In June, my boss passed around Jo Boaler‘s book What’s Math Got To Do With It? to all the math teachers at my school and asked us to read it over the summer. It was originally written back in college but was updated for this year.
I must admit that what with traveling off to Utah for PCMI and then a million other places for the rest of the summer, and also plowing my way through a bunch of Tom Robbins books, I kiiiind of forgot that I was supposed to be reading this until two weeks before the start of school when I looked into the short stack of books I keep by my bed after finishing Fierce Invalids Home from Hot Climates (which I of course heartily recommend). Luckily, Boaler’s book is a super fast read. I ate it up over about three days.
This marks the first time in my life that I have ever felt the need to put those skinny little post-it notes into a book to keep track of what I came across. The content is perhaps more directed toward those who haven’t already drunk the creative-math-teaching kool-aid, but there were a number of specific ideas that I’d like to use and references to research backing up ideas that I’m always trying to convince people (parents, students, other math teachers) are true.
I was planning to write out my notes and that I took and review the bits that I earmarked so they would be easily at hand rather than stuffed into a book that I accidentally spilled green tea onto when I fell asleep on the airplane (sorry, library…). I figured I’d just do it here in case any of it was useful to anybody else!
STUFF TO USE WITH STUDENTS
- Fermat’s Enigma by Simon Singh – This is a book about proving Fermat’s last theorem. Boaler writes, “Any child – or adult – wanting to be inspired by the values of determination and persistence, enthralled by the intrigue of puzzles and questions, and introduced to the sheer beauty of living mathematics should read [it].” Well, that sounds pretty good. I like that in addition to giving students the experience of creative, problem-solving mathematics, they also get a peek into how that translates in the work of professional mathematicians. (pg 22)
- Self-Assessment – This book explains that self-assessment can be helpful for students for the simple reason that it helps students to understand *what* they are supposed to be learning. You can give a student a check-list of ideas they should understand and ask them to fill it out. I could do this after a few days on a new topic or near the end of a unit. I definitely remember being asked, when I was in high school, “what are you learning right now?” and just having no idea. I think that presenting the topics as a check-list will make that question much easier for students to answer. Also, if I collect their responses, then I have a ton of useful information that I can use to determine next steps for the class to take. (pg 96)
- Extend the Problem – This is something I know of and am already planning to do more, but I always enjoy reading a little more about how people do it. Boaler talks about giving out problems and asking students to ask their own, new questions about them. She also says that when students asked good questions in class, they’d go up on the wall.
- Physical Set-Up – one of Boaler’s students, Nick Fiori, apparently created all sorts of physical set-ups for students to then create and answer questions about. There were cards from SET, differently sized/colored beads and string, colored dice, snap cubes, measuring cups, pine cones, etc. I love this idea. It’s actual kinesthetic mathematical work. I’m curious to figure out how to best make this a productive experience for algebra students. (pg 169)
- In Code: A Mathematical Journey by Sarah Flannery – This is a book written by a woman about her mathematical development. I am curious about whether there’s anything that could be useful in here to share with students, especially with an eye for presenting them with an example of a successful female mathematician. (pg 172)
- Making Number Talks Matter by Cathy Humphreys and R. Parker – the idea of these number talks is to help students to think more flexibly about values and to develop number sense.
- Turkey – “A woman is on a diet and goes into a shop to buy some turkey slices. She is given 3 slices that together weigh 1/3 of a pound, but her diet says that she is allowed to eat only 1/4 of a pound.” (pg 44)
- Four fours – Can you make every number from 0-20 by using four 4’s and any mathematical operation? (pg 180)
- Race to 20 – This is a 2-player game. Start at 0. Take turns. Each turn, the player adds either 1 or 2. Whoever hits 20 wins. (pg 181)
- Beans and Bowls – How many ways can you split up ___ beans in ___ bowls? (pg 182)
- Partitions – “The number 3 can be broken up into whole numbers in four different ways: 1+1+1, 1+2, 2+1, 3. Or maybe you think that 1+2 and 2+1 are the same, so there are really only three ways to break up the number. Decide which you like better and investigate partitions for different numbers using your rules. (pg 182)
STUFF TO USE WITH PARENTS
- Moms – It is especially important that mothers never talk about being bad at math. When this happens, it has a nearly immediate negative effect on their daughters’ grades. (pg 177, 187)
- Enthusiasm – Boaler recommends that parents act as enthusiastic as possible when referring to math homework, even if they need to lie to do so. Maybe my students (high school) are a little too old for this to come off as anything but their parents just being lame dorks. My task as a teacher is to assign homework that makes this easier for parents to do honestly. (pg 177)
- Explaining – She also notes that parents should keep their homework help to the guiding, question-asking side. I like what this means for parents of my students. By the end of the year, some parents say they can no longer help students with their math work. But if the math is really over their heads, then they can easily ask their students to explain it to them, which is a really excellent learning tool. (pg 177)
- Back to School Night – I think I would like to take some of my (very short amount of) time on Back to School Night to ask parents to do some of the things that Boaler recommends. I will say that in order for you to help your student to be successful, here are the things that I will ask you to do, as backed by research by a fancy professor at a fancy school. I’ll probably make a worksheet with these ideas on it, which are selected from the things Boaler recommends:
- Praise effort, not ‘smartness.’ (growth mindset)
- Be positive and enthusiastic about math.
- Describe mistakes as an opportunity for growth.
- When helping with homework, ask them to explain and make sense of the work.
- Advanced: Try posing puzzles with logic or numbers to your students. (pg 186-193)
- Math Power by Patricia C. Kenschaft – This is a book for parents of young kids. It is intended to help them to help their kids get into math. (pg 232)
- Memorization sucks – PISA – research shows that “…the students who memorize are the lowest achieving in the world. The highest-achieving students are the ones who think about the big ideas in mathematics.” I believe that this report is the proof behind what Boaler is talking about. It’s about 175 pages long so you will please excuse that I have not read the whole thing. I’ll just leave that link there for myself to get into a bit later… (pg 41)
- Tracking sucks – TIMSS analysis, Stanford study – “…we know from several international students that countries that reject ability grouping – nations as varied as Japan and Finland – are among the most successful in the world, whereas countries that employ ability grouping, such as America, are among the least successful.” My experience definitely shows this to be true – some of my most enriching math experiences have been in groups of math teachers with wildly varying backgrounds (from not majoring in math at all, to having their masters degrees, for example). But obviously, just cramming kids into the same class, with a teacher trained to deal only with narrow sections of ability at a time, is not going to be successful, either. You have to change how you teach. (I plan to write a little bit about the group work structures – borrowed from Complex Instruction – that I’m going to use this year, which are intended to take advantage of heterogeneity.) (pg 103)
- Thoughtful Math and Tests – “Is Dealing with Mathematics as a Thoughtful Subject Compatible with Maintaining Satisfactory Test Score? A Nine-Year Study” by Carolyn Maher – this article supports the idea that teaching math as a thoughtful and creative field will still result in students scoring well on dumb tests (that is, standardized tests). Duh. In my own personal experience, I’ve always done extremely well on standardized tests not because I’ve memorized a bunch of junk, but because I’m good at reasoning and figuring out new things. (pg 225)
- List of Lots of Studies – “Evidence of Student-active Learning Pedagogies” by Jeffrey E. Froyd. A bit of a survey of the research, with some important points highlighted.