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This week, I’ve been working on Jo Boaler’s MOOC “How To Learn Math.” It’s presented via videos, forum discussions, and peer assessment; registration is still open, for those who might be interested.
They’re having some technical difficulties with the discussion forum, so I thought I would use this space to open up the questions I’m wondering about. You don’t need to be taking the course to contribute; all ideas welcome.
Student Readiness for College Math
According to Session 1, math is a major stumbling block in pursuing post-secondary education. I’m assuming the stats are American; if you have more details about the research that generated them, please let me know!
Percentage of post-secondary students who go to 2-year colleges: 50%
Percentage of 2-year college students who take at least one remedial math course: 70%
Percentage of college remedial math students who pass the course: 10%
The rest, apparently, leave college. The first question we were asked was, what might be causing this? People hazarded a wide variety of guesses. I wonder who collected these stats, and what conclusions they drew, if any?
The next topic we discussed was the unusual degree of math trauma. Boaler says this:
“When [What’s Math Got To Do With It] came out, I was [interviewed] on about 40 different radio stations across the US and BBC stations across the UK. And the presenters, almost all of them, shared with me their own stories of math trauma.”
Boaler goes on to quote Kitty Dunne, reporting on Wisconsin Radio: “Why is math such a scarring experience for so many people? … You don’t hear of… too many kids with scarring English class experience.” She also describes applications she received for a similar course she taught at Stanford, for which the 70 applicants “all wrote pretty much the same thing. that I used to be great at maths, I used to love maths, until …”.
The video describes the connection that is often assumed about math and “smartness,” as though being good at English just means you’re good at English but being good at Math means you’re “smart.” But that’s just begging the question. Where does that assumption come from? Is this connected to ideas from the Renaissance about science, intellectualism, or abstraction?
There was a brief discussion of stereotype threat: the idea that students’ performance declines when they are reminded that they belong to a group that is stereotyped as being poor at that task. For example, when demographic questions appear at the top of a standardized math test, there is a much wider gender gap in scores than when those questions aren’t asked. It can also happen just through the framing of the task. An interesting example was when two groups of white students were given a sports-related task. The group that was told it measured “natural athletic ability” performed less well than a group of white students who were not told anything about what it measured.
Boaler mentions, “researchers have found the gender and math stereotype to be established in girls as young as five years old. So they talk about the fact that young girls are put off from engaging in math before they have even had a chance to engage in maths.”
How are pre-school girls picking this stuff up? It can’t be the school system. And no, it’s not the math-hating Barbie doll (which was discontinued over 20 years ago). I’m sure there’s the odd parent out there telling their toddlers that girls can’t do math, but I doubt that those kinds of obvious bloopers can account for the ubiquity of the phenomenon. There are a lot of us actually trying to prevent these ideas from taking hold in our children (sisters/nieces/etc.) and we’re failing. What are we missing?
July 22 Update: Part of what’s interesting to me about this conversation is that all the comments I’ve heard so far have been in the third person. No one has yet identified something that they themselves did, accidentally or unknowingly, that discouraged young women from identifying with math. I’m doing some soul-searching to try to figure out my own contributions. I haven’t found them, but it seems like this is the kind of thing that we tend to assume is done by other people. Help and suggestions appreciated — especially in the first person.
Interventions That Worked
Boaler describes two interventions that had a statistically significant effect. One was in the context of a first-draft essay for which students got specific, critical feedback on how to improve. Some students also randomly received this line at the end of the feedback: “I am giving you this feedback because I believe in you.” Teachers did not know which students got the extra sentence.
The students who found the extra sentence in their feedback made more improvements and performed better in that essay. They also, check this out, “achieved significantly better a year later.” And to top it all off, “white students improved, but African-American students, they made significant improvements…” It’s not completely clear, but she seems to be suggesting that the gap narrowed between the average scores of the two groups.
The other intervention was to ask seventh grade students at the beginning of the year to write down their values, including what they mean to that student and why they’re important. A control group was asked to write about values that other people had and why they thought others might have those values.
Apparently, the students who wrote about their own values had, by the end of the year, a 40% smaller racial achievement gap than the control group.
Holy smoke. This just strikes me as implausible. A single intervention at the beginning of the year having that kind of effect months later? I’m not doubting the researchers (nor am I vouching for them; I haven’t read the studies). But assuming it’s true, what exactly is happening here?
Yesterday I wrote that my students have trouble reading their textbooks. Today I started wondering how my screencasts fit into this. My screencasts so far are often a retelling of some part of the textbook. If I could say “read Ch. 13-4 for tomorrow and write down your questions,” screencasts would not be necessary. Are my screencasts a lost opportunity for reading practice?
Another thing: can text-comprehension strategies also help with math comprehension? What would happen if I taught students to read math the same way they read a sentence? Could I help them stop assuming that “y = 2x” means “2x causes y”? I mean, obviously, lots of times when they see this, x does cause y. But that’s not what the equal sign means, and they end up imputing an incorrect meaning to the left/right positions (in fact, their misconception is closer to the programming language meaning of the assignment operator). This misconception makes them see algebraic manipulation as nonsensical. After all, if x causes y, how can it possibly also be true that y causes x? (x = y/2)