Presentation on theme: "“There is an exceptionally strong relationship between,, and (key aspects of professional learning communities) and.” “There is an exceptionally strong."— Presentation transcript:
“There is an exceptionally strong relationship between,, and (key aspects of professional learning communities) and.” “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.” “The demands of the 21 st century has created a that focus on developing human capital and creativity in their teachers to prepare them for changing the educational landscape.” “The demands of the 21 st 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.” 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.
3 “I lift, You grab.... Was that concept just a little too complex for you, Carl?” … is a group of people working interdependently toward a common goal.
Common Core State Standards CCSSM vs. Mathematics Florida State Standards MAFS Cognitive Complexity of the Content Standards did NOT change. 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. “The new Florida Math Standards ask us ALL to… teach … rethink what it means to teach mathematics, understand … understand mathematics, learn … and to learn mathematics.” Sherry Fraser Faculty member of the Marilyn Burns Education Associates
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.” “The new access points in mathematics identify the most salient grade-level, core academic content for students with a significant cognitive disability.” Bureau of Exceptional Education and Student Services Spring 2014
Vol. 108, No. 2, September 2014 NCTM, MATHEMATICS TEACHER
Why Teachers’ Mathematics Content Knowledge Matters 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…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.
The Instructional Core Principle #1: 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: Principle #2: If you change one element of the instructional core, you have to change the other two..
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 8.EE.7-8 Analyze and solve linear equations and pairs of simultaneous linear equations. 7.EE.3-4 Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 6.EE.5-8 Reason about and solve one-variable equations and inequalities. 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. Alignment in Context: Neighboring Grades and Progressions 16 “You're constantly reusing the same concepts in the growth of the staircase, leading to algebraic ways of thinking that you begin to master linear algebra in grade 8 and go on to a wider set of algebra in the high school.” "Bringing the Common Core to Life" David Coleman · Founder, Student Achievement Partners
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 Mathematics Standards Flip Books For questions or comments about the flipbooks please contact Melisa Hancock at
Mathematics Teaching in the Middle School ● Vol. 14, No. 8, April 2009
Proficiency Scale 6 th
Instructional Strategies for 6.EE 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)
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. Explanations and Examples for 6.EE.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. 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. Learning Progression Document “Expressions and Equations” Grades 6-8, pg. 7
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
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. Instructional Strategies for 8.EE.7 - 8
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.
AlgebraAlgebra: Reasoning with Equations and Inequalities (A-REI.1-12) Algebra Understand solving equations as a process of reasoning and explain the reasoning Understand solving equations as a process of reasoning and explain the reasoning Solve equations and inequalities in one variable Solve equations and inequalities in one variable Solve systems of equations Solve systems of equations Represent and solve equations and inequalities graphically Represent and solve equations and inequalities graphically 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.)
Proficiency Scale HS
Scope and Sequence Curriculum Blueprints
38 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 tools 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 40 A scale of cognitive demand (thinking) based on the research of Norman Webb (1997). Categorizes assessment tasks by different levels of required of a student in order for them to successfully,, and with the task. 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 () intended by the standards, curricular activities, and assessment tasks. 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.”
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 else – Make Judgments – WRITE! 41
MAFS + DOK = Math Standards & Math Practices
Standards for Mathematical Practice
Mathematics Assessment Project Mathematics Assessment Project “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.”
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)
“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.
Benefit #1Benefit #2 Benefit #3Benefit #4 “Students write to keep ongoing records about what they’re doing and learning.” “Students write in order to solve math problems.” “Students write to explain mathematical ideas.” “Students write to describe learning processes.”
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.
Model Eliciting Activities MEAs are a collection of realistic problem-solving activities aligned to multiple subject-area standards. Are you familiar with these “ready–to–use” activities?
6 th Grade - The Best Domestic Car The Best Domestic Car MAFS.6.RP.1.1 MAFS.6.RP th Grade - Run For Your Life Run For Your Life MAFS.7.NS.1.1 MAFS.7.NS th Grade - Pack It Up Pack It Up MAFS.8.G.3.9 MEA LESSON TITLES Middle School mea.cpalms.org
CollegeReview.com MAFS.912.A-CED.1.1 MAFS.912.S-ID.1.1 MAFS.912.S-ID.2.5 MAFS.912.S-IC.1.2 MAFS.912.S-IC.2.6 Shopping for a Home Mortgage Loan 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 MAFS.912.N-Q.1.3Shopping for a Home Mortgage Loan MEA LESSON TITLES High School mea.cpalms.org Which Brand of Chocolate Chip Cookie Would You Buy? MAFS.912.S-IC.2.6 MAFS.912.N-Q.1.1 Plants versus Pollutants MAFS.912.F-BF.1.1 MAFS.912.F-BF.1.2
"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 Alan Cohen