Perceived Realities Rule...Unfortunately
Let me begin with a true story as I remember it. A close friend, when in elementary school, was forced to take the Iowa Basic Skills Exam to determine her placement in a particular math class (homogeneous grouping!) Unfortunately, at the same time, her mom was dying from cancer and she did not care about the test or much else. So, on the exam, rather than look at the questions, she turned the answer sheet sideways and filled in the bullets until she had proudly drawn the outline of a super spaceship.
Unfortunately, the answer sheet was graded by a machine and her low score (7%) placed her into the lowest "slow learners" category/class. It took tons of arguing on her father's part and considerable time elapsed before she was moved to the correct class of high acheivers.
This person later graduated with a math degree from college by age 18 and has been a highly-respected mathematics professor for more than 30 years. What if her father had not intervened for her...explained the underlying problem...and forced a human "someone" to actually look at her bubbled space ship...and fought for her proper placement?
So, why tell this story? It's memory was triggered by my reading of a disturbing article published in the respected Science (January 19, 1973). I recently discovered its reprint in Paul Watzlawick's The Invented Reality (1984), an early text on constructivism.
Stanford psychologist David Rosenham wrote the article: "On Being Sane in Insane Places." Basically, Rosenham had sane people (e.g. psychologists, psychatrist, painter, graduate student, pediatrician) pretend they were hearing voices to the extent that they were admitted to psychiatric hospitals...then immediatly dropped their act and interacted with their normal "sanity." The study's goal was to determine if the hospitals (doctors, nurses, etc.) would ever recognize their sane-ness and release them.
As the Pygmalian-like results were disturbing, I will skip most of it (the mistreatment, use of drugs, etc.). But, the key thing is that none of the pseudopatients were ever diagnosed as being sane. Rather, the majority were released: "the evidence is strong that, once labeled schizophrenic, the pseudopatient was stuck with that label. If...discharged, he must naturally be 'in remission'; but he was never sane, nor, in institution's view, had he ever been sane." Wow!
So why tell these two stories? As math teachers, our students stuffer under "perceived" realities as well. For example:
I could go on....But I suggest that mathematics students (and mathematics education itself) suffers from our own perceived realities.
- On the first exam of the year, a student does poorly (or great), what is your perceived view of that student?
- You hear teachers discuss a difficult student in the faculty lounge, and the next year when you have that student, what is your perceived view of that student?
- You have had a student and then have his/her sibling, what is your perceived view of that student?
- You have a student who got an A last year from a teacher you do not respect and is viewed as easy, what is your perceived view of this student?
- Given a student of a particular sex or certain ethnic group in your math class, what is your perceived view of this student?
Find and read Rosenhan's article and you may see what I mean!