Thread by @benwilbrink

Contexts in math education.
Question: is ‘daily life (and its situations)’ a knowledge domain?
Can one learn to become an expert in ‘daily life’?
I am asking this for a friend who thinks that it is fair to test mastery of math by hiding math problems in situations of daily life.

#contexts A contrasting case might be the ‘culture free test’ (of intelligence) in the definition of the American Psychological Association dictionary.apa.org/culture-free-t…
Oh wait. Culture-free tests are impossible. ‘Culture fair test’ might be better: dictionary.apa.org/culture-fair-t…

#contexts Note. Culture fair tests of intelligence should not show a strong ‘Flynn effect’ (rise in mean IQ over the 20th century). For if they did, they would evidently not be culture fair.
Guess what. Yes, indeed. The Raven test showed the strongest ‘Flynn effect’.

#contexts The contrasting case of the culture fair intelligence test suggests that tests of the mastery of pure math are culture fair tests in a meaningful way. Fine.
Reform math, e.g. RME, changed that, the idea being that math is only math if one can apply it, #transfer it.

Another school discipline, physics, is a heavy user of math. Physics is a knowledge domain, *inclusive* of the appropriate math. A true physics test is a test of mastery of physics, not a test of mastery of math; the math is necessary, not sufficient.
#contexts #paradox

#contexts Why am I doing this exercise? In Holland an attempt is being made (by the minister of education) to reform the goals and goal structure of primary and secondary: curriculum.nu Also math. The proposal further entrenches reform math, based on pseudopsychology.

The arguments for the uses of #contexts in instruction as well as in assessments and examinations of mathematics are are not grounded in sound psychology at all.
I’ll try to show in this thread that #contexts in examinations invalidates them, in the sense of the APA standards.

The Standards are not open access, regrettably. Info on wikipedia en.wikipedia.org/wiki/Standards…

‘Far transfer’ might not be a special phenomenon at all, it is just continued learning (thanks to Stellan Ohlsson, in his 2012 ‘Deep learning’, reviewed: jaredfreeman.com/jf_pubs/Freema…).
If not guided (eg. private), it is problem solving. If guided (eg. vocational), it is training.

Another serious problem with contexts not being drawn from specific knowledge domains is that is obstructs students’ preparation for assessments and exams. One can’t prepare oneself for problem contexts that might just be anything, anywhere, anytime.

Writing the English essay in examinations had the same problem; it tended to be solved by letting students choose from among a small list of subjects. A lot better than just one subject, yet it still does not result in a level playing field for all students.

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