A Contrarian's Take on the Issues of Math Anxiety, Confidence, Motivation, and "Fun"
This discussion strikes pretty close to the heart of this blog. From the recent math conference, here are some comments from speakers, reports, and power-point slides on the issue of math attitudes:
"Attitude is key; we must convince students that math can be fun and easy."
"The important thing [about this technique] is that your students are happy."
"There is no other way to make students mathematicians than to make them happy."
"This technique did not demonstrate an increase in test scores, but it did increase student confidence."
"In particular, [this teaching approach] stresses the principal importance of elimination of mathematics anxiety -- the main barrier to success in mathematics."
Okay; so as always, I'll be the contrarian and come down on the other side of this issue. While others talk about math being beautiful or elegant or fun or (classically) musical, my gut-sense of it is more of a horrible brutal war that you commit to out of dire necessity. Personally, I could find math important, or insightful, or transformative, or useful, or even an addiction, but rarely has it ever been "fun" to me. See the inaugural post for this blog -- The AngryMath Manifesto. I don't see any evidence that confidence is a signal of ability (in fact, some of my most confident students are the most helpless -- see also Socrates), nor do I think that "fun" is either a requirement or even something very informative to talk about (which reiterates stuff I've said vehemently on my gaming blog). Intriguingly, neither does at least one specific research article from this conference:
On the first day of class in Spring 2011, all Precalculus students were given a customized 20 minute Diagnostic Test that check basic Pre-algebra concepts and a Motivation Test that measured student motivation as a prediction of success... However, as Figure 4 shows, there is no correlation between the Diagnostic Test and the Motivation Test (n = 159, r = -0.07). This counter-intuitive outcome indicates that student motivation is not a factor influencing the outcome of the Diagnostic Test. The math scores are low whether or not the students are motivated... it is reasonable to conclude that students are motivated, but genuinely do not know or cannot recall the prerequisites at the beginning of the semester. (Kingan, Clement, and Hu, 2012; "The Gap Project: Closing Gaps in Gateway Mathematics Courses")
Now, I don't find this result "counter-intuitive" in any way (again; in some sense it's the whole point of this blog since day one). To me, I think if anything, the perceptual problem for our remedial students is not that they are insufficiently confident and upbeat; I worry that they are not sufficiently aware of what grave peril that they're actually in (like, a 10% chance of getting a degree within the next 3 years; not something that is communicated to them in an honest fashion), and the amount of time and effort they need to devote to their math studies if this is truly a priority for them.
Likewise, the Dunning-Kruger Effect seems critically important -- the observation that tremendously unskilled people will radically overrate their ability at a certain task. Note in the analysis above, the value r = -0.07; if anything, in this sample high motivation is somewhat correlated with reduced math ability (not that the effect is very strong or significant). So to me, remedial students' "fear" of math is largely an honest and accurate assessment of their very weak skills. If we have an alternative teaching method that raises confidence, but leaves math ability unchanged, then is that not actively harming them -- changing their self-assessment from accurate to inaccurate (exacerbating Dunning-Kruger)?
I suspect that "math-anxiety" is a convenient whipping-boy that frequently lets students, teachers, and administrators avoid talking about actual, concrete math and quantitative reasoning deficiencies (which is frequently sad and hard). Consider another article by Clark: "Antagonism between Achievement and Enjoyment in ATI Studies", which found that when given the chance, both weak and strong learners chose the learning style which produced the least amount of learning (reversed for each type) as preferred -- i.e., the more enjoyable, the least work, the most "fun".
Finally, consider findings by Robert Rosenthal (Harvard researcher, famous for investigations on the Pygmalion Effect):
"The most surprising finding in our research," says Rosenthal, "has to do with what we called the 'psychological hazards' of unexpected intellectual growth." When so-called "lower track" students in the control group at Oak School (students who were not expected to shine) began to show marked improvement and growth, their teacher evaluations on such things as "personal adjustment," "happiness," "affectionate" declined. ("Pygmalion in the Classroom")
Rosenthal sees this as society (teachers) punishing those who break its expectations, but I think an equally defensible interpretation is that actual learning growth is related to struggle and challenge and resistance, and inversely related to happiness.
Perhaps the real over-arching struggle in all of our different teaching techniques is the fight to get students to actually spend the required amount of time studying and practicing their math -- whether we try to do that in-class, out-of-class, with online software, outsourced video lectures, extra math tutors/coaches, or whatever. Ultimately (as I say on the first day in all my classes) it's patience and focus that are both the requirement and the end-goal of remedial math classes -- and, much like the Samurai-mindset, excitability-fun-confidence are likely to be either uncorrelated or negative indicators for those traits.