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