Teaching Quantitative Reasoning with the News
PNW-MAA NExT 2010
Quantitative LiteracyIs Necessary For:
• Personal welfare and quality of life– Health,– Safety– Financial Planning
• Our collective well being– Social decission making– Functioning of democratic society
Carefully lifted from:Achieving Quantitative Literacy by Lynn Steen
BUT….
• Many educated adults remain functionally innumerate– This hasn’t changed in 25+ years.– There is a noticeable “gap” for minority groups
More (algebra?), Trig and Calculus Is not the answer!!
Rather,…
We need to give students the tools to• Think for themselves,• Ask intelligent questions of experts, and to• Confront authority confidently
Politely borrowed fromMathematics and Democracy
How?
Assumption: much of our information comes from reading/listening/watching the news.
So…
Design a course to develop the power and habit of mind to search out quantitative information, critique it, reflect upon it, and apply it to one's public, personal, and professional life.
Q: Can a college level mathematics class be designed around the critical analysis of
newspaper articles?If “no”, then….Done.If “yes”, then
• How to design the course?• How to get the articles and study questions?• What topics/skills could be covered?• What topics/skills would not be covered?
1. Look through some newspapers to find articles which deal with quantitative information.
2. Discuss answers to the above two questions.
Example 1Working with large numbers
How Big is 1 trillion?(or any other large number)
Comparing using ratios, percents, units which make sense.
Example 2
Tax Rates
Comparing numbers: units
Arkansas Democrat-Gazette - June30, 2003Taxpayer airs his woes Re the letter that Roger Bresnahan of Hot Springs Village: I’m one of theses people who make less than $30,000 a year. I pay almost $5,000 a year in federal income tax. He says a person making $200,000 a year pays $53,000 in federal tax a year. So, my friend, a person [making] $30,000, pays $6 on $1,000: a person making $200,000 pays $3.77 on $1,000. I wish I was one of those unlucky people paying $53,000 [so] I could also take my family out to eat every night and put it on an expense account. Oh, woe is me.
BOB MASSERYLittle Rock
Arkansas Democrat-Gazette – July 9, 2003Taxes confuse everyone Re Bob Massery”s letter and his observation that he, paying almost $5,000 federal income tax on $30,000 income, paid $6 per $1,000 and someone else, paying $53,000 on $200,000 income, paid only $3.77 per $1,000: I think his numerators and denominators are mixed up. He paid $1 tax for every $6 income. The other person paid $1 tax for every $3.7 income. Figuring taxes is enough to confuse any of us, regardless of income.
ANN PIERCEPine Bluff
Arkansas Democrat-Gazette – July 10, 2003Way off on his point Re the letter from Bob Massery of Little Rock on his taxpayer woes: Who taught this man math? He says since he make $30,000 a year and pays $5,000 in taxes, he pays $6 on $1,000, while a guy making $200,000 and paying $53,000 in taxes is paying only $3.77 on $1,000. Let me redo the math for him. He is paying $166.67 per $1,000 in taxes and the rich guy is paying $265 per $1,000 in taxes. Not only is his math way off, he is way off on his point that the rich man pays a lower tax rate. Depending on the size of Massery’s family, he probably is getting most of the tax back as a refund – unless he’s using the same style math on his tax return as he did in his letter.
PHILLIP BASINGERSpringdale
Arkansas Democrat-Gazette – July 15, 2003Correcting tax figures Re the letter from Bob Massery, “Taxpayer airs his woes”: I am sure that Massery’s heart is in the right place, but his math is not. He claims that a person making $30,000 a year pays federal taxes of $6 on every $1,000 of income and that his tax bill is $5,000. He claims that a person making $200,000 a year pays federal taxes of $3.77 on every $1,000 of income and his tax bill is $53,000. His implication is that all of this is unfair. Let’s do the math correctly and see what’s fair. I will use the numbers he provided in his letter. Five thousand dollars of taxes on $30,000 of income is not $6 per $1,000, it is $166.67 per $1,000. That represents 16.7 percent of that person’s income. Fifty-three thousand dollars of taxes on $200,000 is not $3.77 per $1,000, it is $265 per $1,000. That represents 26.5 percent of that person’s income. Fair or unfair? Depends on whom you ask. However, if we are to debate the relative merits of this or that tax code proposal, let’s at least start with correct numbers.
BILLY HERRINGTONMaumelle
Example 3
Language
Comparing numbers: percents (numerators and denominators) , graphics
Men ages 16 to 24 who were incarcerated in 2006-7High school dropouts: ____ %High school students: ____High school graduates: ____1 to 3 years of college: ____College students: ____B.A. degree or higher: ____
Male high school dropouts ages 16 to 24 who were incarcerated in 2006-7Black: ____%Asian: ____White: ____Hispanic: ____
Study Finds High Rate of Imprisonment Among DropoutsBy SAM DILLONPublished: October 8, 2009
On any given day, about one in every 10 young male high school dropouts is in jail or juvenile detention, compared with one in 35 young male high school graduates, according to a new study of the effects of dropping out of school in an America where demand for low-skill workers is plunging.
Example 4
Comparing numbers: dollars (and politics)
PERSONAL BUDGET
INFLATION/BUYING POWER
% OF SALARY
Example 5
Comparing numbers: risk (relative, absolute)
Personal health: false positives, survival rates v. death rates
The Great Prostate Mistake
The annual bill for P.S.A. screening is at least $3 billion, with much of it paid for by Medicare and the Veterans Administration.
American men have a 16 percent lifetime chance of receiving a diagnosis of prostate cancer, but only a 3 percent chance of dying from it.
… testing could detect 3.8 percent of prostate cancers.
The results from the American study show that over a period of 7 to 10 years, screening did not reduce the death rate in men 55 and over.
By RICHARD J. ABLINPublished: March 9, 2010
Survival Rates?
Personal Anecdotes?
