Dana Center InitiativesThat May Be of Interest to TMP

Susan Hudson HullCharles A. Dana Center, University of Texas at Austin

TMPAugust, 2008

Advanced Mathematical Decision-MakingAdvanced Mathematical Decision-Making

An alternative for post-Algebra II

“This is a story about the big public conversation the nation

is not having about education, the one that will ultimately

determine not merely whether some fraction of our children

get "left behind" but also whether an entire generation of

kids will fail to make the grade in the global economy

because they can't think their way through abstract

problems, work in teams, distinguish good information

from bad or speak a language other than English.”

Time, Dec. 18, 2006

How to Build a 21st Century Student

National Center on Education and the Economy, 2007

Profile of Successful Workers

Top academic performance

Creative and innovative

Able to learn very quickly

Today’s World

Bill Gates:“Do we know where we're going? Are we clear about our destination – ensuring that every student graduates from high school ready to succeed in college, career, and life?”

What do all students need?

Economic securityMore math and science than we thought--Within a well-balanced curriculumOptions for future choices and redirectionsAppreciating the need for life-long learningThinking, reasoning, communication and problem solving skills for versatilizingThe opportunity to develop their potential-- their right as citizens and human beings; our responsibility as educators

Preparing all students for…

College

Work

Citizenship

Ready for College and Ready for Work: Same or Different?

ACT, May 2006

Whether planning to enter college or workforce training programs,

students need to be educated to a comparable level of readiness in

reading and mathematics…if they are to succeed in college-level

courses without remediation

and to enter workforce training programs

ready to learn job-specific skills.ACT, 2006

So how much math do students need for success in college, work, and citizenship, and what math is it?

What kind of math will they need?

Moving toward national consensus...

Principles and Standards for School Mathematics

Curriculum Focal Points PK-8

National Math Panel Final Report: Foundations for Success

College Board, Achieve, ASA, NCTM

Recent Secondary Recommendations

• Achieve: New definition of high school math

(more statistics, flexible organization)

• College Board:

Standards for College Success

(more statistics, flexible organization)

• American Statistical Association

GAISE: Guidelines for Assessment and Instruction in

Statistics Education

(more statistics, flexible organization)

• NCTM…

• States… Washington!

Emerging themes

• Algebra II is the new Algebra I

• But what is Algebra II?

• Statistics is (arguably) one of the most useful mathematical sciences

• Financial literacy is critical and lacking

• Changing world, changing student needs may call for changing our view of math PK-16

Where do they get what they need?

High school: 4 x 4 (Interesting high school fourth-year courses)

Two-year colleges

Four-year institutions

Workforce training programs

Achieve’s Advocacy for Rigorous Math for All Students

• ADP Benchmarks define the rigorous math content needed by all students for success in college and careers.

• Achieve research, augmented by that of ACT and College Board, shows that a 4th year of math—at least through Algebra II—is associated positively with students’ college readiness.

Achieve’s Advocacy for Rigorous Math for All Students

• Taking rigorous math at least through Algebra II:–Reduces the remediation rate in college–Reduces the gap in college completion rates between

White students and African-American and Latino students by half

–More than doubles a student’s likelihood of earning a college degree at a public 4-year institution compared to students who stop at geometry

–Results in students feeling better prepared for college and careers

• But math in the senior year is the biggest predictor of college success

“The intensity and quality of one’s secondary school curriculum was the strongest influence not merely on college entrance, but more importantly, on bachelor’s degree completion for students who attended a four-year college at any time.”

“What you study, how much of it, how deeply, and how intensely has a great deal to do with degree completion.”

- Adelman, Toolbox Revisited, 2005

“The impact of a high quality, rigorous, high school curriculum on degree completion is more pronounced, positively, for African American and Latino students than any other pre-college academic resources indicator.”

- Venezia, Betraying the College Dream, 2003

Criteria for High-Quality Capstone Courses

• Students should solidify and increase mathematical knowledge and skills at and above the level of Algebra II or its equivalent.

