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1. Common Core Mathematics in a PLC – Sustainable Solutions Dr. Timothy D. Kanold (tkanold.blogspot.com)“These standards are not intended to be new names for old ways of doing business. They are acall to take the next step. It is time for states to work together to build on lessons learned fromtwo decades of standards-based reforms. It is time to recognize that standards are not justpromises to our children, but promises we intend to keep.” —Common Core State Standards Initiative (2010), p.5Matt Larson and I wrote this school leadership book, Common Core Mathematics in a PLC atWork™, Leaders Guide, because during professional development, we often hear from teachers,“You need to share this information with our administrators! We need their support!” And so wechose to provide you with the same message about change that we wrote about to the reader ineach of our four grade level books.At the same time, we often hear from school leaders, “Please help our teachers to betterunderstand and deliver on the message you are giving us!” And so, our grade level books –written by outstanding voices in the field – Skip Fennell, Juli Dixon, Diane Briars, ThomaseniaLott Adams, David Foster, John Carter, Beth Kobett, Gwen Zimmermann, Mardi Gale, HaroldAsturias, Jon Wray, Mona Toncheff and Matt Larson provide a deeper support to the importantwork of your teams that you are expected to lead.As the Common Core story unfolds in your school or district there will be a thousand voicestelling you what to do. We hope the leadership book as well as the other books in our series willhelp you to cut through all of the noise and allow you to just focus on doing a few things reallywell. Think: One paradigm at a time! If you already have the benefit of working as a PLC, youare well on your way to that equity pursuit: “Ready, Set, Action!” Matt and I wish you the bestand invite you to contact us anytime to let us know your story, your concerns and your triumphs!Enjoy!One of the greatest problems with mathematics instruction, and instruction in general in mostschool districts, is that it is too inconsistent from classroom to classroom, school to school, anddistrict to district (Morris & Hiebert, 2011). How much mathematics a fourth-, eighth-, or tenth-grade student in the United States learns, and how deeply he or she learns it, is largely determinedby the school the student attends, and even more significantly, the teacher the student is randomly(usually) assigned to within that school. The inconsistencies teachers develop in their professionaldevelopment practice—often random and in isolation from other teachers—create great inequitiesin students’ mathematics instructional and assessment learning experiences that ultimately andsignificantly contribute to the year-by-year achievement gap (Ferrini-Mundy, Graham, Johnson,& Mills, 1998). This issue is especially true in a vertically connected curriculum likemathematics.The Education Trust (Ushomirsky & Hall, 2010, p.10), in Stuck Schools: A Framework forIdentifying Schools Where Students Need Change—Now, indicates that in an environment wherefunds and capacity are limited at best, educators and policymakers will need to establish clearTimothy D. Kanold, Ph.D. © 2012 tkanold.blogspot.com and Solution Tree press at www.solution-tree.com 1
priorities for implementation. The books in this series are designed to provide that sustainablestory for change in your school or district.The five fundamental paradigm shifts for mathematics: Knowing your focus andyour message.The CCSS for mathematics expectations for teaching and learning, and the new state assessmentsof that learning, usher in an opportunity for unprecedented change of the second-order variety.First-order change is characterized as working within existing paradigms with marginaldisturbance to the system, and is implemented within the existing knowledge and skill set of thoseclosest to the action—the faculty and school leaders. Second-order change requires workingoutside existing paradigms by embracing new paradigms for how you think and practice (Waters,Marzano, & McNulty, 2003, pp. 6–7).Until now, there has been a lot of debate, but no clear turning point with respect to K–12mathematics education improvement. The CCSS for mathematics represent a collective andcollaborative states’ effort to signal that turning point. It is time to disturb the system as currentlydefined. And the CCSS provide the catalyst for that disturbance.There are five fundamental second-order paradigm shifts (outside of existing paradigms) requiredto prepare every student and teacher for the successful implementation of the CCSS inmathematics and for the general improvement of mathematics learning for K–12 students in theUnited States. They are: 1. Professional Development—The CCSS for mathematics require a paradigm shift to move the grain size of change beyond the individual, isolated teacher or leader. It is the grade-level or course-based collaborative learning team (collaborative team) within a PLC that will develop the expanded teacher knowledge capacity necessary for successful implementation of the CCSS for mathematics. Your leadership role is to provide the conditions, structures, and culture necessary to eradicate the old paradigm of isolated teacher decision-making and accidental professional development and growth. 