“College Readiness Standards
in Mathematics”
presented by
Dr. Larry Lesser of
for
Charles A. Dana Center
2008 Higher Education Conference
on “Current Issues in Mathematics and Science Education:
Transition to College”
Larry Lesser, Assoc. Prof.
Mathematical Sciences Dept.
University of Texas at El Paso
www.math.utep.edu/Faculty/lesser
as seen in Sept.’08 Math. Teacher!
OUTLINE
1. My connection to the topic
2. Some national context
3. Some Texas context
4. College Readiness Standards
5. Work of Phase 1 & 2 Vertical Teams
6. Next steps
7. Resources (e.g., handout on web)
8. Q & A, then LUNCH!
3 reasons I’m glad I did this work
• Got to meet and work with some great
people statewide
• Gained familiarity with the bigger picture of
the TEKS and of college readiness
• Gained opportunity to reflect upon my own
trajectory and realize just how much of my
background/work was connected to it
my related background (in Colorado)
• co-authored (McGraw-Hill) college algebra text
(different pace, goals, emphasis on higher-order
thinking than HS course)
• on math content Vertical Team for 1994-95
Colorado Commission on Higher Education
grant “The Next Step: K-12 and Higher
Education Working Differently and Together”
to create ‘seamless’ K-16 alignment between
HS exit standards & college entrance standards
more (Colorado) background
Reformed intro stat course for CCHE grant
“Educational Technology Improvement Project”.
“In 1993, the Colorado General Assembly enacted
HB93-1313, making K-12 public schools develop
content standards and performance-based
assessments by 1997. So these students are
expecting more compatibility with universities in
terms of how admission criteria will be established
and in terms of assessment in university classes
themselves.” (Lesser 1998, p. 54; Tech.Hor.Ed.)
www.math.utep.edu/Faculty/lesser/StatStandards.html
my related background (in Texas)
• as HISD student, I took Adv. Placement & Int’l Baccalaureate
courses
• 2 decades teaching includes 2 yrs full-time HS teaching (in TX)
• Recent Dana Center meetings gave out David Conley’s College
Knowledge and US DOE’s The Toolbox Revisited: Paths to
Degree Completion from High School Through College
• UTEP Provost’s 2007-08 Task Force on Developmental and
General Education Mathematics Course Success Rates (about
2/3 of UTEP grads [1/3 of STEM majors] started with ≥1 dev.
math);
solutions include starting Accuplacer test with HS juniors &
seniors and starting accelerated development program at UTEP
still more (Texas) background
• El Paso’s systemic grants (e.g., MSP)
bring together university, community
college, and high schools (e.g., UTEP,
EPCC, & big 3 ISDs all agreed on same
precalculus & calculus books!)
• El Paso has 4 Early College High Schools:
Socorro ISD & EPCC Mission del Paso;
El Paso ISD & Transmountain EPCC;
Canutillo ISD & Northwest EPCC;
Ysleta ISD & Valle Verde EPCC
Importance of CR
from the start of one’s education
“Mathematics educators at all levels should
be aware of these standards – they aren’t
just for high schools! Many of these
student performance descriptors originate
in elementary schools and are refined
vertically through middle and high school.”
-- former TCTM President JoAnn Wheeler
College readiness:
a subject of national debate
USA Today, September 22, 2008, p. 12A
• Editorial: “43% of CC students are enrolled in a
remedial class. At 4-year colleges, 30%. The
cost for colleges and taxpayers: more than $2
billion/year…Nearly 4 of 5 remedial students had
a HS GPA of B or better.”
• “Opposing view: don’t blame HS” (G. N. Tirozzi):
“If NAEP scores are any indication, some states
have rigorous standards and some don’t.”
