Assessing Early Numeracy - Province of British Columbia

Assessing Early Numeracy - Province of British Columbia
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Assessing Early Numeracy
BC Early Numeracy Project (K-1)
Ministry of Education
Assessing Early Numeracy
BC Early Numeracy Project (K-1)
Ministry of Education
N AT I O N A L L I B R A RY O F C A N A D I A N C ATA L O G U I N G I N P U B L I C AT I O N D ATA
Main entry under title:
Assessing early numeracy : BC Early Numeracy Project (K-1)
Companion document to: Supporting early numeracy. Cf. P.
Includes bibliographical references: p.
ISBN 0-7726-5135-3
1. Numeracy - Testing. 2. Mathematical ability Testing. I. British Columbia. Ministry of Education.
II. British Columbia. Early Numeracy Project.
III. Title: Supporting early numeracy.
QA135.6.A87 2004
372.7’2’076
C2004-960018-4
© 2003 Ministry of Education, Province of British Columbia.
C O P Y R I G H T N OT I C E
No part of this document may be reproduced in any form or by any means,
including electronic storage, reproduction, execution or transmission
without the prior written consent of the Province.
P R O P R I E TA RY N OT I C E
This document contains information that is proprietary and confidential to the
Province. Any reproduction, disclosure or other use of this document is expressly
prohibited except as the Province may authorize in writing.
Permission to copy and use this publication in part, or in its entirety, for non-profit
educational purposes within British Columbia and the Yukon, is granted to all staff
of BC school board trustees, including teachers and administrators; organizations
comprising the Educational Advisory Council as identified by Ministerial Order; and
other parties providing direct or indirect education programs to entitled students as
identified by the School Act.
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A S S E S S I N G
E A R LY
N U M E R A C Y
Table of Contents
About the BC Early Numeracy Project . . . 1
Who Was Involved . . . 2
Project Materials . . . 3
The Assessment and Instructional Support Resources . . . 3
Assessing Early Numeracy: Key Components . . . 6
Using the Assessment . . . 9
Getting Ready . . . 10
Conducting the Assessment . . . 11
Summarizing Results . . . 12
Interpreting the Assessment . . . 14
Follow-Up to the Assessment . . . 15
Whole-Group Follow-Up . . . 18
Math for Families – Supporting Numeracy at Home . . . 18
The Assessment . . . 19
Item 1. Mathematical Awareness . . . 20
Item 2. Recognizing Dot Patterns . . . 22
Item 3. Matching Numerals and Sets . . . 24
Item 4. Ordering Numerals 0-9 . . . 26
Items 5 & 6. Counting Forward and Backwards . . . 28
Item 7. Estimate and Check . . . 30
IItem 8. Invariance and Counting On . . . 32
Item 9. Build and Change . . . 34
Item 10. Pattern Items . . . 36
Item 11. Problem Solving . . . 38
Item 12. Squares Puzzle . . . 40
Item 13. Reading Numerals . . . 42
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Item 14. Printing Numerals . . . 44
Item 15. Coin Sets (Optional) . . . 46
Item 16. Cube Building (Optional) . . . 48
Item 17. 100 Chart (Optional) . . . 50
References . . . 52
Resource Sheets . . . 53
RS1.
Learner Profile . . . 55
RS2.
Early Assessment Record Sheet . . . 56
RS3.
Summary of Early Numeracy Assessment Responses . . . 58
RS4.
Numeral Cards 0–9 for Items 3 and 4 . . . 59
RS5.
Dot Cards for Items 2 and 3 . . . 60
RS6.
Shapes for the Squares Puzzle, Item 12 . . . 61
RS7.
Square for the Squares Puzzle, Item 12 . . . 62
RS8.
Calendar for Item 13 . . . 63
RS9.
Numeral Cards for Item 13 . . . 64
RS10. 100 Chart for Items 13 and 17 . . . 65
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A S S E S S I N G
E A R LY
N U M E R A C Y
About the BC Early
Numeracy Project
T
he BC Early Numeracy Project (ENP) was sponsored by the
Ministry of Education and involved UBC mathematics teacher
educators and teachers from several school districts in the province.
The project’s purpose was to develop assessment and instructional
tools to support early numeracy development, particularly for
children at risk. Three classroom resources, Assessing Early
Numeracy, Supporting Early Numeracy, Whole Group Follow-up
and a parent resource Math for Families – Supporting Numeracy
at Home, are the result.
Three questions focused the project’s development:
●
How can we identify children’s strengths and weaknesses in
early numeracy?
●
How can we provide instruction in kindergarten and grade
one so that fewer students require intervention later?
●
How can we develop intervention plans with appropriate
starting points and effective instructional strategies?
We began by examining current research and practice in mathematics
“This
assessment
has expanded
my
understanding
of what is
possible in
student
thinking.”
teaching to establish what constitutes early numeracy and how best
to assess, recognize and support its development. The team drew
from the Mathematics IRP and a variety of other sources to design
the assessment items. Over a year and a half, we piloted and refined
the items, developed the scoring frameworks and finalized the
assessment resource. Next, we developed instructional resources
to complement the assessment.
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Who Was Involved
U N I V E R S I T Y O F B R I T I S H C O LU M B I A P R O J E C T T E A M
Dr. Heather Kelleher, ENP Project Leader, UBC Faculty of Education
Dr. Cynthia Nicol, ENP Research Leader, UBC Faculty of Education
Dr. Lyndon Martin, ENP Consultant, UBC Faculty of Education
Dr. Ann Anderson, ENP Consultant, UBC Faculty of Education
TEACHER TEAM MEMBERS
Leigh Ariel SD#38 Richmond
Kelly Cannon SD#40 New Westminster
Renata Caverzan SD#39 Vancouver
Dot Clouston SD#38 Richmond
Lilly Frey SD#60 Peace River North
Pamela Hagen, BCAMT and SD#43 Coquitlam
Tracy Harding, UBC and SD#48 Howe Sound
Linda Jensen SD#35 Langley
Jan Kenny SD#40 New Westminster
Gowa Kong, SFU and SD#44 North Vancouver
Chris La Croix SD#60 Peace River North
Janey Lee SD#39 Vancouver
Terrie Levitt SD#35 Langley
Kathy McKnight SD#60 Peace River North
Jan Morrissey SD#40 New Westminster
Janice Novakowski SD#38 Richmond
Linda O’Reilly SD#39 Vancouver
Shirley Peters SD#60 Peace River North
Carole Saundry SD#38 Richmond
Corrine Tacey SD#60 Peace River North
Louise Williams SD#35 Langley
Sally Williams, SD#20 Kootenay-Columbia
D I S T R I C T S I N V O LV E D I N F I E L D T E S T I N G T H E R E S O U R C E S
SD#19
SD#20
SD#22
SD#23
SD#27
SD#35
SD#38
SD#39
SD#40
Revelstoke
Kootenay-Columbia
Vernon
Central Okanagan
Cariboo-Chilcotin
Langley
Richmond
Vancouver
New Westminster
SD#45
SD#48
SD#53
SD#60
SD#67
SD#70
SD#73
SD#74
SD#83
West Vancouver
Howe Sound
Okanagan-Similkameen
Peace River North
Okanagan Skaha
Port Alberni
Kamloops-Thompson
Gold Trail
North Okanagan-Shuswap
M I N I S T RY O F E D U C AT I O N T E A M M E M B E R S
Richard V. DeMerchant
Joanie Donovan
Jill Levere
Dr. Bruce McAskill
The Ministry would like to thank A. Toutant Consulting Group and DGB Typesetting for their
advice and guidance in the production of this document.
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A S S E S S I N G
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N U M E R A C Y
Project Materials
The Assessment and Instructional
Support Resources
Assessing Early Numeracy
addresses several important
components of early numeracy.
It was designed to be used at the
end of kindergarten or early in
grade one, with a focus on
identifying children at risk in
mathematics. The assessment
helps teachers consider which
children would benefit from
intervention support in grade one
and which need extra attention
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Assessing Early Numeracy
BC Early Numeracy Project (K-1)
Ministry of Education
“The ENP
project has
helped me
see how
assessment
can inform
instruction –
assessment is
well worth
the time.”
given to the development of
specific skills.
Supporting Early Numeracy was
designed as a resource for
teaching based on assessment
results. The goal is for assessment
to inform instruction. However,
for the assessment to be fair,
children must have had the
opportunity to learn the concepts
and skills assessed. This resource
provides instructional suggestions
to support grade one students
who are at risk of falling behind.
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P R O J E C T
Supporting Early Numeracy
BC Early Numeracy Project (K-1)
Ministry of Education
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Whole Group Follow-up –is
designed to provide additional
instructional activities to support
numeracy. These activities are
designed for the teacher to use
with the whole class and offer
activities that are of value for all
levels.
Math for Families – Supporting
Numeracy at Home is designed
to provide suggestions for ways
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Whole Group Follow-up
BC Early Numeracy Project (K-1)
Ministry of Education
that families can engage in
mathematics and support numeracy through everyday activities
at home. The activities provided support the assessment and can
be selected by teachers to suggest for support at home. Math for
“I pay more
attention now
to where
students are
developmentally.”
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Families – Supporting Numeracy at Home is also available as a
webpage for parents to access.
A S S E S S I N G
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N U M E R A C Y
The assessment and instructional resources focus on four key
aspects of numeracy:
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Number Skills—the basic tools of numerate thinking,
including counting, reading and writing numerals, and
recognizing visual-spatial quantities without counting.
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Number Concepts—the “understanding” part of numerate
thinking, through sorting, comparing, ordering, patterning,
estimating, quantifying, seeing part/whole relationships,
joining, separating, grouping, sharing and representing.
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Visual-Spatial Thinking—the ability to make sense of visualspatial information.
●
Attitudes—the dispositions that support numerate activity:
the inclination to make sense, to try hard, to persevere, to see
mathematics as fun and relevant, and to see oneself as a
capable thinker and problem solver.
“For the
assessment
to be fair,
children must
have had the
opportunity
to learn the
concepts and
skills being
assessed.”
The educators who developed the Early Numeracy Project materials
believe that supporting young learners to build competency requires:
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building a solid foundation of understanding rather than
focusing on speed or memory
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recognizing and supporting differences in developmental
stage and learning style
●
understanding how children learn mathematics and typical
learning patterns for mathematics
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recognizing visual-spatial strengths and the scaffolding that
visual-spatial thinking provides for making sense of number
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supporting and enhancing children’s mathematical
dispositions and habits of mind
The materials are designed for use by kindergarten and grade one
classroom teachers and learning assistance/resource room teachers.
