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Transcript of Re-Thinking Pre-College Math: Joining a ‘Joyful Conspiracy’ as ‘Reasonists’ in the...
Re-Thinking Pre-College Math:Joining a ‘Joyful Conspiracy’ as
‘Reasonists’ in the ‘Bermuda Triangle’
Bill Moore, Project Director
TMP 2009 Institute
September 8-10, 2009
The Bermuda Triangle
The decision to funnel the most academically at-risk students into colleges that receive the fewest resources has turned out to be something of a disaster…
Community colleges don’t have an obligation to work miracles, but they do have an obligation to do better--to ensure quality teaching and academic counseling, to pay close attention to student outcomes, to try new approaches when the old ones obviously aren’t working…
Camille Esch, “Higher Ed’s Bermuda Triangle,”
Washington Monthly, Sept./Oct. 2009
Some System SAI Data: Pre-College Math
79% of the students enrolled in 07-08 started the year needing college math
31% of those students starting the year with no college math made a math related achievement
Of the total number of students who attempted pre-college math in 2007-08:– 56% made at least one momentum gain:
• 19% made gains in pre-college (basic skills or pre-college math or English)• 32% made gains in college course work (earned at least 15 college level
credits)• 15% made gains in college level math• 11% earned a completion
– 11% made substantial gains in math (passed 2 levels of pre-college math or passed college level math)
– 13% attempted more than one level of math during the year
Basically, you learn two kinds of things in college:
•Things you will need to know in later life (2 hours)…
•Things you will NOT need to know in later life (1198 hours).
These are the things you learn in classes whose names end in ‘-ology’, ‘-osophy’, ‘-istry’, ‘-ics’, and so on. The idea is, you memorize these things, then write them down in little exam books, then forget them. If you fail to forget them you become a professor and have to stay in college the rest of your life. Dave Barry, 1981
College Learning…?
Is It Motivation…?
Or Is It Math…?
Team Discussion
How do your students learn math?
New Psychology of Intellectual Ability and Learning
Intelligence… • is not an inborn, permanent lump in each
person’s head• involves self-monitoring of learning and
thinking processes• is socially and culturally constructed• Is multifaceted
New Psychology of Intellectual Ability and Learning (2)
• No neat and tidy distinction between developing intelligence and learning to think about subject matter
• By-rote sequential instruction does not foster critical thinking or meaningful learning
• Learning is a constructive process• Effective instruction helps students to use
what they already know to arrive at new understandings
Lorrie Shepard, 1992
Team Discussion
What is most important for your students to understand deeply about
math?
Mathematics for Whom?
These rules [about the mathematics curriculum] were made by my grandfather’s generation. Even if our purposes haven’t changed, time alone justifies a fresh look at mathematics pathways to college. The question is not just, what mathematics do freshmen need to take that will allow them to proceed to higher level math courses. It is also, what mathematics do humanities majors need? Pre-law? Pre-med? And so on.
Phil Daro, “Mathematics for Whom? The Top of High School Meets the Bottom of College,” 2009
The “Ladder Myth”The most striking thing about the so-called mathematics
curriculum is its rigidity…The “ladder myth”--the idea that mathematics can be arranged as a sequence of ‘subjects’ each being in some way more advanced, or ‘higher’, than the previous--makes mathematics into a…sad race to nowhere. In the end you’ve been cheated out of a mathematics education, and you don’t even know it…
The ladder myth is a false image of the subject, and a teacher’s own path through the standard curriculum reinforces this myth and prevents him or her from seeing mathematics as an organic whole.
Paul Lockhart, “A Mathematician’s Lament”
(see http://www.maa.org/devlin/devlin_03_08.html)
Team Discussion
How do you help students learn what you want them to
understand?
Improving Mathematics Learning: Where Are We?
• Curriculum materials alone cannot determine instruction; teaching is what matters.
• In order to teacher mathematics well, teachers must know and be able to use mathematical knowledge flexibly to help students learn.
• In order to teach mathematics well, teachers must be able to understand and work from where their students are. Teachers cannot learn for students.
• Good teaching is something to learn, not an inheritance.• Most improvements efforts do not focus sufficiently on
instruction and are not designed for what it takes to make them work in real contexts.
Deborah Loewenberg Ball, 2009
Transfer of Learning
Somethings are, somehow, transferred somewhere.– Somethings: the content/learning you
want transferred– Somehow: what you do as a teacher to
promote/encourage transfer– Somewhere: the targets of transfer
(“near,” “far”)
Transfer cannot be counted on to occur spontaneously. If we educators want transfer, we need to teach for transfer.
Tishman, S., Perkins, D., & Jay, E., 1995
The Thinking Classroom: Learning and Teaching in a Culture of Thinking
Tackling “Elementitis”#:A Whole New Ball Game
1. Play the whole game.2. Make the game worth playing.3. Work on the hard parts.4. Play out of town.5. Uncover the hidden game.6. Learn from the team…and the other team.7. Learn the game of learning.
