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Assessing and SupportingEarly Numeracy

Webcast Two, Feb. 22, 2005

Presented by

Heather Kelleher

Hosted by the B.C. Ministry of Education

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Overview for Early Numeracy Webcast Two

*How are assessment and instruction connected in the ENP resources?

*What kind of support can we provide:•through intervention for those most in need?•through small group focused instruction?•by working with whole group instruction?•by involving parents

*What does research tell us about best practice for all children in primary mathematics?

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Homework for February 22 session:

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

• Discuss at your tables:•What did the assessment confirm for you?•What did you find that surprised you?•What did you find most useful for informing instruction?•Questions?

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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

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Early Numeracy Assessment Learner Profile

Pages 20 and 21

Mathematical AwarenessQuestions

*general awareness*language issues*adapting questions*putting the child at ease

**make it your own

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Number Skills Items

Number Concepts Items

Visual Spatial Items

*see Page 12 for detail

*See Page 58 and back page of the Learner Profile

7www.cust.educ.ubc.ca/projects/tandrpros/ENP

For additional resourcesrelated to the ENP,check out the websitebelow…

This is a useful tool developed after the project was completed…a scoring snapshot for use when you are familiarwith the assessment.

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Assessment informing instruction…

1. Is intervention needed?

2. What can I add to my math program in the way of focused instruction?

*for a small group with specific needs?*for all students?*for specific students?

3. What changes can I make to my whole class teaching to accommodate the learning differences I see?

4. How might I engage parents in supporting numeracy?

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Supporting Early Numeracy

A. Surprise Box- Small Group Intervention Program

B. Focused Instruction for the Classroom…•Estimation•Pattern•Counting and Numerals•Visual-Spatial Patterns•Math Playground

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Purposes of the Surprise Box Program - page 16

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Surprise Box Content - page 15

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Supporting Early Numeracy

A. Surprise Box- Small Group Intervention Program

B. Focused Instruction for the Classroom…•Estimation•Pattern•Counting and Numerals•Visual-Spatial Patterns•Math Playground

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Page 17

•Connection of items to instructional resources

Supporting Early Numeracy

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Estimation Section - page 27 to 46Table of Contents - page 31

Estimation work:

•Builds mental imagery for quantities

•Involves making sense numerically and spatially

•Stretches thinking, encourages logic/analysis

•Encourages us to use what we know …if/then

•Depends on personal benchmarks

•Depends on willingness to risk not being “right”

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What are you looking for in estimation work?

Can the children:•Understand the language used?•Willingly make a guess?•Give reasonable answers?•Independently answer questions?•Comfortably estimate without counting?•Use spatial clues?•Use benchmarks?•Share their thinking about their estimates?

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Pattern Section - pages 47 to 58

Table of Contents page 48

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Pattern Item, Assessment page 36-37Video Clip 1

What can you learn from the video clip?Pattern wise…

•Verbal description, awareness of pattern•Extend one way (requires analysis)•Extend both ways (more complex analysis)•Recognize the chunk that keeps repeating

Learner wise…•Reflective? Analytical? Patient? Alert?•Independent? Confident? …

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•Concrete

•Visual

•Verbal

•Symbolic

•Analysis

•Generalization

Where is Pattern work going?

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Pattern work:•Builds analytical skills

•Sharpens awareness of similarities and differences

•Encourages creativity and independence

•Stimulates communication and higher level thinking

•Changes the way children see the world

•Changes the way children see mathematics

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Counting and Numeral Recognition Section pages 59 to 77 (T. of C. page 62)

•Extra practice for basic skills

•Contextualize skills early and often

•Work for fluency

•Work for connections to number concepts

•Uses multi-sensory activities

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Counting, Item 5 Video clip 2 - K student in January…

Watch, then discuss:

•What are her strengths?•Where does she have difficulty?•What would you consider her comfort range for counting?•How might this information inform instruction in the classroom?

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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

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Item 13. Reading Numerals*Number of digits?*Articulation difficulties? e.g.14/40*Transpositions?*Hurdles: zero? Teens?

Item 14. Writing Numerals*Pencil grip?*Small motor control?*Patterns for forming numerals?*Reversals? Transpositions?*Hurdles?

*Language article.pdf

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Visual Spatial Pattern Recognition Section pages 78-90 (T. of C. page 80)

This section works on:•Visual imagery and visual memory

•Instant recognition of quantities

•Analyzing visual information

•Combining, comparing and ordering visual information

•Modeling using visual patterns

•Spatial sense making

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From thePrimaryAssessmentDraft

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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

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ENP Frame of Reference for the Development of Number

over Time

(This graph is printed in the Supporting Learning Document.)

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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

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2

3

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Australian Early Numeracy Research Project(state of Victoria)

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Item 11 - Problem Solving Directions and Scoring, Pages 38-39

Present a verbal problem…

1. 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?

