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  • If you’ve never attended an elluminate before, here are a few pointers. When documents are sent via the elluminate, click save, and create an elluminate folder in your documents folder on your computer. Just save the documents there, so you can find them later. You can also come back to the elluminate site, and look this session up in the elluminate recordings. Search by date, then topic. Also, it is important that you conduct an audio check. Go to Tools at the top of the window, then click on Audio Setup Wizard, and follow the prompts. To give a smiley face, click on the smiley face icon beneath the participant window. When you want to chat, type into the chat window, and send to “All Participants” so that everyone can read what you have to share. If you wish to speak to an individual, then choose that person from the participant list, and send to “Selected Participant”. Please don’t choose the raised hand icon, as this just makes a noise during the presentation. Instead, type your question into the chat window.
  • Most important words? What is the classroom contract? Restate 3 shifts: “You may be able to explain beautifully, but you can never understand for a child.”
  • Where do these situations come from? How can we create problematic situations?
  • This grouping of the SMP was created by a common core author. It makes the big picture a bit clearer. What do these resemble? Where were they located? How are the SMP different?

3rd Grade Webinar Slideshow 3rd Grade Webinar Slideshow Presentation Transcript

  • Our session will start momentarily.While you are waiting, please do the following:Enter/edit your profile information by going to:•Tools - Preferences - My Profile…•Fill out the info on the “identity” tab and click “OK”•To view the profile of another user, hover your mouse over his or her name inthe participants windowConfigure your microphone and speakers by going to:•Tools – audio – audio setup wizard• Follow the promptsConfirm your connection speed by going to:•Tools – preferences – connection speed
  • Standards For Mathematical Practice Third Grade November 10, 2011 Presenter: Turtle Gunn Toms
  • Welcome!• Thank you for taking time out of your day to join this discussion.• You should end the session today with at least 3 takeaways- something you can do tomorrow, a list of resources, something to think about.• I need your feedback at the end of this session. Feedback helps me become a better teacher, and helps you to reflect on your learning. Please enter feedback in the chat box once we are done.
  • Clearing up confusion:• This webinar is not about CCGPS content, it is about using the CCGPS Mathematical Practices this year with GPS content.• For information about how and why CCSS were developed and adopted, watch: common core- teaching channel and this: common core- math- teaching channel• GPS is taught and tested 2011-12. CCGPS is taught and tested 2012-13.• I will provide a list of resources mentioned during the session and one of the documents that has been downloaded to your computer is also a list of resources and future GPB broadcast dates.
  • Think for 30 seconds, then share- What is learning?What defines an effective classroom?How do students become proficient in mathematics?
  • Answers from classroom teachers• Learning happens when a student can make connections.• Learning happens when a student can make sense of mistakes.• Learning happens when students can think about their thinking.• An effective classroom is a place where students are doing the work.
  • Is my classroom effective?• Learning happens when a student can make connections.• Learning happens when a student can make sense of mistakes.• Learning happens when students can think about their thinking.• An effective classroom is a place where students are doing the work.
  • So what does the teacher do?• Focus on more on learning, less on teaching.• Ask questions related to the ideas the students are constructing, questions that illuminate the learner’s thinking.• Provoke disequilibrium.• Allow productive struggle.• Think differently. Many of us have seen math as something to be learned, practiced, and applied. Now it is understood as interpreting, organizing, inquiring, and constructing meaning using a mathematical lens.
  • Chew on this for a moment: “Am I really interested ingetting to know what is in their heads, or, do I just want them to know what is in my head?” Ann Shannon, 2011
  • How do we create a classroom environment which encourages students to take responsibility for their learning and allows them to become proficient in mathematics?What changes and what stays the same?
  • What needs to go away:• Problem solving Friday• Enrichment for the few• Just giving the answer (teacher or student!)• Isolation of content from process• GPS-ing students (what does that mean?)
  • Starting now: we can begin using Standards for Mathematical Practice• “The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important ‘processes and proficiencies’ with longstanding importance in mathematics education.” (CCSS, 2010)• The mathematical practices require a "re-negotiation" of the classroom contract.• 3 Major Shifts: – Teachers cannot create learning-only learners can do that. – Increased student responsibility- from receptive to active learner – Teacher/student relationship shift- from adversarial to collaborative Black and Wiliam, 2006
  • What happens if we continue to sacrifice understanding?
  • In every classroom, in every mathematical situation:• Students must mathematize their world.• Students must take responsibility for learning.• Mathematics must be made explicit.Hmmm….What does it mean to make mathematics explicit?
