Geometric Reasoning with Shapes and Attributes

1. Geometric Reasoning with Shapes and Attributes K-2 Webinar November 3, 2015  2:45 - 3:45 p.m. Coweta Committed to Student Success

2. AdvancED CCSS Professional Learning We believe as a learning community, we must continually improve.

4. Agenda • Aspects of geometry • Levels of geometric understanding • Characteristics of van Hiele levels • Activities for helping students notice attributes and reason about them • Resources • Wrap-up and reflection Our vision is to ensure the success of each student.

5. Aspects of geometry • Shapes and properties • Properties of two- and three-dimensional shapes • Relationships among shapes based on properties • Transformations • Translations, reflections, rotations • Symmetry and similarity • Location • Coordinate geometry • Visualization • Shapes in the environment, spatial relationships, perspective We believe we must see students as volunteers in their learning.

6. Levels of geometric understanding • Level 0: Visualization • “It looks like …” • Focus only on the shapes available at the time • Level 1: Analysis • “Laundry list” of properties • Understanding of classes of shapes with common properties • Level 2: Informal Deduction • Identify informal relationships among properties • Identify necessary and sufficient properties • Level 3: Deduction • Create proofs about properties • Level 4: Rigor • Reason about different axiomatic systems (e.g., spherical geometry) We believe we must provide challenging, interesting, and satisfying work for students.

7. Source: http://proactiveplay.com/the-van-hieles-model-of-geometric-thinking/ We will provide high-level, engaging work for all learners and leaders.

8. Characteristics of van Hiele Levels • Levels are not dependent on age or maturation. • Advancement through levels requires geometric experiences appropriate for the transition students are making. • When instruction is at a higher level than the student’s working level, students will not be able to understand the concept being developed. “I can follow what you do but I can’t do it myself.” We believe we must provide challenging, interesting, and satisfying work for students.

9. Laying a strong foundation Indicators of Level 0 Indicators of Level 1 “All these shapes are examples of rectangles.” “Squares have four equal sides, four right angles, two equal diagonals, opposite sides are equal, opposite angles are equal… .” Indicators of Level 2 • “This is an upside down triangle.” • “This triangle [the example in front of me] has three different sides.” • Can a student recognize multiple labels? (e.g., rhombus and parallelogram as names for the same shape) • Students can make conjectures and use if-then reasoning. • “I believe that if there are four equal sides and four right angles, then the shape will be a square.” We believe that we are responsible for the success of each student.

10. Working with attributes • What are attributes? A quality or feature regarded as an inherent part of something • How do we help learners understand attributes? Coweta Committed to Student Success

11. Identifying attributes • Which ones matter? • Which ones don’t matter? Common issues • Color • Orientation We believe as a learning community, we must continually improve.

12. Comparing manipulatives Pattern Blocks Attribute Blocks Each shape comes with a variety of attributes Size (small or large) Color (red, yellow, or blue) Shape (triangle, square, rectangle, hexagon, circle) Thickness (thick or thin) • Each shape is a different color. • All shapes based on the same unit length side. Our vision is to ensure the success of each student.

13. Noticing attributes How many bears can sit here? We believe we must see students as volunteers in their learning.

14. Noticing attributes How many bears can sit here? We believe we must provide challenging, interesting, and satisfying work for students.

15. Noticing attributes • Finding shapes in the real world • Look for variety in the shapes • Emphasize the common attributes of a given category of shapes. • Examples from The Greedy Triangle We believe we must provide challenging, interesting, and satisfying work for students.

16. We believe that we are responsible for the success of each student.

17. Coweta Committed to Student Success

18. Reasoning about attributes Making attribute trains Small blue triangle Large blue triangle Large red triangle Large red square Small red square Small yellow square What could come next? We believe as a learning community, we must continually improve.

19. Reasoning about attributes Our vision is to ensure the success of each student.

20. Red Shapes Small Shapes Triangles We believe we must see students as volunteers in their learning.

21. Building on the geoboard • Provide each student with a geoboard. • Invite each student to create a specific shape and make it different from those created nearby. • Triangles • Quadrilaterals • Rectangles • Squares • What do the shapes have in common? • How are they different? • How do you know each of these shapes is a triangle? We believe we must provide challenging, interesting, and satisfying work for students.

22. Building shapes with AngLegs • Give students AngLegs and ask each one to build a quadrilateral. • Compare your shape with your neighbor. • How are they the same? • How are they different? We believe we must provide challenging, interesting, and satisfying work for students.

23. “What’s My Rule?” • Two students share a set of shapes. One is the rule maker and one is the rule guesser. • The rule maker secretly decides on a rule which will sort the shapes into two piles. • The rule maker begins to sort the shapes into two groups: • yes/true (meets the rule) • no/false(does not meet the rule) • The rule guesser watches the sorting and tries to guess the rule. • Take turns being the rule maker and the rule guesser. We believe that we are responsible for the success of each student.

24. “What’s My Rule?” Yes/True No/False Coweta Committed to Student Success

25. Resources • Articles • Developing Geometric Thinking through Activities that Begin with Play • Solving Geometric Problems by Using Unit Blocks • Young Children’s Developing Understanding of Geometric Shapes • Lessons and blackline masters • Geometry Investigations • Discovering Attributes of Geometric Shapes • Attributes of Geometric Shapes • Van de Walle blackline masters • Book and game • Which One Doesn’t Belong? A Shapes Book • Set game ($12.99 to purchase card set; daily online set free for projecting at http://www.setgame.com/set) We believe as a learning community, we must continually improve.

26. Wrap-up and reflection • How can a student’s geometric level of understanding be determined? • What experiences can help students move from one level of understanding to the next? Our vision is to ensure the success of each student.

27. References Andrews, A. (1999). Solving geometric problems by using unit blocks. Teaching Children Mathematics, 5(6), 318-323. Crowley, M.L. (1987). The van Hiele model of the development of geometric thought. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.456.5025&rep=rep1&type=pdf Hannibal, M. (1999). Young children’s developing understanding of geometric shapes. Teaching Children Mathematics, 5(6), 353-357. Mason, M. (n.d.). The van Hiele levels of geometric understanding. Retrieved from http://jwilson.coe.uga.edu/EMAT8990/GEOMETRY/mason,%20marguerite.%20the%20van%20hiele%20levels%20of%20geometric%20understanding.%202002.pdf Van de Walle, J. A., & Lovin, L. H. (2006). Teaching student-centered mathematics, grades k-3. New York: Pearson. Van de Walle, J.A. (2001). Geometric thinking and geometric concepts. In Elementary and middle school mathematics: Teaching developmentally, 4th ed. Boston: Allyn and Bacon. van Hiele, P. M. (1999). Developing geometric thinking through activities that begin with play. Teaching Children Mathematics, 5(6), 310-316. We believe we must see students as volunteers in their learning.