Perkins, David, 2009Making Learning Whole: How Seven Principles of Teaching Can
Transform Education
#“Elementitis”: approaching complexity through teaching elements with the whole game nowhere in sight
Mathematical Thinking: The “Whole Game” for Math?
• Content (core concepts, skills)• Problem-solving strategies/heuristics• Control (how well and efficiently people use the
mathematical resources at their disposal)• Beliefs• Ability to function as a member of the mathematical
community
Alan Schoenfeld, 1994
“What Do We Know About Mathematics Curricula?”
Team Discussion
How do you know students have learned what you want them to
understand?
Assessment Resources• Balanced assessment work:
http://balancedassessment.concord.org/
• Mathematics Assessment Resource Service (MARS): http://www.nottingham.ac.uk/education/MARS/
• Washington Mathematics Assessment and Placement (WAMAP): http://www.wamap.org/
Aspects of Formative Assessment
Where the learners are
Where they are going
How to get there
Teacher Eliciting evidence of learning through classroom activities
Clarifying goals & success criteria
Providing feedback that moves learners forward
Peers Peer-assessment Understanding success criteria
Using students as instructional resources for each other
Students Self-assessment Understanding success criteria
Helping students take ownership of their learning
Dylan Wiliam, “Keeping Learning on Track…”
• Design and implement new curricular models in pre-college math
• Develop a math community of practice supporting teachers in addressing changes in math instructional strategies and classroom approaches
• Refine and extend use of web-based resources providing math assessment support for students and teachers
“The Re-Inventing Pre-College Math proposal builds on and extends the products and successes of the Transition Math Project (TMP), including the College Readiness Mathematics Standards as a
central foundation, shifting the focus of the intervention from high schools to the pre-college math programs in Washington community
and technical colleges.”
IMPROVING STUDENT LEARNING IN MATH
CURRICULUM/INSTRUCTIONAL MATERIALS
INSTRUCTIONAL PRACTICES/
TEACHER SUPPORT
ASSESSMENT & PLACEMENT
•“Bridge course” to college readiness•Alternative (non -calculus) pathways•Modular & contextualized materials
•Professional learning communities•Integrated assignments•Case studies, video approaches
•Classroom -based assessments•New diagnostic assessments•“Balanced” assessments linked to professional development
Defining Characteristics of Project
• Changing the core of educational practice
• Considering role of student and faculty beliefs about learning and mathematics
• Taking an inquiry stance toward practice
• Collaborating in going to “scale”
Changing the Core
We put an enormous amount of energy into changing structures and usually leave instructional practice untouched…We are attracted and drawn to these [efforts] because they’re visible and, believe it or not, easier to do than to make the hard changes, which are in instructional practice…
The prevailing theory of learning suggests that teaching mathematics is not a developmental problem but a problem of aptitude: some people get it, some people don’t. People do not believe that these problems can be solved by inquiry, by evidence, by science…
The ethic of atomized teaching--teachers practicing as individuals with individual styles--is very strong. We subscribe to the extremely peculiar view [that] professionalism equals autonomy in practice.
Richard Elmore, January/February 2002, “The Limits of ‘Change’”
Taking a Stance of Inquiry Toward Practice
• Strive to make a new idea viable, but not pushing it as “the way”
• Consider how other resources and knowledge might be useful with particular agendas (as tools rather than “truth”)
• Shift the emphasis from implementing programs to adapting innovations and generating new knowledge
Deborah Loewenberg Ball, 1994, Developing Mathematics Reform…”
Collaborating to Get to Scale
Scale at the organization level means, are people working in concert around a set
of ideas about what curriculum and pedagogy should look like, and is it
obvious in their practice?
Richard Elmore, “Improvement of Teaching at Scale”
NSF Learning Network Conference, January 2006
Strengthening Pre-Collegiate Education in Community Colleges
(SPECC)• Change/Ability:
– Faculty leadership– Knowledge of students– Visibility of data and evidence– Redefined faculty development
• Sustain/Ability– Campus progress told as a story– Infrastructure flexibility & imagination
Rose Acera, Carnegie Foundation
See profiles for Los Medanos, Pasadena City College, College of the Desert:
http://www.carnegiefoundation.org/general/index.asp?key=26
CSU Transforming Course Design
• Placement and diagnosis• Alternative instructional strategies
– Mastery learning– Online support– Supplemental instruction– Alternative course designs for specific cohorts
• Integrating technology• Efficiency improvements
http://groups.google.com/group/csu-transform-dev-math-teams
Colleagues Committed to Redesign (C2R)
Core ElementsWhole course
redesignActive learningComputer-based
learning resourcesMastery learningOn-demand helpAlternative staffing
Distinct ModelsSupplementalReplacementEmporiumFully OnlineBuffet
National Center for Academic Transformation
http://www.center.rpi.edu/RedesignAlliance/DissemProgram.htm