An Aside about Creative Standard Testing

Coming from Pennsylvania I knew of the achievement testing (e.g. OLSAT, Stanford) and state assessments (the PSSAs - and I have to look up that acronym!), but in coming to Virginia I learned how things were different. Also, I observed some of the changes in the tests (yes, I hear about this in talking with teachers and how textbooks have to evolve to meet the ever-changing standards).

I could spend time talking about the changes in math education to focus on "higher level thinking" and related issues (e.g. the creep of probability / counting to the Algebra curriculum). I'd rather talk today about forcing standards tests to become, well, conforming verbatim to the course.

I found some articles from abroad interesting and worth discussing:

http://www.telegraph.co.uk/education/2016/10/21/rise-of-predictable-exam-papers-due-to-fears-of-social-media-bac/

In this article the discussion is on the use of experimental / creative questions in the standards exams. Links to the questions were provided and duplicated here. I'm interested in feedback since I think these types of problems need to be given and really test comprehension of topics taught.

Hannah's Sweets:

http://www.telegraph.co.uk/education/11652918/Students-vent-their-frustration-at-Edexcel-GCSE-maths-exam.html

Here I actually don't like the write-up of the solution since they used the answer to derive the equation. Rather, the problem says there are n sweets where 6 are orange (I suppose we assume n > 6) so picking 2 successive orange sweets is C(6, 2) / C(n, 2) = 1/3 (here C is the combination function of C(n, r)) which simplifies to 15 / (n * (n - 1) / 2) = 1/3 or 30 / (n * (n - 1)) = 1/3 or n * (n - 1) = 90 yielding the expression to prove (factor n^2 - n - 90 = (n - 10) * (n + 9) = 0 for n = 10 (only positive root) as the solution for n). While the question was weird, it did test process of setting up the problem which tends to be stressed more than the manipulations to solve the problem.

Crocodile Tears:

http://www.telegraph.co.uk/education/educationnews/11921671/Can-you-answer-the-tricky-crocodile-maths-question-that-left-students-in-tears.html

This is another problem which is an optimization question. Contact me if you want this one solved or come to a session and we'll discuss!