Quantitative Literacy assessment

QUANTITATIVE LITERACY ASSESSMENT

Eric Gaze Semra Kilic-Bahi Linda MisenerBowdoin College Colby-Sawyer College S. Maine Community College

What is QL? QL vs. Math Assessment The Bowdoin Story The Colby-Sawyer

Story The SMCC Story

How Much Math Do We Really Need?

- Professor Emeritus U. Ill. Chicago Washington Post 10/22/2010

“Unlike literature, history, politics and music, math has little relevance to everyday life.”

“All the math one needs in real life can be learned in early years without much fuss.”

“Most adults have no contact with math at work, nor do they curl up with an algebra book for relaxation.”

Black and White Victimization’s and Arrests for Crimes of Violence 1997

Number Percent Rate

Victimization

White 7,068,590 82.1 37.1

Black 1,306,810 15.2 46.8

Arrests

White 284,523 56.8 1.5

Black 205,823 41.1 7.4

[i] Per 1,000 people aged 10 and above[ii] Estimates for personal victimization (crimes of violence) derived from 1997 National Crime Victimization Survey[iii] Arrests for violent crime reported in 1997 Uniform Crime Reports


Number Percent Rate

Victimization

White 7,068,590 82.1 37.1

Black 1,306,810 15.2 46.8

Arrests

White 284,523 56.8 1.5

Black 205,823 41.1 7.4


“41.1% of blacks were arrested in 1997, which means 7.4 out of every 1,000 people was a violent black criminal…”

Really? So 56.8% of whites were arrested for violent crimes as well?...

Quantitative Literacy: Communicating (Reading and Writing) with Numbers NOT just Arithmetic


Number Percent Rate

Victimization

White 7,068,590 82.1 37.1

Black 1,306,810 15.2 46.8

Arrests

White 284,523 56.8 1.5

Black 205,823 41.1 7.4


In 1996 the US population was 82.9% white and 12.6% black… Which of the statistics are disproportionate?


Number Percent Rate

Victimization

White 7,068,590 82.1 37.1

Black 1,306,810 15.2 46.8

Arrests

White 284,523 56.8 1.5

Black 205,823 41.1 7.4


In 1996 the US population was 82.9% white and 12.6% black… Which of the statistics are disproportionate?

Confounding variable?

“Race as a proxy for social class.”

-Joel Best Damned Lies and Statistics

Women are 68% percent more likely than men to experience depression in their lifetimes.

Over 75% of women never experience depression in their lifetime.

17.1 percent of individuals have experienced depression in their lifetime.

Over 1 in 5 women and 1 in 8 men have experienced depression in their lifetimes.

Approximately four of every ten depressed individuals is a man.

“In other words, translating a ratio to a percentage is not just a mathematical operation, but also a rhetorical practice in which artistic appeals are manipulated.” - Joanna WolfeRhetorical Numbers: A Case for Quantitative Writing in the Composition Classroom

Statistics: 21.3% of women and 12.7% of men have experienced depression in their lifetime.

Critical Thinkers:

Ask Questions! Reason from Evidence!

And use evidence in the construction of argumentation

Have Q-skills! RATIOS, rates, percentages… Middle School Mathematics

SO HOW COME NO-ONE KNOWS THIS STUFF???

WHY IS IT CULTURALLY ACCEPTABLE TO BE INNUMERATE?

QL vs. Algebra

“Algebra is the key to success in college.”

- Secretary Duncan 4/15/2011

“Endless Algebra- The Deadly Pathway from High School Mathematics to College Mathematics.”

- NCTM President Shaughnessy 2/2011

Who’s Right????

Why all this algebra?

? ? ? CALCULUS!

Gateway to the STEM fields and beyond!

623 2 xxy51 xx

1sin 2

a

acbbx

2

42

2001 Cohort 9th Graders

2001 2005 2005 2005 2007 2011 -

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

4,000,000

4,500,000 4,012,770

2,799,250

1,861,501

1,303,050

277,550 166,530

4.2%STEM graduates

69.8% graduated

46.4% college plans

32.5% college ready

6.9% STEM majors

This is not a pipeline… it is a trickle. 60% of STEM workforce is 45 and older.

How Much Math Do We Really Need?

- Professor Emeritus U. Ill. Chicago Washington Post 10/22/2010

“Unlike literature, history, politics and music, math has little relevance to everyday life.”

“All the math one needs in real life can be learned in early years without much fuss.”

“Most adults have no contact with math at work, nor do they curl up with an algebra book for relaxation.”

“One of the best gifts a math teacher can give a student is to teach them how to solve complex algebraic equations.”

- Secretary Duncan 4/15/2011

“Endless Algebra- The Deadly Pathway from High School Mathematics to College Mathematics.”

- NCTM President Shaughnessy 2/2011

The STEM crisis vs. the QL crisis

They are not incompatible!

The Importance of QL: Mathematics and Democracy

“Quantitatively literate citizens need to know more than formulas and equations.

They need a predisposition to look at the world through mathematical eyes, to see the benefits (and risks) of thinking quantitatively about commonplace issues,

and to approach complex problems with confidence in the value of careful reasoning.

