Nipissing University North Bay, Ontario, Canada Guest Instructor: Dan Jarvis, PhD Email: danj@nipissingu

1. The Revised KindergartenMathematics Curriculum (2006) Nipissing University North Bay, Ontario, Canada Guest Instructor: Dan Jarvis, PhD Email: danj@nipissingu.ca

2. Kindergarten Workshop Agenda • Introduction: The Revised Kindergarten Curriculum (2006) – A Focus on Reform Mathematics (technology, manipuplatives, problems) • Expectations 1-14: A Hands-On Approach to Teaching through the Revised Curriculum (2006) • Break (7:45 – 8:00 pm approximately) • Expectations 15-28: A Hands-On Approach to Teaching through the Revised Curriculum (2006) • Kindergarten Resources: eWorkshop and the Guides to Effective Mathematics Instruction in Number Sense and in Geometry (2003, 2005); NCTM “Focal Points” for Kindergarten (2006)

3. Building on Prior Knowledge/Experience Mathematics in Kindergarten builds on children’s desire to make sense of their world, and helps them develop and demonstrate their mathematical understanding. Young children use mathematics intuitively and develop their understanding of mathematics through their individual approaches to learning, as well as through their prior experience of their linguistic, family, cultural, and community backgrounds. It is therefore important that children’s existing conceptual understanding of mathematics be valued and that children be introduced to mathematical concepts in an appropriate manner and at an appropriate time in their development. Children also need to be given learning experiences that are within the range of things they can do with and without guidance (that is, in their zone of proximal development). (p. 40)

4. Providing Rich Problems and Connections to Real Life Problem solving and reasoning that involve the “big ideas” of mathematics are the foundations of mathematics in the Kindergarten program. Rich mathematical problems involve important mathematical ideas and arise out of real-life situations, and can be approached in a variety of ways so that all children can be involved in exploring solutions. Solving such mathematical problems requires persistence, since they do not have one easy-to-find correct answer. Through active participation in mathematics investigations, including problem solving and discussions, children develop their ability to use mathematics as a way of making sense out of their daily experiences. (p. 40)

5. Providing Balanced Mathematics Instruction When developing their Kind. mathematics program from this document, teachers are expected to weave together the mathematical processes (7) and related expectations from the five mathematics categories [strands], as well as relevant expectations from other areas of learning. . . . It is important that the study of various aspects of everyday life should permeate young children’s mathematical experiences. . . . On the basis of what we know about young children’s learning, mathematics in Kind. must be active, hands-on, child-centred, and problem-based. • Concrete materials • Questioning (range of types; children pose math questions) • Reading books aloud and in shared reading contexts

6. Providing Balanced Mathematics Instruction • Demonstrate learning in a variety of ways (e.g., constructing models, describing ideas in their first language, making drawings) • Investigative learning experiences with math manipulatives and other found objects from the classroom and/or home • Free exploration (teacher observes), focused exploration (teacher suggests), and guided (teacher leads through modeling) activities Developing a positive attitude to mathematics and the ability to persevere in solving problems will have a significant impact on children’s future success. (pp. 41-42)

7. Exploring the Expectations (#1-16) • Number Sense and Numeration (Quantity Relationships; Counting; Operational Sense) [#1-12] • Measurement (Attributes, Units, and Measurement Sense; Measurement Relationships) [#13-16]

8. Specific Expectation Km1 • Investigate the idea that quantity is greater when counting forwards and less when counting backwards • Activity: Count objects forward/backwards using number lines, stacking blocks, etc. • Other Activities?

9. Specific Expectation Km2 • Investigate some concepts of quantity through identifying and comparing sets with more, fewer, or the same number of objects • Activity: Identify more/fewer/some; conservation of number (different arrangements); cardinality (last number equals total in set); abstraction (comparing different objects) • Other Activities?

10. Specific Expectation Km3 • Recognize some quantities without having to count, using a variety of tools • Activity: Dot plate construction; dominoes • Other Activities?

11. Specific Expectation Km4 • Begin to use information to estimate the number in a small set • Activity: Estimate number of objects using an anchor reference (5-frame) • Other Activities?

12. Specific Expectation Km5 • Use, read, and represent whole numbers to 10 in a variety of meaningful contexts • Activity: Write and read numbers (note issues with 2, 4, 7, 8); search for numbers • Other Activities?

13. Specific Expectation Km6 • Use ordinal numbers in a variety of everyday contexts • Activity: Identify ordinal numbers through use of stories (objects, people, etc.) • Other Activities?

14. Specific Expectation Km7 • Demonstrate an understanding of number relationships for numbers from 0 to 10, through investigation • Activity: “Making 10” on 10-frames and mentally • Other Activities?

15. Specific Expectation Km8 • Investigate and develop strategies for composing and decomposing quantities to 10 • Activity: Show number of fingers (less or more than 5; Add/subtract fingers • Other Activities?

