"Bear in mind that the wonderful things you learn in your schools are the work of many generations, produced by enthusiastic effort and infinite labor in every country of the world. All this is put into your hands as your inheritance in order that you may receive it, honor it, add to it, and one day faithfully hand it to your children. Thus do we mortals achieve immortality in the permanent things which we create in common." - Albert Einstein

Wednesday, April 5, 2017

Math Anxiety and Math Performance

Being anxious about math correlates with lower performance in math. This is apparently true across different countries as reported in a paper published in the journal Current Directions in Psychological Science. The negative relationship between anxiety and performance is, of course, not exclusive to math. In martial arts, for instance, both somatic and cognitive anxiety can produce about 80 percent discrimination between winners and losers. A good karate master like the one my children have recognizes the importance of instilling confidence in martial arts students. After all, either freezing or closing one's eyes during a match can easily spell defeat. A positive and growth mindset is clearly necessary and a master does this best by example. Interestingly, research strongly suggests a connection "between adult role models and children’s math anxiety and math achievement". Children whose parents are anxious about math are likely to exhibit anxiety in math and children taught by teachers who are anxious about math learn less in math.

Above copied from
The Math Anxiety-Performance Link. Alana E. Foley, Julianne B. Herts, Francesca Borgonovi, Sonia Guerriero, Susan C. Levine, Sian L. Beilock. Current Directions in Psychological Science. Vol 26, Issue 1, pp. 52 - 58. First published date: February-08-2017
How anxiety affects performance is also seen to directly correlate with high performance. Students who do well in math are more likely to see their scores go down with anxiety. This relationship suggests that anxiety may be forcing good students to use inefficient strategies. Students may not be able to think clearly when anxious.

The paper in Current Directions in Psychological Science does not provide clear evidence behind a bidirectional relationship between anxiety and performance, that is, not only does anxiety leads to poor performance but poor performance also leads to greater anxiety. However, it cites studies that indicate math anxious individuals have difficulty with basic math tasks that are typically learned before elementary school entry, such as judging the magnitudes of pairs of numbers.

My son is entering middle school this coming Fall. In a short chat with his future math teacher, the teacher shows me a set of arithmetic questions that he wants my son to answer. There is a time limit to answer all 70 arithmetic questions, 5 minutes. The purpose is to check fluency. Such a perspective is actually similar to the one taken by my son's karate master. There are practices and drills in karate that help a student develop instincts since in a karate match there is really little time to think therefore some moves and responses need to be automatic. My son's future math teacher speaks in similar terms - a student who has to spend quite some time adding, subtracting and multiplying has no time to see the beauty in math.

Teaching math clearly requires confidence and good role models. Differences in math anxiety across countries also point to the significance of cultural context. Unfortunately, Jo Boaler of Stanford University seems fixated on the idea that the main cause of math anxiety is the way math is taught. In the Hechinger Report, Boaler writes the opinion:
Our future depends on mathematical thinking, but math trauma extends across our country – and the world – due to the ineffective ways the subject is often taught in classrooms, as a narrow set of procedures that students are expected to reproduce at high speed... ...timed tests, speed pressure, procedural teaching – are the reasons for the vast numbers of children and adults with math anxiety.
Boaler cites the same paper from Current Directions in Psychological Science to support her opinion when the paper barely mentions competitive performance and testing environments as possible causes of math anxiety. Students from the East Asian countries perform very well in international math exams yet show high levels of anxiety. Here, there maybe important cultural differences. The higher academic achievement of students in East Asian countries is often attributed to the effort these children and their parents invest in studying. Stankov, in a paper published in Learning and Individual Differences, wrote:
Confucian Asian culture has a long history of high regard for learning and achievement and emphasis on effort to achieve academically. Its collectivist aspect underscores relationships, family closeness, and social harmony. Putting together these two salient features of Confucian Asian culture leads to the perception that individuals strive to achieve not only for their personal success but also for honor of their family and society. A finding from PISA 2003 that Confucian Asian students expressed higher levels of anxiety and self-doubt can be interpreted in terms of this unique cultural aspect of Confucianism. That is, in the minds of Confucian Asian students, the distinction between the self and one's family is not clear-cut and self achievement is also seen as family's achievement. Consequently, Confucian Asian students become aware of and learn to take seriously the implications and consequences of their academic success and failure. From this vantage point, the internal pressure for academic achievement is probably higher in Confucian Asian societies than in the other parts of the world.
Surprisingly, although levels of math anxiety are higher in these Asian countries, their scores are still among the top in the world. Stankov suggests that Confucian Asian students " can tolerate higher anxiety without a detrimental effect on performance — i.e. they are more resilient (“tougher”)." Resiliency may be coming not from the fact that these children are trying to outcompete each other but from their desire to honor their family and community.

Nevertheless, there is no evidence, contrary to what Boaler insists, that anxiety is largely due to the way we teach math. Instead, math anxiety in our children is mainly caused by our (We, teachers and parents) own anxiety and fears about math.

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