Assessing and SupportingEarly Numeracy

Presented byHeather 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.Consultant: Ann Anderson, PhD.

RichmondDot Clouston Janice NovakowskiLeigh ArielCarole Saundry

New WestminsterKelly Cannon Jan KennyJan Morrissey

LangleyLinda JensenTerrie LevittLouise Williams

Peace River NorthLilly Frey Chris La CroixKathy McKnightShirley PetersCorrine Tacey

Vancouver Renata Caverzan Janey Lee Linda O’Reilly

Pamela Hagen, BCAMT/SD#43Tracy Harding, UBC/SD#48Gowa Kong, SFU/SD#44Sally Williams, SD#20

Teacher Team Members

•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?

ENP Focus Questions

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

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?

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

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.

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.

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

If you stack 3 dice, there will be5 hidden faces. Where are they?

I can quickly tell the sum of those hidden faces no matter how youstack the dice. Can you figure outhow?

Solve, compare strategies with a neighbour, then discuss the aspects of numeracy that became apparent.

Kelleher’s Amazing Dice Trick

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.

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

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

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

AU Data (Clarke et al. 2001) Changes in Addition Strategy Use

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

End of K 1 2 3 4

5: advanced strategies

4: basic strategies

3: counting on

2: counting all

1: incorrect

Strategy use at end of grade

1

2

3

4

5

Australian Early Numeracy Research Project(state of Victoria)

U.S.Data, Carpenter & Moser, 1984 Addition Strategy Use, Sums to 18

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Fall,Grade 1

Spring,Grade 1

FallGrade 2

SpringGrade 2

FallGrade 3

Spring,Grade 3

4: strategies, facts

3: counting on

2: counting all

1: incorrect

4

2

1

Strategy use across grades 1-3

3

Madison, Wisconsin, longitudinal study

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

ENP Frame of Reference for the Development of Number Over Time

*This graph is printed in the Supporting Learning document)

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

?

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

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)

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

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

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

What does the assessment highlight?

Content: Number SkillsNumber ConceptsSpatial Thinking

Process: DispositionsStrategiesRepresentationCommunication

• Representation and Communication

• Accuracy

• Strategies and Approaches

• Dispositions and Applications

Numeracy Performance StandardsGrade 1 Quick Scale

Scoring for Performance Standards

Scoring for Early Numeracy Assessment

Page 14 - Connecting with Numeracy Performance Standards

Not YetMeeting

MinimallyMeeting

Meeting FullyMeeting

ExceedingExpectations

1 2 3 4 5

Early Numeracy Assessment Learner Profile

Mathematical Awareness

Dispositions / Habits of Mind

Learning Characteristics

Other Relevant Considerations

* See Page 55 and front page of the Learner Profile

Number Skills Items

Number Concepts Items

Visual Spatial Items

*see Page 12 for detail

*See Page 58 and back page of the Learner Profile

Number Skills Tasks 1 2 3 4 5

3. Matching Numerals and Sets

4. Ordering Numerals 0- 9

5. Counting Forward

6. Counting Back

13. Reading Numerals

14. Printing Numerals

17. 100 Chart (optional)

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 103: Some familiarity with 2 digit numbers4: Comfortable with 2 digit numbers5: Can work with numbers above 100

Number Concept Tasks 1 2 3 4 5

7. Estimate and Check

8. Counting On/I nvariance

9. Build and Change

11. Problem Solving

15. Coin Sets (optional)

Scoring is based on the developmental scheme.

1: No systematic grasp of number2: Counts all from 1, needs perceptual models3: Counts on, mentally represents numbers4: Beginning to use grouping strategies5: Uses known facts, patterns, and relationships

Number Concept Items 7, 8, 9, 11, 15

Visual Spatial Items 2, 10, 12, 16

Scoring reflects an increase in use of mental imagery.

1: No consistent use2: Recognizes and matches shapes3: Uses visual memory to find and use shapes4: Uses dynamic imagery to find and use shapes5: Shows intuitive visual-spatial sense including dynamic imagery

Visual Spatial Tasks 1 2 3 4 5

2. Recognizing Dot Patterns

10. Pattern Tasks

12. Squares Puzzle

16. Cube Building (optional)

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?

Page 17

• Connection of items to instructional materials

Supporting Early Numeracy

Page 20-21

*Video clip 2, girl answering questions

Pages 22-27

Item 2 - Recognizing Dot Patterns

Item 3 - Matching Numerals and Sets

Item 4 - Ordering Numerals 0-9

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

Pages 30 to 33

Item 7 - Estimate and Check

Item 8 - Invariance and Counting On

*Video clip 4 of Adam and Chantelle

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

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

Pages 38-39

Item 10 - Problem SolvingCan 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

Pages 40-41Item 12 - Squares Puzzle

*Video clip 8 - 3 children

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

Homework for Feb. 22 session:

• Try out the assessment with two children: • one verbal and average, then• one who puzzles you.

• Work with your school team to create the time for completing the assessment.

• Bring your assessment data and your questions to the next session.

References:Carpenter, T.P., & Fennema, E., (1999). Children’s mathematics: Cognitively guided instruction. Portsmouth, NH: Heinemann.

Carpenter, T.P., & Moser, J.M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15, 179-202.

Early Numeracy Project Websites:

www.cust.educ.ubc.ca/projects/tandrpros/enp/index.htmlwww.bced.gov.bc.ca/numeracy/

Victoria, AU website for Early Numeracy Research Project information:

www.education.vic.gov.au/search/default.asp