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In many parts of the world, the majority of the population is uncomfortable with math. In a few countries this is not the case. We would do well to change our education systems to promote a healthier relationship with math. But in the present situation, how can we help the students who come to our classes, which they are required to take, with fear and loathing?
How do we help students overcome their math anxieties?
There are a few strategies that are supported by experimental research which I will share here, but they all have to do with stereotype threat. I am sure there are other types of anxiety related to math which would not be helped by these strategies.
First, the wikipedia article on stereotype threat is fairly comprehensive. It describes some studies that have been done, as well as some strategies to combat stereotype threat.
I am "not a math person". Students who believe that there are "math people" and "people who aren't good at math" feel that there is no way to grow. This is much more likely to effect a student who is undergoing stereotype threat. Students who are told that intelligence is "malleable" perform much better.
Awareness of stereotype threat. Making students aware of stereotype threat (that is, explicitly telling them "your race/gender/finances makes you more likely to do badly") can help them on easy tests while simultaneously hurting them on harder tests. There are many studies that support this, but here is one.
Self-affirmation. Self-affirmation (that is, affirming a value important to the individual--not necessarily related to math) can significantly increase performance.
Role Models. Role models who are in the minority that students respect can significantly decrease stereotype threat. This study also points out that students who did not believe the role model deserved (in this case) her success were not helped (but also not hurt).
I agree with the idea that different people might be anxious about mathematics for different reasons...
Culturally, in the United States, we tend to look at capabilities in mathematics as determined by "ability" and from a "fixed" ability" perspective – some people can do math and others cannot. Other nations attribute capabilities in mathematics to effort – everyone can improve at doing mathematics if they put in time and effort. It is likely that anyone with a "fixed ability" mindset will encounter anxiety when they struggle to understand something (oh no! I am struggling to make sense of this! I guess I am not as smart as I thought I was / I guess I'm not good at math!). [Carol Dweck's book – Mindset – gets at this issue!]
So, one thing we can do as teachers, is promote a growth mindset – that effort combined with opportunity to learn (with support) leads to capabilities. A small thing: When people say, "I don't understand!" Instead, it's: "I don't understand YET." More things – look up promoting a growth mindset in math. For instance: here. And Dweck has research that indicates that intervening to promote a growth mindset makes a positive different.
It seems that the first step is to diagnose the problem. What, specifically, causes the fear or anxiety? Getting a history of the student's mathematical experience is a reasonable start. Helpful questions include courses the student has taken, what the student liked best or disliked most, what parts were easiest or hardest, and so forth. This often identifies specific concerns that can be remedied, which usually works better than vague, general reassurances. An organized, systematic approach to assessment usually works better than an intuitive, haphazard one.
When I posted this question over a year ago, I meant to post my own answer after giving others a bit of time to post. I apparently forgot.
My students have had some success in decreasing their anxiety with books like Mind Over Math (Kogelman, Warren), Overcoming Math Anxiety (Tobias), and Managing the Mean Math Blues (Ooten).
I also wanted something that directly addressed their test anxiety in math, and (after much research on math anxiety and the principles of creating guided visualizations) I developed a 14-minute guided visualization, which I titled Math Relax. It is available online for free. Not every student finds it helpful, but some students have felt that it changed their outlook dramatically.
To my view, the most effective strategies deal with anxiety as a collective - and thus political and cultural - issue. The answers provided by adamblan and Mandy Jansen are quite to the point, in that regard, and what I'll add here is just a complement.
Anxiety can be defined as overreaction to falsely perceived risk. Risk taking is socially divided, just like labor is. Risk avoidance behavior is commonly present in children. It can obviously be reinforced positively or negatively, depending on what kind of parental guidance is given, and these decisions are heavily informed by the cultural background of the parents and/or caregivers. It has been argued that biological characteristics are relevant to determining what degree of exposure to danger can a person tolerate (so there would be inclinations based on gender), but anthropological research tells us that human behavior is extremely plastic, so universal truths are scarce here.
That said, what kind of risk is presented to a child in learning mathematics? There is, of course, the social risk of being outcast by failing to fit properly into the assigned stereotype. This fear has been brilliantly addressed by previous answers, so I'll skip it here.
There is possibly, though, a different kind of risk perception, more subtle, and with deeper roots than social prejudice. To put it in simple terms: the human brain consumes a lot of energy, and streams of thought that are (considered) energy efficient tend to be strongly preferred. This also has a social signature: anti-intellectualism is the way societies have to indicate to the individual that to be "lost in thought" is dangerous to herself and to the larger group. Being considered the way of thinking that is more liberated from experiential constraints, mathematics may have been historically associated with the biggest of threats.
In other words, if thinking "complicated" thoughts has been considered, in itself, wasteful and possibly dangerous to the cohesion of the group - and thus risky - then thinking mathematically has to be extremely problematic. This kind of prejudice affects more directly, obviously, those that are not in a position of power. In this case, though, it won't be enough to address cultural stereotypes, because the anti-mathematical prejudice is largely unconscious, and even more pervasive. I'd say that it lies outside of what can be dealt with in a pedagogical environment.
This predisposition can cause enormous suffering, inside and outside of the classroom. It is a clinical problem, and a social one. The issue is particularly urgent on our present time, when the ability to think mathematically is, maybe for the first time in human history, not an accidental feature (virtue or menace), but the most valuable resource that we have, for our continued survival on this planet.
Sue VanHattum, in reference to your question "How can we help students who are very ANXIOUS about math?" I don't know that this will answer your question, but I want to refer you to www.mathmidway.org or [email protected]. Phone is (631) 444-0945. One of the questions in the booklet is "how do you get a 10-year-old excited about the world of numbers?" As the first exhibition created by the nation's only museum centered on mathematics, the Math Midway demonstrates the power of bringing hands-on math to the public. It launches the museum's mission to enhance the museums understanding and perception of mathematics as an evolving, creative, and esthetic human endeavor.The Math Midway make math approachable and enticing, so that children and adults alike can experience the exhilarating moment of mathematical discovery. I'm trying to get the portable math midway into Memphis so it might help our local public school system.
