Quantitative Reasoning at UMass
Boston
Fourteen Years of Experience
Mark Pawlak, Director
Academic Support and Quantitative Reasoning Programs
Quantitative Reasoning at UMass Boston | May 1, 2012
General Education at UMass Boston
In 2002, a new general education program was put in place after 4
years of faculty discussion and planning with the following
principles as its foundation
▸ Critical analysis and logical thought
▸ Verbal and quantitative reasoning
▸ Human diversity
▸ Principal approaches to knowledge
Core elements include
▸ Writing--English Composition I & II
▸ First Year & Intermediate Seminar
▸ Mathematics/Quantitative Reasoning
▸ Distribution courses in several areas
▸ Writing Proficiency Requirement
▸ Capstone in major
Quantitative Reasoning at UMass Boston | June 5, 2012
Assessing Student Learning in Quantitative
Reasoning:
A Dynamic, Evolving Process
Mark Pawlak
Director, Academic Support and Quantitative Reasoning Programs
Chair, Quantitative Reasoning Assessment Committee
University of Massachusetts Boston
Quantitative Reasoning at UMass Boston | June 5, 2012
The Mathematics/Quantitative Reasoning Requirement
▸ All students must “demonstrate competence in
mathematics/quantitative reasoning.”
▸ B.S. students must take Calculus I (a traditional Calculus course)
▸ B.A. students have several choices:
– Test into PreCalculus or Calculus
– Take Statistics (taught by Math, Psychology, Sociology,
Economics, etc.)
– Take College Algebra
– Take a Quantitative Reasoning course
▸ Each semester, approximately 200 - 250 students choose a QR course.
Quantitative Reasoning at UMass Boston | June 5, 2012
Quantitative Reasoning Courses
QR Course Guidelines
▸ Required topics are:
descriptive statistics
linear models
exponential models and/or
probability
use of technology (graphing
calculators or computers)
▸ Students learning outcomes:
engage in critical reading and
analysis
speak, listen and write effectively
use technology to further learning
work independently and
collaboratively
reason logically and quantitatively
Math 114Q
▸ Mathematics offers the primary QR
course
▸ This is the lowest-level course Math
offers
▸ Prerequisite: (outdated) placement test
▸ All sections are taught in a computer lab
▸ QR faculty are primarily adjuncts (90%)
▸ Class size is small (20 - 23 students)
▸ Many students come out of
developmental math courses and are math
phobic; have weak skills; hate math
▸ All topics are motivated using real world
data, course follows an investigations
pedagogy
▸ Technology is used as a tool and as way
of seeing patterns.
Quantitative Reasoning at UMass Boston | June 5, 2012
QR Assessment Cycle
Quantitative Reasoning at UMass Boston | June 5, 2012
Student self-assessment
Self-reflection:
▸ Students complete an “automathography” at the beginning of
the semester and a reflection at the end of the semester – this
is viewed only by the instructor
Course assessment and evaluation:
▸ Student questionnaire given to all students
▸ Demographic data
▸ Self-assessment of technical skills and QR skills
▸ Attempts to measure attitudinal change
▸ Administered online with support from the mathematics
department
▸ Faculty log in to view their students’ responses and coursewide responses.
Quantitative Reasoning at UMass Boston | June 5, 2012
Sample Questions – Student Questionnaire
Quantitative Reasoning at UMass Boston | June 5, 2012
Faculty self-assessment
▸ QR faculty meet each semester to “de-brief”
▸ Discussions include
▸
▸
▸
▸
▸
▸
What worked
What didn’t work
Issues of support and training
Student learning outcomes and course objectives
Assessment information
Resources and information
Quantitative Reasoning at UMass Boston | June 5, 2012
Holistic grading of common final exam problems
▸ QR faculty agree on a set of problems that will appear on all
finals across sections
▸ Generally 5-6 problems, covering main student learning
outcomes
▸ After semester grades have been submitted a sample of finals
from each section is graded holistically
▸ Initially, holistic grading was done by QuAC members
▸ QR faculty now participate in the holistic grading
▸ End of semester QR faculty debriefing and holistic exam
grading are now combined.
Quantitative Reasoning at UMass Boston | June 5, 2012
Sample Exam Question
▸ On April 19, 2012, the Boston Globe reported that “MIT
physicist leads effort to scrap the penny. Finds himself at center
of passionate debate about coin,”
(http://www.bostonglobe.com/business/2012/04/18/mitphysicist-jeff-gore-leads-effort-scrappenny/Xz04E54R4BTkoDTYIOpnJO/story.html )
▸ “[Jeff] Gore, who has become an unlikely national spokesman
for efforts to eliminate the penny, is gaining fresh hope that the
United States might finally dump the coin. Canada recently
announced it would get rid of its one-cent piece by the end of
the year even as the US Mint reported it is losing more money
than ever to produce the coin..
