Reaching for the Ideal
Course Through StudentCentered Course Redesign
NCAT’s Redesign Conference 2008
Gary Hagerty (Presenter)
GaryHagerty@bhsu.edu
Stan Smith (Co-Redesign Participant)
StanleySmith@bhsu.edu
Results
By following much of NCAT’s
philosophies, we moved from a
traditional 3 day a week lecture, to a
student centered approach based around
technology beginning in 2004.
Resulting in a 40% cost reduction and
more possible.
Results
•Passing Rate = 83%
•Increased test scores
•Enrolling in Trig after college algebra
•Increased from about 1% to about 6%
•Increased grades in Trig
•Increased acceptance and support
outside the department
Results
Passing rate
80.00%
70.00%
60.00%
50.00%
40.00%
30.00%
20.00%
10.00%
0.00%
2002FA 2003FA 2004FA 2005FA 2006FA
Passing as defined as a “C” or better –
(83% rate is defined as a “D” or better -- )
Results
Test Results 1
CAAP results for students who completed the CAAP Test prior to
beginning the Redesign versus most recent year.
The subgroup of ACT scores of 20-24 were evaluated to remove as
much outside influence as possible. (This group primarily enrolled
only in College Algebra)
ACT
20-24
2001-2002
2006-2007
Ave
n
Ave
n
58.08
110
59.15
115
P
value
0.0009
NOTE: Using a normalcdf – this change is
approximately increasing from the 49.5
percentile to the 61 percentile.
Results
Test Results 2
A Brief look at CAAP results based on Grades in
College Algebra. This examination was to look for
grade inflation with the desire that the Null
Hypothesis: The means of pre and post groups are
equal to be upheld.
Grade 2001-2002
Ave
n
A
61.6
32
B
58.8
55
C
57.2
97
2006-2007
Ave n
61.1 39
59.0 91
57.4 100
P value
0.38
0.58
0.56
Results
Outside Department
Over the last 3 years I've noticed a trend in the increased general level
of mathematical background and preparedness my students have, this has
been esp. noticeable in my genetics course with regard to algebra.
Another interesting (and encouraging!) trend I've noticed over the past 2-3 years
here is what seems to be a greater overall appreciation for mathematics as a field,
and its value and practical benefits in the real world. This is a very interesting and
welcome trend that I hope continues here at BHSU.
It seems whatever you guys are doing in the math program is having positive
effects on many students. In fact , several students over the past 2 years have
specifically commented on the high quality of the several math classes, most
notably algebra.
Dr. Dan Bergey – Biology 11-2007
Results
Outside Department
Due to the revision of the College Algebra course by
the Mathematics Department, I have observed that
the students in my required mathematics courses for
prospective elementary teachers have better
procedural skills, more confidence in their
mathematics ability, and improved problem solving
competence.
Dr. John Alsup – Math Education
12 - 2007
The Redesign
Overview
The redesign has been developed in three parts
and readably fit into most formats of delivery.
The Big Picture
•Theoretical
•Historical
Connections
•Real World Applications
•Group Work
ALEKS
•Traditional Algorithm development
The Redesign
ALEKS
For the Small Picture, we have chosen to use
technology to deliver Traditional Assignments.
Software Choice – ALEKS
•Individualized
•Programmed (mastery) Learning
•Well Designed
The Redesign
ALEKS
Initial Assessment
Number of students
16
14
12
10
8
6
4
2
0
0-2
3-5
6-8
9-11
12-14 15-17 18-20 21-23 24-26 27-29 30-32
33-
Using the initial assessment from ALEKS, we can advise students.
Red – Indicates weak student who may want to consider enrolling in Intermediate Algebra for a refresher. As this group is often
returning students who have been away from math for a while, they can also choose to put in extra effort and catch up.
Yellow – Weak students, who should probably start in a review chapter in a traditional test.
Green – Strong students, who can start at a typical first chapter in College Algebra.
The Redesign
ALEKS
Content
Consider the traditional course.
