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Office Number:
Education 3260
Phone Number:
(805) 893-7770
E-mail:
education.ucsb.edu clager
Carl Lager
Assistant Professor, Ph.D. (University of California, Los Angeles)
Emphasis:
Teaching & Learning
Research Interests:
Mathematics education; Comprehensibility of mathematics instruction, curricula, and assessment; Large-scale mathematical assessment development; Preparation of pre-service English language learner (EL) mathematics teachers; Professional development of in-service EL mathematics teachers
Biography:
After finishing my B.S. in Applied Mathematics at UCLA, I taught mathematics to middle and high school English learners (ELs) - students whose primary languages were not English and who were not yet proficient in English - in both English and Spanish in the Los Angeles Unified School District for six years. Though earning my M.Ed., teaching credential, and Bilingual CLAD credential (in Spanish) in the interim helped teach me how to use research to inform my practice, the literature did not adequately prepare me to recognize or address their unique instructional and assessment needs. I also saw firsthand many of the language, culture, and identity tensions that my students and their families experienced as well as how certain education policies systematically kept the scholastic “playing field” tilted against them. To level that playing field for my students and other ELs and contribute to the research base, I went back to UCLA to earn my Ph.D. in Education.
While a doctoral student, I helped develop, facilitate, and evaluate the English Language Development – Mathematics Content (ELD-MC) institute, an in-service professional development model for California mathematics teachers and paraprofessionals of ELs grades 3-8 focused on integrating academic English language proficiency with algebraic instruction. The lessons learned spurred me to focus my dissertation research on exploring the language-mathematics interactions that typically challenge middle school ELs responding to developmental algebraic tasks involving a linear function. Surprisingly, I found that some English proficient students participating in the study exhibited some of the same linguistic challenges encountered by ELs. By my graduation in 2002, it appeared to me that though different components of the research applied to different groups of students, many students could benefit from some of its results.
Combining that new knowledge with my prior experience, I moved to Vermont to effect change for New England’s students (ELs and non-ELs alike) in mathematics instruction and assessment on multiple levels. As a Co-PI for the Vermont Mathematics Partnership, I contributed to developing that NSF/USDOE grant’s middle school/high school in-service curricula and helped create professional development focused on making explicit the language components of mathematics instruction. As the Mathematics Assessment Coordinator for the Vermont Department of Education, I brought EL needs to the fore when crafting large-scale assessment policies and reviewing large-scale mathematics items with my colleagues from New Hampshire and Rhode Island to inform the development of the New England Common Assessment Program (NECAP) Mathematics Assessments. In both roles, I, along with my colleagues, recognized the need for more research in these areas to inform our work and to disseminate what we learn.
In Fall 2004, I came to UCSB to carry out that research agenda and to share that knowledge with our students. Funded by an NSF-CCLI grant, I am currently collaborating with Dr. Bill Jacob (UCSB - Mathematics) to develop and research a yearlong mathematics education curriculum that explores early forms of pedagogical content knowledge for upper division, undergraduate STEM majors who are preparing to become secondary mathematics teachers for diverse learners. Funded by an FCDA award, I am currently investigating how and to what extent high school, Spanish-speaking ELs make meaning of and solve actual and modified algebra items released from previous versions of the California High School Exit Exam (CAHSEE-M) and how and to what extent mathematics teachers predict and address the reading comprehension and problem solving challenges their EL students experience when engaging with the items. Findings from both projects inform the creation and research of related professional development for in-service teachers.
On campus, I teach mathematics education courses for our students across all levels. By teaching courses such as Ed 3B – CAT II for incoming mathematics and science majors for the UCSB Science and Mathematics Initiative (SMI), Secondary Mathematics Methods for pre-service secondary mathematics teachers in our Teacher Education Program, and Mathematics and Science Curriculum Analysis for our doctoral students, I get to see and help facilitate the development of our students’ learning trajectories.
I am proud to be a member of the Gevirtz Graduate School of Education team and look forward to continuing to collaborate with and learn from our students and faculty.
Recent Publications:
Lager, C.A., Ruffo, C., & Gordon, M.K. How English Learners Understand and Solve CAHSEE Algebra Problems. University of California Linguistic Minority Research Institute. 2009. [Newsletter Article]
Lager, C. A. The Travieso Activity. In R. Kitchen & E.
Silver (Eds.), Research Monograph of TODOS: Mathematics For All. 1, 61-77. National Education Association. 2008. [Refereed Monograph Article]
Lager, C.A. Reading comprehension for algebra learning [title change]. ComMuniCator, 32(4), 38-42. California Mathematics Council (CMC). 2008. [Refereed Journal Article]
Lager, C.A. Including English learners in secondary mathematics methods courses. In M. Lutz (Ed.), CAMTE Monograph 1 - Secondary Mathematics Methods Courses in California, pp. 59-86. California Association of Mathematics Teacher Educators (CAMTE). 2008. [Refereed Monograph Article]
Asturias, H., Daro, P., Fuson, K., Howe, R., Hunt, L., Lager, C.A., et al. Elementary Mathematics Benchmarks, Grades K – 6. Achieve, Inc. 2008. [Technical Report]
Awards and Honors:
Faculty Career Development Award - UCSB, 2009
Faculty Career Development Award - UCSB, 2008
Affiliations:
American Educational Research Association (AERA)
Association of Mathematics Teacher Educators (AMTE)
California Association of Mathematics Teacher Educators (CAMTE)
California Mathematics Council (CMC)
National Council for Teachers of Mathematics (NCTM)
TODOS: Mathematics for All
