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 79 th 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: 1 st reading and filing of revised math TEKS Jan. 2009: 2 nd 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