–Arithmetic and algebraic processes–Continued experience with functions–Topics from non-traditional areas

Criteria for High-Quality Capstone Courses

• Students should deepen and enrich the ways they think about math to elevate its study beyond rote memorization to a process of analysis and interpretation…

–Conceptual thinking–Justification and reasoning, in context–Experimental thinking and inquisitiveness–Abstraction and generalization–Connections–Technology applications

Criteria for High-Quality Capstone Courses

• Students should develop an appreciation for and experience with a variety of applications of math across disciplines and in practical situations

–Focus on non-routine, interesting problems–Emphasis on modeling and problem solving–Problems that have multiple solution pathways–Encouragement and nurturing of persistence

Rubric and Rating System

• System for evaluating and comparing 4th year capstone courses

• Based on 15 Criteria for High-Quality Capstone Courses

• Use of a rating scale of 0 to 3• Rubric on joint Achieve/Dana Center

website to facilitate rating http://www.utdanacenter.org/k12mathbenchmarks/

Principles and Standards for School Mathematics, NCTM, 2000

More than content

MATHEMATICAL PROCESSESProblem solving

Reasoning

Connections

Communication

Representation

4 years of math for all in the U.S.: What’s happening now?

–Districts are creating their own 4th-year courses, often depending on teacher interest and capacity

–There’s no consistency across districts.–Higher ed is most likely not involved in developing

courses (not true in WA).–There are few resources.–There is little professional development.–There are no common standards.

Proposed Suite of High School Mathematics Courses

• Algebra I / Geometry / Algebra II• or Integrated Math I / II / III• Math Models with Applications

(Algebra I pre-req; before Algebra II)• Precalculus (Alg. II pre-req)• Proposed Course (Alg. II pre-req):

Advanced Mathematical Decision-Making • AP Calculus (or IB)• AP Statistics• Concurrent / dual enrollment

Advanced Mathematical Decision-Making: AMDM

A joint (ad)venture of the Dana Center

and the Texas Association of Supervisors of

Mathematics

With partial funding from the Greater Texas Foundation

AMDM: Audience/Purpose

• Rigorous, relevant course to follow Alg. II• Important math not currently addressed;

assumes some fluency with Algebra I and Geometry

• To serve as a 4th-year math requirement for non-STEM majors and/or students who are workforce-training-program-intending

• Possible elective for calculus-intending students• Coherent part of PK-12 math program

AMDM: Philosophy/Approach

• Modeling and reasoning throughout

• Range of contexts

• Strong financial strand

• Communication and presentation encouraged

• Projects, extended problems appropriate

• Appropriate technology used to extend mathematical understanding and allow complex problem solving

AMDM: Considerations

• Need for student expectations/standards • Need for accompanying high-quality,

comprehensive, coherent instructional materials

• Need for long-term, high-quality professional development and training

• Must be a coherent part of district’s and state’s PK-12 programs

AMDM: What the course is NOT

• Remedial or test prep• Computation-focused• Naked math

(math without outside context)• Algebra III• Algebra II louder and slower• Another statistics course to replace AP

Statistics• Precalculus

AMDM: Content topics• Analyzing information using statistical

methods and probability

• Modeling change and mathematical relationships

• Mathematical decision making in finance and society

• Spatial and geometric modeling for decision making

AMDM Resources: Core Units• Analyzing numerical data

• Probability

• Analyzing statistical studies

• Designing a study

• A discrete look at change

• More continuous models of change

• Spatial and geometric modeling

• Networks and graphs

• Decision making in finance

• Decision making in fair division and selection (supplemental unit)

AMDM: Next steps

• Dissemination of the set of student

expectations for the course (2008)

• Materials development and online

dissemination (2008-09)

• Professional development

• Implementation and support

• Pilot with materials: 2009-2010;

Implementation: 2010-2011

Cathy Seeley, Charles A. Dana Center

Questions to Ponder...

• Do high school Algebra II and Geometry have to change for all students? What about 13-16?

• What if freshman college math were based on statistics or had a statistics alternative?

• At what point should students choose a path (or have it chosen for them)?

• What math and science does a student really need to succeed in college? in a good job?

• What if they come to higher education really knowing the math and science from a 4 x 4 program?

Academic Youth Development Academic Youth DevelopmentShaping the Culture of Ninth-Grade Classrooms

• In the National Math Panel survey, 62% of teachers rated “working with unmotivated students” as the “single most challenging aspect of teaching Algebra I successfully.” (Foundations for Success, p.9)

• In a campus study of 144 students who failed Algebra I, only 3 failed only Algebra.

