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### Academic Affairs Workshop:Mathematics

Quantitative Literacy

Articulation

and Assessment

Bonnie Gold, Monmouth University

bgold@monmouth.edu

Overview

- Does Quantitative Literacy = Statistical Literacy?
- Why should mathematics departments care about quantitative literacy?
- What mathematics should every college graduate know?
- How can we make articulation less of a burden?

Where I’m coming from

- 20 years at Wabash College, Indiana
- Came to Monmouth in 1998 as chair
- Chaired MAA’s Committee on the Teaching of Undergraduate Mathematics
- Member, MAA’s Committee on Articulation and Placement
- Co-chairing MAA’s Assessment committee (and co-editor of 2 books on assessment)
- Member, MAA Committee on Professional Development

My prejudices, upfront

- “College Algebra” is a holdover from the time when students took one year of algebra in high school
- The “traditional” college algebra is not an appropriate quantitative literacy course
- BUT some people (e.g. Don Small) have done significant revisions that are appropriate
- The last course a student takes in a subject should never be named “pre...”

Where YOU’re coming from

- As with many states, your schools vary dramatically
- Several NH schools have done significant work on QL: Colby-Sawyer, Keene State
- Some have no math majors: all mathematics taught is for general education or service toward another major
- There are issues of articulation between schools

Where YOU’re coming from (I think)

- Chief Academic Officers LOVE assessment
- Mathematicians HATE assessment (except what we do in our own courses for our own purposes)
- This workshop aims to build bridges and communication:
- between mathematicians and CAOs
- between mathematicians at different institutions

Assessment and Redesigning Courses

- Assessment cycle begins with looking at your program goals
- These will differ among colleges and universities due to different missions, different types of incoming students
- Are there commonalities?

What is Quantitative Literacy?

The ability to adequately use elementary mathematical tools to interpret and manipulate quantitative data and ideas that arise in an individual’s private, civic, and work life.

Like reading and writing literacy, quantitative literacy is a habit of mind that is best formed by exposure in many contexts.

(From SIGMAA QL’s web page, http://sigmaa.maa.org/ql/about.php)

Why should mathematics departments care about QL?

- Do you want your students to leave your school hating/fearing mathematics, or feeling it’s important and within their grasp?
- They need to be able apply critical thinking to news reports involving mathematics/statistics
- They vote, and sometimes become legislators!

Quantitative Literacy

- Hitting students over and over with what they didn’t learn in high school isn’t advancing quantitative literacy
- “You can be educated in calculus and be uneducated in quantitative literacy” – Milo Shields, Augsburg College, director of the W.M. Keck Statistical Literacy Project (quoted in L.A. Times editorial, “But Who’s Counting”)
- Every college graduate should be able to apply simple mathematical methods to the solution of real-world problems

Does Quantitative Literacy = Statistical Literacy?

- There is no national agreement
- Carleton: QUIRK: Quantitative Inquiry, Reasoning and Knowledge Initiative takes a statistical approach
- The alternative is a modeling approach: for example, Don Small at West Point

QUIRK: 10 Foundational Quantitative Reasoning Questions

I. What do the numbers show?

- What do the numbers mean?
- Where are the numbers?
- Is there numerical evidence to support a claim?
- What were the exact figures?
- How can seeking and analyzing numbers illuminate important phenomena?
- How plausible is a possibility in light of back of the envelope calculations?

QUIRK: 10 Foundational Quantitative Reasoning Questions

II. How representative is that?

- What's the central tendency?
- "For instance is no proof."
- Mean, Mode, and Median.
- Interrogating averages:
- Are there extreme scores?
- Are there meaningful subgroups?
- Who's in the denominator?
- What's the variability (standard deviation)?
- What are the odds of that? What's the base rate?

QUIRK: 10 Foundational Quantitative Reasoning Questions

III. Compared to what?

IV. Is the outcome statistically significant?

V. What's the effect size?

VI. Are the results those of a single study or of a literature?

VII. What's the research design (correlational or experimental)?

VIII. How was the variable operationalized?

IX. Who's in the measurement sample?

X. Controlling for what?

Modeling approach

From Don Small’s talk,

“Refocused College Algebra – A Basis for Quantitative Literacy”

at Northeast Consortium on Quantitative LiteracyColby – Sawyer College, May 17, 2008

(used with permission)

Traditional College Algebra question

“Data from the U.S. Department of Health and Human Services indicates that the cumulative number N of reported cases of AIDS in the United States in year x can be approximated by the equation ,

N = 3,362.1x2 - 17.270.3x +24,032

where x = 0 corresponds to 1980.

In what year did the total reach 550,000?”

Straightforward quadratic equation exercise

A “refocused” version of this exercise would have the students:

- a. Develop a model (give or direct the students to the data, have them form a scatter plot of the data, and then fit a curve to the scatter plot).
- b. Answer the question: In what year did the total reach 550,000?
- c. Interpret the model and the answer to the question. (E.g., is the answer reasonable? Why? Is the model reasonable? Why? Does the model show any intervention effects? For what span of years is the model reasonable? Explain.)

QL Resource: RWLO

- Real World Learning Objects Resource Library:
- an online repository of Internet-based unique and compelling learning objects designed so that community college faculty can easily access and adapt for use in their classes
- http://www.ciese.org/pathways/rwlo/search.php
- Developed for the PT3 Community College Pathways to Improved Teacher Preparation through Technology Project (Pathways) with funding from the U.S. Department of Education

Problem-solving paradigm:

- Sketch and label a picture where appropriate
- Define variables
- List or display the pertinent information
- List assumptions
- Clearly state what the problem is asking.

