Week 2 discussion: Brave minds?
What is intellectual bravery? Why is it important to everyone? How do we develop it? Do you see it in children while doing the lessons?
I read all these wise replies so far and didn't think I had anything to add. So I decided to ask my kids instead. I first asked my 9 year old Joanna, who said "I don't know." (She was struggling with what the word "intellectual" means.) I then asked my 14 year old Rachel. First she said "it means not being afraid to say an answer, even if you might be wrong." (Joanna agreed.)
"Is that all it means?" I countered.
"Well, if could also mean a willingness to tackle a really hard problem, even if you know you may never get an answer to it."
"Is bravery the same as confidence?" I asked. At first they said yes, but then had second thoughts. Finally, Rachel said decisively, "It means thinking outside the box."
I was just reading a book about confidence and the frugality of it. Dictionary defines confidence as "a feeling or belief that you can do something well or succeed at something" - and depends on what those beliefs are based upon. Bravery, our courage, on the other hand, is the ability to face the unknown or something you are not sure you will be able to do well - but you still do it.
It would seem to me intellectual bravery follows a lack of fear to make mistakes. When we are open to our mistakes and don't see them as downfalls but rather as openings for discussion and learning, we are more willing to put our thoughts out for observation and debate. Despite my personal efforts in my home school environment to encourage and celebrate failure, I still have a perfectionist, but only in math, where her intuition is high and she feels expected to excel. It takes effort and a lot of bravery for her in particular to stand before her math team peers and offer her solution to a problem but she still does so. Sadly, she remembers the one time her solution was considered "wrong", though only she perceived it that way, and not the many times her solution was right.
Leanne, what you describe is a serious issue, and there are studies that it affects girls more than boys. It's possible to cure, otherwise, it adds up over the years, especially with negative social pressures in pre-teen years. And yes, the pattern tends to happen only in math! It has to do with girls correctly recognizing that mathematics has beautiful tools for finding and proving real truth - but then erroneously concluding it means they have to be successful in the use of those tools all the time, every time.
It helps if you just notice and discuss these patterns. You can also do a bit of a study together: observe answers in a group, and check if they are right or wrong. You can do it in your daughter's group, or visit a university class, or view a recording of someone's math circle: http://www.mathcircles.org/videos. All problem-solving groups have a high number of wrong answers. Discovery and Socratic groups have divergent answers that may be neither right nor wrong.
Thanks, Maria! It is painful to see her struggle with perfection and I will try some of the ideas you mentioned. Though only 8, she is quite mature and takes well to being spoken to in a logical, adult manner. So, I discussed your response a little with her which went over quite well. It led to a discussion of the many mistakes that were made just yesterday in our math team group, mostly by adults! It was a funny group, with many people attempting the same problems from many angles and gave us all a good shared laugh. I think rational discussion along with your suggestions will help her. By the way, I asked her what she thought "intellectual bravery" meant. She responded that it is being brave enough to show your intelligence, an interesting idea.
This effect is more dangerous for mature kids - precisely because it's based on their sense of responsibility to others. They don't want to pollute the communal space with their wrongness. Yes, discussion and noticing helps - and laughter does too!
Yesterday during the activities I used a strategy that Joe Boaler uses in the border problem video and asked if they all wanted to say their answer together. The kids happily shouted out their common answer. But one of them had a different one, in such a situation I think it takes bravery to speak out, which he did, and trust one's reasoning enough that he could stand out there and explain how he thought about the problem. Intellectual bravery also takes the form of asking "What if" questions and explore beyond the given. A good way to develop it is to regularly engage in the kinds of activities we are exploring this week, and do it within a group that one can trust enough to support the explorations and creativity (reference to recent FB post).
My long-time math circle participants are very aware by now, that when they all have the same answer, it is almost always wrong. They actually made it an informal rule of the math circle, and joyfully explain it to the new students as they join the class. ( " If you think like everybody else, you are almost certainly wrong")
It seems to me that it is closely related to confidence. Confident kids are not afraid of being wrong, so they will say what they are thinking even when they are not sure they are right. I think we can help create an atmosphere where they feel intelectually brave by not reacting negatively when they give us wrong answers to our questions.
When you say "confidence" here, you mean that children are confident that their input will be accepted positively. It is different from the "confidence" when the children believe that they are right - that type of "confidence" is harmful, and actually diminishes teh intellectual bravery.
Bravery I define as doing something in spite of fear, danger, or uncertainty. This is different than confidence, I think, in the aspect that those who are confident do not fear and are fairly certain of the outcomes or their abilities to handle them. Intellectual bravery then, would be to overcome the fear to think and share something with others - fear of rejection by peers or authorities, uncertainty to whether or not your thoughts are true or meaningful. Confidence is a natural outflow of successful trials of bravery. In the context of our math circles, intellectual bravery would be shown by the child who is embarrassed to share but shares anyway. When the child's ideas are received by the group and constructively evaluated and appreciated, the child will have confidence to share again next time. The job of the members of the circle is to know how to constructively evaluate an appreciate all approaches to a problem.
Thank you for your reply. Yes, bravery and confidence is not the same, and, sadly, may actually be quite opposite in some situations. You may tell the children, that one of the reasons we call it a math "circle" is that there is not one whose opinion weights more that the others'. The job of the circle members is to accept and then analyze each and every approach and solution. It is quite possible that the same approach, that is not very effective in a given problem, can turn out to be quite effective in another - so comparing different approaches enriches the overall experience.
