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?
” You don’t hear of… too many kids with scarring English class experience.”
That’s because those who have scarring English class experiences don’t go on to be writers, and so few people hear of their experiences. Our society celebrates mathphobes and shuns those who have trouble with reading or writing, so they remain silent. It isn’t that they don’t exist—just that they are unheard.
Thanks — an excellent reminder. Math teaching advocates sometimes make this analogy — “why is it acceptable to proudly declare ‘I’ve never understood math’? No one happily announces at a dinner party ‘I’ve never understood reading and writing’.” This line of argument has come up in the HLM discussion forum a number of times.
But you’re pointing out a disquieting implication; troubles with reading and writing are stigmatized, leading us to underestimate how often they occur, and to misunderstand them when we do recognize them. The goal has to involve less of that stigma all around, not extending it to those with math troubles in the name of “equality.”
For other readers who are interested, GSWP has several thought-provoking posts on the subject, including one about the value of writing therapists and one about ways that typical curricula can shut down reluctant writers.
Hi, I’m also doing Jo Boaler’s course. There are plenty of people that struggled with English classes, writing essays and analysing texts. I’m married to one, I work with them and I’ve studied with them. All the ones I know went on to become engineers! The “I failed English Lit.” was almost a badge of honour and more than a handful had to sit the supplementary exam to show proficiency in English to enter university. They’re definitely out there, and in fairly large numbers too I believe.
As for what’s happening, I don’t know how many parents I’ve overheard saying something like, “I was never good at math, so don’t worry about it.” That implies that there’s some sort of talent or IQ associated with math.
We’ve been working hard at developing a growth mindset with our students and we’re ramping it up even more this year.
Do you have a link to the Boaler study about the “I believe in you” feedback? I’d love to read it.
Sure. But are they saying those things to their pre-schoolers? This is the kind of comment that’s naturally evoked by poor report cards. Where else is it coming from, in the case of children too young to go to school?
How can we push ourselves to see past the big problems and look at the subtler problems too? I ask because I know lots of people who would die before making a comment like this to a child (or anyone) and yet they find that their children are picking up all kinds of stereotypes. Their kids are watching carefully selected high-quality TV and getting gender-neutral toys for birthdays. You know the families I mean? I think it’s going to be easier to have these conversations when we can see the ways we, the well-intentioned, are playing into it too. I suspect we must be, but it’s so hard to see the log in one’s own eye…
Actually, yes, they are. Having worked as a preschool teacher in a program full of highly involved, careful parents who make their own baby food and don’t own TVs, you would not believe the stuff they say in front of their darlings. Little pitchers have big ears, as they say, but parents forget that.
For example, if I had activities out that would naturally lead to mathematical conversations, a parent might comment, “I’m glad you’re doing that. I was never good at math so we don’t use math at home.” Really? You’ve never been to a store? Or wondered where that missing sock went? But I digress. It’s these subtle things kids pick up.
Patti — that’s really interesting. Thanks for the examples.
At the risk of stereotyping early elementary educators, I think that some of the messages are coming from sensing the discomfort and distaste from their teachers. It has been documented (I should have citations handy but I don’t) that early elementary educators consistently cite math as their least favorite/most challenging/most uncomfortable subject. As a dad of a 10 yr old and a 4 yr old I have become aware of how much they pick up even if I don’t explicitly say anything. They are aware of the vibe I give off at times.
Re: “I believe in you”:
It was one of these two studies.
(Cohen, G. L., Garcia, J., Apfel, N., & Master, A. (2006). Reducing the Racial Achievement Gap: A Social-Psychological Intervention. Science, New Series, 313(5791), 1307–1310.)
Yeager, D. S., Purdie-Vaughns, V., Garcia, J., Apfel, N., Brzustoski, P., Master, A., et al. (2013). Breaking the Cycle of Mistrust: Wise Interventions to Provide Critical Feedback Across the Racial Divide. Journal of Experimental Psychology: General.
I can’t tell exactly which one because they are mentioned together in the video, and of course, videos don’t have citations! So I end up taking the mention from the video, flipping to the resources page, searching for the authors’ names, and hoping that it wasn’t some other study by the same people. Argh, Another strike against video lectures (and in favour of written documents).
I can understand your trauma session. I have had students who used to experience some kind of math “trauma.” Very nice post on math education, because we really need to our system in teaching math. I found technology to be incredibly helpful in teaching math. For example, I’m now using a tool called ClassroomIQ (https://classroom-iq.com). It’s a very efficient grading tool. It helps me grade homework and exams more quickly and easily. It’s a very handy and convenient product to have. Ever after I can get back the grades the day or even the hour after, my students are more active and engaged. I guess this is another way that technology enhances education? Anyway, great thoughts and thanks for sharing!
