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Additional Online Case Studies & Appendices | |
“Surveying Majors in Developing a
Capstone Course”
M. Paul
Latiolais, Joyce O’Halloran, Amy Cakebread Department of
Mathematics and Statistics Portland State
University Abstract
The
Department of Mathematics and Statistics at Portland State University surveyed
its undergraduate majors (and some graduate students) to gather information for
the development of a senior mathematics capstone course. Students were asked
about the importance of a list of performance objectives and their perceived
competency in each objective.
Demographic information was also collected. Results and analysis of the survey are presented, as well the
role of these results in departmental decisions. Background
and goals: What did we hope to accomplish? The
design and implementation of courses in the Department of Mathematics and
Statistics at Portland State University has traditionally been based on what
mathematics departments in research universities do and what faculty in the
department think might be needed.
Removal of courses from the curriculum has been similarly based on what
faculty believe is needed. Asking the
students what they need in a controlled manner has not been done. After lengthy discussions over several years, the department
agreed in June of 2001 on a list of student learning objectives for the
major. Those learning objectives were
in six categories: Mathematical tools,
Connections, Technology, Communications, Independent learning, and Attitudes. In mapping these objectives
to the curriculum, the department discovered that many of the objectives were
not effectively addressed by the curriculum in place at that time. The learning
objectives that were not being met were largely in three areas: Connections, Communication, and Independent learning. See appendix for the list of those
objectives. At the same time, the dean
of the College of Liberal Arts and Sciences urged the department to develop an
assessment of the major as part of the universities assessment initiative. While developing strategies to assess
student learning objectives, the department realized it needed new strategies
to assess students at the senior level.
The department has developed strategies to assess student skills as they
begin abstract math courses, but the department does not have a way to measure
the value added between their first abstract math course and completion of the
undergraduate program. We realized that
we could develop an end of program assessment and address student learning
objectives not yet covered with a senior capstone experience. In order to begin the design of a senior capstone course, we
undertook a systematic survey of current and past undergraduate mathematics
majors’ needs. The intent was to ask
students what they thought was most needed in their studies of mathematics and
whether they would voluntarily take such a capstone course addressing those
needs. With
the help of a graduating senior mathematics major, we designed, piloted and
administered a survey of math students. The survey focused on ten particular
learning objectives from the departmental list, that the department felt were
not being well addressed or well assessed (See Appendix). The survey asked students how proficient
they felt they were in the identified learning objectives and how important
they thought each objective was. The
survey also described a potential model for the capstone course and asked
students for feedback on the course design and whether they would take such a
course. A
pilot survey was administered in the winter of 2002. It provided valuable feedback on how students perceived the
questions that were asked and how to improve the survey to get information we
needed. The survey was subsequently redesigned, changing some of the column
formatting and the phrasing of some questions.
The survey was administered at the beginning of fall term 2002. The
results of the survey will be discussed in subsequent sections. Survey Responses and Analysis
The
survey was administered in two classes; a junior level advanced calculus and a
senior real analysis course. The
advanced calculus course is required of all majors, so thought we could get a
good representation by surveying that class.
The vast majority of students in the real analysis course are typically
seniors, so we could be sure to get their voice by surveying that class. As advanced calculus is a pre-requisite for
real analysis, we would not get any overlap. Student
Demographics A
total of 40 students were surveyed; 30 undergraduate and 10 graduates. As the
chart below indicates, 12 students identified themselves a female; 27
identified themselves as male. One
student did not declare a gender. For
the purposes of statistical analysis we decided to declare that student as “not
sure”.
As can be seen in the AGE chart, the majority of
students were between the ages of 20 and 24.
The work chart shows that the majority of students worked
over 15 hours per week At least one student worked full time.
Student Responses
Students were asked about the importance of student learning objectives
in three areas: Connections,
Communication and Independent
learning. The most interesting result of the survey was
that the majority of students felt each student learning objective
was important. The
tables below are labeled by key words of the learning objectives. The master key is supplied in the appendix.
The most important objective to the students was
“Proficiency
as an independent and critical thinker”.
The second most important objective was “Proficiency in oral
and written communication of mathematics”.
The lowest scoring objective was “Familiarity with historical/social
contexts of mathematics”. It
is not surprising that students valued this objective less.
What is surprising is that they still thought it was important. The department’s mathematics history course
is taught only in the summer and only by non-regular faculty. The course is not required of majors. The social
context of mathematics is not well addressed either. Students infrequently
encounter the relevance of the historical or social contexts of
mathematics.
Students
felt that they were most skilled in “Proficiency as an independent
and critical thinker”, the same objective they felt was most important. Students rated “Ability to work as part of a team to do math” second in their perceived
skill level. A focus group
study of two years ago told us why students might feel they are
good at working in groups; the department’s atrium is full of students
all day long collaborating on mathematics together.
The atrium may be our greatest asset.
The objective scoring lowest in skill level was “Familiarity
with historical/social contexts of mathematics”.
This result is not a surprising from our earlier comments. The department does not offer much in these
areas, hence students do not have the skill.
By subtracting the average responses on
skill from those on importance, we get a sense of areas where students
feel the need for the most improvement.
The difference is the highest for “Proficiency in oral and
written communication…” and the lowest at “Ability to work as part
of a team to do math”. We conclude that students feel that their oral
and written communication need the most improvement. Other skill/importance differences can be seen
in the chart below.
Notice
that even where students felt they were skilled in a particular
objective, they still expressed a need for further improvement.
While
both the junior level advanced calculus and senior level analysis
students felt “Proficiency as an independent and critical thinker”
was the most important skill, the students surveyed from advanced
calculus did not rate the skills overall as important as the analysis
students did. When comparing their skill level, the students from advanced calculus
felt more confident about their skills than the analysis students.