NASSP calls for “rigorous national standards for
K12 education for all students”
Current Ways to Assess CR
(Conley 2007)
www.epiconline.org/crs_regional_meetings/workshop_materials
• HS course taking patterns
challenge: measuring nature and quality of courses
• HS GPA
challenge: mean of HS GPAs has steadily increased, but
not measures of college success
• state standards-based high-stakes tests
challenge: alignment with postsecondary learning; varying
definitions of proficiency; limited in how deeply they can
assess higher-order skills or performance tasks
• placement into college courses
challenge: placement methods and requirements vary
greatly between institutions
Facets of CR (Conley 2007, p.12)
how to assess 4 aspects of
Conley (2007) model of CR:
• key cognitive strategies:
collection of classroom evidence
• key content knowledge:
end-of-course exam
• academic behaviors:
student survey & inventory
• contextual skills and awareness:
questionnaires
an aside: CR is part of
an even bigger view of ‘readiness’
(2008; www.childtrends.org)
• 3 goals: college readiness, workplace
readiness, & healthy youth development
(for transition to adulthood)
• needed competencies organized into
5 domains of youth development: cognitive,
social, psychological, spiritual, physical
success in college math requires
(Conley 2007, p. 15):
• thorough understanding of concepts of
mathematics (especially algebra), beyond
"exposure" or "formulaic understanding"
• ability to "extract a problem from a context,
use mathematics to solve the problem,
and then interpret the solution back into
the context. They know when and how to
estimate to determine the reasonableness
of answers and can use a calculator
appropriately as a tool, not a crutch."
Marcus et al. (2008)
Recommendations for college reform
(e.g., MAA’s “A Collective Vision”, 2004)
parallel
recommendations in NCTM (2000)
Process Standards (problem solving,
reasoning/proof, communication,
connections, representation)
Brown & Conley (2007, p.139, 152)
• “The adoption by states of P-16 legislation is one
more indicator that state policymakers are
reconceptualizing the organizational structure of
their public education systems from preschool
through postsecondary education in ways that
connect the levels more directly.”
• “State HS assessments and the knowledge and
skills necessary for university readiness align in
areas that might be characterized as more basic
and do not align as well in areas requiring more
sophisticated cognitive functioning.”
Brown & Conley (2007, p. 153)
• “…some reasonable degree of alignment
already exists between a high school
education in most parts of the country and
at least a subset of college-readiness
skills. The more pressing question is
whether this baseline level of alignment is
sufficient to result in well-prepared
students at a time when the proportion of
HS graduates pursuing postsecondary
education is increasing.”
Brown & Conley (2007, p. 153)
• “this alignment is not evenly distributed
across the standards. Reading and writing
standards in English and computation and
mathematical reasoning in mathematics
explain most of the alignment. Other
standards areas such as research skills,
critical thinking, statistics, and
trigonometry are seriously
underrepresented or nonexistent in state
tests.”
value of postsecondary education
(Census Bureau data graphed on p.90 of 2007 Report of Commission for a College Ready Texas)
is passing TAKS enough?
• Passing score on exit-level TAKS: 2100
• THECB/SBOE Higher Education
Readiness Certification standard: 2200
• NCEA (Nat. Center for Educ. Accountability)
college readiness benchmark:
2300
• TAKS commended performance: 2400
Texas College Readiness Program
3-year THECB-sponsored project to improve
alignment in Texas between
secondary & postsecondary education
Mandate given in 2006:
3rd Special Called Session of 79th Texas Legislature--
Article 5, House Bill 1 (Section 28.008 of
Texas Education Code: “Advancement of
College Readiness in Curriculum”)
2 phases done, 1 to go!
Phase 1: develop CRS
Phase 2: analyze alignment between CRS
(entry-level “reference courses”) and TEKS
Phase 3: develop or establish minimum
standards for curricula, professional
development materials, and online student
support materials
what is “college readiness”?
THECB says a college-ready student
“has the knowledge and skills necessary
to begin entry-level college courses
with a reasonable likelihood of success
and does not require developmental
education.” (Tex. Admin. Code, 2007)
national sources of CRS
• ACT (American College Testing): CRS
• Achieve: ADP (American Diploma Project)
Benchmarks
• College Board Standards for College Success
• Standards 4 Success from College Knowledge
(David Conley 2003, 2005)
• Some state CRS (e.g., CA, WA) are viewed by
some to be of “national quality”
Texas’ College
Readiness Standards
in 4 areas (Math, English,
Science, Social Studies)
Written by Phase 1 Vertical Team in 2007 (4 meetings!),
Facilitated by EPIC (Educational Policy Improvement Center)
from University of Oregon
Adopted by THECB January 24, 2008
Phase 1 math Vertical Team
(* = co-chair)
HIGHER ED (6)
• Thomas Butts (UT-Dallas)
• Troy Furlough (DCCCD,
El Centro College)
• Selina Vasquez-Mireles*
(Texas State U.)