Quantitative literacy empowers people by giving them tools to think for themselves, to ask intelligent questions of experts, and to confront authority confidently.

These are skills required to thrive in the modern world.”

The Bowdoin QR Exam

Q-score correlates with GPA at R = 0.382 (N = 1,302)

Correlate how students did on a question with their overall exam score (Item-Total Correlation)

The Correlation statistic is between -1 and 1. Negative implies students who do well on the question do poorly on the test overall, i.e. not a good question!

The closer to 1 the stronger the correlation, these questions are measuring the QR “construct” better than others.

The Super 8 all correlate at 0.4 and above.

Lessons Learned

Replace procedural, algorithmic questions with more involved reasoning, critical thinking questions.

Ask students to interpret tables and charts rather than doing it for them.

Focus on quantitative literacy, using numbers in meaningful sentences rather than just computation.

Ask students to postulate possible explanations for statistics rather than traditional logic games.

#2 Taking 90% versus 5.2% increase.

Replace procedural, algorithmic questions with more involved reasoning, critical thinking questions

Ask students to interpret tables and charts rather than doing it for them. If Taxpayer's Income Is... Then Estimated Taxes Are...

Between But Not Over

Base Tax + Rate

Of the Amount Over

$0 $16,700 $0 10% $0$16,700 $67,900 $1,670.00 15% $16,700$67,900 $137,050 $9,350.00 25% $67,900

$137,050 $208,850 $26,637.50 28% $137,050$208,850 $372,950 $46,741.50 33% $208,850$372,950 - - - - - $100,894.50 35% $372,950

#10 Tax is $7,664 plus 8% of the excess over $100,000.

#23 Compare South to International. #29 Use 59.08 in a sentence: “59.08% of

18-64 year olds are under 18 and over 65.”

Focus on quantitative literacy, using numbers in meaningful sentences rather than just computation.

Midwest6%

Mid At-lantic26%

New England43%

Interna-tional

4%

West13%

Southwest3%

South5%

Home Region Class of 2014

[email protected]

Quantitative Literacy: Literacy Redefined

18

QL Across the Curriculum in a Liberal Arts Setting

Semra Kilic-Bahi

Colby-Sawyer College, New London, NH

[email protected] 19

Who We Are

• Small liberal arts college • Rural• 1100 Students

– Coed– Traditional age students– Residential


Math ProficiencySpring 2004

• Basic Mathematical Skills• The Conceptual Understanding• The ability and the flexibility to use those skills in

different contexts – CUPM Curriculum Guide 2004– The Mathematics Learning Study Committee of the National

Research Council “Adaptive Reasoning,”


QL Mission Statement

Spring 2006• Read, understand, interpret, use, and

communicate quantitative information given symbolically, visually, numerically, or verbally.

• Gather and analyze information, construct and test hypotheses, draw inferences, and make well-reasoned decisions.

• Use technology effectively

[email protected]@colby-sawyer.edu 2222

QL Across the Curriculum in a Liberal

Arts Setting

NSF Funded Project – 063313

PI: Semra Kilic-BahiCo-PIs: Ben Steele, Peter White,

Joe Carroll, Cheryl Coolidge

Senior Personnel: John Callewaert, Randy Hanson, Lynn Garrioch

http://www.nsf.gov/


Assessment Plan

• Students– Basic Skills– QL Skills– Attitude (Split survey)

• Faculty– Survey – Workshop Assessment

• Curriculum– Syllabi


Basic Skills and QL SkillsAssessment Instrument

– Trinity College (Judith Moran)– Dartmouth College (Dorothy Wallace)– Wellesley College (Corrine Taylor)– Bowdoin College (Linda Kirstein) – Hamilton College (Mary O’Neil )– Hollis University (Caren Diefenderfer) – Johnson State (Glenn Sproul)


Basic Skills and QL Skills Mapping

Learning Objective Basic Skills Quantitative Literacy Skills

1. Apply basic arithmetical, algebraic and geometric tools in everyday settings and distinguish between the appropriate and inappropriate uses of numerical information.

21

16

2. Use inductive and deductive reasoning and understand fallacies in logic.

2 4

3. Understand, and use descriptive statistics and graphical displays.

2 3

4. Use reasoning to develop and test hypotheses and to draw inferences and make well reasoned decisions from collected data.

0 2


Sample Question-Basic Skills

A survey of football players revealed that 20 % of 1180 players had knee injuries. How many players had knee injuries?

77% Freshmen86% Senior

[email protected]

Sample Question QL

In 2004 your salary increased by 10%. In 2005, you received a 10% pay cut. After the two changes, how does your salary compare to your original salary?

a) It is lower. b) It is higher. c) It is unchanged.

