Quantitative Literacy at MSU

Dennis Gilliland Vince Melfi November 3, 2009 November 3, 2009 STT Colloquium 1

People

• QL Group: DG, VM, Jennifer Kaplan, Alla Sikorskii, Ed Corcoran, Nicole Johnson • Scientific Reasoning Group: Diane Ebert May, Megan Donahue, Gabe Ording • Doug Estry • Funding from the Office of the Provost’s Quality Fund November 3, 2009 STT Colloquium 2

Today’s talk

• Background and history • An ongoing study of QL at MSU • Preliminary data from the study • Conditions of the assessments • Possible implications November 3, 2009 STT Colloquium 3

What is Quantitative Literacy?

• Various definitions in the literature • Verbal literacy is a much older concept, and much studied • Can think of QL as the quantitative analogue of verbal literacy • Another term: Numeracy November 3, 2009 STT Colloquium 4

What is Quantitative Literacy?

• Verbal Literacy: – Many components (grammar, vocabulary, context, …) – Many possible levels • Quantitative Literacy – Many components (arithmetic, algebra, geometry, statistics, reasoning, context, …) – Many possible levels November 3, 2009 STT Colloquium 5

What we’re up against

• “I confess to be one of those people who hate math. I can do my basic arithmetic all right (although not percentages)…” • “Here's the thing, Gabriela: You will never need to know algebra. I have never once used it and never once even rued that I could not use it.”

Richard Cohen, Washington Post syndicated columnist

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QL Task Force at MSU

• Met during 2004-2005 • Final Report: January 2005 (available on MSU academic governance web site) • Members from across the University including Jon Hall, Cliff Weil, Karen King (MTH), Dennis Gilliland (STT) November 3, 2009 STT Colloquium 7

Task Force: QL Levels

•

Prerequisite Knowledge Students should enter with this knowledge

•

Quantitative Literacy Foundation Students should obtain this by junior year

•

Applied Quantitative Literacy Within the student’s major

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Assessing QL

• Wanted to assess QL of current and incoming MSU students • Some relevant assessments already in place: – ACT and SAT scores – Math Placement Exam • Did not want to redo these assessments November 3, 2009 STT Colloquium 9

Assessing QL

• Created a multiple choice assessment • Aimed for broad coverage of skills • Mainly assessed skills at the prerequisite level • No calculators (more on this later?) • Approximately 25-30 minute session November 3, 2009 STT Colloquium 10

The (ongoing) study

• New students: Approximately half of 2008 AOP participants and (almost) all 2009 AOP participants • Current students drawn from a variety of majors, class levels, etc. • Covariates from SIS data: demographic, academic, etc. Not easy to obtain November 3, 2009 STT Colloquium 11

The (ongoing) study

• Data from ~10,000 AOP students – 6448 consenting (most non-consenters were under 18) – No SIS data from non-consenting students • Data from ~1350 current students – 1284 consenting – Many majors: Math, Stat, English, etc.

– Many levels of mathematical and statistical knowledge November 3, 2009 STT Colloquium 12

Other assessments

Assessment Coeff. Of Determ. (R 2 )

ACT Math Math Placement ACT English ACT Science ACT Reading HS GPA 0.261

0.163

0.133

0.089

0.070

0.062

NOTE: All correlations are positive November 3, 2009 STT Colloquium 13

Example QL Item on Volume

A homeowner would like to determine whether his truck can carry the weight of a cubic yard of topsoil. He estimates that the maximum weight of a cubic foot of topsoil is approximately 100 pounds. What would he calculate as the maximum weight, in pounds, of a cubic yard of topsoil?

(a) 300 pounds (b) 900 pounds

(c) 2700 pounds

(d) 1200 pounds (e) Can not be computed with the information given.

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Example QL Item on Volume

In-coming students

(2008) – 24.3%

On-campus classes

Low math prereq – 10.3%, 21.4%, 21.5% Low math prereq from elite program – STT 200 (algebra prereq, many majors) – 20.6% 23.9% STT 315 (business majors with calc prereq) – Freshman comp sci with concurrent calc req – Math and Stat undergrad majors – 23.1% 52.4% 61.3%

(Guessing: 20%)

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Example QL Item on Volume

Some relevant GLCEs and HSCEs:

• M.PS.

• M.UN.

• M.UN.