The materials are designed to help them become more observant in
seeing and hearing what children think and do. The materials do not
replace the classroom mathematics program but provide support in
the form of in-depth assessment and focused instruction.
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Assessing Early Numeracy: Key Components
ASSESSMENT ITEMS
“There is a big
change for me
in terms of how
I assess. … a lot
of kids just
aren’t able to
share their
thinking in a
written format
or even in
pictorial form. ”
Each assessment item provides an opportunity to assess a key
aspect of early numeracy. For each item you will find:
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the purpose of the item
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sample results, if available
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instructions for scoring the item according to the framework
●
what to look for when using the item
●
materials needed
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directions for using the item
●
questions to ask
The items are laid out in a standard format for ease of use, with
sample results and scoring on the left and directions for using the
item on the right.
Item 7. Estimate and Check
This item looks at the child’s meaningful counting range as opposed to the rote
counting chain or song.
Using Item 7
W H AT TO L O O K F O R :
Assessing Student Performance
●
SCORING ITEM 7
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very unrealistic estimate and incorrect
count
3
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In field testing of roughly 200 kindergarten
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counts in unsystematic ways
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(considered reasonable estimates)
●
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12% were right on or within 2 of the 15
counts accurately to 15
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41% were not within +/- 5
uses all of the counting principles listed
above
●
74% were able to accurately count the 15
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5
N/A
Does the child move the objects and count or simply look and count? Is
the method accurate?
59% estimated between 10 and 20
estimates between 10 and 20
as for Level 3 but with confidence and
efficiency
Does the child use a correct and systematic number chain when
counting objects?
students:
does not estimate between 10 and 20
2
Can the child make a reasonable estimate of
number (is 15 within the child’s comfort zone)?
Sample Results for Item 7
Can the child count systematically by 1s, using all of the above skills?
YOU WILL NEED:
to check
Children who find this item a challenge might
benefit from experience with the following
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Estimation
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See Table 2 (p. 17): Linking Assessing Early
a counting mat
a. “About how many do you think are under
here?”
sections in Supporting Early Numeracy:
Surprise Box
15 cubes or other counters
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Randomly place 15 cubes under a counting mat,
show briefly and ask:
I N S T RU C T I O N A L F O L L OW- U P
●
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b. “Count, check and see exactly how many.”
Numeracy with Supporting Early Numeracy
for other sections that can help to develop
this aspect of numeracy.
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LEARNER PROFILE
RS1 Learner Profile is a
RS1. Learner Profile
resource sheet (RS) that
Name: _______________________________ Birthday: ___________ Age: _________________
Teacher: _____________________________ Grade: ______________ Date: ________________
provides a format to note
Not Evident
evidence of the child’s
Always Evident
“You are really
looking at the
development
of kids…what
they
understand,
how they’re
using it. That’s
what is
directing the
instruction.”
MATHEMATICAL AWARENESS SUMMARY (Item 1)
mathematical awareness,
DISPOSITIONS AND HABITS OF MIND:
inclination to make sense
learning characteristics,
confidence and willingness to take risks
dispositions and habits of
perseverance
mind.
interest, curiosity and inventiveness
flexibility in exploring mathematical ideas
pride in mathematical accomplishments
LEARNING CHARACTERISTICS:
Use RS1 Learner Profile
organization (of materials, thoughts, work)
in conjunction with
metacognition (shows or tells his or her thinking)
ability to verbally articulate thinking and procedures
RS3 Summary of Early
ability to model or represent thinking on paper
attention to task and ability to focus
Numeracy Assessment
independence and self-reliance (vs. reliance on others)
Responses to consider
OT H E R R E L E VA N T C O N S I D E R AT I O N S :
which students might
benefit most from extra
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( K – 1 )
support in grade one.
E A R LY N U M E R A C Y A S S E S S M E N T R E C O R D S H E E T
Use the resource sheet, RS2 Early Numeracy Assessment Record Sheet,
for recording student responses to each item.
RS2. Early Assessment Record Sheet
1 0 . P AT T E R N I T E M S – c o n t i n u e d
14. NUMERAL PRINTING
Writes: ✓ or record child’s effort
Analyzing Patterns RGBB RGBB RG…
a) Can you see/describe a pattern? ✓
1
✗
Name: _______________________________ Birthday: ___________ Age: _________________
✓
1 . M AT H E M AT I C A L A WA R E N E S S
6. COUNTING BACK
a) How old are you? ✓
a) Counts back from 10 ✓
✗
b) When is your birthday? ✓
✓
✗
✗
✓
a) estimate ______________________________
f ) What is your telephone number? ✓
g) How old is your mom/dad? ✓
b) count _________________________________
✗
8 . C O U N T I N G O N / I N VA R I A N C E
✗
a) builds 10 ✓
✓ or ✗ recognized without counting
2
4
0
5
3
9
4
0
8
105 2469 6023
✗
Optional Items:
Creating a Pattern Train (only use if necessary)
15. COIN SETS
a) draw student’s construction and description
Show how to make…12 cents
12P
a) 4 plates/2 cookies on each
✗
b) conserves 10 ✓
2 . R E C O G N I Z I N G D OT P AT T E R N S
7
724
Can show with cards?
1 1 . P R O B L E M S O LV I N G
✗
h) What year were you born? ✓
2
15
Can find? Can copy?
Comments:
✗
5
60
Comments:
✓
✗
e) How old is your brother/sister? ✓
3
d) What keeps repeating in the pattern?
7 . E S T I M AT E A N D C H E C K
d) How many brothers or sisters do you have?
47
✗
b) Other
c) How old will you be on your next birthday?
✓
✗
c) Can you continue the pattern at both ends?
✗
6
12
b) Can you figure out which colour comes next?
2N+2P
1N+7P
Answer:
✗
16. CUBE BUILDING
Child’s strategy:
c) provides rationale ✓
estimate:
✗
9
d) counts on ✓
1D+2P
Which coins are used with meaning: P N D
Rating
3x3x3 cube strategy/explanation:
✗
b) 10 candies/2 share
3 . M AT C H I N G N U M E R A L S A N D S E TS
2
4
0
5
3
Answer:
9. BUILD AND CHANGE
✓ or ✗ numeral matched
Predicts
9
a) Change 6 to 4
✓ ✗
b) Change 4 to 8
✓ ✗
c) Change 8 to 5
✓ ✗
d) Change 5 to 12
✓ ✗
Strategy
Does the child:
12. SQUARES PUZZLE
4. ORDERING NUMERALS
1
2
3
4
5
6
7
8
9
a) read 1- and 2-digit numbers (gray boxes)
3
8
14
29
36
75
b) find given numbers and determine the
Notes:
5 . C O U N T I N G F O R WA R D
a) How high can you count? _______________
1 0 . P AT T E R N I T E M S
b) Counts from one to ____________________
Action Patterning clap, clap, pat…
c) Counts on from _______________ correctly.
a) joins in with you ✓
d) Says number after 4____ 10____ 25____
RATING
Circle the pieces the child selects:
✓ or if ordered correctly
0
1 7 . 1 0 0 C H A RT
Child’s strategy:
number one greater 10 ____ 25____ 79____
c) find given numbers and determine the
13. READING NUMERALS
d) write one- and two-digit numerals
✗
b) keeps the pattern going ✓
number one less ___7 ___13 ___40 ___ 100
Reads:
3
✗
49_____ 80_____ 109_____
8
36
83
18
147
407 1847
Optional Calendar:
use patterns to find numbers on a 100 Chart
*finds
42
57
83
If so, continue with pattern items.
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S U M M A RY O F E A R LY N U M E R A C Y
ASSESSMENT RESPONSES
Use the resource sheet, RS3
RS3. Summary of Early Numeracy
Assessment Responses
Name: _______________________________ Birthday: ___________ Age: _________________
Summary of Early Numeracy
NUMBER SKILLS ITEMS
Assessment Responses, to
1
2
3
4
5
COMMENTS
1
2
3
4
5
COMMENTS
1
2
3
4
5
COMMENTS
3. Matching Numerals and Sets
4. Ordering Numerals 0-9
summarize student responses into a
profile of strengths and weaknesses.
5. Counting Forward
6. Counting Back
13. Reading Numerals
14. Printing Numerals
Items are clustered into the three
17. 100 Chart (optional)
content areas of the assessment:
NUMBER CONCEPT ITEMS
7. Estimate and Check
number skills, number concepts
8. Invariance/Counting On
and visual-spatial skills.
9. Build and Change
11. Problem Solving
15. Coin Sets (optional)
“Asking kids to
explain their
thinking gives
you a different
level of
understanding.”
Use the Summaries and Learner
V I S UA L S PAT I A L I T E M S
Profiles when planning for
2. Recognizing Dot Patterns
10. Pattern Items
instructional follow-up.
12. Squares Puzzle
16. Cube Building (optional)
I M P L I C AT I O N S F O R I N S T RU C T I O N :
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A S S E S S I N G
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RESOURCE SHEETS (RS)
RS5. Dot Cards for Items 2 and 3
Pages 55–65 provide the basic
materials required for using the
A
B
C
D
assessment. They need to be
prepared ahead of time by copying
them onto
card stock and
RS6. Shapes for the Squares Puzzle, Item 12
cutting some
into separate
pieces.
E
F
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E A R LY
N U M E R A C Y
Using the Assessment
Being well prepared is important. Review the steps on the following
pages before you conduct the assessment. Keep in mind that your
main goal is to identify children’s strengths and weaknesses in
numeracy.
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Getting Ready
Take some time to prepare for the assessment. Knowing what to
do—and having the supplies you need at hand—will help you feel
more relaxed as you do the assessment and will ensure that the
process goes smoothly. Before you start:
●
familiarize yourself with the directions (Conducting the
Assessment on page 11)
●
prepare the materials listed below (pages 55–65), and
organize them for ease of use (use a container to keep all
materials in one place).
