relations abilities, I came to define my identity as a student as someone who couldn't do math. I took the bare minimum required math to graduate from high school (Algebra II) and am embarrassed to say that I have never taken pre-calculus, trigonometry, or calculus. I didn't like taking courses that were really difficult for me and that I didn't enjoy working hard in (I was willing to work hard in classes that I was interested in); I didn't like failing.
My own dismal experience of math in school shapes my approach to N.'s education in several ways. First, what happens in the early years does matter, and can have a profound impact on a student's later learning. Second, we try to cultivate a holistic and deep understanding of the many facets of mathematical thinking in N. rather than focus on the surface "math facts." Third, speed doesn't matter, understanding does. Fourth, it's okay to fail. Or, better yet, we hope we create a learning environment where there is no failing, only learning, where everything N. does is recognized and valued by us and by him as an important part of his learning and development. I hope he feels that it can be fun to struggle at something that is hard and that his sense of self-worth or his self-definition do not derive from whether something is hard or easy for him. In fact, isn't it better to try to cultivate in children (in adults too!) an open definition of self? What if I hadn't let my struggles with math in first grade become such a strong part of who I thought I was?