The Damage Done

I came across a paper on Piaget cognitive levels and learning in physics. There were lots of interesting things to think about from this paper but one thing in particular caught my attention.

The concept behind this paper is that people go through stages of cognitive development.  In high school we typically get students that arrive with concrete operational thinking, and they hopefully leave as formal operational thinkers. The following two math problems are good ok examples for comparing concrete to formal. Problem A: x = y + 3 and x + y = 17, Solve for x and y. Problem B: Xavier is three years older than Yolanda. The sum of Xavier and Yolanda’s ages is 17. How old are Xavier and Yolanda?

Problem A can be solved with using concrete strategies. Problem B however “requires the type of abstraction that is a characteristic of Formal Operations.” (Harrison, 2015).

Given that I recently wrote about the difficulty that some students have with certain aspects of physics that I think are very basic, this paper was quite timely for me.  The part that really struck we was when Harrison described his attempts to help students that were having problems with basic understanding:

Some years ago, with A.W. Key, we did some investigations and interventions with students in serious difficulty in their physics course. The course was the equivalent of the one that is the subject of this study. We were guided in this work by Piagetian taxonomy, although we were unaware of the CTSR; perhaps when we did it the CTSR was not yet available. Although we didn’t manage to help these students very much if at all, we did hear the same story from them, in one form or another, many times.

When the young person was about 13 or 14 years old they were considered to be good student. In their algebra class they confronted “word problems” such as Problem F above for the first time. The student couldn’t make any sense of how to do the problem, which would be expected fora student not yet capable of Formal Operations. After the teacher repeatedly urges the student to just try harder, the teacher finally loses patience and tells the student they are too stupid for this kind of work! The student believes the teacher, and is now traumatised.

I’m sure that I see the same things with students.  They have early failures with abstract concepts because at the time they are at the concrete operational stage of thinking.  Then, because of a traumatic event or simply because of a fixed mindset, they have great difficulties applying formal operational reasoning once they are actual capable.

This divide between concrete and formal operational thinking is also what was behind my observations with the electrical black box task.  I really wonder if we are doing students a disservice by asking them to think abstractly in cases where it might not be possible?  For example, last year I gave my Grade 9 science students the Lawson Scientific Reasoning Test.  There are some problems/critiques with this test but nonetheless I think that it is capable of telling us if a student is firmly a concrete thinker.  If they are, then what is the point of doing abstract math with polynomials and exponents, or abstract science concepts like conservation laws in electrical circuits (aka Kirchoff’s Laws) or the Bohr model and chemical formulas?  Can we delay these topics and somehow have the students “catch up” later?

Harrison, David M., Factors correlated with students’ scientific reasoning ability in an introductory university physics course, 2015, University of Toronto