Items to prepare or collect ahead of time:
●
copies of RS1 Learner Profile, RS2 Early Numeracy
Assessment Record Sheet and RS3 Summary of Early
Numeracy Assessment Responses – use 11 x 17 paper to
make booklets
●
RS4 Numeral Cards 0-9 – can be made using felt pen on stiff
card (roughly 5cm x 8cm)
●
RS5 Dot Pattern Cards – can be made using cards and stickers
●
RS6 Shapes and RS7 Square Form for Squares Puzzle for
Item 12 (cut out shapes) – run off on stiff card
●
RS8 Calendar for reading one- and two-digit numerals
(optional for Item 13)
●
RS9 Numeral Cards for Item 13
●
RS10 100 Chart for Item 17 (Item 17 is optional)
●
pattern train of 10 Unifix cubes (red, green and blue) for Item 10
●
counting mat (minimum 8.5x11 stiff card)
●
3x3x3 cube constructed from Multilink cubes for Item 16
(Item 16 is optional)
●
Unifix cubes, blocks or other counters familiar to the child
●
paper and pencil (felt pens optional)
●
calculator
●
mixed set of coins, roughly 10 each of pennies, nickels and
dimes for Item 15 (Item 15 is optional)
10
A S S E S S I N G
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N U M E R A C Y
Conducting the Assessment
The first aim of the assessment interview is to better understand the
child’s strengths and weaknesses in numeracy. A second aim is to
determine what kinds of support or scaffolds best support the
child’s learning and allow the child to be successful (e.g., different
wording, use of materials or help organizing materials).
The assessment takes between 20 and 35 minutes, depending on
the child. As you become familiar with using the items, you will
learn how much response time to allow. Before starting, reassure
If the child does not
the child that in this special time together, you want to learn how
understand your directions,
reword them and note what
they think and work in mathematics.
caused the difficulty. Break the
To begin, seat the child to your left (if you are right-handed) so that
assessment into two sittings.
you can record as you go.
If an item is clearly too difficult
With the child’s help, complete the information at the top of RS2
and you have tried some ways
Early Numeracy Assessment Record Sheet, and ask the questions
to scaffold the item, move on to
for Item 1, Mathematical Awareness. Ensure the child is at ease
the next item. These items are
before continuing with the assessment.
starting points for exploring a
Record the child’s responses directly onto the Record Sheet. Upon
child’s strengths and
completion, go back and fill in RS3 Summary of Early Numeracy
weaknesses.
Assessment Responses. If you can arrange it, using a video recorder
End the interview with
to record the first few interviews can be helpful until you become
something the child can do
more familiar with the items and their scoring. (Note: you may need
well (e.g., make a pattern with
parent permission.) Once you are comfortable using the items, it
the cubes) so they leave feeling
may work best to fill out the profiles as you go, making instructional
positive about the experience.
notes for later use.
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Summarizing Results
Scoring criteria are provided for each item, using a range from 1 to 5.
(You will find these criteria beside each item in the assessment.)
Items are grouped into three categories. For each category, there is a
different basis for scoring. The following chart summarizes the key
criteria that distinguish scoring for each category:
Using five stages or levels to describe response to all three sets of
items is not meant to suggest that number and visual-spatial
abilities develop at the same rates in individual children. Rather, the
stages or levels are used to simplify recording and interpretation
and to visually allow patterns of strength to emerge so that
instruction can be built upon children’s abilities.
Table 1: Scoring Criteria
Aspect of Numeracy
Items
Key Scoring Criteria
NUMBER SKILLS
3, 4, 5, 6, 13, 17
Scoring the Number Skills Items:
The five levels gradually increase according to number
size, showing the range of numbers familiar to the child.
1: no systematic grasp of number
2: consistent use of number to 10
3: some familiarity with two-digit numbers
4: comfortable with two-digit numbers
5: can work with numbers above 100
NUMBER CONCEPTS
7, 8, 9, 11, 15
Scoring the Number Concept Items:
The five levels increase by conceptual approach to working with
number (see chart below).
1: no systematic grasp of number
2: counts all from 1; needs perceptual model
3: counts on; mentally represents number
4: beginning to use grouping rather than 1s counting
5: uses reasoning strategies involving grouping and known facts
VISUAL-SPATIAL
2, 10, 12
Scoring the Visual-Spatial Items:
The five levels gradually increase according to proficiency in
the 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
12
A S S E S S I N G
E A R LY
N U M E R A C Y
At the end of the assessment, return to RS1 Learner Profile (page
55), and fill in your summary estimates of the child’s learning
characteristics (these are subjective; use your professional
judgment). The number concept items (Items 7, 8, 9, 11 and 15) and
visual-spatial items (Items 2, 10, 12 and 16) are particularly useful
for assessing these aspects of mathematical disposition. Consider
such things as whether the child relates new ideas to what they
already know (inclination to make sense) or tries different
approaches (flexibility in exploring mathematical ideas).
Summarize the child’s responses to the assessment items on RS3
Summary of Early Numeracy Assessment Responses (page 56). Use
the scoring information for each item as the basis for estimating
the stage of development. The Summary is organized to highlight
clusters of items. This will help you recognize patterns of strengths
and weaknesses in:
●
number skills (mainly recognition and recall in nature)
●
number concepts (mainly conceptual and developmental in
nature)
●
visual-spatial items (items related to visual memory and the
ability to use visual imagery)
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
13
Interpreting the Assessment
Children at any grade level can demonstrate very different levels of
mathematical awareness, interest and ability. Although the BC
mathematics curriculum specifies expectations for each grade,
many children do not fully meet these expectations, while many far
exceed them.
When interpreting the results of this assessment, it is important to
keep in mind that the development of early numeracy is closely tied
to a child’s understanding of number. This understanding depends
on the development of concepts, skills and attitudes. Children may
have highly developed skills,
such as reading and writing
Early Numeracy Project and the BC
Performance Standards
numerals, but little under-
The BC Ministry of Education Performance Standards for
number concepts. Similarly,
numeracy are a good starting point for getting a full picture of
children can understand big
numeracy performance for children in grade 1. Assessing Early
ideas about number while
Numeracy can provide details on mathematics learning for
lacking related skills to
children in grade 1 who do not yet meet or minimally meet
demonstrate or communicate
expectations.
that understanding, or by their
standing of the underlying
lack of confidence to use what
The following illustrates how Assessing Early Numeracy
they know. In practice, concepts
roughly parallels the Performance Standards scoring.
and skills are inextricably
connected—one supports the
other. For assessment
Does Not
Yet Meet
Meets/Fully Meets
Exceeds
purposes, though, separating
out specific components can
help identify strengths and
weaknesses. Recognizing areas
1
2
3
4
5
of weakness helps determine
what learning experiences
children need. Recognizing
learning strengths helps
Both scales above show the range of performance you might
determine how to scaffold
expect for the primary grades. The left end of the range
these learning experiences.
includes children at risk, and the right end includes those
who may benefit from an enriched math program.
14
A S S E S S I N G
E A R LY
N U M E R A C Y
Follow-Up to the Assessment
Once you have completed the Learner Profiles (RS1), Record Sheets
(RS2) and Summaries (RS3), you are ready to decide what actions to
take. You should be able to plan your instruction based on the
needs identified in the assessment. For example, you might begin
by identifying students who would benefit from the various
strategies provided in Supporting Early Numeracy.
CHILDREN’S LEARNING NEEDS
SUGGESTED SUPPORT
Children who struggled with all
These children could benefit
or most of the assessment items
from working in a small-group
are at risk of falling behind.
setting outside the classroom
to build or strengthen early
numeracy skills. The numeracy
intervention strategy designed
with these children in mind is
the Small-Group Intervention
(Surprise Box).
Children who performed well on
These children could benefit
some assessment items and
from using the activities in
struggled with others might
Focused Instruction for the
benefit from experiences
Classroom. These resources
designed to build specific skills.
contain skill-specific activities
that are designed to be used in
small groups or with the whole
class. NOTE: For specific
suggestions See Table 2 (p. 17):
Linking Assessing Early
Numeracy with Supporting
Early Numeracy.
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
15
Supporting Early Numeracy contains the following resources to assist
you in addressing the particular needs of learners in your class.
SMALL-GROUP INTERVENTION
The Surprise Box section provides an instructional sequence for
working with at-risk grade one children in a small-group setting
outside of the classroom. The Surprise Box resource is designed to
develop positive attitudes and kindergarten-level concepts and
skills in a supportive environment.
F O C U S E D I N S T RU C T I O N F O R T H E C L A S S R O O M
This section includes two sets of structured activities and three
“idea files” that can all be used in small groups (or whole groups as
appropriate). The five skill-specific sections include:
●
Estimation—a collection of structured activities that help
children learn a variety of strategies to assist with estimation
and recognize when it is appropriate to estimate.
●
Pattern—a sequence of patterning activities that moves from
simple hands-on, active pattern tasks to more complex
number patterns. This section combines number concepts
and spatial thinking.
●
Counting and Numeral Recognition—an idea file for children
who need more time and systematic reinforcement to reach
proficiency in counting and numeral recognition.
●
Visual-Spatial Pattern Recognition—a sequential set of fiveminute teacher-led activities aimed at developing mental
imagery to support number sense.
●
Math Playground—a resource file of hands-on spatial
explorations for independent centre work, either in the
classroom or for small-group work outside the classroom.
16
A S S E S S I N G
E A R LY
N U M E R A C Y
Table 2: Linking Assessing Early Numeracy with
Supporting Early Numeracy
The following table shows how Supporting Early Numeracy
connects to the different assessment items in Assessing Early
Numeracy. A dark screen indicates a major relationship, a light
screen indicates a minor relationship, and no screen indicates
no relationship.
Estimation
Pattern
Counting,
Numerals
VisualSpatial
Math
Playground
1 Mathematical Awareness
2 Recognizing Dot Patterns
3 Matching Numerals and Sets
4 Ordering Numerals 0-9
5 Counting Forward
6 Counting Backwards
7 Estimate and Check
8 Invariance and Counting On
9 Build and Change
10 Pattern Items
11 Problem Solving
12 Squares Puzzle
13 Reading Numerals
14 Printing Numerals
15 Coin Sets •
16 Cube Building •
17 100 Chart •
• optional items
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
17
Whole-Group Follow-Up
Often children who are discouraged or disengaged benefit from
working as part of a whole class, especially when there are
opportunities for success at a variety of levels. The lessons in the
Whole-Group Follow-Up section are divided into two sets. The first
set builds number skills and concepts; the second set develops
visual-spatial thinking. These lessons can be used with children at
very different levels of development, and they offer something of
value for all levels.
Math for Families – Supporting
Numeracy at Home
Children come to school with a great deal of knowledge about
mathematics based on experiences they have had with their
families. Schools build on this informal knowledge base,
recognizing that an ongoing partnership with families can greatly
assist the continuing development of mathematical understanding
in children.