2. Mathematics Instruction: teaching and learning—The CCSS require a paradigm shift to daily lesson designs that include plans for accommodating the student Mathematical Practices described in the CCSS. These student practices focus on the process of student learning and student development of deeper understanding of mathematics. This paradigm shift requires teaching for procedural fluency and student understanding of the grade level CCSS content and using student understanding as a precursor to procedural fluency. Procedural fluency and conceptual understanding should not and cannot exist without one another (Kilpatrick, Swafford, & Findell, 2001). 3. Mathematics Content—The CCSS require a paradigm shift to “less (fewer standards) is more (deeper rigor with understanding)” at every grade level. This will require new levels of knowledge and skill development for every K–12 teacher of mathematics toTimothy D. Kanold, Ph.D. © 2012 tkanold.blogspot.com and Solution Tree press at www.solution-tree.com 2
understand what the CCSS expect students to learn blended with how students learn it. What mathematical knowledge, skills, understandings, and dispositions should be the result of each unit of mathematics instruction? There is great clarity and low teacher-to- teacher variance on the question, “Learn what and learn how?” 4. Mathematics Assessment—The CCSS require a paradigm shift toward assessment as a multifaceted process that reflects the rigor of the standards and models the expectations for and benefits of formative assessment development around all forms of assessment, including traditional assessment instruments such as tests and quizzes. How you will know if each student is learning the essential mathematics skills, concepts, understandings, and dispositions the CCSS deem most essential, becomes a significant question for each collaborative team. 5. Mathematics Intervention—The CCSS require a paradigm shift toward a team and school response to intervention (RTI) that is required. Much like the CCSS vision for teaching and learning, RTI can no longer be invitational. That is, the RTI needs to become R2TI—a “required” response to intervention. Stakeholder implementation of RTI programs includes a process that requires targeted students to participate and attend. How will you respond and act on evidence (or lack of evidence) of student learning in your school or district? Timothy D. Kanold, Ph.D. © 2012 tkanold.blogspot.com and Solution Tree press at www.solution-tree.com 3
PLCs at Work™: Common Core Mathematics Paradigms INSTRUCTION CONTENT • Fewer standards, greater depth • Deep conceptual understanding • Understanding, focus and coherence • Collaborative lesson design Tool • Common and higher demand tasks • Standards for Mathematical Practice Collaboration Paradigm INTERVENTION ASSESSMENT • Common RRTI Framework response • PLC Teaching-Assessing-Learning cycle • Differentiated, targeted and intensive • In-class formative assessment processes • Student equity, access, support and • Common Assessment instruments as advancement formative learning opportunitties Key CCSS Web Resources 1. The Center on Education Policy (cep-dc.org/) 2. PARCC Consortium (parcconline.org/) 3. The Common Core State Standards documents in Mathematics and ELA (corestandards.org/) 4. The Hunt Institute Mathematics (youtube.com/user/TheHuntInstitute#p/u/14/BNP5MdDDFPY) 5. PARCC Newsletter at (parcconline.org/sites/parcc/files/PARCC-Place-September2011.pdf) 6. Myths and facts about the CCSS (ped.state.nm.us/CCS/plan/read/CoreFacts.pdf) Timothy D. Kanold, Ph.D. © 2012 tkanold.blogspot.com and Solution Tree press at www.solution-tree.com 4
7. SMARTer Balanced resources and Frameworks (www.k12.wa.us/SMARTER/default.aspx) Other Resources for Mathematics 1. For principals insidemathematics.org/index.php/tools-for-teachers/tools-for-principals-and- administrators This portion of the Inside Mathematics website is designed to support school-based administrators and district mathematics supervisors who have the responsibility for establishing the structure and vision for the work of grade-level and cross-grade-level learning teams. What Every Principal Needs to Know About the Teaching and Learning of Mathematics (Kanold, Briars, & Fennel, 2012, Solution Tree) 2. Common Core Standards for Mathematical Practice (Inside Mathematics) insidemathematics.org/index.php/common-core-standards This site provides classroom videos and lesson samples designed to illustrate the Mathematical Practices in action. 