• Doug Hale
(UT-Permian Basin)
• Lucy Michal (El Paso CC)
• Linda Zientek
(Sam Houston State)
SECONDARY ED (4)
• Linda Gann* (Northside ISD)
• Kenneth Grantham
(Dallas ISD)
• Shary Horn (Alvin ISD)
• Diane Reed (Ysleta ISD)
the 10 Texas Mathematics CRS
• • • • • • • • • • Numeric Reasoning
Algebraic Reasoning
Geometric Reasoning
Measurement Reasoning
Probabilistic Reasoning
Statistical Reasoning
Functions
Problem Solving and Reasoning
Communication and Representation
Connections
TX math CRS (NCTM Standards)
• • • • • • • • Numeric Reasoning (number and operations)
Algebraic Reasoning (algebra)
Geometric Reasoning (geometry)
Measurement Reasoning (measurement)
Probabilistic Reasoning (data analysis and probability)
Statistical Reasoning (data analysis and probability)
Functions (algebra)
Problem Solving and Reasoning (problem solving;
reasoning and proof)
• Communication and Representation (communication;
representation)
• Connections (connections)
Organization of math CRS:
math standard
organizing concept
performance expectation
performance indicator
I. Numeric Reasoning
A. Number representation
1. Compare real numbers
a. Determine question(s) that
can be answered with data
Phase 2 math Vertical Team
(* = co-chair)
HIGHER ED (4)
• Mufid Abudiab
(Texas A&M-Corpus Christi)
• Peg Crider
(Lone Star College-Tomball)
• Lawrence Lesser*
(U. of Texas at El Paso)
• Dawn Slavens
(Midwestern State U.)
SECONDARY ED (6)
• Gabriel Estrada
(Pharr-San Juan-Alamo HS)
• Linda Gann*
(Northside ISD)
• Linda Sams
(Cypress-Fairbanks ISD)
• Jane Silvey (ESC 7)
• Rita Tellez (Ysleta HS)
• Angie Watson (ESC 16)
charge of Phase 2 Vertical Team
(TEC 28.008(b)(2)&(3))
• Evaluate whether the HS curriculum
requirements under Section 28.002 and
other instructional requirements serve to
prepare students to successfully perform
college-level course work
our Gap Analysis spreadsheet
• Column A: Texas math CRS performance
expectation
• Column B: Vertical team’s alignment rating
(breakdown of 10 votes) of the Column A
item with the TEKS
• Column C: all specific parts of the TEKS
that constitute the alignment (in some
cases, this was quite lengthy, such as
when “multiple representations” were
involved)
Specific example of where the VT rated
a CRS performance expectation
as being “strongly aligned” with TEKS
CRS III.D.2. “Understand that Euclidean
geometry is an axiomatic system”
TEKS G.1 “Geometric structure.
The student understands the structure of, and
relationships within, an axiomatic system….”
[also, see “The student is expected to:” items]
Specific example rated as “aligned”,
but not “strongly aligned”
CRS V.B.2. “Compute and interpret the
probability of conditional and compound
events.”
TEKS 7.10(A) “construct sample spaces for
simple or composite experiments”
TEKS 8.11(A) “find the probabilities of
dependent and independent events”
Phase 2 VT alignment ratings
• given for each of the (70) performance
objectives of the Texas math CRS
• given for each of the (10) math standards of the
Texas math CRS
• Overall main finding: “The CRS in mathematics
are well-aligned with the TEKS for Secondary
Mathematics”
(see VT’s narrative report at:
www.tea.state.tx.us/teks/CRS_Math_VT_Phase_twoIntro.pdf)
VT-rated alignment of math CRS
(with secondary math TEKS)
Aligned:
Numeric Reasoning
Probabilistic Reasoning
Strongly Aligned:
Algebraic Reasoning
Geometric Reasoning
Measurement Reasoning
Statistical Reasoning
Functions
Problem Solving and Reasoning
Communication and Representation
Connections
Also part of Phase 2 VT’s charge:
(TEC 28.008(b)(2)&(3))
• Recommend how the public school
curriculum requirements [i.e., TEKS] can
be aligned with the CRS
(note:
we could not suggest changes in CRS;
any changes we suggested in TEKS
had to be related to CRS alignment)
Phase 2 math VT’s process
• Pre-meeting HW in mid-July done as individuals:
rate degree (SAW = Strong/Average/Weak) of
alignment between each CRS item and the TEKS
• Meeting in Austin July 23-24, 2008 to discuss and
make draft of gap analysis(GA) and suggestions
for SBOE-appointed math TEKS writing team
• Co-chairs clean up GA, draft narrative, and send
to VT
• VT discuss report on Aug. 4 conference call
• VT emails approval and report deemed final in
time for Aug. 28-29 meeting of TEKS writing team
who attended July 23-24, 2008
Phase 2 VT meeting?