The Ministry of Education website (http://www.bced.gov.bc.ca/
primary_program/) also provides access to Math for Families –
Supporting Numeracy at Home for ways families can continue to
support children’s numeracy development through everyday home
activities. Please encourage parents to use the ideas on the website.
You are also invited to duplicate the parts you would like to share
with families in newsletters, conferences or family mathematics
sessions.
18
A S S E S S I N G
E A R LY
N U M E R A C Y
The Assessment
The assessment consists of a series of items designed for use at the
end of the kindergarten year or early grade one, with a focus on
identifying children at risk in mathematics.
1. Mathematical Awareness
2. Recognizing Dot Patterns
3. Matching Numerals and Sets
4. Ordering Numerals 0-9
5. Counting Forward
6. Counting Backwards
7. Estimate and Check
8. Counting On/Invariance
9. Build and Change
10. Pattern Items
11. Problem Solving
12. Squares Puzzle
13. Reading Numerals
14. Printing Numerals
15. Coin Sets (optional)
16. Cube Building (optional)
17. 100 Chart (optional)
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
19
Item 1. Mathematical Awareness
This item is a warm-up to the assessment and is designed to provide a general
estimate of mathematical awareness. Your goal with this item is to put the child
at ease.
Assessing Student Performance
SCORING ITEM 1
Item 1 is used to gather information and
provide an overall picture of high, medium
and low indications of math awareness.
Sample Results for Item 1
(% of kindergarten students who answered
correctly):
a) 98%
I N S T RU C T I O N A L F O L L OW- U P
b) 57%
Children who find this item a challenge might
c) 93%
benefit from experience with the following
d) 94%
section in Supporting Early Numeracy:
e) 84%
●
Surprise Box
f ) 61%
●
See Table 2 (p. 17): Linking Assessing Early
g) 29%
Numeracy with Supporting Early Numeracy
h) 9%
for other sections that can help to develop
Note: These results show how a sample
this aspect of numeracy.
group of roughly 200 kindergarten children
from across British Columbia responded
when tested in May of their kindergarten
year (May 2002).
20
A S S E S S I N G
E A R LY
N U M E R A C Y
Using Item 1
RS2. Early Assessment Record Sheet
1 0 . P AT T E R N I T E M S – c o n t i n u e d
14. NUMERAL PRINTING
Writes: ✓ or record child’s effort
Analyzing Patterns RGBB RGBB RG…
W H AT T O L O O K F O R :
a) Can you see/describe a pattern? ✓
signs of mathematical awareness—what is relevant to
a) How old are you? ✓
a) Counts back from 10 ✓
✗
✗
✓
g) How old is your mom/dad? ✓
8 . C O U N T I N G O N / I N VA R I A N C E
✗
a) builds 10 ✓
✓ or ✗ recognized without counting
2
4
0
5
3
4
0
8
105 2469 6023
Optional Items:
15. COIN SETS
Show how to make…12 cents
12P
a) 4 plates/2 cookies on each
✗
b) conserves 10 ✓
2 . R E C O G N I Z I N G D OT P AT T E R N S
9
✗
a) draw student’s construction and description
1 1 . P R O B L E M S O LV I N G
✗
h) What year were you born? ✓
7
724
Creating a Pattern Train (only use if necessary)
Comments:
✗
2
15
Comments:
✓
a) estimate ______________________________
b) count _________________________________
✗
5
60
d) What keeps repeating in the pattern?
7 . E S T I M AT E A N D C H E C K
✗
e) How old is your brother/sister? ✓
3
Can show with cards?
✗
b) Other
✗
d) How many brothers or sisters do you have?
47
Can find? Can copy?
c) Can you continue the pattern at both ends?
✗
c) How old will you be on your next birthday?
✓
✗
✓
f ) What is your telephone number? ✓
the child, what the child pays attention to
✓
6. COUNTING BACK
6
12
b) Can you figure out which colour comes next?
1 . M AT H E M AT I C A L A WA R E N E S S
b) When is your birthday? ✓
●
1
✗
Name: _______________________________ Birthday: ___________ Age: _________________
✗
2N+2P
1N+7P
16. CUBE BUILDING
Child’s strategy:
c) provides rationale ✓
estimate:
✗
9
d) counts on ✓
1D+2P
Which coins are used with meaning: P N D
Answer:
Rating
3x3x3 cube strategy/explanation:
✗
b) 10 candies/2 share
3 . M AT C H I N G N U M E R A L S A N D S E TS
2
4
0
5
3
Predicts
9
a) Change 6 to 4
✓ ✗
b) Change 4 to 8
✓ ✗
c) Change 8 to 5
✓ ✗
d) Change 5 to 12
✓ ✗
Strategy
YOU WILL NEED:
1
2
3
4
5
6
7
8
9
Does the child:
1 0 . P AT T E R N I T E M S
b) Counts from one to ____________________
Action Patterning clap, clap, pat…
d) Says number after 4____ 10____ 25____
a) joins in with you ✓
3
8
14
29
36
75
b) find given numbers and determine the
a) How high can you count? _______________
c) Counts on from _______________ correctly.
a) read 1- and 2-digit numbers (gray boxes)
Notes:
5 . C O U N T I N G F O R WA R D
RS2 Early Numeracy Assessment Record Sheet (pages 56-57)
1 7 . 1 0 0 C H A RT
RATING
Circle the pieces the child selects:
✓ or if ordered correctly
0
Child’s strategy:
12. SQUARES PUZZLE
4. ORDERING NUMERALS
●
Answer:
9. BUILD AND CHANGE
✓ or ✗ numeral matched
number one greater 10 ____ 25____ 79____
c) find given numbers and determine the
13. READING NUMERALS
d) write one- and two-digit numerals
✗
b) keeps the pattern going ✓
number one less ___7 ___13 ___40 ___ 100
Reads:
3
✗
49_____ 80_____ 109_____
8
36
83
18
147
407 1847
Optional Calendar:
use patterns to find numbers on a 100 Chart
*finds
42
57
83
If so, continue with pattern items.
56
A S S E S S I N G
E A R LY
N U M E R A C Y
B C
E A R LY
N U M E R AC Y
P R O J E C T
57
( K – 1 )
Complete the personal information at the top of the Record Sheet
with the child, including as many of the questions as are
appropriate. The wordings are flexible—use any wording that will
help the child understand the questions. Besides exploring
general mathematical awareness, ask any other questions you
think might help to put the child at ease before starting the
assessment items.
a. How old are you? (record at top of Record Sheet)
b. When is your birthday? (record at top of Record Sheet)
c. How old will you be on your next birthday?
d. How many brothers or sisters do you have?
e. How old is your brother/sister?
f. What is your telephone number?
g. How old is your mom/dad?
h. What year were you born?
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
21
Item 2. Recognizing Dot Patterns
This relatively easy item provides a successful start to build the child’s
confidence.
Assessing Student Performance
SCORING ITEM 2
How many dot patterns does the child
recognize without counting?
1
does not recognize any patterns
2
Sample Results for Item 2
In field testing of roughly 200 kindergarten
children:
●
99% recognized
2 dots
recognizes up to three pattern cards
●
87% recognized
4 dots
3
recognizes four cards without counting
●
89% recognized
0 dots
●
55% recognized
5 dots*
4
recognizes five cards without
counting
●
94% recognized
3 dots
●
79% recognized
9 dots**
5
recognizes all six cards without
counting
I N S T RU C T I O N A L F O L L OW- U P
*The dot pattern used for 5 involves a 2 and
3 arrangement which is less familiar than the
domino pattern.
Children who find this item a challenge might
benefit from experience with the following
**Many children who missed naming 9
sections in Supporting Early Numeracy:
guessed 10—a reasonable estimate but
one that does not consider the three rows
●
Surprise Box
●
Visual-Spatial Pattern Recognition
●
See Table 2 (p. 17): Linking Assessing Early
of three.
Numeracy with Supporting Early Numeracy
for other sections that can help to develop
this aspect of numeracy.
22
A S S E S S I N G
E A R LY
N U M E R A C Y
Using Item 2
W H AT T O L O O K F O R :
●
RS5. Dot Cards for Items 2 and 3
Does the child recognize perceptual groupings
(visual dot patterns) without counting?
YOU WILL NEED:
●
A
B
C
D
E
F
RS5 Dot Pattern Cards
58
A S S E S S I N G
E A R LY
N U M E R A C Y
Show the child each dot pattern card for one to
two seconds in a random order.
Say: “I am going to show you some cards quite
quickly. Tell me how many dots you see.”
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
23
Item 3. Matching Numerals and Sets
This is another relatively easy item that helps to build the child’s confidence
and provide a successful start to the assessment.
Assessing Student Performance
SCORING ITEM 3
How many dot pattern and numeral card
matches does the student make?
1
Sample Results for Item 3
In field testing of 179 kindergarten children:
●
12% matched zero to three cards
●
30% matched four or five cards
●
58% matched all six cards with numerals
matches three or fewer
2
matches four or five
3
matches all six
4
N/A
5
N/A
I N S T RU C T I O N A L F O L L OW- U P
Children who find this item a challenge might
benefit from experience with the following
sections in Supporting Early Numeracy:
●
Surprise Box
●
Counting and Numeral Recognition
●
Estimation
●
Visual-Spatial Pattern Recognition
●
See Table 2 (p. 17): Linking Assessing Early
Numeracy with Supporting Early Numeracy
for other sections that can help to develop
this aspect of numeracy.
24
A S S E S S I N G
E A R LY
N U M E R A C Y
Using Item 3
W H AT T O L O O K F O R :
YOU WILL NEED:
●
RS4 Numeral Cards 0-9
●
RS5 Dot Pattern Cards
B C
E A R LY
N U M E R AC Y
P R O J E C T
5 6 7 8 9
Can the child match numerals to dot patterns?
0 1 2 3 4
●
RS4. Numeral Cards 0–9 for Items 3 and 4
( K – 1 )
57
RS5. Dot Cards for Items 2 and 3
A
B
C
D
E
F
58
A S S E S S I N G
E A R LY
N U M E R A C Y
Show the child each dot pattern card for one to
two seconds in random order.
Spread out the numeral cards face up in random
order between the child and the dot pattern
cards.
Say: “Find the number to match the dots.”
If the child seems puzzled that there are more
numeral cards than sets of dots, explain: “You
don’t need to use all the numbers.”
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
25
Item 4. Ordering Numerals 0-9
This item builds on the previous one.
