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Re: Hart of Darkness (well, not really)
Posted:
Sep 3, 1995 10:12 AM


It may be informative for some of you to see standarised tests from an overseas perspective.
Historically, the tradition in secondary mathematics in Australia (and in many other countries in the world) is the ultimate in 'standardised tests'  the external examination, written by a Board of Examiners. All students study the same syllabus, do the exam at the same time on the same day, and the exams are marked by a team of paid markers (usually teachers). The results are important, as they determine if a student gets into university, and which courses they can study.
I have taught under this system. It has its good points. It is a reliable (though maybe not valid) method of determining university placement, ie, a student who does well on a test on Monday should do about as well on a different test, covering the same content, on Tuesday. It puts the teacher and the student into a 'partnership', since the teacher no longer stands in final judgement of the student  the Board of Examiners take on that role. Teachers quickly learn which mathematical skills are valued by the Examiners, and are able to drill these skills into their students. And it makes the end of the year a real joy since someone else is marking your papers!
It also has its bad points. I used to teach the 2 year senior mathematics course in a year and a half, and then drill the kids relentlessly using past exam papers for the last semester. I had no control over what content or processes I taught  the syllabus told me what to teach, and to what depth. The goal of the course was to get lots of kids to pass the exam with high marks. That is what successful maths teachers did. The exam period, at the end of two years of study, was highly stressful for most kids.
Queensland has not had external exams for over 10 years. The current syllabuses are far less prescriptive about content and depth than those written for external examination. Shool results, though, still determine university placement. To obtain comparability between classes and schools, the quality of the work of the students (and ultimately the teacher) is decided by a panel of the teacher's peers. The panel has the power to recommend (and ultimately enforce) a change in students' ratings if they feel that the standard of work (eg of a student awarded a low A) isn't comparable to that of other schools.
In the main, the system works well. Teachers have professional pride, and work damn hard to ensure that their exams are fair to the students and still meet the standards of the panel. And teachers have respect for the judgement of their peers on the panel, since these teachers are acknowledged to be amongst the best in the district.
Since the course content is not rigidly prescibed, it is possible for teachers to follow whatever paths emerge from a good lesson, and to trial new forms of assessment. I currently have my classes doing assignments  the year 12s exploring the catenary and my year 11 students being introduced to numerical analysis and iteration to solve systems of linear equations. I surely wouldn't be doing this if I had an external examination hanging over my students' heads. Or, for that matter, a school superintendent who was using a 'standardised test' to demonstrate the improvement in mathematics teaching in his district.
As a side note, I visited the US recently and bought a copy of an AP Maths Test Prep book by ARCO, in the hope of getting some good assessment from it. My main impression, based on this book, is that AP Calculus is BORING. I'm sure many of you are teaching this course in an exciting fashion, but I hope you are not using that book as guide for designing the course! I reckon it speaks volumes against standardised tests.
In summary, I guess I'm saying that I don't like standardised tests. If they are important, ie they determine your salary for next year or get a kid into uni, then you are forced to teach to the test, which is a very bad thing. If they aren't important, then why give them? And I really don't think that standardised tests as they currently exist can truly measure what is learned in a good mathematics classrom.
This turned out to be a longer letter than planned, so this was my 4c worth.
Rex
Rex Boggs  High above the hushed crowd, rex@cqpan.cqu.edu.au  Rex tried to remain focused.  Still, he couldn't shake one Glenmore High School  nagging thought: He was an Rockhampton, Quensland  old dog and this was a new Australia  trick  Gary Larson



