Here is a wonderful piece by Stanford math professor Jo Boaler. I offer it not as part of the Common Core debate but because it lives in a world so far beyond that debate. Whether or not you are a math person, so to speak, you will enjoy this.
Never mind the longer paragraphs. It’s still easy to read. Here’s the beginning:
A few years ago a British politician, Stephen Byers, made a harmless error in an interview. The right honorable minister was asked to give the answer to 7 x 8 and he gave the answer of 54, instead of the correct 56. His error prompted widespread ridicule in the national media, accompanied by calls for a stronger emphasis on ‘times table’ memorization in schools. This past September the Conservative education minister for England, a man with no education experience, insisted that all students in England memorize all their times tables up to 12 x 12 by the age of 9. This requirement has now been placed into the UK’s mathematics curriculum and will result, I predict, in rising levels of math anxiety and students turning away from mathematics in record numbers. The US is moving in the opposite direction, as the new Common Core State Standards (CCSS) de-emphasize the rote memorization of math facts. Unfortunately misinterpretations of the meaning of the word ‘fluency’ in the CCSS are commonplace and publishers continue to emphasize rote memorization, encouraging the persistence of damaging classroom practices across the United States. Mathematics facts are important but the memorization of math facts through times table repetition, practice and timed testing is unnecessary and damaging. The English minister’s mistake when he was asked 7 x 8 prompted calls for more memorization. This was ironic as his mistake revealed the limitations of memorization without ‘number sense’. People with number sense are those who can use numbers flexibly. When asked to solve 7 x 8 someone with number sense may have memorized 56 but they would also be able to work out that 7 x 7 is 49 and then add 7 to make 56, or they may work out ten 7’s and subtract two 7’s (70-14). They would not have to rely on a distant memory. Math facts, themselves, are a small part of mathematics and they are best learned through the use of numbers in different ways and situations. Unfortunately many classrooms focus on math facts in unproductive ways, giving students the impression that math facts are the essence of mathematics, and, even worse that the fast recall of math facts is what it means to be a strong mathematics student. Both of these ideas are wrong and it is critical that we remove them from classrooms, as they play a large role in the production of math anxious and disaffected students. It is useful to hold some math facts in memory. I don’t stop and think about the answer to 8 plus 4, because I know that math fact. But I learned math facts through using them in different mathematical situations, not by practicing them and being tested on them. I grew up in the progressive era of England, when primary schools focused on the ‘whole child’ and I was not presented with tables of addition, subtraction or multiplication facts to memorize in school. This has never held me back at any time or place in my life, even though I am a mathematics education professor. That is because I have number sense, something that is much more important for students to learn, and that includes learning of math facts along with deep understanding of numbers and the ways they relate to each other.
read the rest at Fluency Without Fear.