AVATAR: Aligning Algebra II and College Mathematics

April 2014 | Denton, Texas
BY: Jean Keller and Mary Harris

For two years, Academic Vertical Alignment Training and Renewal (AVATAR) partners in Education Service Center (ESC) Regions 2, 9, 10, 16, and 20 have been working to ensure more students move from high school to college successfully and without remediation in mathematics.  The AVATAR partnerships include an ESC, a local P-16 Council, and at least one high school that is a feeder to at least one two- and four-year institution of higher education (IHE) also in the partnership. These partnerships form Vertical Alignment Teams (VATs) that include secondary and postsecondary teachers and curriculum leaders.  VATs look at student performance and its implications for instruction by using Critical Conversations to explore a range of instructional issues.  This article offers examples from the work of VATs in four Texas regions to illustrate the AVATAR model.

Local and Regional Student Data 
Using local and regional student data provides an important starting point for conversation in each region.  A local PowerPoint draws on statistics reported by the Texas Education Agency (TEA) and the Texas Higher Education Coordinating Board (THECB).  Of particular interest are indicators within the TEA data of College Readiness and THECB data that show how high school graduates perform when they get to college [see http://ritter.tea.state.tx.us/perfreport/tapr/index.html and http://www.txhighereddata.org]. From these data, educators in Region 16, for example, learned about distinct and non-overlapping feeder patterns among the institutions in the region.  As a result, they invited some new partners to round out their partnership.  For educators in Region 2, the data reinforced that the fastest-growing segment of the local population, Hispanic males, was least likely to be successful in college.  Educators in Region 20 learned from UT-San Antonio staff about mathematics performances of students from particular high schools; consequently, they were able to identify student needs, as well as areas of student success, in college math readiness.

High School and College Algebra Syllabi Scrutiny       
Beginning in 2010 in pilot sites and in 2011 statewide, VATs looked at results of assessments in their regions, and many examined local syllabi for Algebra II and College Algebra in light of the Texas Essential Knowledge and Skills (TEKS), End-of-Course Assessments (EOC), Texas College and Career Readiness Standards (CCRS) and student learning outcomes at each level.  Study of the state standards and syllabi from Harlandale High School, San Antonio College, Palo Alto College, and UT-San Antonio, for example, led math educators in Region 20 to conclude that operations with complex numbers are not included in the Algebra II TEKS at the level necessary for the study of college-level algebra at local institutions.  Discussion of syllabi led to scrutiny of assignments and teaching practices. Instructors found that different vocabulary was sometimes being used by students and instructors to describe the same operations. All agreed that this could be confusing to beginning algebra students, who are easily misled by even minor differences in terminology and notation.  Differences in policies concerning the use of calculators by algebra students were striking, as were course policies, such as including homework in the final grade, allowing retakes of quizzes, and permitting extra credit assignments.  Other differences in instructional and grading practices arose from different decisions about how to assess group work. 
Results: Even when VAT members did not agree or felt that institutional policies prevented changes in practice, they were grateful to learn about these differences. High school educators resolved to tell their students more about what is expected in college and how to prepare for it.  College instructors were committed to take into consideration expectations their students might be bringing from high school.

Student Feedback and Interactive Journaling         
Region 16 mathematics educators developed a plan to involve Algebra II students in providing feedback about their journeys from high school to college algebra.  The VAT developed an interactive notebooking procedure through which students could reflect on their own learning experiences beginning in high school and continuing in college.  As the 2013 spring semester ended, Algebra II students In Amarillo ISD and Borger ISD used their notebooks to assess aspects of the algebra curriculum of which they were most and least confident.  Moving on to Amarillo College, Frank Phillips College, and West Texas A&M University, these students can expect to be consulted by the faculty about their experiences in college algebra: how well prepared were they for major components of the curriculum; what aspects of the transition were confusing; what points brought up in their journals represented issues that might be common to other students? 
Results: Interactive notebooking as a cross-institutional assessment tool is attractive to other sites, which will be starting this process with small groups of student informants. 
 
Development of Aligned Lessons
In 2013-14, the Region 9 VAT developed plans for lesson study using a method explicated by Lewis and Hurd in Lesson Study Step by Step (2011).  The intention here was for high school and college mathematics teachers to develop collaborative lesson plans based on content they believed could be better taught. After a preliminary lesson was created, mathematics faculty from Burkburnett ISD, Vernon ISD, Wichita Falls ISD, Vernon College, and Midwestern State University would visit each other’s classrooms to see how and what was being taught.  The focus of these visits was on student learning outcomes, while exploring various teaching methods and techniques. Subsequently, using the measure “I would recommend using this lesson to a colleague,” all team members participated in refining the lessons to better align with mathematics standards. 
Results: Region 9 is beginning to use lesson study. Though this approach is still in the early stages, it has the potential to strengthen professional community in ways that promote content learning, sharing of resources, and discussion of how students learn from secondary to postsecondary.

Sharing Results        
In all four regions, the VAT members often found themselves among the leadership team for guiding professional development curriculum that is provided by ESCs. Consequently, VAT recommendations have had an immediate impact on mathematics professional development.  In Summer 2013, Region 16 VAT members presented their work to regional math teachers at the ESC’s math conference.  In Region 20, math teachers benefitted from the work of Ainsworth (2003) on “Unwrapping” the Standards, an approach to restating standards in language that makes them more comprehensible.  In Region 2, this work merged with the School Mathematics Project at TAMU-Corpus Christi, which has workshops and online vehicles for exchanges of ideas between school and college-based mathematics faculty.  In Region 9, recent presentations for mathematics teachers have focused on alignment-related topics, such as the impact of new Texas Success Initiative (TSI) requirements on developmental education, basic content expectations of students entering college mathematics courses, and use of online resources to help students explore career pathways by mathematics requirements and income projections. 
       
References
Ainsworth, L. (2003).  “Unwrapping” the Standards.  Englewood, CO: Englewood Press.

Lewis, C. C. & Hurd, J. (2011).  Lesson Study Step by Step.  Portsmouth, NH: Heineman.