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Assessing and Supporting Early Numeracy Presented by Heather Kelleher Hosted by the B.C. Ministry of Education

Assessing and Supporting Early Numeracy Presented by Heather Kelleher Hosted by the B.C. Ministry of Education. UBC Faculty of Education ENP Contract Team Project Leader: Heather Kelleher, PhD. Research Leader: Cynthia Nicol, PhD. Consultant: Lyndon Martin, PhD.

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Assessing and Supporting Early Numeracy Presented by Heather Kelleher Hosted by the B.C. Ministry of Education

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  1. Assessing and Supporting Early Numeracy Presented by Heather Kelleher Hosted by the B.C. Ministry of Education

  2. UBC Faculty of Education ENP Contract Team • Project Leader: Heather Kelleher, PhD. • Research Leader: Cynthia Nicol, PhD. • Consultant: Lyndon Martin, PhD. • Consultant: Ann Anderson, PhD. Teacher Team Members Langley Linda Jensen Terrie Levitt Louise Williams Peace River North Lilly Frey Chris La Croix Kathy McKnight Shirley Peters Corrine Tacey Richmond Dot Clouston Janice Novakowski Leigh Ariel Carole Saundry New Westminster Kelly Cannon Jan Kenny Jan Morrissey Vancouver Renata Caverzan Janey Lee Linda O’Reilly Pamela Hagen, BCAMT/SD#43 Tracy Harding, UBC/SD#48 Gowa Kong, SFU/SD#44 Sally Williams, SD#20

  3. ENP Focus Questions •How can we identify children’s strengths and weaknesses in early numeracy? •How can we use this assessment information to inform the development of effective intervention plans? •What kinds of instructional support can we provide in Kindergarten and Grade One so that fewer students require intervention later?

  4. ENP Resources • •Assessing Early Numeracy • •Supporting Early Numeracy • •Whole Group Follow-up • •Math for Families • To download: • www.bced.gov.bc.ca/numeracy/resources.htm • To order: 250-387-6409 1-800-663-6105

  5. Overview for Early Numeracy Webcast One January 13, 2005 • What is early numeracy? • What overlaps can we see between early literacy and early numeracy? • What does numerate thinking look like? • What does research tell us about the development of early numeracy? • What is the ENP assessment and how does it help to assess the development of early numeracy?

  6. Numeracy… • Is also called Mathematical Literacy • Involves all aspects of mathematics, not just • number…spatial sense, measurement sense, data • sense… • Depends on an inclination to make sense • • Involves concepts, skills, and attitudes • Can’t be measured just by what you know • Needs to be considered in developmental terms • …..hence….. Early Numeracy

  7. B.C. Association of Mathematics Teachers… Numeracy can be defined as the mathematical knowledge, problem solving and communication skills required by all persons to function successfully within our technological world.

  8. B.C. Primary Program… Numeracy takes into account the intuitive and constructive nature of early mathematical thinking which grows from children’s need to describe various elements of the world. Numeracy develops at the intersection of the child’s intuition and the real world. B.C.’s Numeracy Performance Standards… Numeracy refers to the application of mathematical understanding in daily activities at school, at home, at work, and in the community. It involves both using mathematical skills and knowing how mathematics can be used to solve problems.

  9. What overlaps can we see between • early literacy and early numeracy? • Sense making • Development of imagery • Interconnection of skills and concepts • Metacognition • Built on a base of language and experience • Developmental patterns to learning

  10. Kelleher’s Amazing Dice Trick If you stack 3 dice, there will be 5 hidden faces. Where are they? I can quickly tell the sum of those hidden faces no matter how you stack the dice. Can you figure out how? Solve, compare strategies with a neighbour, then discuss the aspects of numeracy that became apparent.

  11. What the Dice Trick Can Show… • Mathematical disposition/attitude • Flexibility and creativity in thinking • That there are multiple ways to solve a problem • That working with others can help boost thinking • That working alone first is often a good start • That understanding the problem is key • That making conjectures and testing them is key • That a good problem challenges and engages.

  12. What does numerate thinking look like? • Inclination to make sense • Ability to use what you know to figure out what • you don’t know • Confidence and willingness to try, to persevere, • and to take risks • Flexibility and often creativity to thinking • Ability to articulate and to represent thinking • *Video clip 1: Daniel doing the Problem Solving Task

  13. What does research tell us about the • development of numeracy? • • Early success is related to later success • • Attitude is key • • Spatial reasoning plays an important role • • Requires a sustained emphasis on making sense • • Involves the interaction of skills and concepts • • Developmental aspect to growth in both number • and spatial thinking

  14. Making Sense of Number: • Changes in strategy use • Changes in modality use: - concrete materials - picturing/imagining materials - working abstractly, symbolically • Growth of the range of numbers used • Changes in the math knowledge that is stored and used

  15. Australian Early Numeracy Research Project (state of Victoria) 5 5: advanced strategies 4: basic strategies 3: counting on 2: counting all 1: incorrect 4 3 2 1 Strategy use at end of grade

  16. Madison, Wisconsin, longitudinal study 4 4: strategies, facts 3: counting on 2: counting all 1: incorrect 3 2 1 Strategy use across grades 1-3

  17. ENP Frame for Development of Number Emergent: pre-number reasoning Early: counting all Developing: counting on Expanding: early grouping Established: later grouping *detail provided in “Supporting Early Numeracy” document

  18. ENP Frame of Reference for the Development of Number Over Time *This graph is printed in the Supporting Learning document)

  19. Emergent Number • Pre-counting stage • No systematic means of quantifying • Intuitive reasoning • Spatial strengths • Perception dominates • Multisensory dependence • Ability to recognize spatial groupings, • e.g. dice patterns

  20. ?

