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Knowing how to solve an equation is no longer a valuable human ability; what matters now is formulating the equation to solve that problem in the first place, and then taking the result of the machine solution to the equation and making use of it.

Today, we have instant access to vast amounts of information and to unlimited computing power. Both are now utilities, much like water and electricity. And that has led to a revolution in the mathematics ordinary citizens need in order to lead a fulfilling, productive life. In a world where procedural (i.e., algorithmic) mathematics is available at the push of a button, the need has shifted to what I and others have been calling mathematical thinking.

Unfortunately, many Americans were never taught to understand arithmetic, they were just trained to execute procedures. It's not their kids who are being short-changed. They—the parents—were!

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.

I learned math facts through using them in different mathematical situations, not by practicing them and being tested on them.

Math facts are a very small part of mathematics but unfortunately students who don’t memorize math facts well often come to believe that they can never be successful with math and turn away from the subject.

She describes the language of maths as full of "beauty and elegance".

She did poorly at maths for several years at school because she was not interested in the subject. "I can see that without being excited, mathematics can look pointless and cold. The beauty of mathematics only shows itself to more patient followers,"

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.

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.

Believe it or not, math is changing. Or at least the way we use math in the context of our daily lives is changing. The way you learned math will not prepare your children with the mathematical skills they need in the 21st Century.

Math education is stuck in the 19th Century

Numbers and variables are NOT the foundation of math.