Monday, August 15, 2016

#MTBoSBlaugust Day 10: Mathematical Mindsets

Just finished Jo Boaler's incredible Mathematical Mindsets. Can you tell it gave me a few ideas? 
For anyone who hasn't read it yet, Boaler does an incredible job synthesizing recent research on everything from the influence praise has on toddlers to the influence assessment and classroom environment have on students. She looks at achievement from many angles and offers tons of practical advice and strategies for all grade levels. I feel this insane desire to put one in the mailbox of every elementary teacher I've ever met who told me they "weren't math people." It's that kind of read. 

I wanted to go through some of my favorite ideas in the book and try to marry those to some ideas for my classroom, so bear with me here. Feeling a lot of inspiration mojo today. 

1. No one is "born" with a math-phobia
My brother is a computer scientist and my sister-in-law is a nurse. They both work in extremely math-centric careers and have a large amount of formal math training. Yet the insist that my 2 year old niece already needs me to set some free time aside to tutor her in high school because they won't be able to help and she'll probably struggle just like mom and dad did. It drives me insane. Math phobia is learned (maybe even- dare I say- taught) and I never want her to experience that. I see the unbounded love she has of experimentation right now....I never want her to lose that. 

This particular passage shot out at me the minute I read it...both when thinking about my own family and thinking about my kiddos:
"...researchers concluded that the difference between high- and low-achieving students was not that the low-achieving students knew less mathematics, but that they were interacting with mathematics differently. Instead of approaching numbers with flexibility and number sense, they seemed to cling to formal procedures they had learned, using them very precisely, not abandoning them even when it made sense to do so. The low achievers did not know less, they just didn't use numbers flexibly- probably because they had been set on the wrong pathway, from an early age, of trying to memorize methods and number facts instead of interacting with numbers flexibly. The researchers pointed out something else important- the mathematics the low achievers were using was harder mathematics."
The frustration so many students that have been labeled low face is that they have always trusted that the procedural way a teacher taught them was the only way. When that procedure became too complicated, too distant from their own intuition, they began to think of themselves as failures. And no wonder they've lost trust in themselves and their math teachers by the time they get to high school. I just imagine that kid in the back of the room who refuses to do what's asked of him because he's defeated before he starts....that's the kid who has been trying to keep up by doing harder math all along. Your heart just breaks for them. Of course they hate math. 

2. Homework isn't just a question of practice, it's a question of equity
My husband has always refused to assign homework in his science classes and as a math teacher I've never been able to go quite get there. I was different than many math teachers I've met in that I assigned only a small amount of homework and gave my students a talk on the first day that if they were struggling after ____ amount of time on homework (depending on the grade level), they should stop and come in the next day with questions. But this book really pushed my thinking on the topic.

What was particularly interesting to me was to see the amount of research backing up the neutral or negative effect of homework on student achievement, as well as the discriminatory effects of homework grading practices. In a sense, backing up what I have seen every day since I started teaching. I have taught those kids who have a job (or jobs) to help support their family, don't really eat when they aren't in school, and more or less raise their siblings when a parent is absent, working long hours, or deceased. I've always had a positive enough relationship with these kids to work one on one with them and decrease their amount of work or give them an extension on it. But I saw in their eyes that it stressed them to know that I was making an exception for them. Seeing these observations confirmed with so much research was huge for me. 

What I also loved was that Boaler gave an alternative if you are at a school that requires homework. Instead of giving a list of problems from the book, use that time to help students reflect and self assess. Boaler's homework reflection questions can be found here

Boaler also offers 6 strategies to purposefully make math class for equitable for all. Homework is only one part of a much bigger puzzle. I created this graphic so I can hang it right above my desk. I want these challenges nearby whenever I'm planning. 

Equity is how we better kids lives. It's the whole point of education. I'm excited that I'm becoming more cognizant of it through studies like this. 

3. The 5 C's of Mathematics Engagement

Love these. Some things to shoot for every day. 

4. Designing & Adapting Math Tasks
Boaler offers 6 questions to ask yourself to try to adapt a mathematics task to your classroom and I love them! Another little graphic for my desk so they're never far away! 

