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“Fortune favors the prepared mind.”-- Louis Pasteur
“The advancement and perfection of mathematics are intimately connected with the prosperity of the state.”-- Napoleon
“The illiterate of the future will not be someone who cannot read, it will be someone who cannot learn, unlearn, and then relearn.-- Alvin Toffler
Factors Contributing to Attainment of Factors Contributing to Attainment of a Bachelor’s Degree While in a Bachelor’s Degree While in
CollegeCollege
First-year grades-dummy
variable (0 or 1). A 1
indicates the student’s
grades are in the top two quintiles.
Low credits first year. Did the student
earn less than 20 credits in
the first year?
A proxy for preparedness of high school
studentSocioeconomic status
A proxy for preparedness of high school student
Socioeconomic status
First-year GPA
Whether one attends multiple schoolsNumber of credits earned
in summer schoolEver a part-time studentTotal number of college
math creditsWere grades rising, falling, or flat over timeDid student repeat or
withdraw from more than 20% of courses?
Enrolled continuously?
Students are not studying enough! Median of 49 minutes per hour of credit in Intermediate Algebra Median of 44 minutes per hour of credit in College Algebra
An Investigation of Student Habits in Mathematics Courses
First-year full-time students are spending a mean of 13.3 hours and a median of 13.5 hours per week preparing for class (studying, reading, writing, doing homework or lab work, analyzing data, rehearsing, and other academic activities)
National Survey of Student Engagement
At Joliet Junior College, between Fall, 2006 and Spring, 2007, our retention rates (A, B, or C), ranged between 47.5% and 52.5% in the Intermediate Algebra course.
Retention Matters 78.4% of all awarded Bachelor’s degrees had less than 10% of all attempted courses become drops, withdraws, or incompletes. 6.7% of all awarded Bachelor’s degrees had more than 20% drops, withdraws, or incomplete
~ Answers in the Tool Box
Our students need to be inspired! In 1966, 4.6% of high school seniors who took the SAT were
interested in mathematics as a major. Today, it is less than 0.6%.
The Employment Picture• To compete in the global economy of the 21st century,
knowledge of math is critical. In today’s changing world, employers seek critical thinkers and practical problem-
solvers fluent in today’s technology. U.S. Department of Education
“The challenge facing the U.S. now is twofold. On one hand, the country must breed more top-notch mathematicians at home, especially as foreigners find greater opportunities abroad. This will require revamping education, engaging more girls and ethnic minorities in math, and boosting the number of students who make it through calculus, the gateway for math-based disciplines. “It’s critical to the future of our technological society,” says Michael Sipser, head of the mathematics department at MIT. At the same time, school districts must cultivate greater math savvy among the broader population to prepare it for a business world in which numbers will pop up continuously. This may well involve extending the math curriculum to include more applied subjects such as statistics.”
“Math Will Rock Your World” by Stephen BakerBusinessWeek, January 23, 2006
An Overarching Goal of Education The only person who is educated is the one who has learned how to learn and change. ~ Carl Rogers It is the mark of an educated mind to be able to entertain a thought without accepting it. ~ Aristotle If a man neglects education, he walks lame to the end of his life. ~ Plato In the first place, God made idiots. That was for practice. Then he made school boards. ~ Mark Twain
Kolb Learning StylesKolb Learning Styles Concrete Experience
• Empathetic and "people-oriented."
• Find theoretical approaches to be unhelpful and prefer to treat each situation as a unique case.
• Learn best from specific examples in which they can become involved.
• Oriented more towards peers and less toward authority in their approach to learning
• Benefit most from feedback and discussion with fellow CE learners.
Abstract Conceptualization • Analytical, conceptual approach to learning that relies heavily on logical thinking and rational evaluation.
• Prefers things and symbols over people.
• They learn best in authority-directed, impersonal learning situations that emphasize theory and systematic analysis.
• They are frustrated by and benefit little from unstructured "discovery" learning approaches like exercises and simulations.
Active Experimentation Enjoys active learning that relies heavily on experimentation. Learn best when they can engage in such things as projects, homework, or small group discussions. Dislike passive learning situations such as lectures. These individuals tend to be extroverts.
Reflective Observation
• Rely heavily on careful observation in making judgments
• Prefer learning situations such as lectures that allow them to take the role of impartial objective observers.
