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Defining and Implementing Quantitative Literacy Programs

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Defining and Implementing Quantitative Literacy Programs

Rick Gillman

Valparaiso University

“You know it when you see it.”

A Definition Perspective

A Problems Perspective

A Curriculum Perspective

A Syllabus Perspective

And, last, my Perspective

Every college graduate should be able to apply simple mathematical methods to the solution of real-world problems. The college graduate should be expected to have deeper and broader experiences than those who only graduate from high school and that the level of sophistication and maturity of thinking expected should extend to reasoning which is commensurate with the college experience.

- elements of QL such as: confidence with mathematics, cultural appreciation, interpreting data, logical thinking, making decisions, mathematics in context, number sense, practical skills, prerequisite knowledge, and symbol sense;
- areas of life utilizing expressions of QL, such as: citizenship, culture, education, professions, personal finance, personal health, management, and work; and,
- skills needed for QL, such as: arithmetic, data, computers, modeling, statistics, chance, and reasoning

Quantitative literacy (QL) can be described as the ability to adequately use elementary mathematical tools to interpret and manipulate quantitative data and ideas that arise in individuals’ private, civic, and work lives. As with reading and writing literacy, quantitative literacy is a habit of mind that is best formed by exposure in many contexts.

Suppose that the United States government decided to institute a national lottery, the proceeds of which would be used to retire the federal debt. Based on information that you gather about lottery finances, estimate how much money could be raised (after expenses and prizes) each week in a national lottery. How long would it take to pay off the federal debt assuming that the budget is exactly balanced every year in the future? Do you feel that this is a feasible strategy to pay off the federal debt?

The following ballot initiative appeared before Colorado voters in 1992:

Shall there be an amendment to the Colorado constitution to prohibit the state of Colorado and any of its political subdivisions from adopting or enforcing any law or policy which provides that homosexual, lesbian, or bisexual orientation, conduct, or relationships constitutes or entitles a person to claim any minority or protected status, quota preferences, or discrimination?

What does a yes vote mean?

In the November 25, 2003 edition of the Boston Globe, an article ran with the headline “Colleges trail prisons in funds”. The following is taken from that article.

“For the first time in 35 years, Massachusetts is spending more on prisons and jails than on public higher education, according to a report released yesterday. (The 2004) state budget included $816 million in appropriations for campuses and student financial aid, and $830 million for prisons and jails, said the report from the Massachusetts Taxpayers Foundation. Deep cuts to state spending on higher education have left the system of state colleges and universities in ‘profound’ disarray, the report said, citing two eras of deep cuts that reduced state support to the same level as three decades ago when adjusted for inflation. Higher education appropriations were cut 29 percent between 1988 and 1992, and 27 percent between 2001 and 2004. Spending on higher education dropped from 6.5 percent of the state budget at its peak in fiscal 1988 to less than 3.5 percent for the 2004 fiscal year, the report said.”

Using information in the article, find the following:

What was the amount budgeted by the legislature for higher education in 2004?

Estimate the total state budget in 2004. Show your work.

The portion of the state budget allocated for higher education has decreased from ______ % in fiscal 1988 to ______% in fiscal 2004. Calculate the relative (percentage) change in the portion allocated to higher education between fiscal 1988 and fiscal 2004 and then write your answer using a complete sentence. Show your work.

American Social History

The core of the program is a two-tiered system consisting of a “foundations” course usually taken during the first or second year and “infusion” or applied courses taken in the latter years of undergraduate study. It is anticipated that the foundation course or courses would usually, but not necessarily, be offered by the mathematics department. The courses in the second tier of the program would be offered by disciplines outside of mathematics (frequently within the student’s majors) which would utilize the foundational skill previously developed toaddress problems of interest to the students in context.

- QS courses seek to instill basic competence in statistics: sampling, data organization and representation, measures of central tendency, measures of dispersion, and elementary probability concepts.
- QM courses offer an understanding of mathematics: including such topics as percentages, ratios, proportionality, rates of change, linear functions and systems in two unknowns, but the true essence is a combined algebraic, graphical, and numerical approach to problem solving andan emphasis on word problems.”

- Chance: statistical hypothesis testing, sampling, experimental design, measures of correlation.
- Change: percentages and rates; marginal versus average rates; linear versus exponential growth; importance of units; estimation.
- Trade-offs: cost/benefit and cost/effectiveness analysis; other mathematical techniques for comparison.

- Week 1: Absolute and Relative Quantities; Introduction to Excel
- Week 2: Estimation and Percentages
- Week 3: Making and Interpreting Graphs
- Week 4: Applied Interdisciplinary Module
- Week 5: Introduction to Mathematical Modeling and Linear Models in Particular
- Week 6: Exponential Modeling
- Week 7: Basic Descriptive Statistics and Correlation
- Week 8 and 9: Additional Applied Module or Modules
- Week 10: Presentations

QMPPS syllabus

- unit analysis
- interpretation of charts & graphs
- proportional reasoning
- counting principles
- general percents
- percent increase or decrease
- the use of mathematical formulas
- average
- exponential growth

(or, more accurately, my observations and conclusions about the status of the QL movement.)

- Large Schools: a course in the math dept
- Mid size schools: an array of specified courses
- Liberal Arts: Integrated coursework (mostly) in the social sciences.

- Technical schools have high end expectations (Farmindale)
- Liberal Arts, selective (Macalester)
- Open enrollment public (U Mass)

- Elementary Logic
- Finance and Interest
- Descriptive Statistics
- Finite Probability
- Change
- Modeling w/ linear and exp. ftns
- Estimation and Approximation
- Problem Solving

- How much can actually be done in a math course?
- Do students completing a calculus course have these skills and apply them?
- How is a QL course distinct from a Liberal Arts math course?

There are no benchmark standards for achievement at any level.

How do we assess QL achievement across disciplines?

Thank you.