Rethinking Developmental Mathematics, High School Math Courses, and College Readiness

Advisory Team for Quantitative Reasoning HS and HE coursesCharles A. Dana Center The University of Texas at Austin

September 23, 2013

About the Dana Center

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The Charles A. Dana Center at The University of Texas at Austin works with our nation’s education systems to ensure that every student leaves school prepared for success in postsecondary education and the contemporary workplace.

Our work, based on research and two decades of experience, focuses on K–16 mathematics and science education with an emphasis on strategies for improving student engagement, motivation, persistence, and achievement.

We develop innovative curricula, tools, protocols, and instructional supports and deliver powerful instructional and leadership development.

There are serious disconnects HSHigher Ed

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Source: Complete College America

In mathematics, developmental education is even more common 67% of community college students are referred to one or more

developmental math courses (and 80%+ in some systems)

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Developmental Education Pipeline at Public Two-Year Colleges Fall 2007 Cohort

Cohort total: 99,097

Of students below state standard in mathematics 100

Enrolled in developmental education 83

Achieved college readiness 39

Attempted first college-level course 21

Successfully completed first college-level course 15

Source: Texas Higher Education Coordinating Board

Long developmental sequences increase attrition

Two-year cohort data from a typical large community college in Texas

There are serious disconnects HSHigher Ed

High school preparation often has not led to college readiness…

“Well, I think the biggest thing for them is, here, they’ve graduated from high school but they come and take our placement test and they’re still in pre-college … math and they don’t understand that if they stop taking math in their sophomore year that, you know, they don’t get it…

and I think the sad thing is that they say…‘no one told me that I should be taking math all the way through’.”-community college advisor (Stanford University Project report, 2004)

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If high school had demanded more, graduates would have worked harder

82%80%

Would have worked harder Strongly feel I would have worked harder Wouldn’t have worked harder

High school graduates who went to college

High school graduates who did not go to college

Source: Peter D. Hart Research Associates/Public Opinion Strategies, Rising to the Challenge: Are High School Graduates Prepared for College and Work? prepared for Achieve, Inc., 2005.

Achieve, 2005

Majority of graduates would have taken harder courses

Knowing what you know today about the expectations of college/work …

Would have taken more challenging courses in:

Would have taken more challenging courses in at least one area

Math

Science

EnglishSource: Peter D. Hart Research Associates/Public Opinion Strategies, Rising to the Challenge: Are High School Graduates Prepared for College and Work? prepared for Achieve, Inc., 2005.

Achieve, 2005

The Dana Center is working on a multi-pronged approach to smooth transition HSHigher Ed

Redesign higher education remediation at scale: the Dana Center’s New Mathways Project

Support districts’ high school standards implementation to ensure college-ready mathematics for all students (CCSSM, TEKS)

Introduce a new breed of 4th-year high school mathematics courses that provide an additional pathway into college readiness

Work in the policy sphere to ensure students can transition successfully

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Audience: Students graduating from high school should be college ready

HS HE math

College ready

The Dana Center is working on a multi-pronged approach to smooth transition HSHigher Ed

Redesign higher education remediation at scale: the Dana Center’s New Mathways Project

Support districts’ high school standards implementation to ensure college-ready mathematics for all students (CCSSM, TEKS)

Introduce a new breed of 4th-year high school mathematics courses that provide an additional pathway into college readiness

Work in the policy sphere to ensure students can transition successfully

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NMP audience: Students directly from high school and not college ready in mathematics

HS HE math

NMP Not college

ready

College ready

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NMP audience: Students not directly from high school and not college ready in mathematics

HE math

NMP Not

college ready

Not directly from HS

College ready

New Mathways Project: Setting the agenda

Charles A. Dana Center at the University of Texas at Austin

Led development of original curricula for pathways to college success—Statway and Quantway—in partnership with the Carnegie Foundation

Texas Association of Community Colleges

Represents all 50 community college systems in Texas

Represents the interests of community colleges in state policymaking and budgeting

A unique partnership of colleges setting the agenda for reform

addresses issues from the classroom to state policy

allows for collaboration and input from people at all levels of the system

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The Principles of the NMP Model

A systemic approach to improving student success and completion by reforming developmental and gateway mathematics:1. Multiple pathways with relevant and challenging mathematics content

aligned to specific fields of study

2. Acceleration that allows students to complete a college-level math course within 1 year—more quickly than in the traditional developmental math sequence.

