My thoughts on the book, Mathematical Mindsets by Jo Boaler.
From the first page, I was hooked.
New ideas to implement immediately into my classroom.
At times, it was a confirmation of how I was already conducting my classroom.
My philosophy for teaching math is to "Move Our Thinking".
Obviously, the best way to move our thinking is to be engaged, practice, and ultimately make mistakes.
This concept of "Moving Our Thinking" starts on day one and is referred to almost on a daily basis and we conquer objective after objective in our 8th grade math classroom.
Chapter One and Two of Mathematical Mindsets tackles this exact concept but with a little more depth.
In chapter one, according to Carol Dweck, 40% of students have a fixed mindset where they believe that they are either smart or they are not. These mindsets can be changed, though, to a growth mindset where one believes that that the more they study/work, the more they can learn. "When we learn a new idea, an electric current fires in our brains, crossing synapses and connecting different areas of the brain."
~ Is this why connecting to prior knowledge is so important?
It is important to remember that in the classroom, when students are praised it should not be because they are smart, but instead for what they have learned, the perseverance they used to solve a problem, or how they thought about a problem.
And then I read Chapter 2.
The Power of Mistakes and Struggling
It was like reading my mind.
Only better.
I learned some new stuff!
Synapses were firing away!
Favorite quotes:
"Every time a student makes a mistake in math, they grow a synapse."
I shared this with my students last year and they were very intrigued with how their brains work. We talked about the power of mistakes and how they really help us in the learning process. At times I purposely make mistakes in my instruction (and then there are times when it happens naturally!) but in any case, finding mistakes and learning from them is important. Of course, it's more powerful when students make their own mistakes. This is why taking a risk to solve a hard problem is important. Students are looking for an entry point into the problem and then must connect the mathematical knowledge they have to solve it. If they don't take the risk, they are not even allowing themselves to make a mistake...thus no synapse. I have heard students say to themselves, "I just grew a synapse." I love it.
Based on the reading from "Mindsets" by Dweck, it is important to teach students not only about the two mindsets but also about how their brains work.
Based on the reading from "Mindsets" by Dweck, it is important to teach students not only about the two mindsets but also about how their brains work.
When students struggle "the brain is challenged and this is the time when the brain grows the most."
This is essential for me to remember in my later hours. It seems like during the first couple hours, when the problem is fresh for me as well, I allow students to struggle through the problem. By the time my last class arrives, I find that my questions are much more leading when they stuck. Something I definitely need to work on.
"Mistakes are not only opportunities for learning, as students consider the mistakes, but also times when our brains grow".
Students commented that they would just make mistakes on purpose then to grow more synapses. It was a little disheartening to them to find out that if they made a mistake on purpose, then they already knew it was a mistake, thus they were just making a choice. Not the same thing.
"What separates the more successful people from the less successful people is not the number of their successes but the number of mistakes they make, with the more successful people making MORE mistakes."
Not only is this helpful for my students, but for me as well.
To help my students gain a positive outlook on making mistakes, I did the crumpled paper idea on pg. 15 this last year. This was a great way to get rid of their initial feelings of when they make a mistake and remind them of the brain growth that occurs every time a mistake is made. This is definitely an idea I will be using again this year...only much earlier in the year as we set up our classroom norms.
Another idea that confirmed how I teach my math classes goes back to the 1930s and Jean Piaget that learning is not about memorizing procedures but seeing how ideas fit together. While I have always believed this and strived for this to happen in my classroom, it wasn't until this summer when I was introduced to the Progressions for the Common Core Standards when I got a first hand view of how mathematical ideas vertically align across the curriculum. Now I have an understanding of where my students are coming from and where they are going and how 8th grade math can be the bridge that connects these ideas together.
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