16. Specific Expectation Km9 • Explore different Canadian coins, using coin manipulatives • Activity: Identify Canadian coins; arrange coins by size (note 10-cent difficulty); shop • Other Activities?

17. Specific Expectation Km10 • Demonstrate understanding of the counting concepts of stable order and of order irrelevance • Activity: Recognize faulty # orders (1, 2, 4, 5, 8, …); count objects starting with a different object in the group • Other Activities?

18. Specific Expectation Km11 • Begin to make use of one-to-one correspondence in counting objects and matching groups of objects • Activity: Matching objects within a story • Other Activities?

19. Specific Expectation Km12 • Investigate addition and subtraction in everyday activities through the use of manipulatives, visual models, or oral exploration. • Activity: Tell a story with objects/animals; simple games like “Off to the Race” • Other Activities?

20. Specific Expectation Km13 • Compare and order two or more objects according to an appropriate measure, and use measurement terms • Activity: Sort objects from shortest to longest • Other Activities?

21. Specific Expectation Km14 • Demonstrate, through investigation, an awareness of the use of different measurement tools for measuring different things • Activity: Measuring time/mass/length • Other Activities?

22. Specific Expectation Km15 • Demonstrate awareness of non-standard measuring devices and strategies for using them • Activity: Measure length with feet/hands (discuss problems with non-standard measure using different sized objects) • Other Activities?

23. Specific Expectation Km16 • Demonstrate, through investigation, a beginning understanding of the use of non-standard units of the same size • Activity: Measuring items with paper clips or straws, i.e., same size always • Other Activities?

24. Break (10 min)

25. Exploring the Expectations (#17-28) • Geometry and Spatial Sense (Geometric Properties; Geometric Relationships; Location and Movement) [#17-22] • Patterning (Patterns and Relationships) [#232-24] • Data Management and Probability (Collection and Organization of Data; Data Relationships; Probability) [#25-28]

26. Specific Expectation Km17 • Explore, sort, and compare traditional and non-traditional two-dimensional shapes and three-dimensional figures • Activity: Sorting by given rules and having students make up their own sorting rules • Other Activities?

27. Specific Expectation Km18 • Identify and describe, using common geometric terms, two-dimensional shapes and three-dimensional figures through investigations with concrete materials • Activity: Identify 2D and 3D shapes and figures; use mystery bags/boxes; drawing on the back or in the sand • Other Activities?

28. Specific Expectation Km19 • Compose pictures and build designs, shapes, and patterns in two-dimensional shapes, and decompose two-dimensional shapes into smaller shapes, using various tools or strategies • Activity: Build a given design and have students create/communicate/analyze their own designs with 2-D blocks • Other Activities?

29. Specific Expectation Km20 • Build three-dimensional structures using a variety of materials, and begin to recognize the three-dimensional figures that the structure contains • Activity: Build 3-D structures and have students discuss/analyze the components using mathematical terminology • Other Activities?

30. Specific Expectation Km21 • Investigate the relationship between two-dimensional shapes and threedimensional figures in objects that they have made • Activity: Match up shapes with corresponding 3-D figures; discuss prisms and pyramids for sorting shapes • Other Activities?

31. Specific Expectation Km22 • Demonstrate an understanding of basic spatial relationships and movements • Activity: Actions involving proximity, out/in, above/below, behind/in front • Other Activities?

32. Specific Expectation Km23 • Identify, extend, reproduce, and create repeating patterns through investigation, using a variety of materials and actions • Activity: Recognize and extend given patterns and create one’s own patterns • Other Activities?

33. Specific Expectation Km24 • Identify and describe informally the repeating nature of patterns in everyday contexts, using oral expressions and gestures • Activity: Finish the pattern sentences from everyday life (e.g., morning, noon, and night; breakfast, lunch, dinner) • Other Activities?

34. Specific Expectation Km25 • Sort, classify, and compare objects and describe the attributes used • Activity: Sort objects by given rules and create/justify one’s own sorting rules • Other Activities?

35. Specific Expectation Km26 • Collect objects or data and make representations of their observations, using concrete graphs • Activity: Using T-charts (tallies) or pictographs depict data for a given question • Other Activities?

36. Specific Expectation Km27 • Respond to and pose questions about data collection and graphs • Activity: Analyze data sets collected by the individual or the class (e.g. Census @ School) • Other Activities?

37. Specific Expectation Km28 • Use mathematical language in informal discussions to describe probability • Activity: Using keywords always/sometimes/never, think of situations that would apply to each from everyday life; answer questions posed by a partner • Other Activities?

38. Recent Ontario Ministry of Education Resources • Ontario Curriculum: Mathematics, Revised, Grades 1-8, 9/10, 2005 • Education for All (Special Needs), 2005 • The Kindergarten Program, Revised, 2006 • eWorkshop Video Database; Guides to Effective Instruction in Mathematics

39. NCTM Focal Points: Pre- and Kindergarten