2 SVMI PROFESSIONAL DEVELOPMENT November 13, 2012 hosted by Dublin Unified School District
3 Agenda • Looking deeper at CCMS and Practice CCSS Standards for Mathematical PracticeCCSS Grade Level OverviewsDifferentiationVan Hiele & Mosaic PuzzlesMenu Slices and FALsLunchBreakout Groups• Looking deeper at CCMS and PracticeStandards : :00• Van Hiele & Mosaic Puzzles :00 –10:00• Break : :30• Menu & FAL Slices and Debrief : :00• Lunch : :45• Breakout Groups : :00
4 Make sense of problems and persevere in solving them. Reason abstractly and quantitatively.Construct viable arguments and critique the reasoning of others.Model with mathematics.Use appropriate tools strategically.Attend to precision.Look for and make use of structure.Look for and express regularity in repeated reasoning.
5 Grouping the Practices William McCallumStandards for Mathematical PracticeTucson, April 2011Why do you think Bill McCallum paired them like this?
6 From Jordan School District in Utah – 6th grade interpretation Participants will look at both k-1 and 6th grade versions of each practice.In groups of 8 each of you will take one practice to study.
7 Grouping the Practices SMP Pairs1 & 6 ; 2 & 3 ; 4 & 5 ; 7 & 8Discuss with your SMP partner the similarities and differences between the two practices in the K-1 posters and then the middle school posters.Discuss with your SMP partner why these two practices have been grouped together.Share highlights of your partner talk with your table.Whole group discussionThinking about the pairs that we just saw,
8 Slide 5 of 7 (Time continued) Share that domains call out the design principals on which the CCSS were constructed
9 Geometry Across Grade Levels In your team of 8:Read one of the overview handouts (K/1; 2/3; 4/5, 6, 7, 8, Algebra, Geometry)Circle, underline, or, highlight any geometry concepts and other big ideas that support geometrical reasoning.Share the progression of geometry with your table, beginning with the K/1 overview.Popcorn share out and clarifying questions.Today our focus will be on Geometry.
10 Content standards: CCSS-Mathematics paint the Big Picture of the domainflesh out the domainare not a checklistare independent of California’s math standards
11 DifferentiationPlease read Malcolm Swan’s Improving Learning in Mathematics: Challenges and StrategiesDiscuss at your table:highlights from the article.anything that resonated with you.questions that arose while reading .Whole Group Debrief
12 Setting the Stage for Geometry Take a few minutes to think about and represent in some way [diagraming, webbing, listing, organizing] what you believe are the big ideas in Geometry.Pair/Share your ideas with an elbow partnerGroup Popcorn Sharing
13 Setting the Stage for Geometry Please read the excerpts from Van de Walle and Burns.Discuss at your table:highlights from the article.anything that resonated with you.questions that arose while reading .Whole Group Debrief
14 Van Hiele Levels“I believe that development is more dependent on instruction than on age or biological maturation and that types of instructional experiences can foster, or impede, development.”-Pierre M. van HieleTeaching Children Mathematics
15 Please read Van Hiele’s Levels of Geometric Reasoning Van Hiele LevelsPlease read Van Hiele’s Levels of Geometric ReasoningLevel 0 RecognitionLevel 1 AnalysisLevel 2 Informal DeductionLevel 3 Formal DeductionLevel 4 RigorSome sources list these as levels 1-5, but the descriptors are the same.
16 Level 0 Shapes are what they look like Students recognize and name figures based on the global visual characteristics of the figure.It’s a square because it looks like a house.These shapes go together because they’re pointy or they’re fat.
19 Instruction at Level 0Sorting and Classifying-see how shapes are alike and differentVariety of shapes- minimize the effect of irrelevant features. Build activities around specific properties so students start to understand and see them naturally.
20 Questions at Level O Let’s see if that’s true for other rectangles. Can you draw a triangle that does not have a right angle?In general students should be challenged to see if observations made about a particular shape apply to other similar shapes.
21 Level 1- AnalysisStudents start to see classes of shapes (instead of a rectangle, all rectangles)Start to see properties of shapes or list of attributesThey have trouble with subcategories or sifting through the attributes, such as seeing that squares are also rectangles, quadrilaterals, parallelograms.
22 What’s a rectangle?6th graders were asked: Can a parallelogram be both a rectangle and a rhombus?
23 What’s a rectangle?6th graders were asked: Can a parallelogram be both a rectangle and a rhombus?
24 What’s a rectangle?6th graders were asked: Can a parallelogram be both a rectangle and a rhombus?
27 Other Students Did not notice that Blobbies had 4 sides. Failed to notice that Blobbies had circles in the middle or thought all shapes with circles in the middle were Blobbies.Students used irrelevant properties like parallel sides.Students couldn’t sort with 2 attributes.
28 Instruction at Level 1Focus on properties rather than mere identification.Think about classes: all rectangles, all prisms.
29 Questions at Level 1 Questions that involve reasoning: If the sides of a four-sided shape are all congruent, will you always have a square? How do you know?Can you find a counterexample? How do you know?
30 Instruction at Level 2 Make and test hypotheses and conjectures. Examine properties of shapes to determine necessary and sufficient conditions.Use language of informal deduction: all, some, none, if-then, what if, etc.Encourage students to attempt informal proofs.
31 Implications for Instruction HandoutStudents working at the recognition or visual level needed activities like…Students working at this analysis stage need activities like…Students working at abstraction or informal deduction are ready for…
32 Mosaic PuzzlePlease cut out the puzzle pieces and explore their relationships.
33 Mosaic PuzzleFind all the pieces that can be made from two other pieces.Find all the pieces that can be made from three other pieces.How many different shapes can be made with a pair of pieces?
34 Mosaic Puzzle What two shapes make a parallelogram? What other two pieces make this shape?Do they also work flipped over?Can you make a parallelogram with three pieces?Hint:Try pieces 1,2 and 5; make it in a different way with these 3 pieces. Also try pieces 1,2, 5 flipped over
36 Problem of the Month (POM) and Slices SVMI morning sessions provide:Opportunities to experience the development of specific mathematical content through the grade levels.POMs and Menu Slices provide:multiple entry points to mathematicsopportunity for extension, development, and differentiationan opportunity to analyze and synthesize the progression of mathematics within domainsSeptember and October POMsNovember and December Menu Slices
37 Geometry Menu Slices Work through all the activities in the slice. Choose a color from the pile on your table.Go to corresponding color Menu Station2- and 3- Dimensional ShapesLocation and PositionTransformations and SymmetryVisualization, Spatial Reasoning, and ModelingWork through all the activities in the slice.Complete the Learning Log
38 Geometry Menu Slices Return to your table. Share Learning Log for the Slice you experienced with your table.Whole Group Discussion
39 Please be back in 45 minutes LunchTime: 60 minutes (Slide 1 of 1)Intent: LunchTalking Points/Instructor Notes: N/AMaterials: N/APlease be back in 45 minutes
44 2-D GeometryWhat are the shapes?How did you see them?
45 3-D GeometryHow many cubes?How did you see them?
46 Teacher Techniques • Individual Think Time • Signals - e.g. Use of Thumbs• Pair/Share• Whole Group Share Out• 3 x 5 Card Follow-up Question or Continuation for Next Day Number Talk• 3 x 5 Card Formative Assessment: two different strategies for solving problem• And the conversation continues …
47 Teacher Tools • Overhead Transparencies • Charts • Butcher Paper Recordings• White Boards• Document Reader• Smart Boards• 3 x 5 Card Follow-up Question or Continuation for Next Day Number Talk• And the conversation continues …
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