Intensifying Interventions for Students by Identifying and Remediating Conceptual Understandings in Mathematics (original) (raw)
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Research for Action (RFA) is a Philadelphia-based nonprofit organization. We seek to use research as the basis for the improvement of educational opportunities and outcomes for traditionally underserved students. Our work is designed to strengthen public schools and postsecondary institutions; provide research-based recommendations to policymakers, practitioners and the public at the local, state and national levels; and enrich the civic and community dialogue about public education. For more information, please visit our website at www.researchforaction.org. This research would not have been possible without the generous support of the Bill and Melinda Gates Foundation. We are very appreciative of the efforts of the district points of contact at each pilot site; they facilitated our work in many ways, especially by organizing our fieldwork, which included teacher interviews and classroom observations. Principals, teachers and other educators also graciously gave their time and openly shared their successes and challenges in piloting the tools. RFA staff members traveled across the country to interview educators at the pilot sites and observe classrooms and professional development. Our team was also instrumental in developing interview and observation protocols and synthesizing fieldwork data into analytical memos. Those RFA team
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Teaching mathematics is complex work. Effectively implementing the Common Core State Standards-Mathematics (CCSS-M) requires teachers to engage students in meaningful learning in which students make sense of mathematical ideas and representations, and communicate and reason mathematically. Teachers must also ensure that they are providing mathematical access to all of their students. Instead of expecting teachers to implement the large-scale changes called for in the CCSS-M overnight, change may be more likely and more sustainable if teachers are encouraged to shift their practice incrementally in a continuous improvement model (Star, 2016; Hiebert & Morris, 2012; Stigler & Hiebert, 2004).Accordingly, the expectation should be for small yet powerful changes that teachers can implement relatively easily in their instruction (Star, 2016). For example, teachers may initially implement manageable new ideas that make sense to them, such as:- Math talks to support students to conceptualiz...
Using the iPad to Develop Preservice Teachers' Understandings of the CCSSM
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The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important "processes and proficiencies" with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council's report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy).
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We analyzed 52 middle school mathematics lessons from multiple states and curriculum contexts to understand how teachers were enacting the CCSSM. The teachers stated that all of the lessons were CCSSM-aligned. We categorized curriculum materials according to two approaches, with one approach associated with curriculum programs funded by NSF and the other representing curriculum programs commercially produced, typically from a large publisher. We analyzed the nature of mathematical activity and level of interactions in the lessons. We found significant differences across curriculum approaches in the mathematical activity categories related to cognitive demand and in the level of interaction. The implications are that curriculum programs strongly mediated the enactment of the CCSSM.
Implementing standards-based mathematics instruction: a casebook for professional development
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Adapting Mathematics Core Curricula to Meet the Needs of Students with Disabilities
For the past 2 years, Mrs. Perez, a third-grade teacher, and Mr. Williams, a special education teacher, have co-taught a diverse class of 22 students, including 10 students with disabilities. Although they enjoy their collaborative relationship, Mrs. Perez, an 11-year veteran, would prefer to spend her day teaching reading and early writing instruction; similarly, Mr. William's love for reading and his desire to support students who struggle with reading and writing skill development motivated him to become a special education teacher. Although neither dislikes mathematics, it does not come as naturally to them. Mrs. Perez also feels a great deal of anxiety from the pressure of state assessments in a content area that had been a struggle for her as a learner. It is not surprising that for guidance they both cling to the district-adopted mathematics textbook and its supporting resources. The "toolbox" of resources Mr. Williams has collected and developed over the years for teaching reading, combined with Mrs. Perez's own reading strategies treasure trove, could serve as an accredited series independent of district resources. However, in mathematics, their concern about the content limits them to the core textbook and two resources suggested for struggling learners. Having nearly completed a second year together, they are increasingly concerned about what they are not doing, what the textbook does not provide, and their need for additional supports and solutions to help them truly meet the needs of their 22 students, especially those with disabilities.