toward guiding principles for equity and quality in...
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Toward Guiding Principles for Equity and Quality in Mathematics Instruction
Kathleen PitvorecCraig Willey
Lena Lícon KhistyUniversity of Illinois at Chicago
Acknowledgments Philip KisunzuLena Licón Khisty
CEMELA (Center for Mathematics Education of Latinas/os) is funded by the National Science Foundation under grant – ESI‐0424983. The views expressed here are those of the author(s) and do not necessarily reflect those of the funding agency.
OverviewDriving questions about curricula and Latino students
Curriculum as a source of change
Characteristics of one successful curriculum
Developing a Bilingual Mathematics Framework
Implications of the framework
Driving QuestionsWhat characteristics of a curriculum might provide support for Latino students’ improved achievement?
How can we use these characteristics to support teachers in adapting their implementation of the curriculum they are using?
Why Look to Curriculum Materials?A curriculum (both macro & micro) determines what students learn (NCTM, 2000).
Teachers need curriculum models for new skills and practices (Hiebert, 2003; Hirsch, 2007).
School districts adopt curriculum materials in an effort to “regulate mathematics teaching practices” (Remillard, 2005).
Connecting Curriculum and TeachersAdopting curriculum materials does not insure consistency in a school or district. (S. A. Brown, Pitvorec, Ditto, & Kelso, 2009; Chval, Chavez, Reys, & Tarr, 2008)
The teacher is an agent who designs curriculum, and curriculum materials serve as tools for mediating teachers’ and students’ mathematical activity (M. Brown, 2009).
Finding Out/Descubrimiento (FO/D)Forerunner of integrated curriculum, science‐based with mathematics and language as tools
Research demonstrated significant gains in mathematics content and language development (Cohen, 1994)
Developed by Edward A. De Avila, Sharon E. Duncan, and Cecilia Navarrette (1980)
Specifically designed to meet the needs of bilingual students—children of migrant workers in CA
Provided context for Complex Instruction research (Cohen, 1994)
Professional development in summer to prepare teachers to support students in learning to work collaboratively
Explanations of philosophy and approach in teacher materials.
Finding Out/Descubrimiento (FO/D)
Broken Circles GameObject of Game: Put pieces together so that each group member ends up with a complete circle.
1.NO TALKING OR SIGNALING to other players in any way.
2.This is a GIVING game. NO TAKING PIECES from others.
3.Open your envelop.
4.Assemble your own circle. No one may show you or do it for you.
5.Do NOT place a piece for someone else. You may hand someone one of your pieces. Only give out one piece at a time.
6.The game ends when everyone has a complete circle.
Creating the FrameworkHow do students know what to do, how to approach problem situations, and how to engage in doing mathematics?
What roles do students and teachers have in the problem‐solving process?
What purpose do mathematical activities have and in what way are activities structured to promote engagement in meaningful mathematical activity?
How is literacy defined and developed during mathematical problem solving?
Pyramid of SuccessIdeologyIdeology
Language and Communication Learning Communities
Curriculum Materials
Bilingual
Students’
Learning
Bilingual Mathematics FrameworkCurriculumMaterialsTasks involve:• Doing mathematics•Multiple entry points•Multi‐modal engagement•Decision making•Multiple strategies•Mutual engagement•Cues for negotiating meanings•Related mathematical structures (themes)
Language &Communication•Emphasis on home language resources•Meaningful math talk•Equal status to both languages•Tasks presented in both languages•Language‐rich•Use language to read, write, explain, discuss, argue, justify, question
LearningCommunities•Joint productive activity•Interactional space•Distributed authority•Negotiated norms•Conceptual agency•Students do the intellectual work•Students’ thinking is an object of inquiry•Activity structures support language use
Language &Communication•Emphasis on home language resources•Meaningful math talk•Equal status to both languages•Tasks presented in both languages•Language‐rich•Use language to read, write, explain, discuss, argue, justify, question
ImplicationsThe Bilingual Mathematics Framework may…
Provide a useful resource for developing curriculum design principles that support Latino students.
Provide teachers opportunities to develop new images of what mathematics teaching and learning can look like.
Support teachers in designing their implementations of a curriculum to improve the mathematical experiences, engagement, and achievement of Latinas/os.