• Phase 2 Math Vertical Team
• Math TEKS writing team (to listen actively
and ask clarifying questions of VT,
but not to do gap analysis)
• TEA and THECB officials and staff
• Unofficial observers from other subject
areas yet to go through the process
Further Comments
in Phase 2 math VT report
• VT not able to assess alignment with
Cross-Disciplinary CRS (especially
technology standards)
• Phase 3 VT will need to ensure teachers
understand the rigor and intent of the
standards through professional
development and instructional materials
after the Phase 2 VT’s work…
SBOE-appointed Math TEKS Writing Team met
Aug. 28-29 and started the revision process for
MS & HS math TEKS to incorporate CRS (now
posted by TEA):
• modified existing Knowledge & Skills statements
(MS: 7.10; 7.12; HS: M.3)
• modified existing Student Expectations
(MS: 7.4A, 8.2D, 8.12A; HS: 2A.6C)
• added Student Expectations
(MS: 8.1E; HS: G.8E, G.8F)
example of WT’s reported rationale
“For added clarity and to strengthen the alignment
with the CRS, the WT added the phrase
‘including conversions between measurements
systems’ to 8.2D. This revised SE provides an
opportunity to prepare students for dimensional
analysis, which addresses the VT’s
recommendation to support alignment between
math and science.
To further address the alignment with science and
address the VT’s recommendation to convert
between measurement systems, the WT created
a new high school SE, G.8F [Use conversions
between measurement systems to solve
problems in real-world situations.]”
Excerpt of “revised TEKS”
THECB/EPIC offer 14 Regional CRS meetings
(Oct. 20 - Nov. 13, 2008)
• Goal: to disseminate and to develop
regional plans for support systems and
curriculum alignment
www.epiconline.org/crs_regional_meetings
• Cities: Tomball, Houston, Austin, El Paso,
Lubbock, Midland, Abilene, Denton, Dallas,
Tyler, Edinburgh, Corpus Christi, San
Antonio, Laredo
What’s next?
• • • • • • • • Nov. 2008: 1st reading and filing of revised math TEKS
Jan. 2009: 2nd reading and adoption
Spring/Sum. 2009: TEA determines what’s on EOC’s
Summer 2009: Prof. Development for teachers on
revised math TEKS with CRS
Summer/Fall 2009: Phase 3 Vertical Teams establish
criteria for CRS online student materials
Fall 2009: implement secondary math revised TEKS
Spr./Sum. 2010: PD for CRS online student materials
Fall 2010: Implement online math CRS materials
www.tea.state.tx.us/teks/mathTEKS.html
CRS material also in the
fall 2008 Texas Mathematics Teacher
• “TEA Talks” news (Torres-Martinez,
Pierce, Duncan), pp. 20-22
• “Texas CRS in Mathematics” feature
(Lesser, Gann), p.15
REFERENCES
(on Higher Ed Conference website)
• www.thecb.state.tx.us/collegereadiness/
• www.tea.state.tx.us/HB1/ColRea/
• www.tea.state.tx.us/teks/mathTEKS.html
• www.tea.state.tx.us/math/
• www.collegereadytexas.org
• www.epiconline.org/texas_college_readiness_standards
www.epiconline.org/crs_regional_meetings/workshop_materials
Sources & Acknowledgments
• Texas Education Agency
• Texas Higher Education
Coordinating Board
• Charles A. Dana Center
• Commission for a College Ready Texas
• my phase 2 VT colleagues
THANK YOU!
Larry Lesser (UT-El Paso)
Comments/questions?
www.math.utep.edu/Faculty/lesser