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“The demands of the 21st century has created a need for schools to become learning organizations that focus on developing human capital and creativity in their teachers to prepare them for changing the educational landscape.” “There is an exceptionally strong relationship between communal learning, collegiality, and collective action (key aspects of professional learning communities) and changes in teacher practice and increases in student learning.” 1 Learning Goals Upon completion of this training, participants will… have increased their knowledge of the new Florida State Standards for Mathematics (MAFS). recognize how the coherence of content standards within and across the grades supports the learning progressions of students. encourage the integration of student writing in mathematics in order to increase reasoning and problem solving skills. Identify resources that will provide assistance with implementation of MAFS. be equipped to develop and facilitate Professional Learning Communities (PLCs) at the school site in order to encourage a continuation of collegial learning that supports the advancement of student learning. … is a group of people working interdependently toward a common goal. “I lift, You grab . . . . Was that concept just a little too complex for you, Carl?” 3 Common Core State Standards “The new Florida Math Standards ask us ALL to… CCSSM … rethink what it means to teach mathematics, vs. … understand mathematics, Mathematics Florida State Standards … and to learn mathematics.” MAFS Sherry Fraser Faculty member of the Marilyn Burns Education Associates Cognitive Complexity of the Content Standards did NOT change. Amended, Deleted, Added Standards Standards for Mathematical Practice (SMP) remain for all grades. LITERACY embedded across ALL CONTENT AREAS. MAFS Compared to CCSSM New and Deleted Standards www.flstandards.org Vol. 108, No. 2, September 2014 NCTM, MATHEMATICS TEACHER Why Teachers’ Mathematics Content Knowledge Matters: “Professional Learning Opportunities for teachers of mathematics have increasingly focused on deepening teachers’ content knowledge. Based on research studies… Teachers’ content knowledge made a difference in their professional practice and their students’ achievement. Teachers’ depth of knowledge meant problems were presented in familiar contexts to the children and the teacher linked them to activities they had previously completed. Teachers with stronger content knowledge were more likely to respond to students’ mathematical ideas appropriately, and they made fewer mathematical or language errors during instruction. Principle #1: Increases in student learning occur only as a consequence of improvements in the level of content, teachers’ knowledge and skill, and student engagement. Principle #2: If you change one element of the instructional core, you have to change the other two.. The Instructional Core Alignment in Context: Neighboring Grades and Progressions Algebra: Reasoning with Equations and Inequalities (A-REI.1-12) • Understand solving equations as a process of reasoning and explain the reasoning “You're constantly reusing the same concepts in • Solve equations and inequalities in one variable of the staircase, leading to algebraic ways •the Solvegrowth systems of equations • Represent and solve equations and inequalities graphically of thinking that you begin to master linear algebra in Analyze and solve linear equations and pairs of simultaneous linear equations. 8.EE.7-8 grade 8 and go on to a wider set of algebra in the high Solve real-life and mathematical problems using numerical and algebraic 7.EE.3-4 school.” expressions and equations. 6.EE.5-8 "Bringing the Common Core to Life" Reason about and solve one-variable equations and inequalities. David Coleman · Founder, Student Achievement Partners 5.OA.1-2 Write and interpret numerical expressions. 4.OA.1-3 Use the four operations with whole numbers to solve problems. 3.OA.1-4 Represent and solve problems involving multiplication and division. 2.OA.1 Represent and solve problems involving addition and subtraction. 1.OA.7-8 Work with addition and subtraction equations. K.OA.1-5 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. 13 Mathematics Progressions Project Progression http://ime.math.arizona.edu/progressions/s Project 14 Year at a Glance Nine Weeks Pacing Organized by Units of Instruction (related standards) Essential Questions and Vocabulary Teaching/Learning Goal(s) and Scales Rubric with Student Learning Target Details Progress Monitoring and Assessment Activities MFAS (Cpalms Formative Assessments) Unpacked Content Standards Unit/Critical Area Learning Objectives (Declarative and Procedural) DOK Level SMP Common Misconceptions Mathematics Standards Flip Books For questions or comments about the flipbooks please contact Melisa Hancock at melisa@ksu.edu http://www.katm.org KG Instructional Strategies for K.OA. 1-5 Concrete Representational Abstract Learning Progressions Document, “Operations and Algebraic Thinking”, Grades K-5, pg. 9 Kg Master in Grade 2 Explanations and Examples for 1.OA.7 and 1.OA.8 Students would have had prior learning within the grade understanding the following priorities. MAFS.1.OA.2.3 1st 1st Instructional Strategies for 1.OA.7 Think about how to explain the traditional… FACT FAMILY. Taken from CCFlipbook with Information compiled by Melisa Hancock melisa@ksu.edu Learning Progression Document “Operations and Algebraic Thinking” Grades K-5, pg. 16 Explanations and Examples for 2.OA.1 and 2.OA.1a Explanations and Examples for 2.OA.1 and 2.OA.1a Developing Fact Fluency: Phases of Understanding Common Multiplication and Division Situations Instructional Strategies (3.OA.1-4) Provide various contexts and tasks so that students will have more opportunity to develop and use thinking strategies to support and reinforce learning of basic mult. and div. facts. Encourage students to solve problems in different ways to show the same idea and be able to explain their thinking verbally AND in written expression. Apply skills to solve word problems. 4th 4th 5th 6.EE.1 5th Example of Using Writing to explain thinking… 5th H.Wu Professor of Mathematics University of California, Berkeley Teachers need to be very careful to extend their own knowledge “…when the ramp collapses, the of what a fraction is (IT IS NOT AN ACTIVITY), well as how to “Is it as reasonable to expect students aren’t able to scale a approach teaching addition and subtraction of fractions withiftheir a person to run well his gentle slope, but rather try and walkare is wobbly?” students. Theatdefinitions impressed upon the climb a wall 90 degrees.”and strategies that students needs to be accurate and a continuum from what they already know about whole numbers and their operations. “No matter how much algebraic thinking“Early is introduced in the early grades algebraic thinking algebra, generality and grades“Inand no matter how worthwhile such exercises might be, the approach gives focus on gaining abstraction are expressed in symbolic failure rate Fluency in algebra will continue to be high UNLESS WE RADICALLY conceptual understanding of notation. with symbolic abstract symbols.” REVAMP THE TEACHING OFpart FRACTIONS AND DECIMALS.” manipulation is an integral of algebra proficiency.” H.Wu, Univ. of Calif., Berkeley Fraction Progression Online Module http://www.cgcs.org/site/Default.aspx?PageID=338 The Council of the Great City Schools, University of Arizona’s Institute for Mathematics and Education (IM&E), and Achieve collaborated on the development of an online professional development module to deepen understanding of the Fractions Progression - a critical focus in the standards. This online, interactive module is available free of charge to all users and takes about 60 minutes to complete. The module features: Brief video segments that explain fraction concepts Illustrative tasks associated with the progression Built in, interactive checks for understanding throughout the module Supporting material that can be downloaded and printed https://www.illustrativemathematics.org/fractions_progression https://mathsolutions.wistia.com/projects/r4bjpdzb31 https://www.illustrativemathematics.org/ Rigor is defined as a process where students: Approach mathematics with a disposition to accept challenge and apply effort. Engage in mathematical work that promotes deep knowledge of content, analytical reasoning, and use of appropriate tools; and Emerge fluent in the language of mathematics, proficient with the tools39 of mathematics, and empowered as mathematical thinkers. Focus on complexity of content standards in order to successfully complete an assessment or task. The outcome (product) is the focus of the depth of understanding. RIGOR IS ABOUT COMPLEXITY What is Depth-of-Knowledge? DOK A scale of cognitive demand (thinking) based on the research of Norman Webb (1997). Categorizes assessment tasks by different levels of cognitive expectation required of a student in order for them to successfully understand, think about, and interact with the task. Key tool for educators so that they can analyze the cognitive demand (complexity) intended by the standards, curricular activities, and assessment tasks. 41 Just the Facts – Low Level Processing “Familiar” – Procedures & Routines, 2 + Steps Real-World Problem – Develop Plan - Justification Take what you learned and extend it to something 42 else – Make Judgments – WRITE! http://www.fsassessments.org Grades 3 Florida Standards Assessment Test Item Specifications Grades 4 Florida Standards Assessment Test Item Specifications Grades 5 Florida Standards Assessment Test Item Specifications Grades 6 Florida Standards Assessment Test Item Specifications Grades 7 Florida Standards Assessment Test Item Specifications Grades 8 Florida Standards Assessment Test Item Specifications Algebra 1 EOC Florida Standards Assessment Test Item Specs Geometry EOC Florida Standards Assessment Test Item Specs Algebra 2 EOC Florida Standards Assessment Test Item Specs Test Design Summary MAFS + DOK = Math Standards & Math Practices Standards for Mathematical Practice Linking the Mathematical Practices with the Content Standards Mathematical Practices Learning Community Templates Tasks that Align with the Mathematical Practices Resources to Support the Implementation of the Standards for Mathematical Practice (SMP) http://files.eric.ed.gov/fulltext/ED544239.pdf “Writing in mathematics gives me a window into my students’ thoughts that I don’t normally get when they just compute problems. It shows me their roadblocks, and it also gives me, as a teacher, a road map.” -Maggie Johnston 9th grade mathematics teacher, Denver, Colorado “Using Writing in Mathematics to Deepen Student Learning” by Vicki Urquhart Why are we writing in math class? David Pugalee (2005), who researches the relationship between language and mathematics learning, asserts that writing supports reasoning and problem solving and helps students internalize the characteristics of effective communication. He suggests that teachers read student writing for evidence of logical conclusions, justification of answers and processes, and the use of facts to explain their thinking. http://files.eric.ed.gov/fulltext/ED544239.pdf Integrating writing into the mathematics classroom • Writing can provide valuable insight for teachers into their students’ mastery of math concepts. • Writing often reveals gaps in learning and misconceptions which can help inform teachers for instructional planning and intervention strategies. • Communicating about mathematics through writing helps strengthen student learning which can build conceptual understanding. • Students are able to clarify their thinking about a math topic through writing. • Integrating writing into the curriculum can be easy with a little planning. “Students write to keep ongoing records about what they’re doing and learning.” “Students write in order to solve math problems.” Benefit #1 Benefit #2 “Students write to explain mathematical ideas.” Benefit #3 “Students write to describe learning processes.” Benefit #4 http://www.readwritethink.org Grade Levels: K-2 “Going on a Shape Hunt: Integrating Math and Literacy” • Students are introduced to the idea of shapes through a read-aloud session with an appropriate book. They then use models to learn the names of shapes, work together and individually to locate shapes in their real-world environment, practice spelling out the names of shapes they locate, and reflect in writing on the process. This lesson provides opportunities to engage students using many different learning modalities. Grade Levels: 1-2 “Draw a Math Story: From the Concrete to the Symbolic” • identify and use key mathematical terms in discussion and in writing. • draw a series of pictures telling a sequential story which depicts objects being added or taken away. • tell and write a sequential story which corresponds to their drawings. • state or write equations that correspond to their stories. http://www.readwritethink.org Grades Levels 3-5 “Talking, Writing, and Reasoning: Making Thinking Visible with Math Journals” Getting Started with Math Journals • Sharing a good math-related children’s book or exploring puzzles – such as the Magic Triangle are good ways to begin working with Math Journals. • At the beginning stages of working with Math Journals, it helps students if they are presented with an open-ended prompt instead of having to develop an idea on their own. This kind of prompt is best for revealing students’ thinking, too. • Teachers should collect and view journal entries and make written comments to encourage the written dialogue between the student. Teachers can ask specific questions. Tasks to build literacy through mathematics and science content Inspired and informed by the work of the Literacy Design Collaborative, the Dana Center has created mathematics- and science-focused template tasks to explicitly connect core mathematics and science content to relevant literacy standards for students in grades 7–9. The mathematics template tasks were built from the Common Core State Standards for Mathematics Standards for Mathematical Practice. MEAs are a collection of realistic problem-solving activities aligned to multiple subject-area standards. Model Eliciting Activities Are you familiar with these “ready–to–use” activities? Primary Grades MEA LESSON TITLES Kg – We Love Pets! MAFS.K.CC.2.4 Flower Power Flower Company 1st Grade – MAFS.1.OA.1.1 MAFS.1.OA.3.5 MAFS.1.NBT.1.1 MAFS.1.MD.3.4 mea.cpalms.org 2nd Grade – Carnival MAFS.2.NBT.1.4 MAFS.2.NBT.2.5 Intermediate Grades MEA LESSON TITLES 3rd Grade - Spin Beyblades MAFS.3.OA.2.6 MAFS.3.OA.3.7 4th Grade - Donuts and Decimals MAFS.4.NF.3.6 5th Grade - X-treme Roller Coasters mea.cpalms.org MAFS.5.NBT.1.2 MAFS.5.NBT.1.3 MAFS.5.MD.1.1 "It takes a lot of courage to release the familiar and seemingly secure, and to embrace the new. But there is no real security in what is no longer meaningful. There is more security in the adventurous and exciting, for in movement there is life, and in change there is power.“ Alan Cohen