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: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!
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:
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.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
An InLinkz Link-up