Reaching for the Ideal Course Through Student-Centered Course Redesign

NCAT’s Redesign Conference 2008Gary Hagerty (Presenter)GaryHagerty@bhsu.eduStan 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

ResultsPassing rate

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

2002FA 2003FA 2004FA 2005FA 2006FA

Passing as defined as a “C” or better – (83% rate is defined as a “D” or better -- )

ResultsTest Results 1

NOTE: Using a normalcdf – this change is approximately increasing from the 49.5 percentile to the 61 percentile.

ACT 2001-2002 2006-2007 P value

Ave n Ave n

20-24 58.08 110 59.15 115 0.0009

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)

ResultsTest 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 2006-2007 P value

Ave n Ave nA 61.6 32 61.1 39 0.38B 58.8 55 59.0 91 0.58C 57.2 97 57.4 100 0.56

ResultsOutside 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

ResultsOutside 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

ALEKSInitial Assessment

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

Time

Con

ten

t

Predetermined Course Pace

Consider the traditional course.

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 RedesignThe Small Picture

Ongoing Assessments keep Students in their

Zone of Proximal Development

The RedesignThe 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 RedesignThe Small Picture

By being Self PacedALEKS

Provides a path for recoveryWhen 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 LectureBased 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

HistoryToo 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

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?

A

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, logisticTools for Understanding:

Polynomials, Exponentials, Series and Sequences

Rational and Logical Thought Processes

Finding zerosSkills necessary for continuation: both within math and in other subjects.

Closing

College Algebra needs to remain a Gateway Course

ButWe 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!