3. Common Core Mathematics in a PLC at Work™ professional development book series (Solution Tree/NCTM, 2012 – kanold Series Editor) http://www.solution-tree.com/products/books/common-core-mathematics This series (Kanold, et al) provides unit-by-unit professional development guidance for implementation of the Common Core. 4. NCTM lessons illuminations.nctm.org/ Illuminations provides standard-based resources that improve the teaching and learning of mathematics for all students. These materials illuminate the vision for school mathematics set forth in Principles and Standards for School Mathematics, Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics, and Focus in High School Mathematics: Reasoning and Sense Making. 5. Common Core State Standards blog commoncoretools.wordpress.com/ Timothy D. Kanold, Ph.D. © 2012 tkanold.blogspot.com and Solution Tree press at www.solution-tree.com 5
Follow Bill McCallum’s blog on tools that are being developed to support the implementation of the CCSS. 6. CCSS Mathematics Curriculum Materials Analysis Project (Council of Chief State School Officers, The Brookhill Foundation, and Texas Instruments) mathedleadership.org/docs/ccss/CCSSO%20Mathematics%20Curriculum%20Analysis% 20Project.Whole%20Document.6.1.11.Final.docx The CCSS Mathematics Curriculum Analysis Project provides a set of tools to assist K– 12 textbook selection committees, school administrators, and teachers in the analysis and selection of curriculum materials that support implementation of the CCSS for mathematics. 7. Illustrative Math Project (Institute for Mathematics and Education) illustrativemathematics.org The main goal for this project is to provide guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in implementing the Common Core State Standards for mathematics. 8. Progressions documents for the Common Core Math Standards (Institute for Mathematics and Education) ime.math.arizona.edu/progressions The CCSS in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on childrens cognitive development and by the logical structure of mathematics. The progressions detail why standards are sequenced the way they are, point out cognitive difficulties and provide pedagogical solutions, and provide more detail on particularly difficult areas of mathematics. The progressions documents found here are useful in teacher preparation and professional development, organizing curriculum, and provide a link between mathematics education research and the standards. 9. Common Core State Standards Resources (www.mathedleadership.org/ccss/materials.html; NCSM, 2011) These professional development files are ready to use and designed to help teachers understand how to implement the Mathematical Practices in their classrooms.10. Common Core Look-fors (CCL4s) – Mathematics iPad/iPhone App (splaysoft.com/CCL4s/Welcome.html; Splaysoft, 2011)Timothy D. Kanold, Ph.D. © 2012 tkanold.blogspot.com and Solution Tree press at www.solution-tree.com 6
CCL4s is a comprehensive tool designed to help teacher learning teams deepen their awareness and understanding of the actions and conditions that promote student engagement with the CCSS for Mathematical Practice, with connections to the content standards. An exciting blend of creativity, innovation, and strategic technology use, this app supports purposeful classroom observation though effective staff collaboration. ReferencesCommon Core State Standards Initiative (2010). Common Core State Standards for mathematics. Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdfDweck, C. S. (2007). Mindset: The new psychology of success. New York, NY: Ballantine Books.Ferrini-Mundy, J., Graham, K., Johnson, L., & Mills, G., (1998). Making change in mathematics education: Learning from the field. Reston, VA: National Council of Teachers of Mathematics.Kanold, T. D., & Larson, M. R. (2012). Common Core Mathematics in a PLC (K–12): Leaders Guide [in press]. Bloomington, IN: Solution Tree Press.Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academies Press.Morris, A. K., & Hiebert, J. (2011, January/February). Creating shared instructional products: An alternative approach to improving teaching. Educational Researcher, 40(1), 5–14.Ushomirsky, N., & Hall, D. (2010). Stuck schools: A framework for identifying schools where students need change—now. Washington, DC: The Education Trust.Waters, T., Marzano, R. J., & McNulty, B. A. (2003). Balanced leadership: What 30 years of research tells us about the effect of leadership on student achievement. Aurora, CO: Mid- continent Research for Education and Learning.Wiliam, D. (2011). Embedded formative assessment. Bloomington, IN: Solution Tree Press.Timothy D. Kanold, Ph.D. © 2012 tkanold.blogspot.com and Solution Tree press at www.solution-tree.com 7