To understand deeply or to know quickly? #EDUC115N

“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 weren’t 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.”

Laurent Schwartz, Fields Medal earner, as quoted by Dr. Jo Boaler in EDUC115N How to Learn Math (MOOC)

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Faster Isn’t Smarter

Persistence through doing things…solving things #EDUC115N

“Lots of people think knowledge is what we want, and I don’t believe that because knowledge is astonishingly transitory. We don’t employ people as knowledge bases. We employ people to actually do things or solve things. Knowledge basis comes out of books, so I want flexibility and continuous learning and I need team-working, and part of team working is communication. When you’re out doing any job in any business the tasks are not forty-five minutes max, they’re usually three week dollops or one day dollop or something, and the guy that gives up, oh sod it, you don’t want him. So the things therefore the flexibility, the team work, communications and the sheer persistence.”

Ray Peacock as quoted by Dr. Jo Boaler in EDUC115N How to Learn Math (MOOC)

If we know problem-based and inquiry-based are more engaging and effective,… #EDUC115N

So the typical method in classrooms is students are taught methods, then they solve problems. But in this classroom students got big open problems, and then they learned the methods to help them solve them. The students started at these two schools at the same levels in maths achievement, but the students at the problem based schools, ended up scoring at significantly higher levels on the national exam. And I was able to follow up and find the students eight years later, and they also ended up in more professional jobs.

Jo Boaler, speaking in Session 3, EDUC115N How to Learn Math (MOOC) [one of best courses I have engaged in]

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Boaler, J. (2002). Experiencing School Mathematics: Traditional and Reform Approaches to Teaching and Their Impact on Student Learning. (Revised and Expanded Edition ed.). Mahwah, NJ: Lawrence Erlbaum Association.

Boaler, J. (1998). Open and Closed Mathematics: Student Experiences and Understandings. Journal for Research in Mathematics Education, 29(1), 41-62.

Boaler, J. (2012, 8-15 July). From Psychological Imprisonment to Intellectual Freedom – The Different Roles that School Mathematics Can Take in Students’ Lives. Paper presented at the 12th International Congress on Mathematical Education, Seoul, Korea.