Assessing Student Performance
SCORING ITEM 4
How many numeral cards does the student
order correctly?
makes several mistakes with ordering
1
confuses numerals
2
misplaces one numeral
3
orders 0 to 9 correctly and systematically
4
N/A
5
N/A
Sample Results for Item 4
In field testing of 180 kindergarten children:
●
14% made several ordering errors
●
18% misplaced one numeral
●
68% ordered all numeral cards correctly,
including 0
I N S T RU C T I O N A L F O L L OW- U P
Children who find this item a challenge might
benefit from experience with the following
sections in Supporting Early Numeracy:
●
Surprise Box
●
Counting and Numeral Recognition
●
Estimation
●
Pattern
●
See Table 2 (p. 17): Linking Assessing Early
Numeracy with Supporting Early Numeracy
for other sections that can help to develop
this aspect of numeracy.
26
A S S E S S I N G
E A R LY
N U M E R A C Y
Using Item 4
RS4. Numeral Cards 0–9 for Items 3 and 4
Can the child order numerals from least to greatest?
●
Is the child aware of 0 and its place in the “great scheme”?
YOU WILL NEED:
●
RS4 Numeral Cards 0-9
B C
E A R LY
N U M E R AC Y
P R O J E C T
( K – 1 )
5 6 7 8 9
●
0 1 2 3 4
W H AT T O L O O K F O R :
57
Remove the 0 card. Shuffle the numeral cards
and place them face up randomly on the table.
Say: “Please put the number cards in order from
least to greatest.” (You may need to say, for
example, “starting with the smallest number.”
Note the wording that makes sense to the child.)
If the child is successful, hand across the 0 card.
Ask: “Where would this one go?”
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
27
Items 5 & 6. Counting Forward and Backwards
A correct and consistent verbal counting chain is integral to building an
understanding of counting objects. If ESL children are unable to count in
English, check whether they have established the counting pattern in their first
language. If so, the problem may be a lack of English patterns rather than a
lack of understanding of number.
Assessing Student Performance
SCORING ITEMS 5 AND 6
I N S T RU C T I O N A L F O L L OW- U P
Children who find these items a challenge might
Item 5: Counting Forward by 1s
1
has no consistent counting chain
2
uses a consistent chain to 10 (may not
count on or give next number)
3
uses a consistent chain to about 50
(counts on and provides the next
number within that range)
4
uses a consistent chain to 100 (counts
on and provides the next number within
that range)
5
counts fluently by 1s beyond 100 (counts
on and provides the next number within
that range)
benefit from experience with the following
sections in Supporting Early Numeracy:
●
Surprise Box
●
Counting and Numeral Recognition
●
Estimation
●
See Table 2 (p. 17): Linking Assessing Early
Numeracy with Supporting Early Numeracy
for other sections that can help to develop
this aspect of numeracy.
Sample Results for Items 5 and 6
No sample data available for these items
Item 6: Counting Backwards by 1s
1
has no consistent backwards chain
2
counts backwards from 10 with
some success
3
uses a confident and consistent
backwards count from 10 to 0
4
uses a consistent backwards chain
from 15 or 20
5
counts fluently backwards by 1s in the
100s range
28
A S S E S S I N G
E A R LY
N U M E R A C Y
Using Items 5 and 6
W H AT T O L O O K F O R :
●
Does the child know the order of the number names? What is the
extent of that knowledge?
●
Does the child know what number comes next/before within their
counting range?
●
Can the child count forward and backwards from any number within
their counting range?
●
Is the child confident in changing decades within their counting
range? (e.g., After the 20s come the 30s, so it is 29, 30....)
YOU WILL NEED:
●
no materials
Item 5: Counting Forward by 1s
Ask:
a. How high can you count? Record childs estimate and actual
count.
b. Count for me starting at ___ (choose a number based on their
estimate).
c. Count from ___ (choose a number midway in their known
counting sequence—not 10 or a multiple of 10).
d. When I say these numbers, tell me what comes next: 4___,
10___, 25___, 49___, 80___, 109___.
Item 6: Counting Backwards by 1s
Say:
Count back from 10 (give starting hint if needed).
Count back from ___ (try to determine the range for this skill).
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
29
Item 7. Estimate and Check
This item looks at the child’s meaningful counting range as opposed to the rote
counting chain or song.
Assessing Student Performance
SCORING ITEM 7
1
very unrealistic estimate and incorrect
count
Sample Results for Item 7
In field testing of roughly 200 kindergarten
students:
does not estimate between 10 and 20
2
3
●
counts in unsystematic ways
59% estimated between 10 and 20
(considered reasonable estimates)
estimates between 10 and 20
●
12% were right on or within 2 of the 15
counts accurately to 15
●
41% were not within +/- 5
uses all of the counting principles listed
above
●
74% were able to accurately count the 15
4
as for Level 3 but with confidence and
efficiency
5
N/A
to check
I N S T RU C T I O N A L F O L L OW- U P
Children who find this item a challenge might
benefit from experience with the following
sections in Supporting Early Numeracy:
●
Surprise Box
●
Estimation
●
See Table 2 (p. 17): Linking Assessing Early
Numeracy with Supporting Early Numeracy
for other sections that can help to develop
this aspect of numeracy.
30
A S S E S S I N G
E A R LY
N U M E R A C Y
Using Item 7
W H AT T O L O O K F O R :
●
Can the child make a reasonable estimate of
number (is 15 within the child’s comfort zone)?
●
Does the child use a correct and systematic number chain when
counting objects?
●
Does the child move the objects and count or simply look and count? Is
the method accurate?
●
Can the child count systematically by 1s, using all of the above skills?
YOU WILL NEED:
●
15 cubes or other counters
●
a counting mat
Randomly place 15 cubes under a counting mat,
show briefly and ask:
a. “About how many do you think are under
here?”
b. “Count, check and see exactly how many.”
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
31
Item 8. Invariance and Counting On
This item assesses the child’s ability to accept and hold in mind an established
quantity despite changes to its arrangement.
Assessing Student Performance
SCORING ITEM 8
1
2
Sample Results for Item 8
cannot establish a set of 10 counters
In field testing of roughly 200 kindergarten
recounts to determine how many once
the items are moved
children:
is uncertain of the quantity without
counting from 1
●
96% were able to build a set of 10
●
64% were not fooled by perceptual changes
in the arrangement and still maintained
for the added 2, counts from 1 to 12
3
there were 10
after establishing the 10, does not need
to recount the new configuration
●
can answer “How do you know?”
without counting
●
60% were able to provide a rationale for why
there were still 10
53% were able to count on 2 to the 10
(10…11, 12) without going back to 1
can count on the 2 extra cubes without
having to recount from 1
responds as if you have asked a silly
question
4
5
for the added 2, says 12 without
obvious counting
N/A
I N S T RU C T I O N A L F O L L OW- U P
Children who find this item a challenge might
benefit from experience with the following
sections in Supporting Early Numeracy:
●
Surprise Box
●
Visual-Spatial Pattern Recognition
●
See Table 2 (p. 17): Linking Assessing Early
Numeracy with Supporting Early Numeracy
for other sections that can help to develop
this aspect of numeracy.
32
A S S E S S I N G
E A R LY
N U M E R A C Y
Using Item 8
W H AT T O L O O K F O R ( I N VA R I A N C E ) :
●
Does the child recount from 1 after every change?
●
Is recounting necessary for the child? What does the child’s
explanation indicate?
W H AT T O L O O K F O R ( C O U N T I N G O N ) :
●
Does the child count on from the established 10 or go back and count
from 1?
●
Can the child hold the starting quantity in mind?
YOU WILL NEED:
●
more than 10 counters all one colour
●
two counters of a different colour
a. Ask the child: “Show me 10 counters.” (Move the rest aside.)
Establish there are 10, then change the arrangement by
spreading the counters out.
b. Ask: “How many now?”
c. Ask: “How do you know?”
Repeat if the child is unsure or counts to check. If the child
persists in counting, ask: “Do you need to count?”
d. Establish there are still 10, then add 2 blocks of a different colour.
Ask: “How many are there now?”
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
33
Item 9. Build and Change
This item assesses the concept of increase/decrease, or addition and
subtraction 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.
Assessing Student Performance
SCORING ITEM 9
I N S T RU C T I O N A L F O L L OW- U P
Children who find this item a challenge might
a) Can the child predict the answer ahead of
doing it? Predict [✓] [x] (out of 4)
benefit from experience with the following
Also note: Can the child solve the example
using the strategy of their choice?
●
Surprise Box
●
Counting and Numeral Recognition
●
See Table 2 (p. 17): Linking Assessing Early
1
2
does not predict or solve any of the
examples
Numeracy with Supporting Early Numeracy
can’t predict how many but may know
whether more or less is needed (big
idea), or
may start from 1 to build each new set
rather than changing the starting set
(predicts 0/4)
3
sections in Supporting Early Numeracy:
predicts subtraction examples (a and c)
by looking and naming what to
subtract but cannot predict addition
examples (b and d) without the support
of materials (predicts 2/4)
for other sections that can help to develop
this aspect of numeracy.
Sample Results for Item 9
After field testing, the scoring criteria were
revised. Using the new criteria, results are
as follows:
●
examples independently (1)
●
4
5
correctly predicts and solves examples
(a), (b) and (c) without touching (note
how the child keeps track) (predicts 3/4)
correctly predicts and solves mentally
for all examples (note whether the
child uses known facts or chunking
rather than counting by 1s to determine the needed change) (predicts 4/4)
8% were unable to predict or solve any
17% were able to solve some examples but
not able to predict ahead of time (2)
●
31% were able to predict for two subtraction
examples and solve other examples using
materials (3)
●
30% were able to predict and solve three
examples without materials (4)
●
15% were able to predict all four examples
ahead of working them out (5)
34
A S S E S S I N G
E A R LY
N U M E R A C Y
Using Item 9
W H AT T O L O O K F O R :
●
Does the child recognize whether more or less is needed to make the new number?
●
Does the child incorporate the starting set without having to start from one to build the new set?
●
Can the child visually analyze the subtraction examples to determine what to subtract without
touching the materials?
●
Can the child predict how many to add without actually using the materials to model?
●
How does the child predict for addition? Does the child mentally count on or use visual patterns
or known facts?
Note: Examples (b) and, particularly, (d) require the child to create a mental representation of what
to add, making those examples more difficult. For (a) and (c) students can see what to subtract.
YOU WILL NEED:
●
blocks or other counters
●
a mat to work on
Use these two warm-up examples to establish the item format of predicting first
without touching.
