Scaling Innovation in Developmental Math: Lessons from Research and Practice Susan Bickerstaff,...
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Scaling Innovation in Developmental Math:Lessons from Research and Practice
Susan Bickerstaff, Community College Research CenterBarbara Lontz, Montgomery County Community College
November 8, 2012AMATYC
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We conduct quantitative and qualitative research on• Teaching and learning in higher education• Access to and success in postsecondary education• High school to college transition• Missions, governance and accountability• Workforce education
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The Scope of the Issue
• Over 60 percent of entering community college students are referred to developmental education
• Students assigned to developmental education are less likely to earn a credential
• Developmental education costs up to $2 billion per year at community colleges
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Our Challenge
• Outcomes for students referred to developmental education are discouraging–Vast majority of students do not complete the
sequences to which they are referred–Developmental education is not effective for
students near the cut-off point –Completion rates of non-compliers (i.e., those
who skip the sequence) is similar to compliers
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Innovation in Developmental Education
• National scan of reforms in developmental education suggests that innovation is widespread–Bootcamps, acceleration, compressed courses,
learning communities, curricular changes• However, most reform efforts are small in
scale, and largely unknown outside their institutions
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Instructional Reform Approaches
Structure
Curriculum
Approaches are NOT mutually exclusive
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Structural Reforms
• Focus on reorganization of time and content– Acceleration, compression, modularization,
mainstreaming• Often addresses sequence length, but may not
target student learning• Challenges
– Requires logistical coordination among stakeholders
– May have implications for policy (i.e., articulation)
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Curricular Reform
• Focus on rationalizing or refining content– Modularization, alternative courses (i.e.,
Path2Stats)• Intended to deliver a more relevant curriculum,
or to address misalignment between developmental and college-level courses
• Challenges– Requires faculty to prioritize what knowledge is
taught– May have implications for learning outcomes
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Pedagogical Reform
• Focus on changes to teaching– Teaching for conceptual understanding, project-based
learning• Intended to make explicit connections between
classroom practice and student learning– Changes the nature of learning interactions
• Challenges– Little understanding of the types of pedagogical
changes necessary to improve student learning– Few resources and mechanisms for meaningful
professional learning
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The Scaling Innovation Project
• Community College Research Center and partner colleges work to scale promising reforms at new institutions
• Faculty-driven effort, with intentional focus on classroom practice
• Rather than strict fidelity, faculty work to adapt the reform to the institutional context
• For more information: www.scalinginnovation.org
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Focus on Teaching and Learning
• Our knowledge of teaching and learning in community colleges is limited– What works for which students and in what
contexts?– Student learning not rigorously measured leaving
us little information about instructional quality• Necessary to understand expectations and
experiences of faculty and students• Current system not structured to encourage
pedagogical improvement
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Causes for Concern at MCCC
• The success rates* for the past eight years in our arithmetic classes have been declining
• The success rates fell between 35% - 45%
• Our numbers reflect a national trend of declining math scores
*success rates are grades of C or better
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• All learning outcomes of a traditional arithmetic course are covered but in a different order
• Lessons proceed through concepts, (addition, subtraction, multiplication, division & combinations) using a discovery approach
• Students are assessed on the same skills as the traditional arithmetic course
Concepts of Numbers
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Concepts of Numbers Outline
• Unit 1: History of Numbers• Unit 2: The Real Number System• Unit 3: Comparisons• Unit 4: Addition• Unit 5: Subtraction• Unit 6: Multiplication• Unit 7: Division• Unit 8: Combinations
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Unit 1: History of Numbers
• In understanding the evolution of numbers, students will better understand/appreciate our present system
• The following civilizations are covered:
Babylonian
Greek
Egyptian
Roman
African
Mayan
• The concepts of place value and place holders are explored
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Unit 2: The Real Number System
• All sets of numbers are introduced: natural, whole, integers, rational, irrational & real
• Numbers are classified according to their sets
• Numbers are located on a number line
• “All numbers are created equal.” B.Lontz
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Unit 3: Comparisons
• The concepts of <, > and =
• “like” numbers are compared (integers, fractions with the same denominator)
• “unlike” numbers are compared (irrational numbers with rational numbers, fractions with different denominators, fractions with decimals)
• Numbers that are “like” are easier to compare
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Unit 4: Addition
• Addition (combining) of the following quantities:
whole numbersdecimalsfractionsintegersalgebraic expressions
• Application of the addition concept (perimeter, money problems)
• Identity element, commutative & associative properties, and binary operation concepts are introduced
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Unit 5: Subtraction
• Subtraction (find differences) of the following quantities:
whole numbersdecimalsfractionsintegersalgebraic expressions
• Application of subtraction (temperature, money problems)
• Solving equations that use the Addition Property
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Unit 6: Multiplication
• Multiplications (repeated combinations) of the following quantities
whole numbersfractionsdecimalsintegersalgebraic expressions (distributive prop)
• Exponents
• Application of multiplication (area, circumference, percents)
• Properties (commutative, associative, identity & inverse)
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Unit 7: Division
• Division (repeated subtractions) of the following quantities:
whole numbersfractionsdecimalsintegers
• Application of division (percents, unit pricing)
• Solving equations using the Multiplication Property
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Unit 8: Combinations
• Simplifying expressions involving multiple operations (order of operations)
• Solving multiple step applications, (ratio & proportion)
• Solving algebraic equations:6(x+5) = -2(x -5)
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Outcome DataSuccess Rates: Success is a grade of C or better: Withdraws count as non-success
* the top 13% of Arithmetic Accuplacer scorers were accelerated into the next course (a 4 credit beginning algebra class)
** an additional top 12% of Arithmetic Accuplacer scorers were accelerated into the next course (a 4 credit beginning algebra class)
MAT010 Concepts of Numbers versus MAT010 Traditional Course
Fall2008
Spring 2009
Fall2009
Spring 2010
Fall2010
Spring2011
Fall2011
Spring 2012
Concepts of Numbers
74% 63% 68% 60%* 58%** 57.4% 57.72% 61%
N = 19 N = 19 N = 19 N = 255 N = 380 N = 289 N = 704 N = 316
Traditional Arithmetic
45% 34% 41% 40% 40% 37.8%
N = 664 N = 429 N = 567 N = 236 N = 284 N = 150 N = 0 N = 0
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What students say …
• “She explained the math to us in a way that I have never experienced. I thought it was taught to us to make sense.”
