Re-Thinking Pre-College Math: Joining a Joyful Conspiracy as Reasonists in the Bermuda Triangle

1. 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

2. 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

3. 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 All information references the 07-08 group of workforce and transfer students.�All information references the 07-08 group of workforce and transfer students.�

4. College Learning�? This wouldn�t be so painfully funny if it weren�t grounded in at least some reality�and whether we like it or not the perception is a common one. There�s a little pain of self-recognition in this admittedly exaggerated (and funny) perspective�but real learning is more than just what you need to know later (and hopefully more than just 2 hours worth!)This wouldn�t be so painfully funny if it weren�t grounded in at least some reality�and whether we like it or not the perception is a common one. There�s a little pain of self-recognition in this admittedly exaggerated (and funny) perspective�but real learning is more than just what you need to know later (and hopefully more than just 2 hours worth!)

6. Melanie Oudin, youngest quarterfinalist at US Open since Serena Williams in 1999Melanie Oudin, youngest quarterfinalist at US Open since Serena Williams in 1999

7. Team Discussion How do your students learn math?

8. 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 In the same way language, gestures, mannerisms, etc. are shaped by a child�s interactions with family and communityIn the same way language, gestures, mannerisms, etc. are shaped by a child�s interactions with family and community

9. 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 In the same way language, gestures, mannerisms, etc. are shaped by a child�s interactions with family and communityIn the same way language, gestures, mannerisms, etc. are shaped by a child�s interactions with family and community

10. Team Discussion What is most important for your students to understand deeply about math?

11. 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

12. 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.

13. Team Discussion How do you help students learn what you want them to understand?

14. 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.

15. 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.

16. Tackling �Elementitis�#:A Whole New Ball Game Play the whole game. Make the game worth playing. Work on the hard parts. Play out of town. Uncover the hidden game. Learn from the team�and the other team. Learn the game of learning. Perkins, David, 2009 Making Learning Whole: How Seven Principles of Teaching Can Transform Education

17. 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?�

18. Team Discussion How do you know students have learned what you want them to understand?

19. 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/

20. Aspects of Formative Assessment

21. 1) Review, share, analyze existing work around Washington and the country with respect to pre-college math curricula Select cohort of collges to participate directly in grant project 2) Engage faculty involved in the project in discussions of current research on learning and pedagogical approaches in mathematics Develop Inquiry Groups around targeted instructional strategies to provide ongoing support and technical assistance for project colleges (become ongoing resources for the system as a whole after the grant ends) 3) Integrate Washington Math Assessment and Placement (WAMAP.org) more fully into the pre-college math curriculum at the cohort of colleges involved Continue refining the platform and work to make it more widely available, as a free, open-source tool, to both college and high school math teachers1) Review, share, analyze existing work around Washington and the country with respect to pre-college math curricula Select cohort of collges to participate directly in grant project 2) Engage faculty involved in the project in discussions of current research on learning and pedagogical approaches in mathematics Develop Inquiry Groups around targeted instructional strategies to provide ongoing support and technical assistance for project colleges (become ongoing resources for the system as a whole after the grant ends) 3) Integrate Washington Math Assessment and Placement (WAMAP.org) more fully into the pre-college math curriculum at the cohort of colleges involved Continue refining the platform and work to make it more widely available, as a free, open-source tool, to both college and high school math teachers

23. 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�

24. 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��

25. 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

26. 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? Individual; organizational; system Organizational issues: Alignment & coherence of individual and collective norms, expectations Alignment of resources: time, people, money Structure supports learning Strategic functionIndividual; organizational; system Organizational issues: Alignment & coherence of individual and collective norms, expectations Alignment of resources: time, people, money Structure supports learning Strategic function

27. 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

28. 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

29. Colleagues Committed to Redesign (C2R) Core Elements Whole course redesign Active learning Computer-based learning resources Mastery learning On-demand help Alternative staffing Distinct Models Supplemental Replacement Emporium Fully Online Buffet