Thursday, July 21, 2016

Rewriting Mathematical Mindsets

This idea has been swimming around my mind for a while and I wanted to get it out there into the world and see if anyone might be able to shoot some holes in it or make it better. I had no plans on doing this with my students unless I see a dire need for it (especially in the very unpolished state it currently exists), but it's the kind of conversation I feel like we don't have with our kids enough. 

This all started when I read this article, The Myth of 'I'm Bad at Math'. My experience with students who have developed a negative mathematical mindset is often that there is some advantage they find in thinking the way they do. If they "just aren't a math person" or "can't do math," it can grant them permission to accept defeat instead of confronting their struggle directly. Often, with time and patience, these kids discover they can do math and (shhhh, don't tell anyone) they might even like some aspects of it.  This is the "self-help"-y conversation I've had with a friend or parent or therapist as I've gotten older....when a mindset I've taken on provides some advantage to me that might be hurting me overall. It's not intentional; it's survival. And ain't no way I ever would have been able to come up with that on my own at age 15. 

I've chosen a few of the phrases that make me saddest as a math teacher and want to take a more critical view of them:

In my ideal little hypothetical classroom, I would assign these out to different groups (and maybe have the kids generate some of their own, since my words aren't always theirs). I would have each group answer these questions:

What advantage does this mindset provide to someone?

What problems do you see with this mindset?

How can we "re-write" this mindset?

It can be something as simple as adding the word "yet" to totally change a perspective. It would also give us the opportunity to talk about the fluidity of learning and bridge perfectly into a growth mindset discussion. If kids would buy into the convo, I feel like it could be beneficial for them. 

I feel like this extends to honors and AP classes too, where the mindsets might be different but the survival instincts are still the same. Those mindsets might look more like this:
So all you amazing educators, feel free to shoot holes or make suggestions or give feedback. I feel like if we truly want kids to buy into growth mindset, we should be helping them examine their current mindsets and why they might not be the most beneficial for them. Too often kids in math only own their failures. If they learn to own their mindsets, maybe they can learn to own their progress and their successes too. 

And of course, it immediately made me think of good old Eleanor. 

Wednesday, July 20, 2016

First Day of School: Setting the Tone & Common Mistakes

I'm in the midst of what might be the longest summer of my life- moving from a southern school that gets out early to a northern school that goes back late. I've already had almost 7 weeks to get moved, get settled, actually get my driver's license, insurance, addresses, etc transferred over, and spend time exploring my new town. I still have almost 7 weeks left to enjoy time with family, learn more about my school community, catch Pokemon while my husband drives so he "doesn't miss any", and start to think about building my reputation at a new school with a new group of kids and administration. 

One of the most important parts of the first day for me is the act of setting the tone with my kiddos. I have very different expectations than what some students have experienced previously in a math class....expectations that students see themselves as members of a team and be ready to both give and receive help from others, that students communicate their learning each day in a variety of ways, and that understanding is a fluid thing that can ebb and flow based on content and work ethic. And while I knew every minute is precious in an AP Calc class and the focus is content, you don't ever get another first day of school. 

Establish Class Norms & Expectations
The first thing I love to do is get the students talking about what is important to them in a class. I've done it two different ways in the past and I'm still debating with which method I like best- or if some beautiful, perfect hybrid of them exists. I'd love to hear some thoughts from you guys! Below are the questions I've used in the past and few I'm thinking of adding this year. This is more than I'd use with a class. I'm going to narrow from these options:

  • I expect my teacher to...
  • I expect my classmates to...
  • I expect myself to....
  • I learn best when...
  • When I don't understand something in class, I want....
  • I get distracted in class when...
  • I'm excited about this class because......
  • I'm nervous about this class because.....
  • When I hear "Calculus," I think....
  • Other? 

Method #1: Gallery Walk
Write questions on big paper and post around the room. Have students complete a gallery walk, putting a post it with their individual answer under each respective question. 

I like: elicits every student's response, gets students up and moving, consider all questions (not just their assigned one)

I wonder: will students start to feel it's repetitive when they already see their answers up on the wall, if kids can focus on a teacher-led discussion about a ton of questions they've already considered and a whole class worth of answers
Method #2: Mini Group Presentations
Assign each group a specific question to answer with the expectation that they present their responses to the class. Ask the class to add any additional ideas after the group presents. 

I like: students get to become "experts" on their question, focusses on student presentation with teacher facilitation to guide, kids listening to kids (not just me)

I wonder: will quieter kids be willing to share their thoughts on questions to which they aren't assigned

Whichever method I wind up choosing, I always conclude by trying to establish a maximum of 4 expectations (I don't love the word "rules" and I don't love a long list of them) that cover the ideas we've addressed. Looking for those "big ideas," as usual. 

Common Mistakes Sort
I want to get my students engaged in some mathematics on day 1. I totally overwhelmed my kiddos last year in my honors calculus class by doing what I thought was a super awesome problem based activity, but just wound up being overwhelming for them after having not done math all summer. We were examining why cups roll in different sized circles ( Mathematics Assessment Project does a great examination of this as does the oh-so-wise Dan Meyer) and I stand by that it's a great activity that can be extended up through limits and more. It definitely got my kids thinking , postulating, and testing, but it didn't have the mathematical benefit it could have if I'd saved it until a little later in the unit. 

Instead, I'm going to get them engaged with some common algebraic mistakes (the biggest calculus pitfall) and start practicing their communication skills- both oral and written. I adapted this from Errors and the Algebra of Calculus from Cengage. 

I plan to have these cut out for each group and have partners match the incorrect algebra with its correct counterpart. Then, they need to work together to explain the error in the "wrong" one. I can move around the room and do some informal assessing of my new students. This can segue directly into all sorts of necessary algebra skills- factoring, simplifying rational expressions, working with exponents and radicals, and more. I know a lot of AP Calculus teachers don't believe in review at the beginning of the year, but with the offering of both AB and BC Calculus at my school, I know my AB sections will have students who could use the time focussed on background skills. Of course, targeted review of prerequisite skills throughout the year will be key, but trying to head off some common mistakes and let the students see something with which they are familiar may help build some confidence at on Day 1.