Contexts in math education

[Twitter original thread Dec 17th 2019, 12 tweets, 5 min read]

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.

A contrasting case might be the ‘culture free test’ (of intelligence) in the definition of the American Psychological Association
https://dictionary.apa.org/culture-free-test

Oh wait. Culture-free tests are impossible. ‘Culture fair test’ might be better:
https://dictionary.apa.org/culture-fair-tests

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’.

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 [Utrecht based Realistic Mathematics Education], 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

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 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 https://en.wikipedia.org/wiki/Standards_for_Educational_and_Psychological_Testing

‘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: http://jaredfreeman.com/jf_pubs/Freeman_DeepLearningReview_CognitiveTechnology_2013.pdf)
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 it 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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Annotations and literature on the subject of contextual questions in assessments:
http://www.benwilbrink.nl/projecten/contexten.htm

Also on transfer:
http://www.benwilbrink.nl/projecten/transfer.htm

A classic article on preparation for assessments:
Adriaan de Groot (1970). ‘Some badly needed non-statistical concepts in applied psychometrics’
http://benwilbrink.nl/publicaties/70degroot.htm

The ‘Flynn effect’:
James R. Flynn (2012). Are We Getting Smarter? Rising IQ in the Twenty-First Century. Cambridge University Press. TEDx-talk: http://www.ted.com/talks/james_flynn_why_our_iq_levels_are_higher_than_our_grandparents

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