Time
When looking at the traditional spread of students enrolled in a College Algebra Course
(previous slide), one needs to question the traditional wisdom of a course designed around
every starting on the same assignment and moving at the same speed
The Redesign
ALEKS
After the first Assessment
•Mastery Learning
(Bloom)
•Self-Efficacy
(Bandura)
The Redesign
The Small Picture
Ongoing Assessments keep
Students in their
Zone of Proximal Development
The Redesign
The Small Picture
Intermediate Objectives allow for
the instructor to control the
primary curriculum so that all
students are working in the same
content at the same time.
•Polynomials
•Rational/Inverse/Composition
•Logs and Exponents
•Series and Sequences
•Matrices
The Redesign
The Small Picture
By being Self Paced
ALEKS
Provides a path for recovery
When needed
(A student ends up in the Hospital for a week and another week at home in
bed without being able to work. ALEKS allows us to individualize for this
student and develop a plan to assist the student in gaining the necessary
skills to successfully pass the course)
Stepping Aside
ALEKS
At this point, ALEKS can be used
as a complete program.
Western Missouri State U uses ALEKS as the
sole delivery tool in remedial math courses with
an 80% passing Rate and success in general
education courses at the level of those who place
directly into the general education courses.
Stepping Aside
ALEKS
At this point, ALEKS can be used
as a supplemental program.
Boise State and Louisiana Tech use ALEKS to
support algebra and trig skills in Calculus
Courses, obtaining a 15-20% increase in grades
and continuation rates.
The Redesign
The Big Picture
1/3 Lecture
Based on
•Theory
•History
•See Hagerty, Smith Goodwin, The unique effects of including history in College Algebra. MAA’s
Convergence Journal
http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=1629#discussion
•Usefulness
The Redesign
The Big Picture
The Redesign
The Big Picture
History
Too often, students leave school never realizing that
knowledge is the answers to someone’s prior
questions, produced or refined in response to
puzzles, inquiry, testing, argument, and revision. To
teach from questions means rhetorically asking, “If
knowledge is made up from answers, then what
were the questions that gave rise to textbook or
teacher answers and current subject-matter
knowledge answers?”
-- Understanding by Design
Wiggens and McTighe 1998
The Redesign
The Big Picture
Usefulness
Graph of absorption of a medication into the blood stream
followed by elimination and metabolism of the medication.
Graph is created by a piecewise rational function
The Redesign
The Big Picture
Usefulness
By translating the function on the last page and adding together translated functions we
can look at the level of medication at any time period if the medication is take every four
hours (red) or every two hours (blue). Green line represents the level where the
medication is effective and yellow line represents where the level is toxic.
Question: Is the purpose of mathematics to develop people can remember the quadratic
formula or people who can understand the mathematical concepts when they present
themselves?
The Redesign
APPLICATION
1/3 Group Work
Application
Oriented
The Redesign
APPLICATION
Application were designed after
discussing with others on Campus as
to their needs:
Business – Profit, Loss, Maximum sales. Financial
Models, Prediction models.
Science – Decay, Population Growth (Logistic model)
Psychology, Kinesiology, Education – Behavior Change
The Redesign
APPLICATION
By creating applications with
other departments in mind,
we are working on tearing
down the
compartmentalization boxes.
The Redesign
APPLICATION
A
Curve A represents a profit curve.
Why do we want to find the x-intercepts?
Will a business student recognize that the x-intercepts in this problem are what
will be called “break even points” in business if we continue to teach algebra
in isolation?
The Redesign
A Student Perspective
I did not like math in high school. I could never
understand or remember any of the details to make
the math work or to apply it to anything tangible. I
intended to take College Algebra and be done with
math forever. However, the way that college algebra
was set up allowed me to master every part of the
course and fill in my weak areas. I am now a
mathematics major who is seriously looking into a
career in cryptanalytics. I wouldn't be a math major
today if I'd enrolled in a normal college algebra
course.
Peter Lemke class of 2009
Closing
College Algebra needs to remain a
Gateway Course Because:
Modeling: Polynomial, exponential, logistic
Tools for Understanding:
Polynomials, Exponentials, Series and Sequences
Rational and Logical Thought Processes
Finding zeros
Skills necessary for continuation: both within
math and in other subjects.
Closing
College Algebra needs to
remain a Gateway Course
But
We must unlock the Gate for
all.
Closing
Tools Such as ALEKS and
Redesign allows for the
unlocking of the Gate and all
can push it open!