\doc\web\99\17\authass.txt
From: "Gary Reid"
As some of you may be aware, Ontario is creating new curriculum for high
school. 1999/2000 is the year for Grade 9 implementation.
A group of "reformers", influenced heavily by NCTM, have pushed the
constructivist approach to the forefront of how mathematics should be
taught. This is in response to the "straw man" who is a man, usually
older, with a piece of chalk and a chalkboard, drilling and killing math
students with endless meaningless exercises. Now we are to introduce new
lessons with an "investigation" where students are to discover "their own
truth" together with their mathematically-adept brothers and sisters in a
highly-charged social setting [i.e. groups].
To facilitate this approach, the so-called authentic assessment criteria,
has been rolled out big-time. To make a long story short, can anyone help
me with the sources [Hansen and Firestone] that are quoted in the following
"research" article created by the EQAO, a government-created, allegedly
"arms-length" agency intended to create tests for students to determine
conformance to the new curriculum.
Thank you for your help............... Sorry if its kind of long....
EQAO has sponsored a second research paper "Varieties of Assessment:
Issues >of Validity and Reliability" (June 1999) by Anthony Barley
(Lakehead) and Alexandra Lawson (OISE).
On page 16 under Validity in Mathematics Assessment the Validity
Question asked is: Does the instrument design match the theory of
learning
underpinning the curriculum to be measured?
This follows over the next paragraphs:
"Over the last decade, mathematics reformers have suggested radical
changes to mathematics instruction; the changes are based upon the view
that children learn by actively constructing their own mathematical
knowledge rather than by receiving information whole from the teacher. In
1989, the National Research Council exhorted teachers to reform their
teaching methods by changing their "view [of] mathematics as a rigid system
of externally dictated rules governed by standards of acurracy, speed and
memory" (p.44)
The essential tenets of the movement have been carefully delineated by
the NCTM in its "Standards (1989)" and the Ontario Association for
Mathematics Educators in its "Focus on Renewal (1993)." ...."Alternative
assessment is seen by reformers as a fundamental aspect of both the
accurate measurement and the development of a constructivist program; that
is, one based on problem solving. Therefore, proponents of the mathematics
reform movement have strongly advocated the replacement of traditional
paper and pencil tests with alternative assessments (authors cite various
sources here)...If the mathematics curriculum considers children's
construction of knowledge to be of greater value than the rote memorization
of facts, the assessment tools must be designed accordingly. The
assessment design must allow students to develop "mathematical power"
through their ability to "explore, conjecture and reason logically, as well
as the ability to use a variety of mathematical methods to solve
non-routine problems" (NCTM, 1995, p.5)."
A second question (P. 17) that the research paper asks is: "Is there
evidence that the assessment has led to or will lead to better teaching
methods and therefore to improved student achievment?" Answer: From a
review by Hansen (1993) of all the studies, "the evidence favouring the
efficacy of mandated accountabilty as a tool for reform is weak at
best.
(p.11)" but it goes on to say, "The case study by Firestone, (et. al.)
(1998) of the effects of the large scale, performance-based mathematics
assessments in five school districts in Maryland and Maine found
significant changes in the alignment of teachers' content material to the
test items but little evidence of change in instruction methods."
"They believe that weak mathematical instruction is due to teachers' deeply
ingrained belief that mathematics is simply the application of memorized
rules, as well as to the limitations of their own knowledge....Therefore,
while authentic assessment may point out the shortcomings of thier
instuctional methods, much more is needed to help teachers make the next
step in mathematical reform. From this perspective, teachers need to
spend time relearning mathematics in a constructivist or problem-based
manner in order to be able to teach in this fashion. Genuine mathematical
reform of teachers' practices, the type of reform that might result in
children understanding more about mathematics, is highly challenging.
The importance of performance-based assessment in the reform of teaching
is
due to the new information it offers teachers about what their students
really understand. Such assessments have the potential to make teachers
think about mathematics in a new way as a result of their experience with
constructivist-based mathematical instruction."
The closing paragraph of the study states: "Validation would entail a
close examination of many of the features considered in this paper, for
example, the significance of theories of learning in the assessment
design." (p18)