I recently finished reading Jo Boaler’s book What’s Math Got To Do With It? and I need a way to reflect on what I had learned and consider ways to implement her research in my own teaching. This is Part 3 of a (probably) 4-part series.
I’m going to use quotes from the book and expand on them with my own thoughts. Chapters 3 through 6 primarily outline the findings that Jo has gathered from her research over the years, and I’m going to cover Chapters 5 and 6 in this post. The last few chapters (later post) discuss how to actually implement the things Jo has uncovered in her research with children.
Chapter 5 – Stuck in the Slow Lane: How American Grouping Systems Perpetuate Low Achievement
This chapter was depressing too. It’s actually really frustrating to read about all the things we do in this country that are extremely widespread and extremely counter-productive. Imagine that.
In the US, we group students based on their prior achievement. This is usually called ability-based grouping which, frankly, says all you need to know about the system. We assume that students who are placed in a certain group have a certain ability, ignoring everything that we have learned recently about how the brain works, and how mindset influences a student’s success. Any type of tracking or ability-based grouping leads to a fixed mindset (in all students – those at the top, bottom, and middle) which contributes to their lack of success in school. (It’s self-perpeutating.) Students at the bottom and in the middle believe they can never improve, and their teachers only give them easier work, so they wind up being right – they can’t improve. Students at the top have to maintain the image of being the best, so they never challenge themselves and become obsessed with appearing to be perfect. See? Damaging.
When students are split up in this way, they also don’t have a variety of students to work with, which has major advantages. “In mixed-ability classes the students are organized to work with each other and help each other” (p. 112). The students who need help can ask other students for it. This has two major advantages in my experience – the teacher doesn’t have to be everywhere at once, and the students tend to understand it better if they hear it from another student anyway. The student who is doing the helping also benefits because “the act of explaining work to others deepens understanding” (p. 112).
In order for mixed-ability grouping to be effective, two conditions must be in place.
- “The students must be given open work that can be accessed at different levels and taken to different levels” (p. 116). The students who struggle with the material need to have a place to start, and the students who get it easily need to have a way to extend the problem as much as they want.
- “Students are taught to work respectfully with each other” (p. 117). I’m worried about this one because I feel like I don’t know how to teach this. I need to make sure that I am hearing all the interactions among my students so I can correct any that are disrespectful.
Chapter 6 – Paying the Price for Sugar and Spice: How Girls and Women Are Kept Out of Math and Science
This chapter was fascinating. This was the chapter that I was reading on a short flight home from vacation and kept handing the book to my roommate who was sitting across the aisle from me and telling her to read passages.
In short: The biggest difference that Jo has found between the way girls learn math and the way body learn math is that boys are ok with just being given a procedure and being told to do it, while girls want to know why it works.
Quotes from students themselves demonstrate this best:
He’ll write it on the board and you end up thinking, “Well, how come this and this? How did you get that answer? Why did you do that?” (p. 123)
It’s like you have to work it out and you get the right answers but you don’t know what you did. You don’t know how you got them, you know? (p. 124)
K: I’m just not interested in, just, you give me a formula, I’m supposed to memorize the answer and apply it, and that’s it.
JB: Does math have to be like that?
B: I’ve just kind of learned it that way. I don’t know if there’s any other way.
K: At the point I am right now, that’s all I know. (p. 126)
Math is more, like, concrete, it’s so “It’s that and that’s it.” Women are more, they want to explore stuff and that’s life kind of, like, and I think that’s why I like English and science. I’m more interested in, like, phenomena and nature and animals and I’m just not interested in, just, you give me a formula, I’m supposed to memorize the answer and apply it, and that’s it. (p. 127)
Jo discusses a study that was done based off what she had uncovered about gender roles in these courses, and concludes, “…the girls wanted opportunities to inquire deeply, and they were averse to versions of the subjects that emphasized rote learning” (p. 128). On the other hand, boys “would tell me that they were happy as long as they were getting answers correct. The boys seemed to enjoy completing work at a fast pace and competing with other students, and they did not seem to need the same depth of understanding” (p. 123). In fact, Jo found that about one third of boys also valued understanding why similar to the way the girls did.
We urgently need to reorient mathematics and other subjects so that they focus on understanding and deep inquiry. When such changes are made girls choose STEM subjects in equal numbers to boys, and this is a goal that we should prioritize in the United States, not only for the futures of girls and women but for the future of the STEM disciplines. (p. 136-137)
How can I do this in my classroom? I need to focus on teaching WHY things work the way they do, not just how they work. I need to have students discuss and chew on these explanations and make sure that they hold themselves and each other to the ideal that reasoning is more important than calculation.