Day 3 Session 7
Day 3 – Session 7 EXPECTED OUTCOMES • Enhance knowledge base of the Common Core Standards for Mathematics; • Enhance knowledge of the Common Core Standards for Mathematical Practice; and • Discuss an Integrated Approach to Collegial Learning with Critical Thinkers and Questioners.
Parking Lot Questions • A question you need to park (save) until the end of a presentation. • It's a fancy way of saying, "Please hold all questions until the end of the presentation." Send to: 37607 and in the message line text Code # 83374 and your response. Example: 83374 How does this all fit together?
Addressing the Needs of All Learners – Working w/ELLs Problem Solving and Response to Instruction/Intervention Differentiated Instruction - FDLRS Students with Disabilities as 21st Century Learners Course Descriptions w/CC Literacy Standards Progress Monitoring State Evaluation System – Marzano & Danielson Text Complexity Anchor Standards for Literacy Comprehension Instructional Sequence Progression Scales Establishing Learning Goals Aligned to CC Literacy Standards http://www.fldoe.org/bii/
Rate your level of understanding!How would you rate your level of understanding for the Common Core Standards for Mathematical Practices? • 174418 No understanding. • 174441 Limited understanding (I have heard of them). • 174473 Partial understanding (I could have a discussion). • 174509 Adequate understanding (I could present an overview ). • 174519 Thorough understanding (I could train others). Send to: 37607 and text Code # to respond
Created by Karol Yeatts Presented by Jackie Speake
Ensuring Education Building Foundation CCSSO Focus Aligned Developmental Levels Coherence Clarity Evidenced-based Domains Application Balanced Critical Areas Fluency Clusters Habits of Mind Knowledge Guided by Principles Joint effort International Benchmarked Learner-focused Life-long skills Illustrative Mathematics McCallum Progressions Organized Robust, Relevant, Real-world National Focus NGA Quality Procedural fluency Opportunities Mathematical Practice Proficiency Research-based PARCC Rigor Teachers Whole Child Approach Standards Vision Sense-making Understanding Zimba X Y Timeline
High School Conceptual Categories • Number and Quantity (N) • Algebra (A) • Functions (F) • Modeling (*) • Geometry (G) • Statistics and Probability (S) A-Z http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
Domains for K-12 A-Z
Algebra Overview • Seeing Structure in Expressions • Interpret the structure of expressions • Write expressions in equivalent • forms to solve problems • Arithmetic with Polynomials and Rational Functions • Perform arithmetic operations on • polynomials • Understand the relationship between • zeros and factors of polynomials • Use polynomial identities to solve • problems • Rewrite rational functions • Creating Equations • Create equations that describe • numbers or relationships • Reasoning with Equations and Inequalities Cluster Headings Cluster Headings Cluster Headings Domain Domain Domain Domain A-Z
Cluster Headings Standards Domain
Florida’s Numbering ofthe Common Core State Standards MACC.912.A-SSE.1.1.a Subject Grade Domain Cluster Standard Heading A-Z
Standards for Mathematical Practice • Develops dispositions and habits of mind • “Characteristic of an educated person” • Precision in thought • Precision in the use of language and terms • Precision of argument • Sense making happens through conversations http://www.youtube.com/watch?v=9pKcO9E4Flw&feature=relmfu http://youtu.be/9pKcO9E4Flw A-Z
Standards for Mathematical Practice “The Standards for Mathematical Practice are unique in that they describe how teachers need to teach to ensure their students become mathematically proficient. We were purposeful in calling them standards because then they won’t be ignored.” - Bill McCallum
Use appropriate tools strategically • Make sense of problems and persevere in solving them 8 Standards for Mathematical Practice 5 1 • Reason abstractly and quantitatively Attend to precision 2 6 Look for and make sense of structure • Construct viable arguments and critique the reasoning of others 7 3 Look for and express regularity in repeated reasoning • Model with mathematics 4 8 A-Z
Florida’s Common Core State Standards Implementation Timeline F- full implementation of CCSS for all content areas L – begin full implementation of content area literacy standards including: (1) use of informational text, text complexity, quality and range in all grades (K-12), and (2) CCSS Literacy Standards in History/Social Studies, Science, and Technical Subjects (6-12) B - blended instruction of CCSS with Next Generation Sunshine State Standards (NGSSS); last year of NGSSS assessed on FCAT 2.0 A-Z 16 http://www.fldoe.org/bii/pdf/CCSS-ImplementationTimeline.pdf
Poll Question How many Common Core Standards for Mathematical Practice are there? Send to: 37607 Text: 202818 plus your message Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
Standards for Mathematical Practice Overarching Habits of Mind of a Productive Mathematical Thinker 1. Make sense of problems and persevere in solving them 6. Attend to precision Reasoning and Explaining Modeling and Using Tools Seeing Structure and Generalizing 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning 22
The Standards for Mathematical Practice Please locate the Common Core State Standards for Mathematics. Take a moment to examine the first three words of the narrative description for each of the 8 mathematical practices. What do you notice? Mathematically Proficient Students… Page 6
Digital Task Your Digital Task is to: • Read your assigned Mathematical Practice. • Identify the words (verbs) that illustrate the student actions for this practice. • Text the words on one continuous line with spaces between each word. • Example: #..... create analysis model describe demonstrate….
