We got the keys this morning to our new apartment, but are going to wait to move in until next Monday when we will have internet there. We are excited though for a new place and new neighborhood to explore!
Tonight for the second half (7:30-9:00pm) of the grad school course "Psychology of Learning Mathematics at the Primary Level" there was a visiting professor whose guest lecture with us was "Mathematics Anxiety: Myth or Monster." Mathematics is the most common subject in school that students experience feelings of anxiety. Broadly, math anxiety is a term "used to describe panic, helplessness, paralysis and mental disorganization that arises among some people when they are required to solve a mathematics problem" (Tobias and Weissbrod, 1980). There are two different constructs of anxiety: State Anxiety (A-Sate) and Trait Anxiety (A-Trait). The concepts of state and trait anxiety have been defined by Spielberger Gorsuch and Lushene (1970) as follows:
- State anxiety (A-State) may be conceptualized as a transitory emotional state or condition of the human organism that is characterized by subjective consciously perceived feelings of tension and apprehension and heightened autonomic nervous system activity. A-State may vary in intensity and fluctuate over time.
- Trait anxiety (A-trait) refers to relatively stable individual differences in anxiety proneness, that is to differences between people in the tendency to respond to situations perceived as threatening with elevations in A-State intensity.
For instance, a student who is otherwise not anxious but feels not mathematically competent may develop A-State anxiety when asked to solve a non-standard mathematical problem. Conversely, a student who is high in A-Trait will show strong signs of anxiety whether the problem is mathematical in nature or not.
To help us understand the feeling of A-State math anxiety the professor presented this room full of math teachers with these two non-routine math problems:
In this room full of math teachers, you could feel and hear the initially anxiety-driven reactions. He gave us a 5 minute time limit to solve them both. Many of the teachers ended the 5 minutes with a blank paper and true feelings of frustration. I think I've done enough of these type problems throughout my years in math team competitions to know to look for a pattern so I was able to solve both during the time period. But I know that wasn't the point of the demonstration :) It was quite interesting though to think about how many students feel in math classes especially when they have not experienced much success in the subject area and/or have not been taught strategies to deal with the unpleasant feeling of not knowing what to do or where to start when presented with a problem that is not identical to the type of problems they have seen and practiced. Some levels of anxiety though are good for us. This curve illustrates the relationship between anxiety and performance:
At the far left, our mind is "asleep". When we do not encounter any situations, we do not perform. In order to function we will need increasing awareness. Some anxiety is good, for example, doing homework and taking tests make our mind work. Peak performance occurs when our anxiety optimally alerts the body. However, as anxiety continues to increase, it interferes with performance until at the far right we are paralyzed by anxiety. Students with test anxiety describe their minds going blank, and students with mathematics anxiety are those at the far right of the graph. The lecture was quite interesting because it provided a real simulation as well as a lot of research related to the effects of math anxiety on students. As teachers (and parents) we can teach kids coping skills and more specifically a set of problem-solving steps/skills that can be used intentionally to approach solving a novel problem.
The professor did not ever go over or expose the solutions to the above problems he presented us with--which would drive my students crazy if I never validated their answers or explained to them how to solve (if they had not be able to on their own). So, scroll down for the my worked solutions:
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