• “Show me 5 blocks. Now change it to 3 blocks. What did you do?” (e.g., I had to
take away 2 blocks.)
• “This time tell me first . . . (fold your arms or sit on your hands) . . . “How can you
change your 3 blocks to 6 blocks? What will you need to do?” After the child’s
response, ask them to go ahead and do it.
• You are working toward having the child tell you first what needs to be done, to see
if they can predict the change. Provide another example if needed.
EXAMPLES FOR SCORING:
a)
b)
c)
d)
Change 6 to 4
Change 4 to 8
Change 8 to 5
Change 5 to 12
Predict
[✓] [x]
[✓] [x]
[✓] [x]
[✓] [x]
Can the child visually analyze the parts and whole?
Can the child mentally construct the needed part?
Can the child visually analyze the parts and whole?
Can the child mentally construct the needed part?
Predict: “Tell me first. What do you have to do to change your 6 blocks to 4 blocks?”
Solve:
“Check to see if you are right.” Or if there is no prediction, ask: “Show me how you can
find out.”
You may need to ask: “How did you figure it out?”
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
35
Item 10. Pattern Items
This sequence of pattern items looks at the child’s developing ability to work
with simple patterns, a prerequisite to number patterns.
Assessing Student Performance
SCORING ITEM 10
I N S T RU C T I O N A L F O L L OW- U P
Children who find this item a challenge might
Action Patterning
Can the child:
●
join in with you
●
keep the pattern going when you stop
(analyze and extend a pattern)
●
benefit from experience with the following
section in Supporting Early Numeracy:
●
Pattern
●
See Table 2 (p. 17): Linking Assessing Early
Numeracy with Supporting Early Numeracy.
maintain a rhythmic pattern
Analyzing a Pattern
How many questions (out of four) are
answered correctly? Score according to the
number correct.
Sample Results for Item 10
Action Patterning
●
1
0 correct
2
1 correct
3
2 correct
4
3 correct
5
4 correct
Creating a Pattern Train
87% of the field test students were able to
complete the action patterning successfully
Analyzing a Pattern
●
22% answered two or fewer questions (1, 2, 3)
●
52% answered three questions correctly (4)
●
33% answered all questions correctly (5)
Creating a Pattern Train
There are no sample results for this item.
This optional check, if completed
successfully, would be equivalent to a 3 on
the scoring chart.
36
A S S E S S I N G
E A R LY
N U M E R A C Y
Using Item 10
W H AT T O L O O K F O R :
●
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?
YOU WILL NEED:
●
a pattern train of 10 Unifix cubes using red, green,
blue, blue (i.e., RGBB, RGBB, RG)
●
additional Unifix cubes of the same colours
a. Action Patterning (warm-up)
Use this item as an active break.
b. Show the pattern: clap, clap, pat knees; clap, clap, pat knees. Ask: “Can you
figure out the pattern? When you do, join in with me. Keep going.”
c. Analyzing a Pattern
Show the Unifix pattern train (RGBB RGBB RG) and ask: “Look at this. Can
you see a pattern?”
“Can you describe the pattern?”
“Can you figure out which colour comes next?”
“Can you continue the pattern at both ends?”
“What keeps repeating in the pattern?”
d. Creating a Pattern Train (optional check)
If the child is unable to analyze the above pattern, see if they can make their
own pattern train with Unifix cubes and answer the following questions:
“Can you describe your pattern?”
“Can you describe it another way?” or “Can you give this pattern another
name?”
“What keeps repeating in your pattern?”
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
37
Item 11. Problem Solving
This item reflects the student’s problem-solving confidence, ability and
experience.
Assessing Student Performance
SCORING ITEM 11
I N S T RU C T I O N A L F O L L OW- U P
Children who find this item a challenge might
Score each problem independently. If
students perform at more than one level in
parts of the item, choose the most
representative level overall to record.
1
does not work out answer even with
teacher help
requires teacher support to get the
answer
2
benefit from experience with the following
sections in Supporting Early Numeracy:
●
Surprise Box
●
Sample Number Lessons (These lessons are
available in Whole Group Follow-up)
See Table 2 (p. 17): Linking Assessing Early
●
uses materials to directly model the
problem
Numeracy with Supporting Early Numeracy
for other sections that can help to develop
strategy unclear
this aspect of numeracy.
cannot explain or model the solution
independently gets the correct answer
3
uses materials to directly model the
problem
can explain or model the solution
Sample Results for Item 11
With the examples used in the field testing
(which were somewhat harder):
independently gets the correct answer
4
5
does not need materials to directly
model the problem
uses mental counting strategy (e.g.,
fingers, taps)
●
approximately 25% had no idea what to
do (1)
●
approximately 50% were able to solve the
problems by direct modeling using
can explain or model the solution
counters and with some teacher support
successfully solves each problem using
an internalized reasoning strategy
involving known facts or chunking
(2 and 3)
can explain or model the solution
●
approximately 25% were able to solve the
problems without using counters (4 and 5)
does not need materials, but may use
them to explain thinking
38
A S S E S S I N G
E A R LY
N U M E R A C Y
Using Item 11
W H AT T O L O O K F O R :
●
Does the child find meaning within real problem contexts presented verbally?
●
Can the child represent problem situations with concrete materials (Level 2 or 3)?
●
Can the child represent problem situations using fingers or drawings (Level 4)?
●
Can the child represent problem situations using mental reasoning (Level 5)?
●
Is the child able to communicate their understanding of the problem solutions?
YOU WILL NEED:
●
counters
●
pencils and paper
Provide counters, paper and pencil and let the students know they can use whatever they like to
solve the problems. Present the problems verbally first, to see if they can do them independently. If
students don’t know what to do, repeat the problem. For students who simply say the answer, ask
them to show you how they know. Make a note where language appears to be an issue.
a. “If you had 4 plates and 2 cookies on each plate, how many
cookies would you have altogether?”
“How did you figure that out?”
Teacher help: “What if we use these plates and counters?” Then
repeat the question.
What support does the child need to be successful?
b. “If you and I share 10 candies, how many candies will we each get?”
“How did you figure that out?”
Teacher help: “Let’s pretend these counters are candies.” Then
repeat the question.
What support does the child need to be successful?
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
39
Item 12. Squares Puzzle
The Squares Puzzle provides useful information on the child’s use of visualspatial imagery and highlights analytical thinking, perseverance and
confidence. (For a second look at mental imagery involving 3-D solids, use the
Cube Building item, optional Item 16.)
Assessing Student Performance
SCORING ITEM 12
See Table 2 (p. 17): Linking Assessing Early
●
Numeracy with Supporting Early Numeracy
How does the child deal with the Squares
Puzzle? You are looking to see if the child:
1
does not complete the puzzle
2
requires several hints and scaffolds to
complete the puzzle
3
successfully fits pieces into a square
after only one clue (e.g., “Let me show
you something that might help you.”)
4
after some trial and error,
independently fits three of the pieces
into a square
5
initially selects three correctly, then fits
them without assistance (may see two
ways to make the square)
for other sections that can help to develop
this aspect of numeracy.
Sample Results for Item 12
In field testing of 193 kindergarten children:
●
27% did not complete the puzzle (1)
●
48% required teacher help to complete the
puzzle (2 or 3)
●
15% completed the puzzle independently
through trial and error (4)
●
11% pointed out the three pieces and fitted
them into place with ease (5)
I N S T RU C T I O N A L F O L L OW- U P
Children who find this item a challenge might
benefit from experience with the following
sections in Supporting Early Numeracy:
●
Visual-Spatial Pattern Recognition
●
Math Playground
●
Sample Visual-Spatial Lessons (These lessons
are available in Whole Group Follow-up)
40
A S S E S S I N G
E A R LY
N U M E R A C Y
Using Item 12
What to look for:
●
Does the child use analytical thinking (e.g., learns from trying different shapes, eliminates
possibilities) or random thinking (e.g., does not apply information from previous tries)?
●
Does the child mentally manipulate shapes to determine which piece to use, or do they need to
use the actual shapes to experiment?
●
Can the child apply a hint (hold the mental image of a shape, then find the pieces and apply the idea)?
YOU WILL NEED:
RS6. Shapes for the Squares Puzzle, Item 12
●
RS6 Shapes for the Squares Puzzle
●
RS7 Square Form for the Squares Puzzle
B C
E A R LY
N U M E R AC Y
P R O J E C T
( K – 1 )
59
RS7. Square for the Squares Puzzle, Task 12
B C
E A R LY
N U M E R AC Y
P R O J E C T
( K – 1 )
23
Place the six shapes randomly in front of the child.
Show the card with the square shape and ask: “Look at these
pieces. Three of them will make this square shape. Look carefully.
Which three do you think will work?”
Let the child choose, then say: “Go ahead and make the square
for me.”
If the child is stumped, demonstrate how the two small right
triangles go together to make the larger right triangle, and say: “Let
me show you something that might help you.”
Offer other support as needed. Once it is clear what the child can
accomplish independently and you have scored the item, help the
child complete the square.
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
41
Item 13. Reading Numerals
This simple item provides a quick survey of which numerals the child is able
to recognize and name from a limited set of examples. These sound-symbol
relationships do not necessarily indicate understanding but are important
skills in constructing an understanding of our number system.
Assessing Student Performance
SCORING ITEM 13
Besides this item, there are several
opportunities in this assessment to collect
data on numeral recognition:
Item 3—matching one-digit numerals with
dot patterns
●
Counting and Numeral Recognition
●
See Table 2 (p. 17): Linking Assessing Early
Numeracy with Supporting Early Numeracy
for other sections that can help to develop
this aspect of numeracy.
Item 13—optional calendar item
Sample Results for Item 13
Item 17—optional 100 chart item
In field testing of 181 kindergarten children:
Use your observations from any or all of
these items to summarize performance
according to the following:
1
does not read any numerals consistently
2
reads one-digit numerals fairly
consistently
3
reads all one-digit and some two-digit
numerals
4
reads two-digit numerals consistently
5
reads two- and three-digit numerals
comfortably
●
6% did not read any numerals consistently (1)
●
23% read one-digit numerals (2)
●
13% read some two-digit numerals (3)
●
24% read all two-digit numerals (4)
●
19% read three-digit numerals or higher (5)
I N S T RU C T I O N A L F O L L OW- U P
Children who find this item a challenge might
benefit from experience with the following
sections in Supporting Early Numeracy:
●
Surprise Box
42
A S S E S S I N G
E A R LY
N U M E R A C Y
Using Item 13
W H AT T O L O O K F O R :
●
Does the child recognize numerals, and within what number range?