• “You did not teach me math but you helped me learn math.”
• “With this course, I feel that I have learned so much and got to fully understand math and became good at it. I am a lot more confident about math now.”
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What faculty say …• I can’t imagine ever going back to the traditional
way of teaching this material.Chris Matus, West Chester University
• My students enjoy math more and therefore, I enjoy teaching more. Introducing them to some algebraic ideas early on has made prealgebra easier to teach and more natural for the students.Steve Solomon, MCCC adjunct
• To be honest, I didn’t think I would like it but my mind has been changed; the students enjoy it and I look forward to teaching it again.Joe Freiwald, MCCC retired FT faculty
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Scaling a Promising Practice
• Institution buy-in– financial– time for development
• Department approval‒ bringing to a larger scale‒ faculty willingness to try something new‒ training
• Monitoring/Assessment• Replicating Process
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Scaling Innovation
In Fall 2011, the Concepts course redesign received a William And Flora Hewlett Scaling Innovation Project two-year grant through the Community College Research Center (CCRC) to replicate at other colleges (Reading Area Community College & Berkshire Community College) and improve learning within
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Scaling Innvation
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Deeper Learning
• Implementation Team• Universal Portal• CoN-NECT
- course improvements- journaling (reflections)- video segments- class observations- best practices
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Deeper Learning
• Implementation Team• Universal Portal• CoN-NECT (inserting logo here; still working on it)
- course improvements
- journaling (reflections)
- video segments
- class observations
- best practices
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Scaling Instructional Reforms: Preliminary Findings
1. Stakeholders need varied support in committing to change
2. During early implementation, structural and curricular concerns supersede instructional issues
3. Importance of collaborative structures for sustainability and refinement
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Ready to act, and have ideas for improvement
Ready to act, but unsure how
Satisfied with status quo, but
open to new ideas
Reluctant to change
Supporting Stakeholders in Committing to Change
These dispositions are reflective of personal perspectives and institutional culture
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Disruption to Faculty Identity
It’s really hard to get faculty to look at teaching differently or changing curriculum in drastic ways when they’ve invested their identity in that way of teaching. ‘You’re not challenging a certain curriculum, you’re challenging me or the essence of who I am.’ It’s too bad, but that can get in the way. - Faculty Leader
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Facilitating a Moment of Dissatisfaction
• Acknowledgement that I can help students do better
• May come through review of data, literature, or conversations with colleagues– Seeing student progression across courses in the
sequence• Acceptance that it will be challenging
– Productive professional struggle is normal– Reframing “failures” into opportunities for
professional growth
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Structure and Curriculum: Questions about the What
• Course format and scheduling‒ Registration, scheduling, space, instructional
supports, staffing, credit hours, financial aid• Curricular questions
‒ Textbook, course materials, assessments, assignments
‒ Content-specific questions (i.e., How do you teach ____?)
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Moving from What to How
• Embedding “design principles” into curriculum and structure‒ Small class size invites pedagogy that is responsive to
student needs‒ Fewer practice problems invites conceptual rather
than procedural instruction‒ Project-based assignments invite teaching for
application
• Examining artifacts of practice‒ Video, classroom observations, assignments, student
work
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Coalitions for Sustainability and Refinement
• Diverse coalitions can build buy-in and ensure the reform is sustained– Full-time and adjunct faculty, administrators,
counselors/advisors, instructional support staff, institutional researchers, and students
• By reviewing data, the coalition can process for ongoing refinement– Course grades, student persistence to subsequent courses,
student success in subsequent courses, qualitative data• Disaggregated by student characteristics
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For more information:
Please visit us on the web at
http://ccrc.tc.columbia.edu,where you can download presentations, reports,
CCRC Briefs, and sign-up for news announcements.
Community College Research CenterInstitute on Education and the Economy, Teachers College, Columbia University
525 West 120th Street, Box 174, New York, NY 10027 E-mail: [email protected]: 212.678.3091