-- the Forum May 1993 --
Betty Field & Ed Chandler, PVCC
Editor's note: Betty and Ed team teach MAT 235 following the
Harvard Calculus model, a non-traditional method which
emphasizes the introduction of concepts from three
perspectives: numerically, analytically, and graphically
("the rule of three"). Students are also expected to do
writing and to use technology tools, i.e., symbolic and
graphics software like
Students in our Calculus with Analytic Geometry III (MAT
235) course are required to keep a portfolio of the work
they produce throughout the semester. The portfolio is worth
100 points (about 20% of the final grade) and should include
the following items:
- assigned homework problems from each section of the
- additional completed problems, including one non-
trivial problem selected by the student from each chapter
- oral presentations support materials
- other work as assigned
The portfolios undergo a peer review and an instructor
review near or at the end of each chapter. The standards for
evaluating the portfolio contents include:
- concise and well-written materials, including the use
of complete sentences to explain the work and the outcomes.
- good attempt at solving the problems, which includes
showing appropriate thought and reasoning even though a
final resolution may not have been achieved.
- valid results which follow from the work.
At the beginning of the semester, students receive the
initial set of rules for preparing their portfolios. The
rules and criteria for evaluation are included in the
syllabus. Students are also given an additional handout with
specific directions as to what is to be included in the
portfolio. Students are asked to include not only homework
problems or assignments, but extra things they produce which
highlight their strengths and abilities. For example, they
can choose to solve one extra problem from each chapter that
meet our conditions: problems have to be non-trivial. If
there are any doubts about the appropriateness of a problem,
students are to check with us before investing time working
The purposes of the writing component include:
- Writing does assist the learning process, "writing for
learning." Writing helps clarify concepts for the students;
helps the students organize, understand, make connections,
clarify processes and solutions; helps the students
understand the assumptions made about the solutions to
problems; helps the students interpret the results of their
- Writing is an important element in the students'
future academic and professional life.
Our students are also expected to plan and deliver an oral
presentation covering the content for one of the chapters.
All materials prepared for presentation (topic outline,
visuals, handouts, etc.) must be included in the portfolio
Another component of the portfolio is the comments from peer
review and students' response to those comments. The concept
is to give students a chance to change things, to improve
them before the final grade. Students exchange portfolios
before the instructors see them. Sometimes we assign the
peer reviewers and sometimes we let them choose their own.
The peer reviewer comments are included in the portfolio and
the reviewers is graded on their comments. We examine the
student work to see if s/he has responded (changed their
work) as a result of the review. We believe that both
students learn from the peer review process. It has been as
meaningful to the reviewer as to the one being reviewed.
Portfolios are evaluated primarily on content. All students
receive an evaluation sheet with written comments. If
students have any questions or concerns about the comments,
they are encouraged to discuss their concerns with one of
the instructors. This semester we assigned a score to each
section of the portfolio completed and reviewed. We did not
think that was an ideal strategy since some students felt
that because they had completed the section and received a
score, they did not have to deal with it anymore. We tried
to change that attitude by telling students that after they
received feedback from us, they could still improve their
work and modify their score by changing the portfolio and
adding to it.
One of our motivations for incorporating portfolios into the
course was to experiment with alternative assessment. We
also believe that students should be able to collect their
best materials and put them in a portfolio that they could
carry to an employer to show. It is part of professional
growth. It has been difficult, however, to make students
understand the idea and to make them see the value of
collecting samples of their work to show change and growth.
We were hoping that students would on a regular basis
contribute to their portfolios, get feedback about the
portfolio, and make improvements based on the feedback. At
one point we thought that we would do very informal
evaluations several times during the semester and then the
final evaluation at the end of the term. We realized early
on that students were not putting anything on the portfolio;
they were not keeping the portfolio up-to-date, so we
changed our thought process and expectations and imposed
some portfolios deadline.
Portfolio is a new concept for both students and
instructors. However, we still believe in the value of
portfolio as an assessment tool and as a learning tool, and
would do it again with third semester calculus students.
Guidelines for Test Construction
Identify knowledge, skill, or performance that has real-
world application. Define the learning objectives.
Develop test items that ask learners to invoke real-world
application: create, design, produce, write, evaluate,
analyze, synthesize, calculate, solve.
Develop scoring criteria:
- Match the scoring criteria to the type of assessment
- Identify and define quality performance.
- Gather samples of student's work that exhibit a range
- Discuss with peers the characteristics between
effective and ineffective product, solution, performance,
etc. Criteria should hold up to several judges looking at
the assessment measure and reaching the same conclusion
about the learner's attainment of the objectives.
Constructing Multiple-Choice Test Item
- Match the test item to the learning objective.
- Each multiple-choice item should include a stem and
3-4 plausible distracters. The stem should present a single,
definite statement of a problem; should always include a
verb in the statement; and should present the problem in a
concise, clear, simple manner.
- The stem should include only the necessary information
to understand the problem. Avoid irrelevant, trivial, and
obvious material. Avoid unnecessary repetition of material
in the options by including as much of the item as possible
in the stem.
- Ensure that all the distracters are plausible and that
only one response is correct or the best answer.
- Be sure each item is independent of all others. A
question should not provide a clue to another question later
in the test.
- Use positive statements as much as possible. If
negative statements must be used, then CAPITALIZE,
underline, or highlight the negative term.
- Arrange the options in logical order (by number,
alphabetically, chronologically), if possible. If there is
no logical order, randomize.
- Avoid copying statements verbatim from the text when
designing stems and options.
- Write options in grammatically parallel form whenever
- Avoid using options such as "all of the above" and
"none of the above."
- Avoid providing clues to the correct option:
- Length: do not make the correct choice the longest
- Verbal association: do not include different forms of
the same word in both the stem and the correct option.
- Grammatical: all the options must complete a
grammatically correct statement. Beware of the use of "a,"
"an," plural forms, and gender forms.
- Determiners: beware -- "all," "never," and "always" are
usually associated with the incorrect responses. "Usually,"
"sometimes," "typically," and "maybe" are usually related to
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