8.04.2016

How To...Mathematical Mindsets: How Do I Start?

In my own personal effort to #ExpandMTBoS, I'm starting a new category of blog posts called 'How To' so I can share the strategies behind the resource. I hope new and veteran teachers alike can find something useful. Click on the tag to the right for more posts!

If you're like me, the last five posts were probably overwhelming.

Part 1 {here}
Part 2 {here}
Part 3{here}
Part 4 {here}
Part 5 {here}

Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching
Jo Boaler

There's a lot of things to change, fixm and improve. I tried to break this massive shift to my brain into categories of practical things to do.

Easy: things I can do from day one this school year with no prep
Medium: things I can do in the next couple of months or with some prep

Easy
• Ask students to think visually first
• Ask students for the different ways they see and solve problems
• Ask students to look for patterns, similarities, and differences
• In every math conversation, ask students to reason, to explain why they chose particular methods and why they made sense.
• Honor hard work and the struggle over effortless achievement
• Think of all the ways to be mathematical. No one is good at all of these ways of working, but everyone is good at some of them.
• Classroom mantra/poster: Always give help when needed, always ask for help when you need it.
• Do not include early assignments {review?} from math class in the end-of-class grade .
• Do not include homework, if given, as any part of grading.
• Honor student thinking- say, "incorrect but helpful"-there is always some logic there.
• When students want me to tell them how to do a problem say, "Do you want my brain to grow or do you want to grow your brain today?”
• Praise people for having good thinking and for being accomplished, learned, hard working, and persistent; not being smart or fast or for effortless achievement
• To take student thinking deeper say, "You may know a rule for solving this question, but the rule doesn't matter today, I want you to make sense of your answer, to explain why your solution makes sense."
• Teachers can encourage students to use intuition with any math problem simply by asking them what they think would work, before they are taught a method.
• Tell students, "I am not concerned about you finishing math problems quickly; what I really like to see is an interesting representation of ideas, or a creative method or solution."
• Ask students to draw connections between concepts in mathematics when working on problems. Encourage students to propose different methods to solve problems and then ask them to draw connections between methods, discussing for example, how they are similar and different
• Ask students to play the role of being the skeptic; explain that they need to demand to be fully convinced. Students really enjoy challenging each other for convincing reasons, and this helps them learn mathematical reasoning and proof. When students act as a skeptic, they get an opportunity to question other students without having to take on the role of someone who doesn't understand.
• Offer all students high-level math content and believe they can do it
• "One of the greatest gifts you can give to your students is your knowledge, ideas, and feedback on their mathematical development, when phrased positively and with growth messages".
Medium

• For definitions, give nonexamples and barely examples instead of perfect examples
• Introduce and build a growth mindset!
• Introduce the headache before the aspirin
• Replace class lectures with instructing reporters who go back and instruct their group.
• Participation quizzes! {Yay Sam!}
• Put student questions on posters,
• Always allow students to resubmit any work or test for a higher grade {I already do quiz retakes but I let students use their notes on tests. Should still allow them to redo tests as well?}
• Take students' ideas and make incorrect statements for the students to challenge
• Instead of asking students to simplify ask students to find all the ways they can represent that are equivalent.
• Tell students what they should know and let them reflect on how much of it they know. Frequently.
• Self and peer-assessment {"Questions that ask students to think about errors or confusions are particularly helpful in encouraging students' self-reflection, and they will often result in the students' understanding the mathematics for the first time."}
• Number Talks
• Ask students to compare and choose methods to problem solve
Hard
• Give group tests and randomly choose one paper from the group to grade.
• Do not use a 100-point scale.
• Give diagnoistic comments instead of grades. "The students receiving comments learned twice as fast as the control group, the achievement gap between male and female students disappeared, and student attitudes improved."
• Study after study shows that grading reduces the achievement of students. Share grades with school administrators but not with the students.
• Give students rich mathematical tasks that are low floor, high ceiling
• Open up the task so that there are multiple methods, pathways, and representations.
• Include inquiry opportunities.

Do you feel better now, seeing that the easy section has the most things to do?

Did you notice that most of them include the verbs ask, tell, show, say, show, think, honor, encourage? Those are all forms of talking and I don't know about you, but I am pretty dang good at that.

Look how we can make great change with small changes in our words and demeanor. I am encouraged that there are so many positive things I can do for my students RIGHT AWAY.

Hooray.

All day.

1. This is a very helpful summary of the book "Mathematical Mindsets" by Jo Boaler. I have been reading it this summer and have found so many ideas that I want to try in my classroom, but it does seem a bit overwhelming. Where do I start? Thank you for taking the time to write out your ideas to help answer that question.
Math to the 7th Power

1. I hope it helps you write out your own ideas! :)

2. I agree with Sara. I haven't read Mathematical Mindsets yet, but it's on my list. However, reading your reflections has been helpful until I get a chance to read the book myself. Your easy list here seems overwhelming to me. Based on what you've read, are there 3-5 things that you think would make the biggest impact?

1. I would say all the ones under easy that start with the word 'Ask'. Those are all manageable since it only involves me substituting what I would normally do for better questions. I plan on making a list to hang near my SMART board so I can focus on asking those questions in particular.

3. Hi Elissa,

I loved reading this post as I had never heard of this book before, but now, as a pre-service teacher I am looking forward to reading it! I think all of those things you have listed are so crucial and so important to implement within a classroom to allow students to be curious and unleash their full mathematical potential, whatever that may be. You have listed so many things that am sure have proven to be effective – however from your perspective, could you narrow some down in terms of maybe what gives you the highest level of reward? I would love to implement each and everyone within my classroom, however I know that as a first year teacher, I am sure I will struggle with that. I would love to hear more about how these changes have positively effected your students learning and classroom environment.

4. 1. Ask students to think visually first
2. Ask students for the different ways they see and solve problems
3. Ask students to look for patterns, similarities, and differences
4. In every math conversation, ask students to reason, to explain why they chose particular methods and why they made sense.
5. To take student thinking deeper say, "You may know a rule for solving this question, but the rule doesn't matter today, I want you to make sense of your answer, to explain why your solution makes sense."
6. Teachers can encourage students to use intuition with any math problem simply by asking them what they think would work, before they are taught a method.
7. Tell students, "I am not concerned about you finishing math problems quickly; what I really like to see is an interesting representation of ideas, or a creative method or solution."

Those would be my top 7 that I feel like I have done a good job with so far this year and have made a difference.

It's also really easy to not give homework. =) But I never did homework so I can't really speak to what reward it may have on students who are used to it.