2. What does the child need to make sense of the problem?3. What dispositions are evident?

Video Clip 3

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Further items, Primary Assessment Draft available at: www.cust.educ.ubc.ca/projects/tandrpros/enp/resources.html

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What supports the development of numeracy

for all students?

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A focus on thinking and problem solving…•using a wide range of problem solving contexts that build on students’ interests

•attention to building a repertoire of problem solving strategies

•building metacognitive awareness

•emphasis on communicating and sharing thinking

•minimizing reading hurdles; using verbal problems and drawing

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Communicating and representing ideas…

•Drawing•Talking•Acting•Constructing•Connecting•Explaining•Making predictions

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The princess had 6 jewels in her crown.The king gave her 2 more jewels.How many jewels are in her crown now?

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Videos available through www.nctm.org

Children’s Thinking: Cognitively Guided Instruction

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Emphasizing number relationships…

•A focus on using what you know

•Moving beyond counting

•Thinking part/whole

•Building on spatial connections

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Rethinking your approach to basic facts…

•Minimize emphasis on speed while students are dependent on counting

•Reconsider the use of e.g. Mad Minute

•Use a strategic approach to facts

•Emphasize part/whole relationships

•Emphasize inverse relationships

•Consider use of visual organizers that highlight number relationships

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Key Strategies to Encourage:

1. Make a Ten

2. Doubles and Doubles plus/minus One

3. Groupings by twos, threes, fours, fives…

4. What’s the missing part for subtraction

5. Decompose/Recompose for multi-digit

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Estimating early and often…

•Using mental imagery to reason out estimates

•Explaining how estimates are derived

•Estimating quantity, time, length, mass, distance, cost, …every day opportunities

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Valuing thinking, promoting thinking like a mathematician….

•What a neat solution for…

•You really used your head…

•That shows creative thinking…

•I like how you…

•That is a unique idea…could you explain how…

•Can someone build on Jon’s idea?

•Can someone say that in another way?

•Mary is thinking like a mathematician…she is making a conjecture / predicting / estimating / verifying…*Mathematician article.pdf on UBC website

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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)

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Squares Task…what to look for…

Dispositions:Confidence, perseverance, …

Spatial Awareness:Selection of specific piecesUse of dynamic imageryUse of rotations, flips

Thinking:Analytical approach, planning ahead…Learning from attempts vs. random

Video Clip #5

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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?

From the Dental Admissions Test (DAT)For a sample, try…http://www.datprofessor.com

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Spatial task…Triangle Jigsaws, page 17, Whole Group Follow Up

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Spatial tasks:•engage all learners

•develop visual imagery, spatial sense, and analytical thinking

•expand the ability to think in flexible ways

•stimulate use of mathematical language

•create a mind set that is conducive to meaningful learning

•develop positive attitudes towards mathematics.

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Using spatial thinking:

•Playing, constructing, drawing, •Measuring•Mapping•Patterning•Geometry•Graphing•Mental math•Using graphic organizers

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What more can children’s responses What more can children’s responses to spatial tasks teach us about their to spatial tasks teach us about their mathematical thinking? mathematical thinking?

Understanding of numberUnderstanding of numberMental mathMental mathMetacognition Metacognition Problem solvingProblem solvingProportional reasoningProportional reasoning

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Emphasizing process and positive attitudes…

•Promote and value effort, persistence, and concentration

•Focus on important mathematical ideas and make that focus clear to the children

•Use a range of materials/representations/ contexts

•Listen attentively and hold back from telling children everything

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Using open ended tasks and activities…

Examples:

• How many ways can you ……make 50 cents?……arrange 5 squares?

• What is the same and what is different about…

• I counted something in the room. There were exactly four. What might it have been?

• I drew a shape with four sides. Draw what my shape might look like?

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Using more probing questions…

•How did you work that out?

•Could you do that another way?

•What happens if…

•Can you see a pattern?

•How are these two objects the same and how are they different?

•Why do you think…

•Tell me how you….

*Questioning article.pdf

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Building spatial thinking into your program in more systematic ways…

•Rich materials

•Purposeful and engaging tasks

•Lots of hands on, open ended explorations

•Lots of graphic organizers

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Math for Families

•ideas and activities that support the development of numeracy at home

Key Ideas*have fun with math*talk about math*focus on thinking*model positive attitudes*respect variations in growth*math is everywhere

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References and Resources

Primary Assessment Draft available at: www.cust.educ.ubc.ca/projects/tandrpros/enp/resources.html

Primary Problems to Ponder available at http://www.bctf.bc.ca/psas/BCAMT/

Power of Ten cards available at www.poweroften.ca

BEAM resources available at http://www.beam.co.uk/

National Council of Teachers of Mathematics:Teaching Children Mathematics…excellent journalwww.nctm.org for CGI materials