Digital Task Text Numbers Practice #1 – code 119825 Practice #2 – code 108045 Practice #3 – code 108045 Practice #4 – code 128304 Practice #5 – code 128404 Practice #6 – code 128418 Practice #7 – code 128424 Practice #8 – code 128951 Send to: 37607 and text the CODE # for your mathematical practice and then your response 25
Mathematical Practice 1 - Make sense of problems and persevere in solving them. Text 119825 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
Mathematical Practice 2 - Reason Abstractly and Quantitatively Text 108045 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
Mathematical Practice 3 - Construct viable arguments and critique the reasoning of others. Text 108045 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
Mathematical Practice 4 - Model with mathematics. Text 128304 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
Mathematical Practice 5 - Use appropriate tools strategically. Text 128404 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
Mathematical Practice 6 - Attend to precision. Text 128418 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
Mathematical Practice 7 - Look for and make sense of structure. Text 128424 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
Mathematical Practice 8 - Look for and express regularity in repeated reasoning. Text 128951 to 37607 Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
AN INTEGRATED APPROACH TO COLLEGIAL LEARNING WITH CRITICAL THINKERS AND QUESTIONERS
QUESTIONING STRATEGIES Eliciting Supporting Extending Source: “Strategies for Advancing Children’s Mathematical Thinking”, Teaching Children Mathematics. The National Council of Teachers of Mathematics, Inc. 2001.
Eliciting • Elicit many solutions to one problem • Wait for, and listen to, students’ descriptions of solution methods • Encourage elaboration • Use students’ explanations as a basis for the lesson’s content • Convey an attitude of acceptance toward students’ errors and efforts • Promote collaborative problem solving • Decide which students need opportunities to report. Supporting Extending Source: “Strategies for Advancing Children’s Mathematical Thinking”, Teaching Children Mathematics. The National Council of Teachers of Mathematics, Inc. 2001.
Science Example Questioning Strategies: Elicit many solutions to one problem and promote collaborative problem solving SC.912.L.17.20 Predict the impact of individuals on environmental systems and examine how human lifestyles affect sustainability. (Also assesses SC.912.L.17.11, SC.912.L.17.13, SC.912.N.1.3, and HE.912.C.1.3.) MACC.K12.MP.4 Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another.
Science Example Salt water is an abundant resource but unusable for irrigation and drinking. As demands on freshwater sources increase, the use of desalination processes to remove salt from ocean water is increasing. Conduct research on current desalination. Based upon research what are some of the benefits and impacts of desalination on the surrounding ocean environment Complete a two way table.
Science Example Complete a desalination lab determining the effects of desalination on ocean plant growth and complete a data table and graph to scientifically and mathematically draw conclusions. Effects of Desalination on Plant Growth Graph Height of Plant A B C Plants
Supporting • Remind students of conceptually similar problem situations. • Provide background knowledge. • Lead students through instant replays. • Write symbolic representations of each solution method on the board. • Encourage students to request assistance. Eliciting Extending Source: “Strategies for Advancing Children’s Mathematical Thinking”, Teaching Children Mathematics. The National Council of Teachers of Mathematics, Inc. 2001.
SOCIAL STUDIES EXAMPLE Questioning strategy: Lead students through instant replays to support all students by going through one student’s solution in a step-by-step fashion. SS.912.G.1.3 Employ applicable units of measurement and scale to solve simple locational problems using maps and globes. MACC.K12.MP.6 Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.
SOCIAL STUDIES EXAMPLE What is the average distance of movement west of the population center of the United States every ten years between 1790 and 1940? Between 1940 and 2000? What were the causes of the difference?
Extending • Maintain high standards and expectations for all students. • Encourage students to draw generalizations. • List all solution methods on the board to promote reflection. • Push individual students to try alternative solution methods. • Promote use of more efficient solution methods. • Cultivate a love of challenge. Eliciting Supporting Source: “Strategies for Advancing Children’s Mathematical Thinking”, Teaching Children Mathematics. The National Council of Teachers of Mathematics, Inc. 2001.
CTE Example Questioning Strategy: Encourage students to draw generalizations. Agriscience Foundations 05.04 Identify the nutrients required for plant growth from the periodic table and explain their functions. 07.03 Solve time, distance, area, volume, ratio, proportion, and percentage problems in agriscience MACC.912.AREI.2 Understand solving equations as a process of reasoning and explain the reasoning. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
Parking Lot Questions • A question you need to park (save) until the end of a presentation. • It's a fancy way of saying, "Please hold all questions until the end of the presentation." Send to: 37607 and in the message line text Code # 83374 and your response. Example: 83374 I am still confused about how to integrate the mathematical practices ...
Collegial Learning:The Intersection of Education Rod Duckworth, Chancellor Career and Adult Education Florida Department of Education
Meeting a Growing Need “Without high quality, knowledge intensive jobs and the innovative enterprises that lead to discovery and new technology, our economy will suffer and our people will face a lower standard of living.” - National Academy of Sciences