You see, all of our brains actually GROW and make new connections when we make mistakes and think about them. There is no brain growth if you can just sail through a problem set! That is why it is so important for our students to make mistakes -- and then we need to VALUE those mistakes and help them learn from them.
People with so-called fixed mindset are usually afraid of making mistakes. We need our students (and ourselves!) to have a GROWTH mindset - the attitude that I'm not perfect nor smart already, but making mistakes helps me learn and grow my brain.
Jo has written a book, What's Math Got to Do with It?: How Parents and Teachers Can Help Children Learn to Love Their Least Favorite Subject. I do not have it... but based on what I saw on Amazon and on her course I took, I expect it to be very helpful.
So, how does this tie in with testing and speed? In one session, Jo gave some reasons why she thinks students feel bad about making mistakes (and they do, don't they?).
- In schools (but it can happen in homeschool too), students get a VERY clear message that success is about "doing well on tests," which is very damaging.
The problem with this thinking is that students cannot then see the role MISTAKES play in learning, and how making mistakes can lead to SUCCESS — if you embrace them, value them, and learn from them.
Quoting from Alina Tugend:
If students are afraid of mistakes, then they're afraid of trying something new, of being creative, of thinking in a different way. They're scared to raise their hands when they don't know the answer, and their response to a difficult problem is to ask the teacher rather than try different solutions that might - gasp be - wrong. They are, as one teacher told me, victims of excellence.
- The second reason had to do with the emphasis on SPEED in math classrooms. Neuroscience is showing us that mathematics should NOT be associated with speed. A number of studies in recent years show that TIMED TESTS cause math anxiety. I think that doesn't come as a surprise at all... Researchers have found that when people are stressed, that stress just blocks their working memory. This can simply prevent students from recalling math facts in tests though they know them.
If you are wondering about automaticity... there are better methods of teaching a quick recall of math facts that ALSO give students conceptual understanding and help them develop number sense. Jo said that number sense is so critical to young children that it is known to be what separates high achievers from low achievers in maths!
Check for example these videos of mine that explain the methods I have used with my children. I have gotten lots of good feedback from others as well:
- Strategies for addition and subtraction facts
- Learning the multiplication table of 3 with a structured method
I thought this was pretty interesting... Jo also said, "In my experience, mathematicians are some of the slowest people I've met. And I don't say that to be insulting to mathematicians, but the reason they're often slow is because they're thinking deeply."
Here's an interesting quote from one of France's greatest mathematicians, Lauren Schwartz, who won the field medal in math. She is reflecting on her time in school and notes how she is SLOW.
"I was always deeply uncertain about my own intellectual capacity. I thought I was unintelligent. And it's true that I was, and I still am, rather slow. I need time to seize things, because I always need to understand them fully. Even when I was the first to answer the teacher's questions, I knew it was because they happened to be questions to which I already knew the answer. But if a new question arose, usually students who read as good as I was answered before me, and towards the end of the 11th grade I secretly thought of myself as stupid and I worried about this for a long time. I never talked about this to anyone but I always felt convinced that my imposture would someday be revealed. The whole world and myself would see that what looked like intelligence was really just an illusion.
Now that never happened. Apparently no one ever noticed it, and I'm still just as slow. At the end of the eleventh grade, I took the measure of the situation and came to the conclusion that rapidity doesn't have a precise relationship to intelligence. What is important is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn't really relevant. Naturally, it's helpful to be quick, like it is to have a good memory. But it's neither necessary nor sufficient for intellectual success."
If you'd like to read more, see this article: The Role of Mistakes in the Classroom or check out Jo's book on Amazon (using the "look inside" feature).