Freshmen 15% Seniors 26%

27


Assessment SummaryFall 2007-Spring 2011

N Average Min Max StdDev FRESHMENBasicSkills 1070 47 0 92 16.55

QuantitativeLiteracy 1070 41 0 88 14.86SENIORSBasicSkills 315 52 12 96 17

QuantitativeLiteracy 315 48 0 96 18



Internal Consistency-Reliability (Cronbach’s Alpha)

Basic Skills QL Skills

Freshmen N = 1040

α = .72 α = .68

Seniors N = 315

α = .73 α = .75


Further Correlations

CumGPA SATMath SATVerb QLTot BSTotal

CumGPA 1 .216** .212** .188** .175**

SATMath .216** 1 .973** .065 .211**

SATVerb .212** .973** 1 .053 .159*

QLTot .188** .065 .053 1 .473**

BSTotal .175** .211** .159* .473** 1

**. Correlation is significant at the 0.01 level (2-tailed).

*. Correlation is significant at the 0.05 level (2-tailed).


Attitude Survey

Thanks to:– Math Across the Curriculum, Dartmouth College (Dorothy

Wallace and Jane Korey)– MAC^3 Survey (Anne Chase) – Trinity College (Judy Moran) – An Instrument to Measure Mathematics Attitudes

Martha Tapia, Berry College, GA George E. Marsh II, The University of Alabama


Attitude Survey

ORDER

1. Survey I10 questions

2. Basic Skills3. QL Skills

4. Survey II10 questions

ATTRIBUTES

• Self-confidence • Anxiety • Value • Enjoyment • Motivation


Survey Results4 point Likert Scale- two questions


NSSE

“to what extent did your experience at this institution contribute to your knowledge, skills and personal development in analyzing quantitative information.”

First Year

2006 2007 2008 2009 Senior 2006 2007 2008 2009

Quite a bit or Very much

64% 68% 59% 64% Quite a bit or Very Much

66% 83% 80% 72%


Recent Developments

• James Madison University-Student Opinion Survey Motivation Survey

• Pilot evaluation of E-portfolios by using QuIRK rubrik developed by Carleton College

ANDQuantitative

Literacy

Who Are Our Students?

48% are Female

41% are above the age of 24

11.8 % are Minority (4.8% for the state of Maine)

And …….

66 % are first generation college

80.29% receive some sort of aid (Pell, Loans, grants,

VA),

70% place into at least one developmental course, most likely math

What is Offered?

MATH 050Introduction to Algebra

MATH 020Numerical Mathematics

MATH 120Symmetry,

Shape, and Space

MATH 145College

Algebra and Trigonometry

MATH 125Discrete

Mathematics

MATH 140College Algebra

MATH 160College

Trigonometry

MATH 190Precalculus

MATH 260Calculus 1

MATH 270Calculus 2

MATH 230Statistics

MATH 115Fundamentals of Elementary

School Mathematics I

MATH 220Finite

Mathematics

Southern Maine Community College Mathematics Department

MATH 280Calculus 3

MATH 110Contemporary Mathematics

MATH 116Fundamentals of Elementary

School Mathematics II

What Is Taken?(Fall 2011)

851

466

19 17458 672

88

70

39

10

203

10

5

Southern Maine Community College Mathematics

Department Spring 2012

203

4

What is our student success rate in the gateway course MATH 050 ?

Fall 09 and Fall 10

Course CompletionGrade # % # %A 44 6% 66 8%A- 37 5% 38 5%B+ 29 4% 53 7%B 59 8% 55 7%B- 45 6% 57 7%C+ 45 6% 45 6%C 67 9% 49 6%Successful 326 43% 363 45%C- 33 4% 41 5%D+ 17 2% 25 3%D 67 9% 51 6%F 78 10% 105 13%AF 96 13% 90 11%I 0 0% 1 0%NS 26 3% 14 2%W 112 15% 116 14%Unsuccessful 429 57% 443 55%Grand Total 755 100% 806 100%

MATH 050 Fall 2008 MATH 050 Fall 2009

KEY PROBLEM

For every 10 students who start in a fall semester:– Only 9 are still coming to class by Oct. 15;– Only 8 earn one (or more) grade of C or better;– Only 7 continue to the spring semester;– Only 5 continue to the following fall semester;

and – Only 2 graduate within three years.

.

Fall 2010 Report

Voluntary Framework of Accountability

“As a nation we have focused on increasing access to higher education but have neglected completion and success rates. Among community college leaders there is a growing concern that providing access to students is not enough and that colleges must also assume responsibility for increasing the success rates for students.” http://www.aacc.nche.edu/Resources/aaccprograms/vfa/Pages/default.aspx

What is The Position of SMCC?

http://www.aacc.nche.edu/Resources/aaccprograms/vfa/Pages/default.aspx

StrategiesWhat Are We Doing?

• Making services more available• Using more technology to increase access• Developing virtual tutoring and advising• Identifying and redesigning gateway courses• Using technology for learning solutions into gateway

courses.• Sharing successful instructional redesign strategies• Using Freshman Interest Groups and learning

communities to support students

How Can Quantitative Learning Help Us Meet our Goal?

Quantitative Literacy assessment

Documents

violent crimes

uniform crime reportsin

uniform crime reportsblack

uniform crime reports41

white victimizations

aboveii estimates

violent black criminalreally

experienced depression