  • Making the mathematics explicit:• Children create and use graphic depictions receiving guidance and feedback from the teacher.• Learner’s reasoning is made as explicit as possible to help students see what another is thinking.• Student sharing of ideas and strategies is paramount.• Teacher looks for significant ideas to highlight. LouAnn Lovin, 2011
  • Mathematizing Third Grade• To mathematize, one sees, organizes, and interprets the world through and with mathematical models.• The potential to model the problematic situation must be built in.• Problematic situations must allow students to realize what they are doing. They must be able to “imagine concretely”.• Problematic situations must prompt learners to ask questions, notice patterns, wonder, ask why, and ask what if. (Young Mathematicians at Work, Catherine Twomey Fosnot, 2001)
  • “Only if children come to believe that there are always multiple ways to solve problems, and that they, personally, are capable of discovering some of these ways, will they be likely to exercise- and thereby develop- number sense.” Laura Resnick, 1990
  • CCGPS Standards for Mathematical Practice These are the backbone of the practices.
  • What teachers do:1. Make sense of problems and persevere in solving them.• Provide time and facilitate discussion in problem solutions.• Facilitate discourse in the classroom so that students UNDERSTAND the approaches of others.• Provide opportunities for students to explain themselves, the meaning of a problem, etc.• Provide opportunities for students to connect concepts to “their” world.• Provide students TIME to think and become “patient” problem solvers.• Facilitate and encourage students to check their answers using different methods (not calculators).• Provide problems that focus on relationships and are “generalizable”.6. Attend to precision.• Facilitate, encourage and expect precision in communication.• Provide opportunities for students to explain and/or write their reasoning to others.
  • 1. Make sense of problems and persevere in solving them.• In third grade, students know that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Third graders may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, “Does this make sense?” They listen to the strategies of others and will try different approaches. They often will use another method to check their answers.6. Attend to precision.• As third graders develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and in their own reasoning. They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, when figuring out the area of a rectangle they record their answers in square units.
  • 1. Make sense of problems and persevere in solving them.• In third grade, students know that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Third graders may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, “Does this make sense?” They listen to the strategies of others and will try different approaches. They often will use another method to check their answers.6. Attend to precision.• As third graders develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and in their own reasoning. They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, when figuring out the area of a rectangle they record their answers in square units.
  • • What can we do to make sure students make sense of problems and persevere in solving them?• How can we ensure students attend to precision?
  • Word Problems vs Problematic Situations• Word problems: Teachers assign them after they have explained operations, algorithms, or rules, and students are expected to apply these procedures to the problems.• Problematic situations: Used at the beginning- for construction of understanding, generation and exploration of mathematical ideas and strategies, offering multiple entry levels, and supportive of mathematization. (Young Mathematicians at Work, Fosnot, 2002)
  • Problem #1• $1.33 - .74 or• Etc…
  • Problem #1 18x 4 4x18 Here are two multiplication problems which have the same answer. Find some other multiplication problems which have the same answer. Show how you know.(Adapted from Young Mathematicians at Work, Fosnot, 2001)
  • Problem #1 (round 2)About how many children Danger: DO NOT EXCEEDof your age would be safe to 950 pounds.take the elevator at onetime?(Young Mathematicians at Work, Fosnot, 2001)
  • Math Anchor Charts!
  • Reasoning and explaining1. Reason abstractly and quantitatively. What teachers do:• Provide a range of representations of math problem situations and encourage various solutions.• Provide opportunities for students to make sense of quantities and their relationships in problem situations.• Provide problems that require flexible use of properties of operations and objects.• Emphasize quantitative reasoning which entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them and/or rules; and knowing and flexibly using different properties of operations and objects.6. Construct viable arguments and critique the reasoning of others.• Provide ALL students opportunities to understand and use stated assumptions, definitions, and previously established results in constructing arguments.• Provide ample time for students to make conjectures and build a logical progression of statements to explore the truth of their conjectures.• Provide opportunities for students to construct arguments and critique arguments of peers.• Facilitate and guide students in recognizing and using counterexamples.• Encourage and facilitate students justifying their conclusions, communicating, and responding to the arguments of others.• Ask useful questions to clarify and/or improve students’ arguments.
  • Reasoning and explaining1. Reason abstractly and quantitatively.• Third graders should recognize that a number represents a specific quantity. They connect the quantity to written symbols and create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities.4. Construct viable arguments and critique the reasoning of others.• In third grade, students may construct arguments using concrete referents, such as objects, pictures, and drawings. They refine their mathematical communication skills as they participate in mathematical discussions involving questions like “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking.