• Tend to be introverts.
Concrete Experience Prefers specific examples; does not like generalizations; prefers information from peers, not instructor
Abstract Conceptualization Hands-on activities that require thought, prefer to work alone
Active Experimentation Enjoys small group discussions; experimentation; does not like lecture
Reflective Observation Lecture, reading, traditional homework
Take the “Index of Learning Styles Questionnaire” by Barbara Soloman and Richard Felder of North Carolina State University
http://www.engr.ncsu.edu/learningstyles/ilsweb.html
Lecture
Reading
Audio Visual
Demonstration
Discussion Group
Practice by Doing
Teach Others/Immediate Use
5%
10%
20%
30%
50%
75%
80%
Adapted from The Learning Triangle: National Training Laboratories, Bethel Maine©mindServegroup 2005
•The Treisman ModelStudy alone to develop skillsCome together to hone and verify skills
Flash video or podcasts Lecture at Home Example Using SCORM to report results
http://www.virtualpublishing.net/scorm2/scorm2.html
Online Homework Systems• Increased retention rates and success (A, B, C) rates• Increased success rates in subsequent courses
Group worksheets Activities
Personal Response Systems• Increased attention• Increased attendance• Increased retention• Verify that students are watching videos
True or False
The median is a resistant measure of central tendency.
Draper and Brown• Students are twice as likely to attempt to construct an
answer to a question using a PRS compared to a question that required them to raise their hand.
University of Missouri • In General Chemistry the percentage of A’s increased
from 23% to 40% and the percentage of C’s and D’s decreased from 34% to 21%.
Eidenhoven University• Pass rates are less than 60% in traditional courses, while
pass rates in courses using Personal Response Systems is 80%.
Rice Paddies and Math Tests• European farming versus Chinese Rice Paddies
Feudal farming versus autonomous rice paddies Low-incentive work versus be a success or don’t eat Eighteenth century European farming (about 1200 hours of
work annually) Rice paddies (about 3000 hours of work annually)
• Naming Numbers English: 24 is “twenty-four”; Chinese: 24 is “two-
tens-four” Find thirty-seven plus twenty-two
English: Convert to symbolism (37 + 22), then find 7 + 2 and 30 + 20, ultimately get 59.
Chinese: three-tens-seven plus two-tens-two
Russian Proverb: If God does not bring it, the earth will not give it.
Chinese Proverbs:
In winter, the lazy man freezes to death
If a man works hard, the land will not be lazy.
No one who can rise before dawn three hundred sixty days a year fails to make his family rich.
In a study entitled “Task Persistance in Japanese Elementary Schools” by Priscalla Blinco, it was found that Japanese first-graders spent an average of 13.93 minutes trying to work a difficult puzzle, while American first-graders spent an average of 9.47 minutes.
Apply yourself both now and in the next life. Without effort, you cannot be prosperous. Though the land be good, You cannot have an abundant crop without cultivation.
-- Plato
“You are not here merely to make a living. You are here to enable the world to live more
amply, with greater vision, and with a finer spirit of hope and achievement. You are here to
enrich the world. You impoverish yourself if you forget this
errand.”
--Woodrow Wilson, 28th president of the US
• Adelman, Clifford. 2004. Principal Indicators of Student Academic Histories in Postsecondary Education, 1972 – 2000. Washington D.C.: U.S. Department of Education, Institute of Education Sciences• Adelman, Clifford. 1999. Answers in the Tool Box: Academic Intensity, Attendance Patterns, and Bachelor’s Degree Attainment. Washington D.C.: U.S. Department of Education• Cerrito, Patricia B.; Levi, Inessa. An Investigation of Student Habits in Mathematics Courses. College Student Journal. Dec. 1999, Vol. 33 Issue 4 • Deal, Ashley (2007) Classroom Response Systems: A Teaching with Technology Whtepaper. Carnegie Mellon University. • Draper, S. and Brown, M. (2004) Increasing interactivity in lectures using an electronic voting system. Journal of Computer Assisted Learning 20, 81 – 84• Treisman, Phillip Michael (Uri) (1985). A study of the mathematics performance of black students at the University of California, Berkeley. Unpublished doctoral dissertation, University of California, Berkeley.
