Now the title of the blog is Growth versus Fixed mindsets and our board has taken that approach for mathematics. Many of us grew up with the thought that math is a skill that only a few can handle, you either got it or didn't but this is a fixed mindset. Yes certain topics can be hard for students but that doesn't mean we cannot achieve understanding.
Take a look at this video:
if it doesn't work: https://www.youtube.com/watch?v=btDHUHZ6fAw
What are your thoughts of the video?
In Peel or at least at the two schools I have done PD at this has been connected to the various evolution or reforms in mathematical teaching. For many (if not all) of us mathematics was taught a lot differently then it is now. This is very scary for some and often challenges our ideals and schemas. When these believes are challenged is when we often get resistance. At both Ray Lawson (had ours first week of Sept) and Burnt Elm, we challenged the participates to think about their own schemas and believes and to adapt a growth mindset to their learning.
Our session started with a review of Stein, Engle, and Smith's Orchestrating Productive Mathematical Discussions: Five Practices for Helping Teachers Move Beyond Show and Tell. We actually talked about their book but this article sums it up quite nicely. If you read the article would love to know your thoughts? What spoke to you about this article? What resonated as the most important point?
I then was asked to tell a personal testimony of my mathematical journey. I know that I have been preaching reform for some time now but I have not always felt this way. Before I became a teacher I volunteered at a school who was just starting using reform. For me this was a shock to the system. Math for me was never hard, in fact at this point in time I was taking my University Calculus class. I felt that if algorithms where invented then they should be used. I also strongly felt that steps and procedures could easily teach students how to do math. I was lucky enough to be pushed by an amazing principal who allowed me to question the process, give me research and see it in action. Its interesting to look back at this and see that really I was discovering these ideals through a constructivist approach: I had to explore, have a mentor and then experiment with my findings. As time went on I noticed how students were achieving amazing results in mathematics and sustaining them but more importantly their attitudes towards math changed. I saw all students engaged in lessons, learning math and being mathematicians. The more I taught the more I saw these observations consistently happening. Not only this but while teaching at Brookmede I was able to be a part of a school which consistently implemented Reform mathematics. During this time not once did I have to review last years concepts with the students, I started each year with that years concepts. Yes I had students who were developmentally not ready for the grade but they all could tackle the problems, worked together collaboratively and loved math. To me that was enough. I share this story because if I had a fixed mind-set and believed that the way I was taught is the best way then I wouldn't have seen the benefit of teaching through problem solving. Now that being said I am always revisiting my teaching practise and I think we always have to be. Growth is growth! Change must happen.
The session then turned into a great problem solving lesson. One in which the teachers got to feel that disequilibrium that comes with learning mathematics.
“@MrSoclassroom: Some great math talk happening here. Grt job burnt elm and @JayWigmore pic.twitter.com/uTa0Zksb20” #EngageMath
— Jason Wigmore (@JayWigmore) October 10, 2014
After debriefing the problem we had a great discussion from a teachers perspective. The questions we discussed where:
1) Why were the strategies chosen in the debrief?
This brought out a cool discussion about levels or accessibility to the problem and talk. A lot of the times when strategies are chosen its because we want to honour student voice but in reality we do have to think about the math. The first strategy should be one that can have the most students engaged with the lesson. One that allows the most talk and will lead to the next progression of the lesson. It was during this time too that we addressed the thought that our goal should never be to get kids to jump from a basic understanding right away to the abstract, this is what causes the gaps in learning. It is far richer to move them up to the next stage in development. To do this as a teacher we have to think through the possibilities and understand what our students may or may not accomplish.
2) What is the role of a teacher in this format?
3) What is the impact on the student?
After this session, the principal open the discussion up for general questions. It was great to hear all of the questions being asked and it reminded me of the journey that I went through. Let me highlight a few of these questions:
1) Are you telling me Algorithms are bad?
No I am suggesting that there is a lot of understanding that goes into learning algorithms that many of our elementary students do not have. We need to think about the middle piece that goes into the learning of math. We often forget as adults all of the processes that we had to go through to learn a concept.
2) What about facts?
I know that I have answered this question before and it always gets me that people associate Reform with not teaching facts. In fact as we have discussed in #engagemath there is a balance and yes FACTS ARE IMPORTANT. One needs facts to solve math but how we go about learning facts is a different matter. Jo Boaler suggests that fluency does not mean speed. In fact I would suggest that speed is a fixed mind set. A mind set that can often discourage children from learning math. I teach facts through games which does three things. One it teaches fact recall. Two it teaches communication, understanding and strategy and three it build relationships. Here is a link to my math games.
3) What is the most important aspect of setting up a classroom like this?
Classroom setup is vitally to building problem solvers. Students need to feel comfortable, held accountable and know that mistakes are learning opportunities. I always find that the best way to do this is wait. Waiting time is so under utilized as a teacher. We want to fill the void but if you just wait one more minute longer you will be surprise at what students say. Here is some things that I have collected on math talk.
Overall, it was an amazing PD session at both Burnt Elm and Ray Lawson (though Ray Lawsons did not happen on Friday). Peel teachers continue to be amazing both in their thinking and sharing. When I do talk about math I am reminded the learning that I had to go through and I know that we are all in various spots but keep that growth mindset not only for your self but your students too. That being said I would love to here your thoughts on anything discussed here:
1) Reform Mathematics
2) Growth versus Fixed Mindsets
3) Teaching through problem solving
4) Five practises
Also if you have any questions or comments please contact me or leave them below.