Learning mathematics is not a spectator sport. The rigorous mathematical knowledge sought for at all levels of instruction requires deep thinking and persistent sense making from students. Communication about mathematics among students and between students and the teacher is the vehicle for bringing thinking to the surface, clarifying ideas, moving ideas forward, revealing misconceptions, and making key mathematical connections clear, transferable, and memorable. Mathematical discourse is the verbal and written communication that is centered around deepening thinking about and making sense of mathematics. Brummer and Kartchner Clark (2014) state, “students must think about, read about, talk about, and write about information in order to synthesize it and to retain it” (p. 21). Students cannot learn only by being told or shown information. Through language students communicate in ways that engage them in reasoning and talking about math (Fogelberg et al., 2008; McKee & Ogle, 2005). The math standards of all states emphasize the importance of student communication of mathematical ideas, making mathematical discourse a required process in learning mathematics.

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Linda Diamond, CORE’s President, shares research and best practices for effective professional learning for K-12 educators.

Research on Professional Learning

Despite a solid and long body of research, school districts continue to futilely emphasize one-off workshops rather than invest in the ongoing, job-embedded professional learning and coaching necessary to change practice. Like Sisyphus, our educators are condemned to participate in the same poor quality professional development over and over with little hope of obtaining sustained support to lead to full implementation. The research on professional development for teachers consistently points out the need to provide ongoing, robust support and coaching to transfer knowledge and skills learned in workshops to classroom practice. READ MORE

All schools and all educators intend to meet the needs of all their students. Indeed, educating all students is the promise of a democracy. Nonetheless, in many American schools, this promise is largely unfulfilled. Teachers struggle to meet the needs of their increasingly diverse classrooms. It is not uncommon to find a single classroom in which ten different languages are spoken, the teacher must manage three to four varying skill levels, and must address the disparate needs of children who live in poverty and children who live relatively comfortable lives. How then is the goal of “all” students to be realized? How does the teacher “leave no child behind”?

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Linda Diamond, CORE’s President, shares her thoughts on the importance of high fidelity implementation of instructional materials. Linda was one of the original founders of CORE and developed their basic training and leadership materials. She continues to develop CORE’s professional programs, school change models, and professional products. Linda was formerly the Director of Curriculum, Staff Development and Evaluation for the Alameda City Unified School District as well as an elementary and middle school principal. She worked as a policy analyst with RPP International, an education research and public policy forum. Linda served on the California State Superintendent’s Task Force on Reading and was co-author of Building a Powerful Reading Program, which helped establish the foundation for reading policy and legislation in California. She is the co-author of CORE Assessing Reading: Multiple Measures and the nationally acclaimed CORE Teaching Reading Sourcebook.

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While many schools and districts use assessment data to determine student needs, only a few are utilizing the data to differentiate support for teachers, make decisions about intervention programs, and monitor program implementation. Some districts use assessment data to determine system-wide professional development needs, allocate coaching time, identify students who need frequent progress monitoring, and purchase and implement intensive intervention programs designed to support at-risk students. Schools using this approach recognize the power of assessment-driven instruction. They use a variety of tests for different purposes, with particular attention to progress monitoring tests focused on critical reading instructions.

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