  • Reasoning and explaining1. Reason abstractly and quantitatively.• Third graders should recognize that a number represents a specific quantity. They connect the quantity to written symbols and create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities.4. Construct viable arguments and critique the reasoning of others.• In third grade, students may construct arguments using concrete referents, such as objects, pictures, and drawings. They refine their mathematical communication skills as they participate in mathematical discussions involving questions like “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking.
  • • How can we encourage students to reason abstractly and quantitatively?• How can we support students in explaining their thinking and examining the thinking of others ?
  • Problem #2 120+ 73 = ___ 73+ 120 = ___ • Etc…(and what about relational equality?)
  • Problem #2Ms. Breedlove loves to read! She is always reading. Right now she is reading a book about math and her friend Molly is reading the same book. Can you help her solve these problems?The book Ms. Breedlove and Molly are reading has 107 pages. Ms. Breedlove is on page 64. How many more pages does she need to read to finish reading the book?Molly is reading the same book, but she is only on page 43. How many more pages does Molly need to read to finish the book? (Young Mathematicians at Work, Fosnot, 2001)
  • Modeling and using tools (what teachers do)1. Model with mathematics.• Provide problem situations that apply to everyday life.• Provide rich tasks that focus on conceptual understanding, relationships, etc.5. Use appropriate tools strategically.• Provide a variety of tools and technology for students to explore to deepen their understanding of math concepts.• Provide problem solving tasks that require students to consider a variety of tools for solving. (Tools might include pencil/paper, concrete models, empty number line, ruler, calculator, etc.)
  • Modeling and using tools1. Model with mathematics.• Students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, acting out, making a chart, list, or graph, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed. Third graders should evaluate their results in the context of the situation and reflect on whether the results make sense.3. Use appropriate tools strategically.• Third graders consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may use graph paper to find all the possible rectangles that have a given perimeter. They compile the possibilities into an organized list or a table, and determine whether they have all the possible rectangles.
  • Modeling and using tools1. Model with mathematics.• Students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, acting out, making a chart, list, or graph, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed. Third graders should evaluate their results in the context of the situation and reflect on whether the results make sense.3. Use appropriate tools strategically.• Third graders consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may use graph paper to find all the possible rectangles that have a given perimeter. They compile the possibilities into an organized list or a table, and determine whether they have all the possible rectangles.
  • Problem #3
  • Problem #3Miss Guy has a very energetic puppy. The puppy loves to playoutdoors, so Miss Guy decided to build a pen to allow her petto be outside while she is at school. She just happens to have50 feet of fencing in her basement that she can use for the pen.What are some of the ways she can set up the pen that uses allthe fencing? Children must figure out forWhat are the dimensions of the rectangular pen with the most themselves, inspace available for the puppy to play? their own ways.Write a letter to Miss Guy explaining her choices and which penyou would recommend she build. Be sure to show how youmade your decisions and include a mathematicalrepresentation to support your solution. (Exemplars, Miss Guy’s Puppy Problem)
  • (Exemplars, Miss Guy’s Puppy Problem)
  • (Exemplars, Miss Guy’s Puppy Problem)
  • What tools and situations can we provide?• http://www.youtube.com/watch?v=7AmOJGb8fiA&• “To do 26 + 37, I will first add 4 to 26 to get 30. I still have 33 to add on. Next I will add 30 to get 60, and finally add the remaining 3 to get the answer 63.”
  • Children must figure out for themselves, in their own ways. Mackenzie burns 220 calories a day running home from school. How many calories will she burn in 5 days?Thank you, Krystal and Henry County!
  • Seeing structure and generalizing (what teachers do)1. Look for and make sense of structure.• Provide opportunities and time for students to explore patterns and relationships to solve problems.• Provide rich tasks and facilitate pattern seeking and understanding of relationships in numbers rather than following a set of steps and/or procedures.8. Look for and express regularity in repeated reasoning.• Provide problem situations that allow students to explore regularity and repeated reasoning.• Provide rich tasks that encourage students to use repeated reasoning to form generalizations and provide opportunities for students to communicate these generalizations.
  • Seeing structure and generalizing1. Look for and make sense of structure.• In third grade, students look closely to discover a pattern or structure. For instance, students use properties of operations as strategies to multiply and divide (commutative and distributive properties).8. Look for and express regularity in repeated reasoning.• Students in third grade should notice repetitive actions in computation and look for more shortcut methods. For example, students may use the distributive property as a strategy for using products they know to solve products that they don’t know. For example, if students are asked to find the product of 7 x 8, they might decompose 7 into 5 and 2 and then multiply 5 x 8 and 2 x 8 to arrive at 40 + 16 or 56. In addition, third graders continually evaluate their work by asking themselves, “Does this make sense?”