●
Can the child name or read numerals, and within what number range?
●
Does the child read numerals left to right?
●
Does the child make any consistent errors, such as with teen numbers or zeroes?
●
Can the child articulate differences (e.g., seventeen and seventy)?
YOU WILL NEED:
RS9. Numeral Cards for Item 13
RS8. Calendar for Item 13
RS10. 100 Chart for Items 13 and 17
Name: _____________________________________________________ Date: ________________
●
RS9 Numeral Cards (3, 8, 36, 83,
18, 147, 407, 1847)
●
●
RS8 Calendar (optional)
3
18
8
147
36
RS10 100 Chart (optional)
Mo n d a y
6
Fr i d a y
Saturday
1
2
3
4
5
2
3
4
5
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
9
10
27 28 29 30
31
33 34 35 36
51
53 54
71
40
48 49 50
59
61 62 63 64 65
407
8
13 14 15 16 17 18 19 20
44 45
83
68 69
74 75 76 77 78 79
91
1847
A S S E S S I N G
E A R LY
N U M E R A C Y
27
28
30
94 95 96
100
31
a) Read: 3, 8, 14, 29, 36,75
b) Find: 10, 25, 79. Write the number that comes next.
c) Find: 7, 13, 40, 100. Write the number that comes before.
d) Find the three shaded boxes that are empty. Write the numbers.
B C
E A R LY
N U M E R AC Y
For more information on two-digit numerals,
use the calendar or 100 chart (these items are
optional). Ask: “Can you tell me what this date
is on the calendar?”
( K – 1 )
29
DIRECTIONS:
Say: “Read these numbers.” (Show 3, 8, 36, 83,
18, 147, 407, 1847.)
P R O J E C T
Thursday
7
P R O J E C T
Show the child the numeral cards one at a time.
Discontinue at the first sign of difficulty.
N U M E R A C Y
We d n e s d a y
21 22 23 24 25
Use the term numbers with the children rather
than the more mathematically correct term
numerals.
E A R LY
Tu e s d a y
85 86 87 88 89
62
B C
1
May
Su n d a y
61
( K – 1 )
B C
E A R LY
N U M E R AC Y
P R O J E C T
63
( K – 1 )
Note any areas of
difficulty such as:
●
reversals, as in
reading 81 for 18
●
teens (reading and
writing)
●
0s (particularly for
three digits and
above)
●
language confusions
(e.g., saying eighty
for eighteen)
43
Item 14. Printing Numerals
Not all children are ready to print numerals in kindergarten, so this may be a
skill that has not developed. However, it is important to know whether the child
can do it in order to plan appropriate follow-up instruction.
Assessing Student Performance
SCORING ITEM 14
I N S T RU C T I O N A L F O L L OW- U P
Children who find this item a challenge might
Is the child able to print numerals? Use the
following scale for scoring:
1
benefit from experience with the following
sections in Supporting Early Numeracy:
does not print any numerals consistently
2
finds and copies numerals from 0 to 9
3
prints all one-digit numerals from
memory
4
prints two-digit numerals from memory
5
prints three-digit numerals correctly
●
Surprise Box
●
Counting and Numeral Recognition
●
See Table 2 (p. 17): Linking Assessing Early
Numeracy with Supporting Early Numeracy
for other sections that can help to develop
this aspect of numeracy.
Sample Results for Item 14
●
involving three or more digits
In field testing of 180 kindergarten children:
●
82% were able to print all 10 single digits.
Numerals were distinguishable, but quality
13% were able to correctly write numerals
N OT E S :
●
Numerals that were reversed (e.g., a mirror
image of 3) were not counted as wrong. If the
varied.
numeral was distinguishable, it was counted
For the multi-digit items:
as correct, reversed or not. 18% of the numerals
●
33% were unable to write any multi-digit
numerals
considered correct were reversed.
●
62% of the kindergarten children reversed at
●
22% wrote one two-digit numeral correctly
least one numeral, and most of these children
●
16% were able to write two of the two-digit
were able to print all 10 numerals.
numerals (most errors involved the teen
Reversals are developmentally typical for the
numerals)
age group so were not counted as an error.
●
16% were able to write all two-digit
numerals (47, 60, 15)
●
For the multi-digit numerals, reversals were
again ignored. However, transpositions (as in
writing 74 for 47) were counted as incorrect.
44
A S S E S S I N G
E A R LY
N U M E R A C Y
Using Item 14
W H AT T O L O O K F O R :
Children who are unable to print may be able to
Does the child recall numeral shapes from
show how to represent each number if you
memory?
remove the printing component. Doing this
●
Does the child use a comfortable pencil grip?
allows you to focus on the child’s mental
●
Does the child use consistent and reliable
imagery for the numeral, rather than on hand-
●
eye coordination. If unable to print from
motor patterns?
●
●
●
Does the child have difficulty with fine
memory, can the child:
motor control?
●
find and copy numerals?
Does the child have difficulty with reversals?
●
show numerals with digit cards?
For which numerals?
●
display numerals on a calculator?
Does the child confuse teens and multiples
OPTIONAL:
of 10 (e.g., 16/60)?
YOU WILL NEED:
●
paper (you may use the back of the 100
●
RS10 100 Chart for reference
●
numeral cards
●
calculator
chart)
●
pencils or felt pens
Single Digits:
As the child works, note:
Say: “Write these numbers as I say them:
1, 6, 3, 5, 2, 7, 9, 4, 0, 8.”
If the child is unable to recall numerals, provide a 100
chart to see if they can find and copy. If the child is
successful with one digit, continue.
Multi-digits:
E A R LY
N U M E R A C Y
pencil grip
●
fine motor control
●
reversals
●
need for reference
shapes to copy
●
Say: “Write these numbers as I say them:
12, 47, 60, 724, 105, 2469.”
B C
●
P R O J E C T
( K – 1 )
comfort with the item
Is this easy or hard work
for the child?
45
Item 15. Coin Sets (Optional)
This item assesses the child’s ability to use coins with meaning, which requires
coin recognition, recall of coin values and many-to-one correspondence
(e.g., a nickel is worth 5, not 1).
Assessing Student Performance
SCORING ITEM 15
I N S T RU C T I O N A L F O L L OW- U P
Children who find this item a challenge might
Which level best describes the child’s
performance?
1/2 does not recognize any coins
comfortably works with pennies
3
benefit from experience with the following
sections in Supporting Early Numeracy:
●
Counting and Numeral Recognition
●
See Table 2 (p. 17): Linking Assessing Early
Numeracy with Supporting Early Numeracy
does not use nickels or dimes unless
counted from one
for other sections that can help to develop
this aspect of numeracy.
uses two coin types at a time
4
can show values in more than one way
uses three or more different coins
5
Sample Results for Item 15
In field testing of 181 kindergarten children:
can make up all values in different ways
●
78% were unable to recognize any coins
(1/2)
Most kindergarten children (78% in the field
●
15% were able to use pennies (3)
●
7% were able to use two or more coins (4/5)
test) were unable to do this item. However, for
children who are familiar with coins and their
use, this item can highlight important
information for follow-up teaching. It is also a
useful item for recognizing children who
require an enriched mathematics program.
46
A S S E S S I N G
E A R LY
N U M E R A C Y
Using Item 15
WHAT TO LOOK FOR:
●
Is the child familiar with money? Which coins does the child use with meaning?
●
Can the child count on from a starting coin (e.g., 5…6, 7, 8)?
●
Can the child manipulate “chunks” of 5s or 10s and use appropriate counting chains (i.e., count
by 5s and 10s)?
●
Is the child able to shift thinking and counting patterns depending on the coins?
●
Does the child demonstrate organizational and analytical strategies (e.g., counting the highervalued coins first) and metacognitive ability (i.e., can explain their thinking)?
YOU WILL NEED:
●
a collection of pennies, nickels and
dimes (roughly 10 of each)
Show the child a mixed set of coins. Ask if any look familiar. Only
use this item if the child can recognize at least two types of coins
and their values.
Ask: “Do you recognize any of these coins?”
If yes, ask the following questions to see how many coin types the
child is able to use.
“Show me how to make 12 cents. Can you make 12 cents another
way? Are there any other ways?”
(12P, 1D+2P, 2N+2P, 1N+7P)
If necessary, ask if a specific coin can be used.
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
47
Item 16. Cube Building (Optional)
This item provides a window into the child’s analysis of 3-D solids and their
ability to use mental imagery for problem solving. Use it for further
information on the child’s visual-spatial strengths.
Assessing Student Performance
SCORING ITEM 16
I N S T RU C T I O N A L F O L L OW- U P
Children who find this item a challenge might
How does the child approach the problem?
1
2
3
benefit from experience with the following
does not understand the item
sections in Supporting Early Numeracy:
doesn’t complete the item
●
Visual-Spatial Pattern Recognition
guesses or randomly counts faces
●
Math Playground
●
Sample Visual-Spatial Lessons (These lessons
counts squares on each side of the
cube and explains that you have to
count the sides
4
counts outer and inner blocks and
explains that you have to count outer
and inner
5
counts layers of nine blocks and
explains the layers
are available in Whole Group Follow-up)
●
See Table 2 (p. 17): Linking Assessing Early
Numeracy with Supporting Early Numeracy
for other sections that can help to develop
this aspect of numeracy.
Sample Results for Item 16
This item was not part of the field test.
48
A S S E S S I N G
E A R LY
N U M E R A C Y
Using Item 16
W H AT T O L O O K F O R :
●
How does the child go about answering the question?
●
How does the child describe his or her thinking?
●
What understanding does the child have of the structure of 3-D solids
(mental imagery for 3-D solids)?
YOU WILL NEED:
●
a 3x3x3 cube constructed from
Multilink cubes (cm cubes are
too small)
Show the child the cube. Ask: “How many little
cubes do you think it took to build this bigger
cube?”
Give the child the cube to handle. Note how the
child uses the cube to help with thinking. Ask:
“Why do you think it is ___? How could you
figure it out?”
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
49
Item 17. 100 Chart (Optional)
If this item is appropriate for the student, it can replace or provide further
assessment data to support other items, such as Item 14, Numeral Printing.
This item can be completed as a whole-class or small-group activity, with the
exception of reading the numbers.
