If you are not a member of youcubed.org, you should be. It's a great resource for teachers and parents about the most current research into how to teach math. The site was set up by Jo Boaler, professor of Mathematics Education at the Stanford Graduate School of Education, who is a mathematics hero.
One of Boaler's points for which I have strong personal feelings, is that timed tests in mathematics are absolute garbage (absolute garbage are my words, not hers, but that's because of the personal connection). Timed tests were something I dreaded as a child. I knew that I could never pass them with the required speed. All I could hope for was to get them over with without too much embarrassment. They absolutely convinced me that I was no good at mathematics. I wish I'd have known then what I know now, which is:
Mathematics is not about speed. It is about depth of thought. If you want an example of this, you can read about Chinese mathematician Shing-Tung Yau.
Children with exceptional math skills are just as likely to preform poorly on timed tests as children with poor math skills.
Timed tests create a situation of anxiety, which actually shuts down the brain's ability to think.
Perhaps the worst thing about timed tests is that they don't teach anything. Children with poor math strategies try to use those poor strategies quickly and children with excellent math strategies try to use their excellent strategies quickly. At the end of the test, nothing has changed about the way the children are approaching mathematics. This is a major problem, because the thing that really separates children's mathematical ability, is the way they approach problems. Children who struggle with math use clumsy and inefficient strategies. Children who excel at math use elegant and efficient strategies. For example, imagine you gave a kindergartener two piles of objects, and ask them to count the piles separately. One pile has 6 objects and one pile has 4 objects. You then ask him how many there are all together. A student whose strategies are underdeveloped starts counting all of the objects again--even though they previously counted both piles. A student whose strategies are more efficient might start at 6 and count on. A student with excellent strategies might move one of the objects in the pile of 6 to the pile of 4, creating a problem of 5+5=10. It is the method that students use that leads to efficiency, not the time in which they do the task. Timing our inefficient mathematician is only going to result in him trying to count faster.
When I was a student, I was deeply embarrassed of the fact that I couldn't remember all of my multiplication tables. I was terrified that my math teacher might discover that I could never remember what 8x6 was and always had to start with 7x6=42+6=48. Now I've discovered that this kind of flexibility with numbers is exactly what mathematicians need. In fact, my computer programmer husband and I have had many discussions about the math classes he took in college and how they were about teaching him this kind of flexibility on a higher level, how they taught him to problem solve, and about how accuracy was always more valuable than speed.
So, if we want to improve our student's ability to do math, please, please, please, never pull out a timer, because we never want our children to get the idea that math is about speed. Just like good writers are concerned with how well something is written, and not how fast they can type, and good scientists are concerned with how accurate their results are, and not how quickly they came up with the results, good mathematicians should be concerned with the processes of mathematics, not the speed of their sums.
--- Contributed by Lyndsey