I tried the second intervention in a 9th grade physics class because it seemed too easy not to. Here’s the references:
Miyake, A. et al. “Reducing the Gender Achievement Gap in College Science: A Classroom Study of Values Affirmation.” Science 330.6008 (2010) : 1234–1237. 27 Feb. 2013. .
Kost-Smith, Lauren E. et al. “Replicating a Self-affirmation Intervention to Address Gender Differences: Successes and Challenges.” AIP Conference Proceedings. 2012. 231. 27 Feb. 2013. .
Thanks so much Brian — saves me hunting through the course resources page. What was it like for you and your students when you tried this intervention?
Students responded positively, and they certainly weren’t expecting it. It also gave me a clue as to what was important to them. Sorry that wordpress stripped out the URLs!
Some of them were surprised at being asked to write, but I used the researcher’s statement that communication was important in this subject, yada, yada. I did enjoy reading about their values. I’ll do it again next week, and I plan to pay more attention to their reactions. If you’d like the instructions I give them (PowerPoint), I can send it to you.
Interesting. Yes, I’d love to see the prompts you use — you can email me at shiftingphases (at) gmail (dot) com. Thanks again!
I appreciate your summaries and responses. It’s interesting to compare. 1-Have you looked at the References link on the top right of the course page? While I haven’t looked at any of the references, it looks to me like she has documented her statements. 2-I suspect that the “single intervention at the beginning of the year” starts a feedback loop. The first intervention leads to 1 small success, which promotes working harder, which leads to another success which promotes… etc.
Yes, definitely, I think all the statements are substantiated. It’s not always completely obvious which study is about which intervention, unfortunately.
As for the chain reaction, that’s the only explanation I can think of too. If anyone has read these studies, please don’t hesitate to tell us more about how exactly the experiments were carried out.
Whistling Vivaldi, by Claude Steele goes into lots of depth on stereotype threat, and how the research studies were done. It’s also very readable. I had read up on this for a number of years before getting this book last month. I still learned a lot. (I think you’ll be satisfied with the references, too.)
Thanks for filling in some of the gaps, Sue. If you’ve blogged about your thoughts, feel free to link here — I’m sure others would be interested too.
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With regard to Mrdardy’s comment about elementary school teachers, I read an article (should have the source but don’t) that if an elementary teacher (female) is sort of math phobic or dislikes math, this attitude rubs off and affects the attitudes of girls but not boys in her class. At one point I read the whole study. It is, they conjecture, because girls identify with their female teacher and see her as a role model, but boys do not. Certainly helps explain why STILL so many girls are under-represented in mathematics.
Wow — that would be an interesting read. If you do stumble across the citation, please send it along! In the meantime, I’ll keep my eyes open. Thanks for the lead.
Hi, I work with 7th-12th grade students. I’m interspersing the growth mindset with all the regular curriculum.
I know I’m kind of late entering this blog, but I’ve finished the course and and the first things I did with my students were how the brain grows, a short video that the fixed mindset vs growth mindset and a Michael Jordan video talking about all the mistakes he’s made. I also found a fixed mindset circumference video that I told the students was NOT how I wanted our classroom to be. I had them take a fixed vs growth questionnaire to see which way they were leaning. So we’ve talked about how important mistakes are and how important struggling and persevering are.
http://www.youtube.com/watch?v=IbzEiAj02ks (Michael Jordan 30 sec)
http://www.youtube.com/watch?v=FcJOKLpRXTQ (fixed mindset circumference)
This week I’m having them write a paragraph setting a positive goal for this year and having them highlight two positive math statements (I gave them a list to help them out) that they were willing to work on this year. Once they finish their paragraphs I’ll give them some specific feedback and try the “I’m giving you this feedback because I believe in you.”
I’d like to hear how people are incorporating all that we learned into their classrooms and how the students are reacting.
Hi Darliss, thanks for all the specific suggestions. I especially like the idea of showing a video of what I hope the class will not be like. I’m struggling to help some of my students break the habit of using memorized information in an unproductively authoritative way — jumping in to present what they “know” to be the “right” answer any time a less confident student asks a question. I’ve tried responding with “how do we know that?” as a way to get them thinking about what evidence could support their point, but the problem is that they have no evidence, so it ends up making them look foolish in class. I wonder if a video about what not to do could help us.
You might also consider having them make a video for other students portraying what growth mindset and fixed mindset is in different situations.
Students are frequently erroneous in their evaluations toward oneself; in some cases they think things are fine when they aren’t, however all the more regularly they think things are going defectively when they are fine–or superior to fine.