1. A rubric is an instrument that serves as a guideline
for evaluating student work. While there have been a great
deal of attention paid to use of scoring rubrics in
mathematics assessment, oftentimes, there is little
discussion of exactly what a rubric is.
2. Throughout this module, we will explore the various
types of rubrics as they are applied to a mathematics
context. Most important are the types of considerations we,
as mathematics educators, must make in developing
appropriate and effective rubrics. As we progress through
the How far, how fast? How many, how much? module, we will
examine these issues in light of the opening activities and
the poster-building activities.
Informal assessment that occurs during the
instructional period. As we teach, or as the
students are doing an activity, how do we know if
the students are understanding the intended
concepts? Most often, this type of assessment comes
from asking questions in class as they work and
seeing their progress.
At the conclusion of a lesson, activity, or
project, how do we evaluate a students work
and understanding of the mathematics? Most often,
we associate summative assessment with grades, test
scores, project grades, etc.
Although any grade is
before the final grade is a type of summative
assessment, all of those grades serve a dual
purposethey give information about a students
progress and understanding of topics covered. Thus, most
graded work is also a type of formative
assessment as well.
- A scoring scheme that focuses on product completion
rather than process components.
- If we give all or nothing credit, it is,
in essence, a holistic type of grade.
- A popular example of a holistic rubric is: 0
pointsno effort and no work done; 1
pointstudent attempted to do the work and partially
completed the assignment or it is partially correct; 2
pointsassignment completed and all work is
- This is often used when the effort is more important
than the correctness of individual parts of an
assignment. Example: One might only grade specific
problems given in homework, but will give a holistic
grade to signify if the homework assignment was attempted
- A scoring scheme that focuses on the process and
components of an assignment more than its attempt and
- The goal is to analyze a problem, project, or
assignment to decide the relative importance of each part
of the task and to categorize these elements. Points are
then assigned according to the level of sophistication or
correctness in each category.
- Sample categories for an analytic rubric are:
correctness of mathematical procedures, strategies for
setting up a problem or solving a problem, the use of
appropriate representations, effective communication of
ones understanding and strategies, etc.
- ISBE uses a three-category analytic rubric for
extended-response items on the ISAT: Mathematical
knowledge (procedure, correct solution), strategic
knowledge (reasonableness, problem-solving strategies),
and explanation (communication, justification).
- WHAT about our familiar term in
mathematics education, PARTIAL CREDIT?
Partial credit assigned on any one mathematics problem is
an analytic rubric that focuses on ONE category: