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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. www.flstandards.org “The new access points in mathematics identify the most salient grade-level, core academic content for students with a significant cognitive disability.” IMPORTANT TO NOTE: “These access points are NOT ‘extensions’ to the standards, but rather they illustrate the necessary core content, knowledge, and skills that students with a significant cognitive disability need at each grade to promote success in the next grade.” Bureau of Exceptional Education and Student Services Spring 2014 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 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. 16 Mathematics Progressions Project http://ime.math.arizona.edu/progressions/s Project 17 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 [email protected] http://www.katm.org Mathematics Teaching in the Middle School ● Vol. 14, No. 8, April 2009 Proficiency Scale 6th Instructional Strategies for 6.EE.5 - 8 In order for students to understand equations: The skill of solving an equation must be developed conceptually before it is developed procedurally. Students should think about what numbers could be a solution BEFORE solving the equation. Experience is needed solving equations with a single solution, as well as with inequalities having multiple solutions. Conceptual understanding of positive and negative numbers and operation rules is introduced in grade 6. Students need to practice the process of translating between mathematical phrases and symbolic notation. (ie. write equations from situations/stories, write a story that references a given equation/inequality) Explanations and Examples for 6.EE.7 Students create and solve equations that are based on real world situations. It may be beneficial for students to draw pictures that illustrate the equation in problem situations. Solving equations using reasoning and prior knowledge should be required of students in order to allow them to develop effective strategies. Learning Progression Document “Expressions and Equations” Grades 6-8, pg. 7 As word problems grow more complex in grades 6 and 7, analogous arithmetical and algebraic solutions show the connection between the procedures of solving equations and the reasoning behind those procedures. 7th It is appropriate to expect students to show the steps in their work. Students should be able to explain their thinking using the correct terminology for the properties and operations. Continue to build on students’ understanding and application of writing and solving one-step equations from a problem situation to multi-step problem situations. Progression Document “Expressions and Equations Grades 6-8” pgs. 13-14 Instructional Strategies for 8.EE.7 - 8 Pairing contextual situations with equation solving allows students to connect mathematical analysis with real-life events. Experiences should move through the stages of concrete, conceptual and algebraic/abstract. System-solving in Grade 8 should include estimating solutions graphically, solving using substitution, and solving using elimination. Progression Document “Expressions and Equations Grades 6-8" pg. 14 Write an equation that represent the growth rate of Plant A and Plant B. Solution: Plant A H = 2W + 4 Plant B H = 4W + 2 • At which week will the plants have the same height? Solution: The plants have the same height after one week. Plant A: H = 2W + 4 Plant B: H = 4W + 2 Plant A: H = 2(1) + 4 Plant B: H = 4(1) + 2 Plant A: H = 6 Plant B: H = 6 After one week, the height of Plant A and Plant B are both 6 inches. Two domains in middle school are important in preparing students for Algebra in high school. Number System (NS) – Students become fluent in finding and using the properties of operations to find the values of numerical expressions. (Began as Number Operations with Fractions, NF grades 3-5.) Expressions and Equations (EE) – Students extend their use of these properties to linear equations and expressions with letters. (Began as Operations and Algebraic Thinking, OA grades K-5.) Algebra: Reasoning with Equations and Inequalities (A-REI.1-12) • Understand solving equations as a process of reasoning and explain the reasoning • Solve equations and inequalities in one variable • Solve systems of equations • Represent and solve equations and inequalities graphically Proficiency Scale HS Scope and Sequence Curriculum Blueprints 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 tools38 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. Content Complexity Florida Standards: Definitions July 2014 “Content complexity ratings reflect the level of cognitive demand that standards and corresponding instruction impose upon a student. The evolution of Florida’s standards and assessment alignment is illustrative of the state’s ongoing effort to support the development of a curriculum and assessment system that exemplifies the qualities of focus, coherence, and rigor embodied by the new FL standards.” 40 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 41 else – Make Judgments – WRITE! MAFS + DOK = Math Standards & Math Practices Standards for Mathematical Practice Mathematics Assessment Project http://map.mathshell.org “I would say that CCs are collaborative lessons that are built around one concept and are structured in ways to allow an initial entry point that every student can access in some way. They really allow a group of students to explore their understanding of the concept.” http://mathpractices.edc.org/ 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 “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 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? Middle School MEA LESSON TITLES 6th Grade - The Best Domestic Car MAFS.6.RP.1.1 MAFS.6.RP.1.2 7th Grade - Run For Your Life MAFS.7.NS.1.1 MAFS.7.NS.1.3 mea.cpalms.org 8th Grade - Pack It Up MAFS.8.G.3.9 CollegeReview.com High School MAFS.912.A-CED.1.1 MAFS.912.S-ID.1.1 MEA LESSON TITLES Plants versus Pollutants MAFS.912.F-BF.1.1 MAFS.912.F-BF.1.2 MAFS.912.S-ID.2.5 MAFS.912.S-IC.1.2 MAFS.912.S-IC.2.6 Shopping for a Home Mortgage Loan Which Brand of Chocolate Chip Cookie Would You Buy? MAFS.912.S-IC.2.6 MAFS.912.N-Q.1.1 MA.912.F.3.9 MA.912.F.3.10 MA.912.F.3.11 MA.912.F.3.12 MA.912.F.3.13 MA.912.F.3.14 MA.912.F.3.17 mea.cpalms.org MAFS.912.N-Q.1.3 "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