Assessing Student Performance
SCORING ITEM 17
Rate the child’s overall performance with the
item:
1
Sample Results for Item 17
This item was not part of the field testing.
unable to complete any examples
consistently
2
can successfully work with the onedigit items
3
uses counting to successfully complete
most of the examples
4
completes almost all of the 16 boxes
correctly
5
uses patterns rather than counting to
complete all boxes correctly and
independently
I N S T RU C T I O N A L F O L L OW- U P
Children who find this item a challenge might
benefit from experience with the following
sections in Supporting Early Numeracy:
●
Counting and Numeral Recognition
●
Pattern
●
See Table 2 (p. 17): Linking Assessing Early
Numeracy with Supporting Early Numeracy
for other sections that can help to develop
this aspect of numeracy.
50
A S S E S S I N G
E A R LY
N U M E R A C Y
Using Item 17
W H AT T O L O O K F O R :
●
Can the child read one- and two-digit numbers (gray boxes)?
●
Can the child find given one- and two-digit numbers?
●
Can the child determine the number that is one greater?
●
Can the child determine the number that is one less?
●
Can the child write one- and two-digit
numerals?
RS10. 100 Chart for Items 13 and 17
Name: _____________________________________________________ Date: ________________
●
Can the child use patterns to find numbers on a
1
100 chart?
21 22 23 24 25
2
3
4
5
31
33 34 35 36
51
53 54
44 45
8
9
10
71
27 28 29 30
40
48 49 50
59
61 62 63 64 65
YOU WILL NEED:
7
13 14 15 16 17 18 19 20
68 69
74 75 76 77 78 79
85 86 87 88 89
●
RS10 100 Chart
●
pencil or felt pen
91
94 95 96
100
DIRECTIONS:
a) Read: 3, 8, 14, 29, 36,75
b) Find: 10, 25, 79. Write the number that comes next.
c) Find: 7, 13, 40, 100. Write the number that comes before.
d) Find the three shaded boxes that are empty. Write the numbers.
B C
E A R LY
N U M E R AC Y
P R O J E C T
( K – 1 )
63
Reading, Writing and Finding Patterns on the 100 Chart:
a. Point to each number (3, 8, 14, 29, 36, 75) and ask: “What
number is this?” Can the child read one- and two-digit
numbers?
b. Say: “Find 10, then write the number that comes next (after).”
Repeat for 25 and 79. Can the child write the appropriate
numerals?
c. Say: “Find 7, then write the number that comes in front of it.”
Repeat for 13, 40 and 100. Can the child find given numbers and
the numbers before or after?
d. Say: “Find the three shaded boxes that are empty. Write the
numbers that belong in them.” Can the child use patterns to
find numbers on the chart?
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
51
References
The references, resources and acknowledgements used in the development of this project can be
accessed on the UBC website: http://www.cust.educ.ubc.ca/projects/enp.html
The Early Numeracy Project documents can be accessed online at the following Ministry website:
http://www.bced.gov.bc.ca/primary_program/
52
A S S E S S I N G
E A R LY
N U M E R A C Y
Resource Sheets
RS1. Learner Profile . . . 55
RS2. Early Assessment Record Sheet . . . 56
RS3. Summary of Early Numeracy Assessment Responses . . . 58
RS4. Numeral Cards 0–9 for Items 3 and 4 . . . 59
RS5. Dot Cards for Items 2 and 3 . . . 60
RS6. Shapes for the Squares Puzzle, Item 12 . . . 61
RS7. Square for the Squares Puzzle, Item 12 . . . 62
RS8. Calendar for Item 13 . . . 63
RS9. Numeral Cards for Item 13 . . . 64
RS10. 100 Chart for Items 13 and 17 . . . 65
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
53
54
A S S E S S I N G
E A R LY
N U M E R A C Y
RS1. Learner Profile
Name: _______________________________ Birthday: ___________ Age: _________________
Teacher: _____________________________ Grade: ______________ Date: ________________
Not Evident
Always Evident
MATHEMATICAL AWARENESS SUMMARY (Item 1)
DISPOSITIONS AND HABITS OF MIND:
inclination to make sense
confidence and willingness to take risks
perseverance
flexibility in exploring mathematical ideas
interest, curiosity and inventiveness
pride in mathematical accomplishments
LEARNING CHARACTERISTICS:
organization (of materials, thoughts, work)
metacognition (shows or tells his or her thinking)
ability to verbally articulate thinking and procedures
ability to model or represent thinking on paper
attention to task and ability to focus
independence and self-reliance (vs. reliance on others)
O T H E R R E L E VA N T C O N S I D E R AT I O N S :
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
55
RS2. Early Assessment Record Sheet
Name: _______________________________ Birthday: ___________ Age: _________________
1 . M AT H E M AT I C A L A WA R E N E S S
6. COUNTING BACK
a) How old are you? ✓
a) Counts back from 10 ✓
✗
b) When is your birthday? ✓
✗
✗
b) Other
c) How old will you be on your next birthday?
✓
✗
7 . E S T I M AT E A N D C H E C K
d) How many brothers or sisters do you have?
✓
a) estimate ______________________________
✗
e) How old is your brother/sister? ✓
f ) What is your telephone number? ✓
g) How old is your mom/dad? ✓
b) count _________________________________
✗
Comments:
✗
✗
h) What year were you born? ✓
8 . C O U N T I N G O N / I N VA R I A N C E
✗
a) builds 10 ✓
b) conserves 10 ✓
2 . R E C O G N I Z I N G D OT P AT T E R N S
✓ or ✗ recognized without counting
2
4
0
5
3
✗
✗
c) provides rationale ✓
✗
9
d) counts on ✓
✗
3 . M AT C H I N G N U M E R A L S A N D S E T S
9. BUILD AND CHANGE
✓ or ✗ numeral matched
2
4
0
5
3
Predicts
9
4. ORDERING NUMERALS
a) Change 6 to 4
✓ ✗
b) Change 4 to 8
✓ ✗
c) Change 8 to 5
✓ ✗
d) Change 5 to 12
✓ ✗
Strategy
✓ or if ordered correctly
0
1
2
3
4
5
6
7
8
9
5 . C O U N T I N G F O R WA R D
a) How high can you count? _______________
1 0 . P AT T E R N I T E M S
b) Counts from one to ____________________
Action Patterning clap, clap, pat…
c) Counts on from _______________ correctly.
a) joins in with you ✓
d) Says number after 4____ 10____ 25____
✗
b) keeps the pattern going ✓
✗
49_____ 80_____ 109_____
If so, continue with pattern items.
56
A S S E S S I N G
E A R LY
N U M E R A C Y
1 0 . P AT T E R N I T E M S – c o n t i n u e d
14. NUMERAL PRINTING
Writes: ✓ or record child’s effort
Analyzing Patterns RGBB RGBB RG…
a) Can you see/describe a pattern? ✓
1
✗
12
b) Can you figure out which colour comes next?
✓
✗
47
3
5
60
2
7
15
9
724
4
0
8
105 2469 6023
Can find? Can copy?
c) Can you continue the pattern at both ends?
✓
6
Can show with cards?
✗
Comments:
d) What keeps repeating in the pattern?
✓
✗
Optional Items:
Creating a Pattern Train (only use if necessary)
15. COIN SETS
a) draw student’s construction and description
Show how to make…12 cents
12P
1 1 . P R O B L E M S O LV I N G
a) 4 plates/2 cookies on each
1D+2P
2N+2P
1N+7P
Which coins are used with meaning: P N D
Answer:
16. CUBE BUILDING
Child’s strategy:
estimate:
Rating
3x3x3 cube strategy/explanation:
b) 10 candies/2 share
Answer:
17. 100 CHART
Child’s strategy:
Does the child:
12. SQUARES PUZZLE
RATING
a) read 1- and 2-digit numbers (gray boxes)
Circle the pieces the child selects:
3
8
14
29
36
75
b) find given numbers and determine the
Notes:
number one greater 10 ____ 25____ 79____
c) find given numbers and determine the
13. READING NUMERALS
number one less ___7 ___13 ___40 ___ 100
Reads:
d) write one- and two-digit numerals
3
8
36
83
18
147
407 1847
Optional Calendar:
B C
E A R LY
N U M E R A C Y
use patterns to find numbers on a 100 Chart
*finds
P R O J E C T
( K – 1 )
42
57
83
57
RS3. Summary of Early Numeracy
Assessment Responses
Name: _______________________________ Birthday: ___________ Age: _________________
NUMBER SKILLS ITEMS
1
2
3
4
5
COMMENTS
1
2
3
4
5
COMMENTS
1
2
3
4
5
COMMENTS
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 CONCEPT ITEMS
7. Estimate and Check
8. Invariance/Counting On
9. Build and Change
11. Problem Solving
15. Coin Sets (optional)
V I S UA L S PAT I A L I T E M S
2. Recognizing Dot Patterns
10. Pattern Items
12. Squares Puzzle
16. Cube Building (optional)
I M P L I C AT I O N S F O R I N S T RU C T I O N :
58
A S S E S S I N G
E A R LY
N U M E R A C Y
RS4. Numeral Cards 0–9 for Items 3 and 4
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
5 6 7 8 9
0 1 2 3 4
B C
59
RS5. Dot Cards for Items 2 and 3
A
B
C
D
E
F
60
A S S E S S I N G
E A R LY
N U M E R A C Y
RS6. Shapes for the Squares Puzzle, Item 12
B C
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
61
RS7. Square for the Squares Puzzle, Item 12
62
A S S E S S I N G
E A R LY
N U M E R A C Y
RS8. Calendar for Item 13
May
Sunday
B C
Mo n d a y
Tu e s d a y
We d n e s d a y
Thursday
Fr i d a y
Saturday
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
63
RS9. Numeral Cards for Item 13
64
3
18
8
147
36
407
83
1847
A S S E S S I N G
E A R LY
N U M E R A C Y
RS10. 100 Chart for Items 13 and 17
Name: _____________________________________________________ Date: ________________
1
2
3
4
5
7
8
9
10
13 14 15 16 17 18 19 20
21 22 23 24 25
31
27 28 29 30
33 34 35 36
44 45
51
53 54
48 49 50
59
61 62 63 64 65
71
40
68 69
74 75 76 77 78 79
85 86 87 88 89
91
94 95 96
100
DIRECTIONS:
a)
b)
c)
d)
B C
Read: 3, 8, 14, 29, 36,75
Find: 10, 25, 79. Write the number that comes next.
Find: 7, 13, 40, 100. Write the number that comes before.
Find the three shaded boxes that are empty. Write the numbers.
E A R LY
N U M E R A C Y
P R O J E C T
( K – 1 )
65
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