2011 | ABRIDGED
MATHEMATICS FRAMEWORK
|
8
Mathematical Complexity
of Test Questions
Mathematical complexity deals with
what
the
students are asked to do in a task. It does not take
into account
how
they might undertake it. In the
distance formula task, for example, students who
had studied the formula might simply reproduce
it from memory. Others who could not recall the
exact formula might derive it from the Pythagorean
theorem, engaging in a different kind of thinking.
To read more about the
.
Three categories of mathematical complexity—low,
medium, and high—form an ordered description
of the demands a question may make on a
student’s thinking. At the low level of complexity,
for example, a student may be asked to recall a
property. At the moderate level, the student may be
asked to make a connection between two properties;
at the high level, a student may need to analyze the
assumptions made in a mathematical model. Using
levels of complexity for the questions allows for a
balance of mathematical thinking in the design of
the assessment.
The mathematical complexity of a question is not
directly related to its format (i.e., multiple choice,
short constructed response, or extended constructed
response). Questions requiring that the student
generate a response tend to make somewhat heavier
demands on students than questions requiring a
choice among alternatives, but that is not always the
case. Any type of question can deal with mathematics
of greater or less depth and sophistication.
An ideal balance in the NAEP Mathematics
Assessment for all three grade levels is to devote half
of the total testing time on questions of moderate
complexity and the remainder divided equally
between questions of low and high complexity.
Low-complexity questions
require students to recall
or recognize concepts or procedures specifed in the
framework. These questions typically specify what
the student is to do, such as carry out a procedure
that can be performed mechanically.
Sample Question:
Questions in the
moderate-complexity
category
involve more fexible thinking and choice among
alternatives than do those in the low-complexity
category. The student needs to decide what to do
and how to do it, bringing together concepts and
processes from various domains. For example, the
student may be asked to represent a situation in more
than one way, to draw a geometric fgure that satisfes
multiple conditions, or to solve a problem involving
Multiply:
8.5
x4.9
Answer:
5.