As a child I had to learn lots of things by rote – times tables being a particular memorable one. As a class we would chant them together, then round the class, then randomly pointed at. I don’t remember hating it, I do remember doing them and I do remember them being reinforced by my parents – around the table, walking to school, almost every spare minute!
I now know my tables, instantly, with corresponding division facts. We didn’t know why they were needed, we were told to do it and we did. Throughout maths lessons at school, university and even as an adult I am very grateful that I “just know” these simple facts. I have, over the years, done quite a bit of tutoring and have always stressed that knowing your tables is a really, really useful skill. A lot of the children I have taught have been very quick to count up on their fingers 3, 6, 9, 12 etc but then can’t easily say what 3 x 40 is as they don’t have the instant recall of 3 x 4 and want to keep going on fingers although I suspect that the majority would have lost track before 114, 117, 120!
Several years ago whilst teaching a Y6 class we had a visit to an “old schoolhouse” where we sat in a lesson with the teacher hitting the desk with a cane and making me stand in the corner with my dunce’s hat on for some perceived misdemeanour. Back at school with my lower group I thought we’d play at continuing this style of lesson (minus cane and dunce’s cap!) and I got them to stand behind their chairs repeating a line at a time after me and then reciting, “to find a fraction of a number…..times by the top …..and divide by the bottom.” Much laughter ensued as they copied and recited, and then sat in silence to do the questions written up on the not so historical interactive whiteboard. A few weeks later during the SATs test find 5/7 of 56 (or similar) came up. I Saw the faces of the children from my group light up, I could see them mouthing the words, and the majority came up with the correct answer. Those children had no understanding of why 40 was the right answer, but they knew what to do!
I am certainly not advocating that we go back to learning methods with no understanding – I was training to be a teacher before I found out why my method of subtraction, which was apparently called subtraction by compensation, worked. But I do sometimes feel that for some children who need to learn how to manage in “real life” that a method that always works and a few number facts learned by rote wouldn’t hurt.