Course:
Instructor:
Intro to Calculus
Dr. Jonathan Fredericks
Text
Intro to Calculus - large class;
prerequisite for several science
study focus areas.
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Course has longstanding
problem with student retention
– students many times either
fail or drop the course.
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Problem
Larger classes may create challenges for
instructor to get to know students and their
interests, as well as whether students
understand the material.
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Larger classes with students from different
study focus areas may create difficulties for
instructor to tap into students’ interests, to
challenge and motivate them, i.e., provide
enhanced opportunities for engagement.
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Poor persistence and retention is
problematic to the college/university,
especially for a course that is a prerequisite
for further study. Colleges/universities want
to increase enrollment, and of equal
importance, want to increase persistence
and retention!
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Dr. Fredericks lectures on key
concepts and underlying
rationale of equations; writes
notes on board as he describes
concepts and equations.
Case Study #1 – Solutions
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The length and passivity of lectures and
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their demand for sustained attention and
concentration are significant barriers that
render lectures ineffective.
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Even though the words spoken in lecture are
accessible because they can be heard and
their meanings recognized, they raise
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barriers stemming from high demands on
Solutions
Ask students to create name cards, with their name and
major/study focus area. Have student display these
cards each day in class so that instructor can see them,
can call students by name, and can develop awareness
of each student’s focus area.
Adopt instructional technologies that increase
communication and allow for alternate modes of
expression AND allow instructor to know immediately
whether students understand the content (e.g., clickers)
Ensure that examples, content and assignments are
relevant to people from diverse backgrounds,
experiences, and study focus areas, facilitating class
engagement.
Seek feedback from instructor and students (UDL
instructor and student surveys), determining
weaknesses in course and areas where UDL is needed.
Implement UDL in response to data from instructor and
student surveys.
Track student perceptions and outcomes, before and
after UDL implementation.
Share results with administration and colleagues,
making case for dissemination of UDL.
Write equations and content on board, then face class
for discussion! Include students in equation solving
through use of clicker technology.
Make lectures interesting and exciting, connecting the
information to current events, life experiences, and
student focus areas.
Break up lecture time with activities, class
participation, etc.
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Students take notes and try to
capture equations and
comments while Dr.
Fredericks speaks and writes
on board.
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linguistic and cognitive abilities, including
memory, attention and the amount of
background knowledge they assume.
Because Dr. Fredericks has his back to the
class during much of the lecture, he may be
unaware of whether students are engaged or
understanding the information he is
covering.
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Instructor is unaware whether students are
grasping content.
Limited opportunities for students to
interact with content and express to one
another what they are learning.
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Dr. Fredericks regularly asks if 
there are any questions.
However, students seldom ask
many questions in class.
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Exam results reveal that
Case Study #1 – Solutions
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Students are not benefitting from class
discussion & participation, and may not be
understanding key concepts of the course.
As a result, they may not even know what
to ask.
Instructor does not know whether students
are understanding the course concepts and
content.
Instructor has no method for determining
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Give assignments that are relevant to students. Take
time in class for students to describe how they
completed those assignments and what they learned.
Use informative PowerPoint slides to accentuate
important equations and theories. Make sure these
slides are available to students before class.
Implement techniques to make the lecture structure
more explicit and memorable and to reduce the
cognitive load (e.g., by using repetition, explicitly
stating the structure of the talk early and often,
summarizing the points and making examples that are
relevant to students’ lives and focus areas).
Make learning active and participatory.
Represent key concepts graphically, verbally and
kinesthetically, involving students whenever possible.
Adopt instructional technologies that increase
communication and enhance learning opportunities
(WebCT discussion, clickers, SmartBoards, etc.)
Allow class time for students to work together on
assignments.
Assign note-taking randomly to 5 – 6 students each
week – post their notes on line for all to benefit from.
Post outline of lectures on line (e.g., P.Pt. slides) before
class and allow students to print these notes and add
lecture content to this outline.
Use clicker technology to engage students in lecture
and to gather feedback anonymously as to whether they
are understanding the equations and theories being
presented.
Involve students in demonstrations of equations and
theories, making sure that these activities are pertinent
to students’ lives.
Again, use clicker technology to determine each
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students do not understand
principles well enough to solve
equations on their own.
whether students are understanding the
content of the course until test results reveal
the gaps.
Homework assignments,
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designed to compliment and
reinforce course content, are
turned in at the beginning of
each class. This process takes
several minutes and many
times results in questions about
grading and excuses for late
work.
Students are not understanding the
information provided in the syllabus re:
homework assignments, expectations of
course, grading and consequences for late
work .
Dr. Fredericks is frustrated by
the rates of failure in his
course. He invites students to
come and see him during his
limited office hour times, and
he stays after class for a few
minutes each day. Few
students come to arranged
office hours, fewer make
appointments.
Student feedback is not
positive, with concerns
expressed about the relevancy
of the content to their majors,
difficulty staying awake in
Case Study #1 – Solutions
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Students most likely have jobs, commutes,
and other challenges that prevent them from
coming to limited office hours or staying
after class.
Students may not realize until it is too late
the importance of communicating with their
instructor.
When students are unhappy, the word gets
around. If students feel their concerns are
not being addressed, their attitude about and
performance in the class will be affected.
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day/week whether students are understanding the key
concepts of the course.
Post practice exams online from previous semesters.
Allow students to anonymously fill out a question card
about class content one time each week. Use one class
session each week to read and answer questions.
This gives students information they need and gives
instructor feedback as to whether students understand
the content.
Make course syllabus available on the Web prior to the
first day of class.
Create class activity with FAQs from the syllabus,
facilitating opportunity for students to become familiar
with important information.
Create rubric with class assignments, possible points &
due dates. Include space for students to track their
points & know their grades.
Allow assignments to be submitted online, with
optional date and time limits.
Offer office hours in flexible formats: face-to-face,
email, telephone, etc.
Provide alternative opportunities in and out of class for
students to communicate their questions and concerns
(e.g., FAQs via clickers, weekly question cards, TA
meetings, etc.)
Use online discussion groups to extend “contact time.”
Respond to student feedback. Make course relevant to
their lives and study focus areas. Make efforts to have
class sessions be interesting, relevant and
exciting.Offer flexibility with office hours, including
different times of availability, on-line communication,
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class, and frustration with
limited availability of office
hours.
Case Study #1 – Solutions
and small group discussions, Q & A opportunities and
work sessions.
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