5. Heterogenous Grouping Helps All Students
So often when a student is grouped with those deemed "outside his or her ability level," you run into issues with the outside world. Parents worry their student will be left behind or not challenged enough and can be extremely vocal about expressing it. Boaler emphasizes that this has been disproved many times and it's helpful to read some of the research to have for discussions with parents and administration. She also discusses Complex Instruction, which examines student engagement in relation to their (actual or perceived) status in a group and works to directly create equity and student accountability.

One thing I will take from this is more of an emphasis on the use of group roles. I used them when I taught middle school, but have moved away from them in high school. I want to give them another go this year with this framework to help and see how it works. I think it might be especially helpful in my standard level classes, where group work can be more of a struggle. 

I particularly loved this quote from the section on Complex was a huge part of my STEM group norms at my last school:

6. Assessments Shape Mindsets
Students label themselves by their test grades and this identity can be such an impediment to mathematical growth. In such a performance-centric world, Boaler encourages a complete reexamination of assessment practices. 

One strategy I loved was one a 20 year veteran teacher had shared with her. Students were told to answer as many questions on an assessment as they could, then draw a line across the page when things got too difficult. Any questions below this line could be answered with the help of a textbook. The work beneath the line then became the fodder for classroom discussion. This was more about assessing students in an effort to continue their learning journey- a true example of formative assessment. 

Boaler also discusses Assessment for Learning (in contrast to assessment of learning). This demands:

  1. "Clear communicating to students what they have learned"
  2. "Helping students become aware of where they are in their learning journey and where they need to reach"
  3. "Giving students information on ways to close the gap between where they are now and where they need to be"
I love the idea from this section of generating "I can" statements for each unit of your course and having students use their as a self-assessment. If anyone has geometry or AP Calc AB resources for this, please feel free to share :)

Boaler gives lots of advice on grading and I'm still working on wrapping my head around the practicality of a lot of these. One that will particularly influence my grading scheme is the idea of a 10 point separation between letter grades A-D, then a 60 point separation to an F. She suggests using a point scale of 0-4 to keep grading more mathematically fair and I like this system for homework. 

7. Growth mindsets can be built by teachers
The final chapter of the book is strategies for growth mindset teaching and they are helping me shape my first day activities that I shared previously. In my Post It Note activity from a previous blog, I was still working on shaping the questions I wanted students to answer. Boaler gives a list of the positive norms she encourages in class and I am going to frame my questions around these.
Read more about here norms HERE

She also talked about participation quizzes, a method to encourage productive group work. This fits perfectly with my previous post about AP Calc study groups and I'll definitely be using it with them. Here's a summary of the strategy.  

Lastly, she talked about the way that teachers interact with students in the classroom. I want each of my students to truly believe I think they can learn and I want to make a conscious effort to give growth praise and help, not fixed praise and help. Praising my kids for their efforts, their specific strategies, and their failures will be more beneficial for them and provide me better information about my kiddos in the long run. It will make me a better aunt and (someday) a better parent, too. 

To anyone who hasn't read the book yet, I highly encourage it. It is a game-changer for anyone who feels like they're in a rut or wants some new ideas and it contains tons of research and strategies for your benefit, no matter the level you teach. 

Next, I'm diving into Make It Stick! My kids won't know what hit them this year! 

P.S. Anyone else feel like we need to start an MTBoS Book Club? Do some online book studies? 


  1. Thank you for sharing this. I just finished a grad class on theory and landed on growth mindset. I read some articles by Jo Boaler but haven't had a chance to read the book yet. My algebra students are all self-contained with very fixed mindsets. My goal for this year is for them to learn to celebrate our mistakes. I'm also going to start doing the "My favorite no" activity after warm-ups. I agree. A book club and discussion would be a lot of fun!

  2. We actually do have a MTBoS book club! :) We usually use the #EduRead hashtag and have done book studies since at least 2010. :) Currently, the book being read is Make It Stick using the hashtag #MakeItStick. I'm hoping this fall to do one on Mathematical Mindsets.

  3. We actually do have a MTBoS book club! :) We usually use the #EduRead hashtag and have done book studies since at least 2010. :) Currently, the book being read is Make It Stick using the hashtag #MakeItStick. I'm hoping this fall to do one on Mathematical Mindsets.

  4. Woah, I had no idea there was a book study too! I can't wait for the math mindsets one.

    This was a great part and helped me solidify some of my understanding from having read the book.