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I NSTRUCTIONAL S HIFTS IN M ATHEMATICS D EVELOPING P ERSEVERANCE & P ROBLEM -S OLVING S KILLS J’lene Cave Genevieve Silebi Shanon Cruz Jenny Kim
Ice Breaker – Marooned Activity: You are marooned on an island!!! What five items will your team bring knowing that you are stranded? One team representative will: Text 207355 and your message to 22333. Then share your responses with neighboring table.
In your table groups, please discuss the following: What Math professional development have you experienced? How do you think this will help us implement CCSS?
ELA Instructional Shifts -Balancing Informational and Literary Text -Building knowledge in disciplines -Incorporating staircase of complexity -Engaging in text-based answers -Writing from sources -Using transferrable academic vocabulary ELA Instructional Shifts -Balancing Informational and Literary Text -Building knowledge in disciplines -Incorporating staircase of complexity -Engaging in text-based answers -Writing from sources -Using transferrable academic vocabulary MATH Instructional Shifts -Focus -Coherence -Rigor MATH Instructional Shifts -Focus -Coherence -Rigor ANCHOR STANDARDS K - 12 ANCHOR STANDARDS K - 12 CONTENT GRADE LEVEL STANDARDS MATHEMATICAL PRACTICES K - 12 MATHEMATICAL PRACTICES K - 12 CONTENT GRADE LEVEL STANDARDS
K EY I NSTRUCTION S HIFTS OF THE C OMMON C ORE S TATE S TANDARDS FOR M ATHEMATICS Focus strongly where the Standards focus Coherence think across grades, and link to major topics within grades Rigor in major topics pursue conceptual understanding, procedural skill and fluency, and application with equal intensity.
6 © 2011 California County Superintendents Educational Services Association Mathematics Teacher Overview
The Standards for Mathematical Practice Take a moment to examine the key words of each of the following 8 mathematical practices… what do you notice?
10 The Standards for Mathematical Practice 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
So how do we apply these mathematical practices in our classrooms? How does it look and sound? What are teachers doing? What are students doing?
Standard 1: Make sense of problems and persevere in solving them Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Essential CharacteristicsTeaching Methods -present mathematical challenges where students are asked to explain and clarify their thinking process Examples of What Students Will Be Doing -use multiple representations to explain their solution to a problem Non-examples of What Students Will Be Doing -solve computational, drill problems on worksheets Standard 1: Make sense of problems and persevere in solving them
Create a Frayer Model Poster Essential Characteristics Teaching Methods Examples of What Students Will Be Doing Non-examples of What Students Will Be Doing Standard for Mathematical Practice - Each table will be assigned one of the Mathematical Practice. - Create a Frayer Model Poster connecting student actions & teacher actions. - Take a Gallery Walk
Frayer Model Poster Gallery Walk Display your poster. Take a post-it and examine the posters to the right of your group’s poster. Look for evidence of student engagement in the math and write down your thoughts on post-its. Rotate to the right and continue until you have finished examining all posters. Be ready to share out your observations and “ahas.”
NLMUSD FOCUS Mathematical Practice 1: Make sense of problems and persevere in solving them. Mathematically Proficient Students: Explain the meaning of the problem to themselves Look for entry points Analyze givens, constraints, relationships, goals Make conjectures about the solution Plan a solution pathway Consider analogous problems Try special cases and similar forms Monitor and evaluate progress, and change course if necessary Check their answer to problems using a different method Continually ask themselves “Does this make sense?” Gather Information Make a plan Anticipate possible solutions Continuously evaluate progress Check results Question sense of solutions
NLMUSD FOCUS Mathematical Practice 3: Construct viable arguments and critique the reasoning of others Use assumptions, definitions, and previous results Make a conjecture Build a logical progression of statements to explore the conjecture Analyze situations by breaking them into cases Recognize and use counter examples Justify conclusions Respond to arguments Communicate conclusions Distinguish correct logic Explain flaws Ask clarifying questions
Let’s do some math!
Critiquing Arguments Compare and contrast the two different strategies by Learner A and Learner B. What is similar? What are the differences? What questions do you have about these strategies? Which strategy do you think was most effective? Why?
Fifth grade students critiquing each others' arguments
Review and Reflect on the Learning Experience: Turn and Talk: How might your experience as a learner in this lesson inform your own teaching? What connections can you make to previous Math PD?
MATHEMATICAL PRACTICE #1
MATHEMATICAL PRACTICE #3
Individual Reflection: How will you plan to incorporate opportunities for students to use mathematical practices 1 and 3 in your instruction? How will you know students are applying these mathematical practices?
School CC Team Review and Reflect on Day 2: In your teams, chart your responses or make a visual representation to the guiding question: What does our staff need to know about implementing Mathematical Practices #1 and #3? Include at least 5 key ideas.
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