Districts face a crisis in Algebra I, … but it’s not only Algebra

Model of the program

• Student audience: 8th graders rising to 9th grade Algebra I; regular students

• Teachers: those who will be teaching Alg I in the fall

• Summer component: 14 days, 4 hours per day, 2 AYD teachers with up to 30 students

• Fall: students scheduled into Alg I courses, 5 students per class, in AYD teacher’s classes (this will mean hand-scheduling)

• Academic year component: 4-6 “gatherings” per year with students and teachers

• All resources for AYD program online through Agile Mind

• Districts agree to share data and learnings with the Dana Center AYD researchers and evaluators

AYD key design elements

Goals of the AYD Initiative

Three primary goals:

• Improve student performance in Algebra I and all high school mathematics courses.

• Build a classroom culture focused on respectful engagement in academics.

• Increase the capacity for teaching to rigorous mathematics standards.

What is Academic Youth Development?

AYD helps students develop

• academic identities as learners who recognize, value, and seek out high-quality education.

• skills to enable them to help create and contribute to a learning community.

Social psychology influences

The program incorporates ideas from social psychology:

• Effective effort: Improving and getting better at something requires the right kind of effort.

• Attribution: Success is attributed to task-specific causes (e.g. effort), not to global causes (e.g. luck or native intelligence).

• Malleable intelligence: Intelligence is something that can be influenced and shaped through actions and beliefs.

Beliefs, attitudes, and behavior

AYD focuses on the beliefs, attitudes, and behavior of a cadre of emerging student ‘allies’ algebra teachers can rely on to

• model effective engagement and academic success.

• help support and shape the Algebra I classroom culture for learning mathematics.

• build a strong relationship between teachers and students.

AYD shapes and supports a culture in which . . .

• Engagement, participation, positive motivation, and risk-taking are developed and embraced.

• Students don’t have to choose between being smart or being cool.

• Effort and persistence are recognized and valued.

• Mutual accountability is fostered and expected.

AYD becomes an integral part of a comprehensive approach to improving student outcomes in math

– Bonding between teachers and students– Changes in beliefs and attitudes– Students will be able to articulate their own role in

learning– Students are increasingly able to work and learn

together

AYD: What can schools expect?

Supporting the Broader Vision

AYD is one necessary but not sufficient component of improving

the campus/district Algebra I program.

Algebra Intensification Algebra IntensificationSupport for double-blocked Algebra I in 9th grade

Algebra I for students likely to struggle: A critical district concern

Many campuses offer double-block Algebra I for struggling students; however…

• There are few, if any, resources for 90-minute classes

• Teachers are often inexperienced, or brand new

• Teachers are often left on their own

• Most resources don’t address social or emotional needs of struggling students

So, these classes have limited success.

Transforming thinking about Algebra for struggling students

• Multifaceted architecture of intensification that addresses multiple key areas simultaneously—e.g., extra instructional time, attention to curriculum and instructional materials; modified instructional approaches; student motivation and social supports; and teacher knowledge and expectations.

• Teacher support geared toward communities of teachers within and across schools; the program will be conceived and built to help districts address this issue at scale—i.e., we are proposing a districtwide solution to a problem that had previously been conceived of as a problem to be solved by individual math teachers and schools.

• Builds from effective existing materials, adapting them for use within a single coherent program framework, and will also develop new materials as needed.

Algebra I Intensification

Developing a comprehensive prgram for underprepared students in Algebra I:

• Effective approaches and materials for teaching mathematics

• Latest research on… Language development and literacyMotivationSpecial Ed supportsAssessmentYouth development

Dana Center, University of Illinois at Chicago, Urban Mathematics Leadership Network, Agile Mind

(funding from Gates and Carnegie Foundations, Dana Foundation, Chicago Community Trust)

Algebra I Intensification

Creating a coherent set of materials, including• Complete Algebra I curriculum (Agile Mind Alg I) and

assessment• Opportunities for just-in-time review or reteaching skills

students are not proficient in• Academic Youth Development components integrated

throughout• Detailed and specific instructional advice for teachers• Supports and protocols for reaching special needs students

(Content Enhancement Routines from the University of Kansas Center for Research and Learning)

• Resources for leaders on how to interpret formative and summative data and support students and teachers

• Other supports

Algebra I Intensification

• Developing 4-5 prototype units 2008-09• Pre-piloting/co-developing with teachers from

Austin, Chicago, Evanston, Los Angeles• Core curriculum developed by 2009-10• Piloting in UMLN districts (at least)

Dana Center InitiativesThat May Be of Interest to TMP

What do you think? Are there ways to use these resources or the ideas from the resources to

support teaching and learning?Let us know what you are thinking…

Thank you! Susan Hull

shhull@mail.utexas.edu