Another school year has begun, and so I want to report on the first day of class. The report won’t make as much sense without knowing what has been on my summer reading list.
On top of that, I’ve been taking Jo Boaler’s course on How to Learn Math.
After reading what I have read, I knew that somehow the first day of class had to be different this year.
In the 4th session of Jo Boaler’s course, she talks about a framework for a growth mindset task that they developed at Stanford.
Growth Mindset Task Framework
2. Different ways of seeing
3. Multiple entry points
4. Multiple paths / strategies
5. Clear learning goals and opportunities for feedback.
Consider the following task for a geometry student as students are beginning to think about inductive reasoning.
Finish the sequence: 2,3,5,8,12,17,…
A few years ago I changed this task for day 1 of geometry.
Now the directions are to find and explain at least two ways to finish the sequence.
So what is the difference between the two tasks?
I want students to realize from the first day of class that there will often be more than one way to answer tasks, that we are not all going to see the same thing, and that being able to explain our thinking is important. Even if we arrive at the same solution, we might use different paths to get there. I also want students to realize that part of being a good student is being a good listener, so that we can really begin to get at constructing viable arguments and critiquing the reasoning of others.
I collected student responses to the sequences using TI-Nspire Navigator.
Our discussion encompassed recursive sequences, prime numbers (and composite), the Riemann Hypothesis, RSA Encryption, powers of 2, memory storage for electronic devices, the Fibonacci sequence, and more.
In light of this task, I passed out the CCSS Math Practices Handout that our department made last year and asked my students to reflect on which practices they had already used in class (they suggested make sense of problems and persevere in solving them, reason abstractly and quantitatively, construct viable arguments and critique the reasoning of others, look for and make use of structure, look for regularity in repeated reasoning).
We talked about using the practices to do math, and I told them that I will want them to reflect on using a practice at least once each quarter using the CCSS MP journal prompts that I had copied on the back of their handout.
Finally, we had a discussion about fixed and growth mindsets. I sent the following poll and asked students with which statements (from the first chapter of Mindset) they agree.
Dweck suggests that those who agree with the first two statements tend towards a fixed mindset regarding their intelligence and those who agree with the last two statements tend towards a growth mindset regarding their intelligence.
One class of students marked the statements as shown below.
I shared some of the research that Dweck cites about growing your brain bigger (creating synapses) when you make and learn from mistakes. I also told my students that I can look back in my own life and see a change from a fixed mindset into a growth mindset. We are certainly not finished having this conversation, but I hope that my students will begin to realize that they can do something to change their intelligence and embrace the work that will require.
So here’s to another school year as the journey continues ….