• (HS) • (HS) 05 05 06 .10 Solve applied problems about volumes of rectangular prisms using multiplication and division and using appropriate units. .02 Know the units of measure of volume: cubic centimeter, cubic meter, cubic inches, cubic feet, cubic yards, and use their abbreviations (cm3, m3, in3, ft3, yd3).

.01 Convert between basic units of measurement within a single measurement system, e.g., square inches to square feet.

L2.3.1 Convert units of measurement within and between systems; explain how arithmetic operations on measurements affect units, and carry units through calculations correctly. G1.8.1 Solve multistep problems involving surface area and volume of pyramids, prisms, cones, cylinders, hemispheres, and spheres.

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Example QL Item on Rate

The figure below gives the rate at which water is entering or leaving a reservoir over a period of seven hours. A positive rate indicates that water is entering the reservoir, while a negative rate indicates that water is leaving the reservoir. During the period between 5 and 6 hours, the volume of water in the reservoir is a. increasing

b. decreasing

c. not changing d. Can not be determined from the information given.

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Example QL item on Rate

In-coming students

– 27.4%

On-campus classes

Low math prereq – Low math prereq from elite program – 25.6%, 21.4%, 27.7% 27.4% STT 200 (algebra prereq, many majors) – STT 315 (business majors with calc prereq) – Freshman comp sci with concurrent calc req – Math and Stat undergrad majors – 33.9% 47.5% 52.0% 54.8%

(Guessing: 25%)

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Example QL item on Rate

At an ice cream factory, a cylindrical cone, like the one pictured below, is being filled by liquid ice cream at a constant rate, until it is full. Which of the following graphs is the best representation of the relationship between the height of the ice cream and the amount of time?

a. Graph A

b. Graph B

c. Graph C d. Graph D

Graph A Graph B

time

Graph C

time

Graph D

time STT Colloquium time November 3, 2009 19

Example QL item on Rate

In-coming students

– 45.1%

On-campus classes

Low math prereq – 28.2%, 28.6%, 31.5% Low math prereq from elite program – 57.5% STT 200 (algebra prereq, many majors) – STT 315 (business majors with calc prereq) – Freshman comp sci with concurrent calc req – Math and Stat undergrad majors – 53.2% 61.6% 70.9% 80.7%

(Guessing: 25%)

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Example QL item on Correlation

For one month, 500 elementary students kept a daily record of the hours they spent watching television. The average number of hours per week spent watching television was 28. The researchers conducting the study also obtained report cards for each of the students. They found that the students who did well in school tended to spend less time watching television than those students who did poorly. Listed are several possible statements concerning the results of this research. Choose the statement that you most agree with based on this study.

(a) Teachers should instruct parents to limit the amount of television their children watch to two hours per day.

(b) If a student decreased the amount of time spent watching television, his or her performance in school would improve.

(c) Even though students who did well watched less television, this doesn't necessarily mean that watching television hurts school performance.

(d) I do not agree with any of the statements.

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Example QL item on Correlation

In-coming students

– 39.8%

On-campus classes

Low math prereq – 61.5%, 57.1%, 63.8% Low math prereq from elite program – STT 200 (algebra prereq, many majors) – 60.3% 49.9% STT 315 (business majors with calc prereq) – Freshman comp sci with concurrent calc req – Math and Stat undergrad majors – 64.0% 60.5% 74.2%

(Guessing: 25%)

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Generalization; Context

• STT 315 final exam 2007 • A “Bayes Theorem” question stated exactly in the form as in earlier STT 315 HW and exams: 81.5% correct • A “Bayes Theorem” question drawn from the assessment: 26.8% correct November 3, 2009 STT Colloquium 23

Motivation

• An important issue • A separate study – Students divided randomly into two groups – One group was paid a flat fee to complete the assessment – One group was paid an amount per correct answer – Paid per correct answer group took more time, but two groups’ performance was the same November 3, 2009 STT Colloquium 24

SIS data

• Demographic data (gender, race, etc.) • Academic data (ACT/SAT scores, HS GPA, college major, college GPA, etc.) • Just received these data • More soon November 3, 2009 STT Colloquium 25

Possible implications

• Prerequisite knowledge (K-12 schooling) • Foundational knowledge (MSU) • Foundational satisfied before junior standing??

• Applied QL (in the major) • Curricular changes?

• Math graduation requirement? QL requirement?

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Other models and issues

• James Madison University • University of Virginia • University of Michigan • Implications of possible federal reporting requirements?

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Thank you

November 3, 2009

Cartoon from xkcd.com/552/

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