Integrating Statistics into College Algebra Sheldon P. Gordon gordonsp@farmingdale.edu

Integrating Statisticsinto

College Algebra

Sheldon P. Gordongordonsp@farmingdale.edu

College Algebra and Precalculus

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

The Focus in these Courses

Most college algebra courses were originally

intended and designed to prepare students for

calculus.

Most of them are still offered in that spirit.

But only a small percentage of the students have

any intention of going on to calculus!

Enrollment Flows

Several studies of enrollment flows out of college algebra:

• Only about 10-15% of students in college algebra are in majors that require calculus.

• On the order of 3-5% of the students who start college algebra courses ever start Calculus I

• About 10-12% of those who pass college algebra ever start Calculus I

Who Are the Students?

Based on the enrollment figures, the students

who take college algebra and related courses

are not going to become mathematics majors.

They are not going to be majors in any of the

mathematics intensive disciplines.

Why Students Take These Courses

• Required by other departments

• Satisfy general education requirements

• For a few, to prepare for calculus

Curriculum Foundations Project

A series of 11 workshops with leading educators from 17 quantitative disciplines to inform the mathematics community of the current mathematical needs of each discipline.

The results are summarized in the MAA Reports volume: A Collective Vision: Voices from the Partner Disciplines, edited by Susan Ganter and Bill Barker.

Common Themes from All Disciplines

• Strong emphasis on problem solving

• Strong emphasis on mathematical modeling

• Conceptual understanding is more important than skill development

• Development of critical thinking and reasoning skills is essential

Common Themes from All Disciplines

• One overriding recommendation from all the disciplines was for a greater emphasis on statistical reasoning.

• Most courses for non-majors (and even those for majors in some areas) make almost no use of mathematics in class. Math arises almost exclusively in the lab when students have to analyze data and this is where their weak math skills are dramatically evident.

What Students Really Need from Math

• The ability to make sense of data – to interpret graphs and tables

• Statistical measures of data• Estimating the mean of a population from a sample

The Curriculum Problems We Face

• Students don’t see college algebra as providing any useful skills for their other courses. •At most schools, college algebra is the prerequisite for introductory statistics.• Introductory statistics is already overly crammed with too much information.• Most students tend to put off taking the math as long as possible. So most don’t know any of the statistics when they take the courses in other fields.

Some Ideas for College Algebra

Data is Everywhere! We should capitalize on it.

1. A frequency distribution is a function – it is an effective way even to introduce and develop the concept of function.

2. Data analysis – the idea of fitting linear, exponential, power, polynomial, sinusoidal and other functions to data – is already becoming a major theme in some college algebra courses. It can be the unifying theme to link functions, the real world, and the other disciplines.

Some Ideas for College Algebra

3. The normal distribution function is

2 2( ) / 21

2( ) xN x e

It makes for an excellent example involving both stretching and shifting functions and a function of a function.

Some Ideas for College Algebra 4. The z-value associated with a measurement x is a nice application of a linear function of x:

xz

Some Ideas for College Algebra

5. The Central Limit Theorem is another example of stretching and shifting functions -- the mean of the distribution of sample means is a shift and its standard deviation,

produces a stretch or a squeeze, depending on the sample size n.

xn

Some Conclusions

Mathematics is a service department at almost all institutions. Few, if any, math departments can exist based solely on offerings for math and related majors.

And college algebra and related courses exist almost exclusively to serve the needs of other disciplines.

Some Conclusions

If we fail to offer courses that meet the needs of the students in the other disciplines, those departments will increasingly drop the requirements for math courses. This is already starting to happen in engineering.

Math departments may well end up offering little beyond developmental algebra courses that serve little purpose.