  21. Early Number • Count all from one • 1 to 1 correspondence • Ordinal view of number • Systematic counting chain to ten • minimum • Conservation of number (invariance) • not established • Dependent on models, perception

  22. Developing Number • Counting-on with tally • Conservation of number • Cardinal view of number • Inclusion relation (e.g., sees 3 as part of 5) • Can mentally represent number (no longer • completely dependent on perception)

  23. Expanding Number • Stage of early grouping • Shifting to many-to-one correspondence • Reversibility and part-whole are established • Known facts and patterns are used for • reasoning rather than counting by ones • Place value is extending the number range

  24. Established Number • Multi-unit conceptual framework • Fully operational grouping structures • Efficient use of facts, relationships, • and strategies • Extensive mental representation • Can keep track of several things at • once

  25. Assessing Early Numeracy: • for using at the end of Kindergarten or in Grade One,or L.A./Resource • individual, 20-30 minute task-based interview • developmentally framed, rather than grade or age referenced • assessment FOR learning and informing instruction • generates a profile of learner strengths

  26. What does the assessment highlight? Content: Number Skills Number Concepts Spatial Thinking Process: Dispositions Strategies Representation Communication

  27. Numeracy Performance Standards Grade 1 Quick Scale • Dispositions and Applications • Strategies and Approaches • Accuracy • Representation and Communication

  28. Page 14 - Connecting with Numeracy Performance Standards Scoring for Performance Standards Scoring for Early Numeracy Assessment

  29. Early Numeracy Assessment Learner Profile * See Page 55 and front page of the Learner Profile Mathematical Awareness Dispositions / Habits of Mind Learning Characteristics Other Relevant Considerations

  30. *See Page 58 and back page of the Learner Profile Number Skills Items Number Concepts Items Visual Spatial Items *see Page 12 for detail

  31. Number Skills Items 3,4,5,6,13,17 Scoring reflects growth in number range: 1: No systematic grasp of # 2: Consistent use of # to 10 3: Some familiarity with 2 digit numbers 4: Comfortable with 2 digit numbers 5: Can work with numbers above 100

  32. Number Concept Items 7, 8, 9, 11, 15 Scoring is based on the developmental scheme. 1: No systematic grasp of number 2: Counts all from 1, needs perceptual models 3: Counts on, mentally represents numbers 4: Beginning to use grouping strategies 5: Uses known facts, patterns, and relationships

  33. Visual SpatialItems 2, 10, 12, 16 Scoring reflects an increase in use of mental imagery. 1: No consistent use 2: Recognizes and matches shapes 3: Uses visual memory to find and use shapes 4: Uses dynamic imagery to find and use shapes 5: Shows intuitive visual-spatial sense including dynamic imagery

  34. If a square paper were folded as indicated by the solid lines, then a hole were punched as shown, what would the unfolded paper look like?

  35. Supporting Early Numeracy Page 17 • Connection of items to instructional materials

  36. Page 20-21 *Video clip 2, girl answering questions

  37. Pages 22-27 Item 2 - Recognizing Dot Patterns Item 3 - Matching Numerals and Sets Item 4 - Ordering Numerals 0-9

  38. Pages 28, 29 Item 5 - Counting Forward Item 6 - Counting Backward Optional Task 17 - Hundred Chart *see pages 50, 51 and RS10 *Video clip 3 - 3 year old girl counting

  39. Pages 30 to 33 Item 7 - Estimate and Check Item 8 - Invariance and Counting On *Video clip 4 of Adam and Chantelle

  40. Pages 34, 35 Item 9 - Build and Change This item assesses the concept of increase/decrease (addition and subtraction), but without symbols. It also explores whether children can visually analyze part-whole relationships and whether they can use mental imagery to generate a missing subset. *video clip 5 of Adam and Chantelle

  41. Pages 36, 37 Item 10 - Pattern Items • Does the child recognize and continue an action pattern? • Can the child analyze a visual pattern to extend it? • Can the child apply the pattern rule to both ends of the pattern? • Can the child identify the pattern stem or chunk that repeats? *video clip 6 - 3 examples

  42. Pages 38-39 Item 10 - Problem Solving • Can the child: • understand the problem • solve the problem and if so, with what sort • of representation and what kind of strategy • • communicate understanding of the problem • What does the child need to make sense of the problem? • *Video clip 7 - 2 children

  43. Pages 40-41 Item 12 - Squares Puzzle *Video clip 8 - 3 children

  44. Pages 42, 43…Item 13 - Reading Numerals Pages 44, 45…Item 14 - Printing Numerals Optional items: Pages 46, 47…Item 15 - Coin Sets Pages 48, 49…Item 16 - Cube Building Pages 50, 51…Item 17 - Hundred Chart

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