inquiry-based learning: pedagogy, research and practice · inquiry-based learning: pedagogy,...
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Inquiry-Based Learning:
Pedagogy, Research and
Practice
Philip K. Hotchkiss
Julian F. Fleron
Westfield State University
PBL Math Teaching Summit
July 17, 2015
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There are several groups at college/university level promoting IBL:
• The Academy of Inquiry-Based Learning (AIBL)
• http://inquirybasedlearning.site-ym.com/
• The Educational Advancement Foundation (EAF)
• http://www.eduadvance.org/
• The Legacy of R. L. Moore
• http://legacyrlmoore.org/
• 4 centers
• University of Michigan
• University of Chicago
• University of Texas at Austin
• University of California, Santa Barbara
• Primary focus on mathematics majors
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• IBL Calculus
• http://www.iblcalculus.com/
• POGIL
• http://pogil.org/
• IBL for Pre-service Teachers
• UC Santa Barbara
• Mathematics for Liberal Arts
• Discovering the Art of Mathematics (DAoM)
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Research supporting IBL:
• In a study on the effectiveness of IBL at the college level that was conducted by S. Laursen,
M. L. Hassi, M. Kogan, A. B. Hunter and T. Weston, it was found that
1. Students in the study reported deeper learning due to having to figure the mathematics
out for themselves; in fact, these learning gains were statistically significantly correlated
to the fraction of time spent on student centered activities and anti-correlated to the
faction of time listening to instructors talk.
2. Students in IBL courses self-report higher gains in persistence than students in non-IBL
courses.
3. Students also reported gains in independence, enjoyment, and confidence as well as
gains in thinking and problem solving skills that they believed would benefit them in
other areas.
4. IBL courses provided better support for the lower achieving students while not harming
the higher achieving students.
http://www.colorado.edu/eer/research/documents/IBLmathReportALL_050211.pdf
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Research supporting IBL continued:
• Among the conclusions of a meta-analysis of 225 studies involving active learning in science,
technology, engineering and mathematics (STEM) disciplines by Scott Freeman, Sarah L.
Eddy, Miles McDonough, Michelle K. Smith, Nnadozie Okoroafor, Hannah Jordt, and Mary
Pat Wenderoth were the following:
1. Active learning increases student performance across the STEM disciplines.
2. Average examination scores improved by about 6% in active learning sections.
3. Students in active learning sections were 1.5 times less likely to fail then students in
traditional lecturing sections.
http://www.pnas.org/content/early/2014/05/08/1319030111
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There are four of us on the Discovering the Art of Mathematics project. Every semester
each one of us teaches 1 or 2 sections of 30-40 students of a general education course
called Mathematical Explorations.
Generally students in this course are non-mathematics and science majors; students in
this class are primarily drawn form the following majors:
• English
• History
• Music
• Psychology
• Criminal Justice
• Social Work
• Art
• Mass Communications
This type of course is what is called a Mathematics for Liberal Arts (MLA) course.
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According to a 2010 survey by the American Mathematical Society
(AMS), the MLA student cohort was the 5th largest cohort of
mathematics students with 232,000 each semester.
In 2005, 79% of MLA courses at community colleges were taught using
the standard lecture mode. By 2010, this percentage had increased to
85%.
We are going in the wrong direction.
We want to empower these disenfranchised students by using IBL.
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Discovering the Art of Mathematics (DAoM), is an innovative
approach to teaching mathematics to liberal arts and humanities students,
that offers the following vision:
MLA students will be actively involved in authentic mathematical
experiences that
• are both challenging and intellectually stimulating,
• provide meaningful cognitive and metacognitive gains, and,
• nurture healthy and informed perceptions of mathematics,
mathematical ways of thinking, and the ongoing impact of
mathematics not only on STEM fields but also on the liberal arts and
humanities.
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Imagine that you are a student and this is the first day of your required
mathematics class.
1. What might this feel like to you?
2. What type of energy do you have?
3. Do you have discussions with your students about their mathematical
experiences and their feelings about mathematics? How?
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Let me just start with the fact that I’ve attempted college at least three
times. I swear every failed attempt is due to Mathematics.
As it stands, I'm terrified of this class.
For me personally doing math is immediately associated with struggle
and hardship. It feels like no matter how I try I am unable to firmly grasp
math as a whole or as its individual formulas. Math has always felt like a
weight I am unable to lift.
Quotes from Student Biographies
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Mathematics is the art of explanation. If you deny students the
opportunity to engage in this activity - to pose their own problems, to
make their own conjectures and discoveries, to be wrong, to be creatively
frustrated, to have an inspiration, and to cobble together their own
explanations and proofs - you deny them of mathematics itself. So no,
I’m not complaining about the presence of facts and formulas in our
mathematics classes, I’m complaining about the lack of mathematics in
our mathematics classes.
-Paul Lockhart A Mathematician’s Lament
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Mathematical Question: For integers a, b > 0, what are all possible
outputs of the equation 3a+5b?
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1. What did you observe?
2. Were there things that you think were empowering to the students?
3. Where was the teacher?
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1. What did you observe?
2. How does the mathematical argument in the student’s presentation
compare to the group’s original discussion?
3. What role do the student comments play?
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Where/How has IBL played a central role in students’ investigation of
this problem?
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Guiding Principle 1: Learning
Mathematical ideas should be explored in ways that stimulate curiosity,
create enjoyment of mathematics, and develop depth of understanding.
Massachusetts Curriculum Frameworks
Guiding Principles for Mathematics Programs
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1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Massachusetts Curriculum Frameworks
Standards for Mathematics Practice
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The Big Question:
How do you create environments where this type of inquiry happens with
students whose mathematical skills, interest levels and
attitudes/perceptions of mathematics are so challenging?
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College students study the best paintings, the most glorious music, the
most influential philosophy, and the greatest literature of all time.
Mathematics departments can compete on that elevated playing field by
offering and making accessible to all students intriguing and powerful
mathematical ideas... Indeed, these courses [general education and
introductory mathematics courses] should be developed and offered with
the philosophy that the mathematical component of every student's
education will contain some of the most profound and useful ideas that
the student learns in college.
-Committee on the Undergraduate Program in Mathematics, 2004
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Does your mathematics class contain “the most profound and useful
ideas that students learn”?
• If so, share one.
• If not, name one that could/should be included.
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Discovering the Art of Mathematics
http://artofmathematics.org
Julian Fleron
Philip Hotchkiss
Volker Ecke
Christine von Renesse