Thursday, July 28, 2016

Creating Mathematical Mindsets

Our summer book study is getting even more exciting, as we start to get down to practical ideas! If you've missed the first few chapters, no worries; you can catch up below:
We've just started a Facebook group & would love for you to join! Click here or search Mathematical Mindsets book study in groups.
Approaching mathematics conceptually is having a mathematical mindset. Children need to see math as a subject they should think about, make sense of, and grow in. A mathematical mindset is active! There was SO much information to ponder upon in this chapter! A section that caught my eye was How Important is Math Practice? When parents ask about the importance of practicing math with pages of homework and problems, Boaler responds with, "It is important to revisit mathematical ideas, but the practice of methods over and over again is unhelpful. . . worksheets that repeat the same idea over and over turn students away from math, are unnecessary, and do not prepare them to use the idea in different situations." (p. 42) Boom! Another very compelling argument against textbook examples and worksheets is that most practice examples give the most simplified and disconnected version of the method, so students have no sense of when or how to use the method in a different situation. The book gives some fascinating examples that I could picture my students having the same misconceptions! 

My Takeaway
The most important advice to give students is to encourage them to PLAY with numbers and shapes, and to notice patterns. Far too often, we discount the importance of exploration time with manipulatives, blocks, and puzzles. When my oldest daughter was just a toddler, she used to take 2 or 3 of her wooden puzzles and dump them on the floor. After mixing them up, she would sit back and gleefully put each puzzle back together. I was always in awe of how she would examine each wooden piece, then put it in just the right place. Home this summer from college, she's been relaxing in the evenings by working on 1000-piece jigsaw puzzles! When Sudoku first came out, she was in heaven! She used to do them in under 10 minutes, using a pen! When I asked her why she didn't use pencil so she could erase, she said she studied the numbers and placement before writing the answers.  Clearly, math comes easy to her, although she has always said she hates math (in school)  :(
Three Tips for the Classroom:

When using technology, use more meaningful math apps and games in the classroom (not just drill & kill apps!) Boaler recommends Wuzzit Trouble, a game/app that significantly improves number sense, disposition to math, readiness to learn math. The game progresses to more challenging puzzles, and different versions are available for specific math topics.  I have to admit. . . I downloaded the app to try it out & my 11-year old daughter grabbed my phone to show me how to play (I last remember playing Atari Space Invaders & Pacman . . . that goes to show how old my technology gaming skills are! LOL) She quickly understood the logic and strategy, although she also says she hates math. . . I tried to convince her that she was doing math!
Another game Boaler recommends is Mathbreakers, a video game similar to Minecraft (and don't all your students love Minecraft?!) but it uses numbers. It teaches number sense conceptually. Although it is a game to purchase, there is discounted educator pricing. You can download and check out the free demo here.
 Limit timed math facts testing! Gulp. . . "For about one-third of students, the onset of timed testing is the beginning of math anxiety." p. 38 Guilty!! Although my students only take timed multiplication facts tests once a week,  I'd love to gain back that time with real instruction and exploration of math concepts! Yes, I still believe that knowing their math facts will give students greater ease when applying them to more difficult problems, but speed is NOT the key to understanding! To build math fact family awareness, Rick Morris at New Management has a FREE download of triangle math facts.  I'm thinking I'll no longer make them mandatory or recorded in my grade book, but as a practice option during math workshop. (And while I'll continue to educate my parents about how to help their children conceptually with math, I'll also give them the link so they can download some of these practice sheets. . . it makes parents feel better knowing they're tangibly giving their child something familiar)
I want to (consistently) build Number Talks into our math time! A Number Talk involves posing a math problem, then asking students to explain how they solve the problem mentally. Number talks build number fluency and automaticity. This is a fascinating 15-minute video on Number Talks: students explain HOW they came to a solution, then Boaler shows what their strategy looks like as a visual representation. I've watched this video multiple times!

How do you help your students with number sense and awareness? Do they understand the flexibility of numbers? Please share!
An InLinkz Link-up


  1. Great post!

    Great minds!! I am going to do Number Talks as well! I'm starting next week. I downloaded Wuzzit Trouble too, but just started playing with it this morning. I'm hoping to work in some of the activities from her Fluency without Fear paper for math facts.

    PS... I used your Mathterpieces idea this week. I took a photo of each set of pages and used them as task cards (shh...don't tell). Thanks for the hint!

    1. I'll have to check out the Fluency without Fear, too!! I can't wait to hear how we're both implementing when school begins!

  2. Great ideas. People don't apply growth mindset to math enough! How is it ok to say "I'm not good at math" but it would be frowned upon to say "I'm not good at reading."??? Kids need to learn the power of "Yet!!"

    1. I agree!! I love the Power of Yet!! I'm so excited to fully get kids to buy in and change their mindsets, particularly in the area of math!

  3. Great suggestions Kathie! I, too, am a huge Number Talks fan! As a middle school instructional coach, I can see the power it has in elementary school to help our students gain flexibility with numbers that will then help them be more successful in middle school!

    1. I always love hearing what middle school expects students to come in knowing. And how great would it be if our 6th graders arrive with that mathematical mindset! How lucky your teachers must be to have a knowledgeable instructional coach!

  4. As a third grade teacher, this chapter struck a chord with me. I love the emphasis on understanding multiplication facts vs memorization but am wondering if she advocates working with x3, x4, etc facts like traditionally done or is it a more universal approach? I downloaded the cards she referenced, but was disappointed it was only 11 pages.

    1. Great question; I'm not sure how Dr. Boaler teaches math facts. I think I'm going to sign up for her course: and also to recommend her FREE course for students (all levels): She covers the following areas: Knocking Down the Myths About Math
      Math and Mindset
      Mistakes and Speed
      Number Flexibility, Mathematical Reasoning, and Connections
      Number Patterns and Representations
      Math in Life, Nature and Work