Exploratory Learning

How do we teach students to

- Learn from a text?
- Question?
- Penetrate below the surface level when reading?
- Identify critical ideas?
- Challenge conclusions?
- Identify underlying assumptions?
- Identify domains of applicability?

Quantitative Literacy Goals

- Students become aware that a wide range of issues for today’s citizens involve mathematics and statistics
- Students gain confidence in their ability to consider these issues without avoiding the mathematics involved
- Students gain confidence in their ability to approach problems involving mathematics

Quantitative Literacy Goals

A quantitatively literate college graduate should be able to:

- Interpret mathematical models such as formulas, graphs, tables, and schematics, and draw inferences from them.
- Represent mathematical information symbolically, visually, numerically, and verbally.
- Use arithmetical, algebraic, geometric and statistical methods to solve problems.
- Estimate and check answers to mathematical problems in order to determine reasonableness, identify alternatives, and select optimal results.
- Recognize that mathematical and statistical methods have limits.

(From Quantitative Reasoning for College Graduates, MAA Report, 1994)

QL Content: best practices

- A required course or two is not sufficient.
- Students need a broad program that instills certain “long-term patterns of interaction and engagement.”
- This starts with a “foundation experience” to raise entering students’ proficiency.
- Then a “continuation experience”, a “framework of mathematics across the curriculum, an array of courses (both within and outside mathematics).”

QL Methodology: Best practices

- Shift the responsibility for student learning from the instructor to the student
- Active learning: students engaging in problem-solving
- Students must find the problems interesting (whether pure mathematics or from a real-world context
- Problems must be within the students’ reach (with a stretch!)

To do this requires small classes, faculty with strong backgrounds, and release time for course development

Model QL programs

- At the Richard Stockton College of NJ

all students must complete three quantitative-reasoning-designated courses:

- At least one Quantitative-Reasoning-Intensive course
- At least one Quantitative-Reasoning-Across-The-Disciplines
- At Colby-Sawyer, QL starts with a mathematics course, and is reinforced by modules developed for a wide range of course across the curriculum

At Monmouth

- MA100 Mathematical Reasoning and Problem Solving
- MA105 Mathematical Modeling in the Social Sciences
- MA115 Mathematical Modeling in the Biological Sciences
- MA117, 118 Quantitative Analysis for Business
- MA125, 126 Calculus I, II
- MA203, 204 Foundations of Elementary Mathematics

Monmouth Math Gen Ed Outcomes

- Recognition of the role of mathematics in society: Students will demonstrate an understanding of various mathematical relationships and their applications in real-world problems
- Mathematical modeling: Students will demonstrate the ability to read a story problem, determine relevant variables and constants, and describe the mathematical relations among the variables.
- Problem solving: Students will demonstrate the ability to use algebraic, geometric, numerical, graphical, and/or statistical methods to solve problems, including via technology
- Model verification: Students will demonstrate the ability to estimate and check answers to mathematical problems in order to determine reasonableness, identify alternatives, and select optimal results.
- Interpreting results: Students will demonstrate the ability to interpret, evaluate, and draw inferences from, answers, graphs and data in terms of the language of the problem.

Articulation

- States vary enormously in their statewide expectations, both in mathematics and for articulation

In NJ, Lampitt bill, passed in 2006, took effect in 2008:

- A.A. / A.S. degree from NJ community college fully transferable as first two years at New Jersey public four-year institutions
- Such transfer students will be considered to have completed all lower division General Education requirements

NJ Articulation Conference 2008

- Found wide variation at the intermediate algebra/college algebra level
- Some difference in the math major, with differential equations and linear algebra
- Also some schools offer “transition to proof” courses at various levels
- Discussion of what to do with D in prerequisite courses
- Discussion of mathematics needed by future elementary teachers
- Distinction between students in math-intensive and non-math intensive majors

Take-home concerns for faculty

- It takes work to develop a good quantitative reasoning program
- This starts with rethinking your goals
- Many existing courses may be used, often with modifications
- Because of articulation issues, it requires working with other schools

Take-home concerns for administrators

- Good quantitative literacy programs require small classes for active learning
- Faculty need some release time to develop such courses, and support to work with faculty from other schools
- Faculty need professional development to teach these courses, especially new and adjunct faculty

Some QL resources

Publications and reports:

- 2008 Calculation vs. Context: Quantitative Literacy (PDF Format)
- 2006 Current Practices in Quantitative Literacy (MAA Bookstore)
- 2004 Achieving Quantitative Literacy: An Urgent Challenge for Higher Education. (MAA Bookstore)
- 2003 Quantitative Literacy: Why Numeracy Matters for Schools and Colleges. (MAA Bookstore)(PDF Format)
- 2001 Mathematics and Democracy: The Case for Quantitative Literacy. (MAA Bookstore)(PDF format)
- 1997 Why Numbers Count: Quantitative Literacy for Tomorrow's America. (The College Board)
- 1994 Quantitative Reasoning for College Graduates. (Report of an MAA Committee)

More QL resources

- MAA's Special Interest Group on Quantitative Literacy (sigmaa.maa.org/ql)
- National Numeracy Network (http://serc.carleton.edu/nnn/)
- Selected Quantitative Literacy Programs in U.S. Colleges and Universities (PDF)
- http://www.stockton.edu/~quad/index.htm
- W.M. Keck Statistical Literacy Project (www.augsburg.edu/statlit/)
- http://www.colby-sawyer.edu/academics/experience/quantitative/resources.html

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