on June 27, 1998
why do we need more than math tests?
I've just come back from almost a week of assessing student portfolios
with 4th, 8th and 10th grade teachers from seven districts in North
Carolina. As we predicted, we found much more evidence of student
competence in writing than we did in math.
What we did find in math caused us to rethink the evidence needed to
judge whether a student is demonstrating competence in meeting grade
level standards in math. Prior portfolio reviews in Vermont coupled
with our own experience showed that objective measures, such as multiple
choice, short answer and most word problems, do an adequate job of
assessing fundamental knowledge of math concepts and procedural skills.
Some (rare) well constructed multiple choice can also indicate more
sophisticated conceptual knowledge. The biggest problem we encountered
was that individual teacher-made tests were not very helpful in
determining whether students had mastered such core knowledge and
procedures unless it was summarized by a comprehensive list of grade or
course objectives, such as that provided by an instructional management
But we concluded that overall these traditional objective measures do
not do an adequate job of monitoring the development of student
understanding. We decided that this developing understanding is best
revealed on two ways: 1) application of concepts to solve structured and
ill-sturctured problems (structured problems are typical school problems
in which the problem and usually the strategies to solve it are evident
in the problem, and usually there is only one right answer.
Ill-structured is more like real life, in which even the problem, much
less how to solve if, are not evident, and there may be a range of both
strategies and solutions) 2) communication, including oral, written and
visual, in which students must explain their logical reasoning,
strategies and steps, links to other math concepts, and/or conclusions
to a variety of audiences.
Prompts (shorter time span, more school like problems) and tasks (more
authentic, real world and usually longer term projects) do a much better
job of revealing developing conceptual understanding than most objective
Our focus of work during the coming year will incorporate work we are
doing with our project with similar statewide work. We will be focusing
on classroom assessment tools which teachers find useful to monitor
their students' achievement of standards and make instructional
decisions, as well as useful for providing feedback to students and
their parents which will help students understand what they need to