Time for Change in College Algebra

Reza O. Abbasian and John T. SiebenTexas Lutheran University

Each year, more than 1,000,000 students take college algebra and related courses [1].

1. Lutzer, David J., James W. Maxwell, and Stephen B. Rodi, 2000 Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States, MAA Reports, MAA (2002), Washington, DC.

Lots of students take College Algebra

College Algebra History:

When college algebra and pre calculus courses were originally created, they were designed with the goal of preparing many of the, at that time, weaker students to go on to calculus in the sense of developing those algebraic skills that were necessary for success in calculus. [2]

2. WHAT’S WRONG WITH COLLEGE ALGEBRA?Sheldon P. Gordon, Professor of Math, SUNY Farmingdale August 2005United University Professions, Working Paper Series 2005

Does College Algebra get students into Calculus?

Steve Dunbar has tracked over 150,000 students taking mathematics at the University of Nebraska – Lincoln for more than 15 years[3]. He found that:

• only about 10% of the students who pass college algebra ever go on to start Calculus I

• about 30% of the students who pass college algebra eventually start business calculus.

3. Herriott, Scott and Steve Dunbar, Who Takes College Algebra?, PRIMUS, 2009.

William Waller at the University of Houston – Downtown tracked the students from college algebra in Fall 2000. Of the 1018 students who started college algebra[4]:

•only 39, or 3.8%, ever went on to start Calculus I at any time over the following three years.

4. Waller, William, Tracking Students from College Algebra, (unpublished manuscript).

The Fall, 2001 there were 1028 students in the college algebra cohort at the University of Houston – Downtown. Of the 1028 students who started college algebra:

•only 2.8%, ever went on to start Calculus I at any time over the following three years.

What then should be the role or roles of college algebra?

If it is to be a stepping stone into calculus, then the traditional course must change as presently 10% or less of its students successfully complete calculus I.

From Don Small, U.S. Military Academy, West Point, NY 10996

If college algebra is to be a service course in terms of satisfying distribution requirements, then it must change to emphasize applications across the disciplines.

From Don Small, U.S. Military Academy, West Point, NY 10996

If it is to be a mathematics appreciation course, then it must change to emphasize student involvement in problem solving and discovery.

From Don Small, U.S. Military Academy, West Point, NY 10996

We take the position that college algebra has become a service course that in large measure serves the non STEM students at the University.

Very few students in the partner disciplines will need to factor anything as complicated as x8 - y8. However,

virtually all of them will need the ability to

• examine a set of data and recognize a behavioral pattern in it,

• assess how well a given functional model matches the data,

• recognize the limitations (often due to uncertainty) in the model,

• use the model to draw appropriate conclusions, and

• answer appropriate questions about the phenomenon being studied.

To achieve these goals the following knowledge and skills seem essential:

•A deep understanding of the function concept, function notation, and the meaning of variable.•A knowledge of different families of functions, including the ability to distinguish between the different families graphically, numerically and algebraically.

•The ability to select the appropriate tool, be it pencil-and-paper, graphing calculators, spreadsheets, or CAS system, to solve the equations that arise from using the models.

•The ability to interpret the mathematical results and to communicate these ideas to others.

The MAA has been involved in an examination of the appropriate role of College Algebra in the modern university curriculum

“Voices of the Partner Disciplines” is a report from a series of disciplinary workshops organized by the Curriculum Renewal Across the First Two Years (CRAFTY) subcommittee of the Committee for the Undergraduate Program in Mathematics (CUPM)

© 2004 by The Mathematical Association of AmericaEdited by Susan L. Ganter, Clemson University andWilliam Barker, Bowdoin College

Across the country, between November 1999 through February 2001 eleven workshops were held. Each workshop involved 20 to 35 participants, mainly chosen from the discipline under consideration. Each workshop was a dialogue between members of the partner discipline [3] with mathematicians present only to listen and serve as a resource.

3.Partner disciplines include biology, business and management, chemistry, computer science, engineering, health science, physics, and teacher preparation.

A few recommendations from this report follow:

Students need to understand• meaning and use of variables, parameters, functions and relationships•how to formulate linear, exponential and logarighmic functions from data or general principles•graphical representation of data in a variety of formats•the use of realistic data sets from the partner disciplines•the use of appropriate technology

TechnologyIt was suggested in more than one workshop that the graphing calculator was not the tool of choice in the disciplines. The use of computers is preferred and the use of the Excel Spreadsheet was mentioned several times.

We have started using Excel because:

•Our partner disciplines are Excel users•Excel is powerful and does the job for us•students bring many different calculators, making instruction difficult•students say they can't afford the book, let alone a new calculator•the University furnishes lots of computers with Excel•And most students have their own computers with Excel installed

The report also offers observations on instructional techniques

“Use a variety of teaching methods since different students have different learning styles. In particular, encourage the use of active learning, including

•In class problem solving opportunities•Class and group discussion•Collaborative group work, and•Out of class projects

Colleagues in partner disciplines support the need for alternatives to traditional lecture courses, which brings us to the final part of our experiment.

March 11, 2012

Sal Khan

The Khan Academy

Sal Khan (with the support of Bill Gates) has recorded over three thousand five to ten minute lessons on arithmetic, algebra, elementary calculus, etc.

What Sal has not covered we can offer ourselves

The professor assigns the lessons in a logical sequence. The student watches the lesson outside of class. Note that the student can watch the lesson as many times as necessary.

In class the professor supervises group work on practice sets and projects

The traditional format of “in class lesson” followed by “out of class practice” is turned on its head. The lesson is out of class, the practice and application is done in a classroom with the professor as resource.

Elementary and Secondary Schools have reported improvements in student success. There is no reason why we can’t make this work for our students as well.

We are currently teaching two sections per semester of an algebra course based on functions, data, and modeling. This course implements the majority of the suggestions we presented in this paper. Over the summer we will incorporate the practices of the Khan Academy and will report to you next year on our progress.

Thank you,Reza and John