▸ The following graphs are from the article:
Quantitative Reasoning at UMass Boston | June 5, 2012
Question: The print version of the article noted that in 2011 there were 4,289
million pennies shipped. Confirm that this number of pennies is consistent with
the 2011 data from the two graphs below .
Quantitative Reasoning at UMass Boston | June 5, 2012
Common Final Exam sample problem 2
1. An article about the US Postal Service in the New York Times on December 4,
2011 stated that
First-class mail — items like bills and letters that require a 44-cent stamp —
fell 6.6 percent in 2010 alone, continuing a five-year-long plunge. Last year …
there were 9.3 billion pounds of ‘standard mail’ — the low-cost postage
category available to mass advertisers — but only 3.7 billion of first-class mail.
www.nytimes.com/2011/12/04/sunday-review/the-junking-of-the-postalservice.html)
a. A graphic next to the article said that standard mail in 2010 amounted to 30.3
pounds for every adult and child in the US. Verify this 30.3 pounds per person
figure.
b. How many pounds of first class mail did the Post Office deliver in 2009?
c. First class mail mostly consists of bills, credit card statements, personal letters
and greeting cards. First class postage is 44 cents for the first ounce and 20 cents
for each additional ounce. Estimate the total cost of the postage on first class mail
in 2010.
Quantitative Reasoning at UMass Boston | June 5, 2012
Scoring Rubric – sample question
2 = full understanding; 1 = partial understanding;
0 = little or no understanding
mean
median
Demonstrated ability to identify and extract relevant data
from complex verbal text and apply it to problems.
1.4
1.2
Able to verify textual claims through an appropriate set of
calculations.
1.0
1.0
Accurately performed backward percentage calculation to
determine a prior year value.
0.9
1.0
Performed a complex calculation involving estimation and
multiple unit conversions.
1.0
1.0
Quantitative Reasoning at UMass Boston | June 5, 2012
Outcomes:
What we have learned
▸ Students appreciate how math (algebra) can be meaningful in the real
world
▸ Students gain proficiency in using Excel and value it for use in future
coursework & employment
▸ Student develop habit of Internet searching (primarily Google) and
back-of-the-napkin problem solving to verify data claims and apply
this to other contexts
▸ Faculty uniformly address QR topics and competencies with varied
emphasis
▸ Some mathematics topics remain challenges for teaching and learning
Quantitative Reasoning at UMass Boston | June 5, 2012
Assessing QR Assessment
Challenges
Lessons
▸ Timely compilation of common
final exam
▸ Timely administration of
questionnaire
▸ Conducting timely holistic
grading; assessing results and
discussing with faculty
▸ Faculty buy-in to course and
program modifications based on
assessment
▸ Importance of continual
evolution and refinement of
instruments and methods
▸ Adequate resources for faculty
release time & administrative
support are needed to conduct
assessment; collect and analyze
data
▸ Importance of faculty involved
in modifying course/program
based on results of assessment
Quantitative Reasoning at UMass Boston | June 5, 2012
Some new initiatives & goals at UMass Boston
▸ Recruiting statistics faculty from relevant majors and all
colleges to QUAC to review alignment of MA 114Q with their
courses
▸ Developing appropriate placement instruments for MA 114Q
and for statistics
▸ Collaborating with Carnegie Foundation Statway and Quantway
initiatives to accelerate developmental math coursework
▸ Recruiting STEM science faculty to embed relevant QR
assignments in their courses
▸ Using the QR VALUE rubric to complement current holistic
assessment of student learning in MA 114Q
Quantitative Reasoning at UMass Boston | June 5, 2012
Resources
Numeracy article: QRCW Rubrics
http://scholarcommons.usf.edu/numeracy/vol4/iss2/art8/
▸ SIGMAA on Quantitative Literacy:
http://sigmaa.maa.org/ql/
▸ Common Sense Mathematics (UMass Boston)
http://quantitativereasoning.net/
See also:
▸ “Quantitative Reasoning at the University of Massachusetts Boston,” M. Mast
and M. Pawlak, in Current Practices in Quantitative Literacy, edited by R.
Gillman, MAA publications, 2006
Contacts:
▸ mark.pawlak@umb.edu
▸ maura.mast@umb.edu
Quantitative Reasoning at UMass Boston | June 5, 2012