  • Seeing structure and generalizing1. Look for and make sense of structure.• In third grade, students look closely to discover a pattern or structure. For instance, students use properties of operations as strategies to multiply and divide (commutative and distributive properties).8. Look for and express regularity in repeated reasoning.• Students in third grade should notice repetitive actions in computation and look for more shortcut methods. For example, students may use the distributive property as a strategy for using products they know to solve products that they don’t know. For example, if students are asked to find the product of 7 x 8, they might decompose 7 into 5 and 2 and then multiply 5 x 8 and 2 x 8 to arrive at 40 + 16 or 56. In addition, third graders continually evaluate their work by asking themselves, “Does this make sense?”
  • How is this different from what we used to think? What are patterns in mathematics? How can make them explicit?• Subitization• Ten frames• Number word patterns• Doubling• 0-99 chart• Benchmark (friendly) numbers• Spatial patterns• Patterning is the search for regularity and structure
  • Problem #4Continue the pattern: 1x12=12 2x6=12 3x4=__ Etc… (and what about relational equality?)
  • Where can we start?• GaDOE Teaching Guides• http://public.doe.k12.ga.us/ci_services.aspx?PageReq=CIServMath• Learning Village• https://portal.doe.k12.ga.us/LearningVillageLogin.aspx• List Serve• join-mathematics-k-5@list.doe.k12.ga.us• join-mathematics-6-8@list.doe.k12.ga.us• join-mathematics-9-12@list.doe.k12.ga.us• join-mathematics-districtsupport@list.doe.k12.ga.us• join-mathematics-administrators@list.doe.k12.ga.us• join-mathematics-resa@list.doe.k12.ga.us• Inside Mathematics• http://www.insidemathematics.org/• Teaching Channel• http://www.teachingchannel.org/videos?categories=topics_common-core• Arizona• http://www.ade.az.gov/standards/math/2010MathStandards/• New York City• http://schools.nyc.gov/Academics/CommonCoreLibrary/SeeStudentWork/default.htm• North Carolina• http://www.ncpublicschools.org/acre/standards/extended/• Ohio• http://www.ode.state.oh.us/GD/Templates/Pages/ODE/ODEPrimary.aspx?page=2&TopicRelationID=1704
  • Resource to find in your school:• Teaching Student-Centered Mathematics, Grades K-3• Teaching Student-Centered Mathematics, Grades 3-5• Teaching Student-Centered Mathematics, Grades 5-8 By John Van de Walle and LouAnn Lovin Provided courtesy of GA Dept. of Education
  • Turtle’s Recommended Reading• Number Talks, Sherry Parrish• My Kids Can, Judy Storeygard• Young Mathematicians at Work, Catherine Twomey Fosnot• Thinking Mathematically, Carpenter, Franke, and Levi These are Turtle’s recommendations, not DOE recommendations.
  • Two great resources, free online for the moment…• http://www.stenhouse.com/shop/pc/viewprd.asp?idProduct=9336&r=sb10r077 http://www.stenhouse.com/shop/pc/viewPrd.asp?idproduct=9509&idcategory=78
  • Downloads Yes, there are a few.• NCTM articles• Ten frame and dot card packet• Empty numberline explanation• GA Dept. of Ed resources• This powerpoint (you can watch again in elluminate recordings, by the way) Enjoy and discuss with your colleagues.
  • Recommended Viewing• Teaching Channel- CCSS videos- http://www.youtube.com/watch?v=1IPxt794-yU&• K-5 Standards for Mathematical Practice prezi- http://prezi.com/zkopzkys49kk/k-5-ccgps-standard• Learner.org- math videos- http://www.learner.org/resources/series32.html
  • 3 things?• Something to do tomorrow?• Resources?• Something to think about? Homework!• Watch this- http://www.learner.org/resources/series32.html#program (#20- Shapes From Squares) Talk about it…try it! (see the Third Grade Homework document for details)• Still hungry? Prezi.com- search for CCGPS- more resources, more food for thought. Enjoy!
  • Feedback• Choose one of these, and enter it into the chat window. Please put the symbol next to the thought. For example: “I never thought of gathering feedback from students!” or, “I am already using journals! +”• An AHA! (!)• A question (?)• Something positive from today’s session (+)• Something you will change as a result of today’s session, or that you wish I would change. (c)
  • Thank you for all you do. Keep calm and carry on.