(Makes you wonder what happens to students to make them less confident
about their skills between advanced calculus and analysis classes!) Overwhelmingly, the analysis students felt
they lacked “Proficiency in oral and written communication”.
Females rated “Awareness of applicability of math in other disciplines”,
“Familiarity with historical/social contexts of mathematics”,
and “Ability to build and use mathematical models” as the areas where they would
like to improve on most. Males,
on the other hand, rated these as the lowest differences. That is, the men felt that the rest of the areas needed more improvement.
Females felt they had sufficient skills in “Ability to work as part of a team “ and “Ability to use the library and other non-classroom resources to
solve a problem in math”. These
gender differences may be attributable to the women being older
than the men.
The
graduate students felt “Proficiency
in oral and written communication of mathematics to peers as well
as to people with less math background” and “Proficiency as an independent
and critical thinker” were most important, while the undergraduates
felt “Proficiency as an independent and critical thinker” and “Ability
to ask the right questions to learn something new or apply something
known to a new situation” were most important.
The graduates felt “Proficiency in oral and written communication”
was where they needed improvement.
The undergraduates felt “Ability to ask the right questions”
was most needed. Neither the graduates nor the undergraduates felt they had as much
skill as they would like in any category.
Open Ended Questions After
asking students to rate importance and skill level on the objectives,
the survey asked them specifically for areas in which they would
like to improve their proficiency, from the list and in other areas
not on the list. We also asked them why it was important to
become more proficient in these areas.
Of the 40 respondents, 27 students answered this question. Of objectives from the list, “Proficiency in
oral and written communication” was the favorite with 13 out of
27. When asked about areas not on the list, only
6 students out of 40 answered.
Writing proofs was the favorite choice here with 4 of them. These answers seemed to reflect a desire of students to see more
of the objectives we listed in the survey as part of the departmental
curriculum.
Lastly,
the survey asked students to critique a senior capstone course described
to them as follows:
“We are proposing a two-term course—worth two
credits per term. Topics for the two terms would include the history
of mathematics, the application of mathematics, and the applicability
of mathematics to specific disciplines.
Each student would be required to give oral presentations
and written reports. All students would help give feedback to presenters throughout the entire process.
During the first term, students would
work in groups to do a variety of short research activities. The second term would consist primarily of
two activities:
1)
Assisting students going through their first term
2)
Creating an independent research project around one
of the topics addressed in the previous term (or a topic suggested
by the faculty).
Second term students would present their work at a public event.
This two-term course could potentially satisfy
the University Studies capstone, but approval would be discretionary and would require the addition of a community service
component.”
They
were also asked if they would take such a course. Only 11 students responded to those questions. Critiques were not significant, although many
felt that the course needed to offer more course credit and should
satisfy the university’s capstone requirement.
Nine of the 11 students said that they would take such a
course.
The
ethnicity category was omitted from the analysis because of the
lack of diversity in those surveyed.
75% of the students surveyed were white with the other categories
holding either 4 or 1. Since
only 3 surveys were from non-math majors, this category was also
omitted. Due to the invalid and often incorrect answers to the question of
the number of credits a student had, this category was omitted. GPA estimates were mostly above a 3.0 and also
were omitted from the analysis due to the lack of diversity.
Insights:
What did we learn?
In any study like this, results include
the questions that arise. One immediate question we had was, “If
we gave the same survey to linear algebra students, would the responses
be different?” The two courses surveyed are very difficult
for our students. Their
perceived need for these skills may be underlined by the difficulty
of the material they are trying to learn.
The Senior Capstone Our declared purpose of the
survey was to help us design the senior capstone course. Based on
the survey results, what should be included in the senior capstone
course? Keeping in mind that students considered all
of the listed objectives important, they all need to be incorporated
into this course to some degree.
The survey indicated that students feel confident about their
communication skill level. At
the same time, their responses also indicated that they would like
to be more proficient in this area. Hence written and oral communication will drive
the format of this course, with students presenting foundational
information as well as solutions to problems.
With "proficiency as an independent and critical thinker"
rated the highest in importance, a discovery format would best serve
the students. The discovery
process could include meta-cognition addressing the objective of
"asking the right questions to learn something new."
As far as course content, it will be important to explore
connections within mathematics and between mathematics and other
disciplines.
Because several student responses
emphasized the desire for a senior capstone course which would satisfy
the university’s capstone requirement, we are incorporating the
required community-based component.
Specifically, the course (to be offered for the first time
as a 2-quarter sequence starting January 2004) will include presentations
to inner city high school students.
Integrating community-based learning into this course will
involve readings and discussions about the role of mathematics in
our society, thereby addressing the “social context of mathematics”
learning objective.
A one-quarter “pilot” capstone
course (with no community-based component) was offered Spring 2003,
in which students explored applications of mathematics independently,
made presentations in class, and wrote a final paper. Experience with the pilot course demonstrated the need for a 2-quarter
experience, both for exploration and in order to incorporate community-based
learning.
Appendix
Student Learning Objectives
For the BS/BA Degree in Mathematics Department of Mathematics and Statistics Portland State University Connections
Applications=Awareness of applicability of math in other disciplines History=Familiarity with historical/social contexts of mathematics Contexts=Ability to make connections in math from one context to
another Models=Ability to build and use mathematical models of concrete
situations or real phenomena Statistics=Ability to use data an
Essential skill d statistical
techniques to solve a problem or make a supportable conclusion Communication
Delivery=Proficiency in oral and written communication of
mathematics to peers as well as to people with less math background Teamwork=Ability to work as part of a team to do math Independent
learning
Independence=Proficiency as an independent and critical thinker Library=Ability to use the library and other non-classroom
resources to solve a problem in math Questioning=Ability to ask the right questions to learn something new
or apply something known to a new situation |