3. Intentional use of strategies to help students develop skills as learners and experience college success

4. Curriculum design and pedagogy based on proven practice

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The NMP Courses

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The NMP Courses

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The Dana Center is working on a multi-pronged approach to smooth transition HSHigher Ed

Redesign higher education remediation at scale: the Dana Center’s New Mathways Project

Support districts’ high school standards implementation to ensure college-ready mathematics for all students (CCSSM, TEKS)

Introduce a new breed of 4th-year high school mathematics courses that provide an additional pathway into college readiness

Work in the policy sphere to ensure students can transition successfully

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Audience: Students graduating from high school should be college ready

HS HE math

College ready

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Audience: Students graduating from high school with college credit are, de facto, college ready

HS HE math

Proposed pathways to readiness for college math

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Alg I Geom Alg IIGrades 6, 7, 8

Precal AP Stat

AMDM/AQR

(and other 4th yr )

QR (and other dual

enroll)

College mathematics

Successful completion certifies college readiness in mathematics

If the goal of college readiness is for students to succeed in college-level courses, students need access to—and experience in—college-level courses.

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Quantitative Reasoning: A proposed new dual enrollment course

Built using similar outcomes as college-level QR courses

Emphasizes content meaningful to students’ professional, civic, and personal lives

Develops skills in interpreting, understanding, and using quantitative information

Teaches algebraic and modeling skills through quantitative literacy lens

Emphasizes critical thinking and strategic reasoning

Designed for non-STEM intending students

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Quantitative Reasoning: A proposed new dual enrollment course

Quantitative Reasoning from a National Perspective

Eric Gaze, Ph.D.

President-elect, National Numeracy Network

Bowdoin College, Brunswick, Maine

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Quantitative Reasoning: What is it?

The Dana Center is working on a multi-pronged approach to smooth transition HSHigher Ed

Redesign higher education remediation at scale: the Dana Center’s New Mathways Project

Support districts’ high school standards implementation to ensure college-ready mathematics for all students (CCSSM, TEKS)

Introduce a new breed of 4th-year high school mathematics courses that provide an additional pathway into college readiness

Work in the policy sphere to ensure students can transition successfully

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The Dana Center is working on a multi-pronged approach to smooth transition HSHigher Ed

What are the policy implications we need to consider?

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Contact Information

General information about the Dana Center: www.utdanacenter.org

Higher Education work: www.utdanacenter.org/higher-education/

To receive monthly updates about the NMP, contact us at: mathways@austin.utexas.edu

Staff contacts: Susan Hudson Hull (mathematics): shhull@austin.utexas.edu Amy Getz (NMP general project issues): getz_a@austin.utexas.edu Connie Richardson (NMP QR development): cjrichardson@austin.utexas.edu Kathi Cook (HS course program): klcook@austin.utexas.edu Lindsay Fitzpatrick (policy issues): lindsay.fitzpatrick@austin.utexas.edu

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Quantitative Reasoning Outcome Planning

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High School Course Descriptors

Proportional reasoning, ratios, rates, percents, vectors, matrices, network models, mathematical models, voting, selection, geometric representations, inaccessible distances, probability, expected value, analysis of statistics, conduct statistical studies, function models, multiple representations, reasoning, evaluation, communication, connections, vectors, matrices, polynomials, rational expressions, equations, inequalities, trigonometric functions, similarity, right triangles, measurement, dimension, geometric modeling, statistics, probability, interpreting data, making inferences, justifying conclusions, decision-making, numerical reasoning, probability, statistical analysis, finance, mathematical selection, modeling, algebra, geometry, trigonometry, discrete, analyze real-world numerical data, risk, return, analyze statistical summaries, make decisions, conduct statistical studies, communication, ranking, selection, modeling, predicting, evaluating, modeling change, finance, networks, geometric modeling

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High School Course Descriptors

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Higher Ed Course Descriptors

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Combined Course Descriptors

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Occurrences

> 5 times 4 times 3 times 2 times 2 times 2 times

statistics data communication analysis interpreting exponential

probability finance consumer analyze linear functions

modeling geometric mathematics applications logic inequalities

models geometry measurement change making information

reasoning mathematical percentages conclusions matrices proportion

statistical rates conduct number studies

theory representations decision of systems

selection equations processing vectors

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Single Occurrences

algebra discrete function network real tables

central distances game networks return tendency

citizenship division graph numeration right triangles

coding drawing inaccessible patterns risk trigonometric

combinatorics effective inferences polynomials scales trigonometry

connections evaluating informed predicting science units

conversions evaluation interest proportional set value

counting evidence justifying proportionality sets voting

decision-making expected make ranking similarity world

decisions expressions management ratio sophisticated

descriptive fair measures rational summaries

dimension from multiple ratios symmetry

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Statistics

The student makes decisions based on understanding, analysis, and critique of reported statistical information and statistical summaries.The student is expected to:(A) Identify limitations or lack of information in studies reporting

statistical information, including when studies are reported in condensed form;

(B) Interpret and compare the results of polls, given a margin of error;

(C) Identify uses and misuses of statistical analyses in studies reporting statistics or using statistics to justify particular conclusions; and

(D) Describe strengths and weaknesses of sampling techniques, data, and graphical displays, and interpretations of summary statistics or other results appearing in a study.

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Task

What are the “buckets”?

Learning outcomes

Performance descriptors