1 2 3 4 5 6 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. ii 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 B C E A R LY N U M E R A C Y P R O J E C T ( K – 1 ) iii 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 iv 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. B C E A R LY N U M E R A C Y P R O J E C T ( K – 1 ) 1 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. 2 A S S E S S I N G E A R LY 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 1 2 3 4 5 6 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. B C E A R LY N U M E R A C Y 1 2 3 4 5 6 P R O J E C T Supporting Early Numeracy BC Early Numeracy Project (K-1) Ministry of Education B C E A R LY N U M E R AC Y ( K – 1 ) P R O J E C T ( K – 1 ) I 3 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 1 2 3 4 5 6 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.” 4 Families – Supporting Numeracy at Home is also available as a webpage for parents to access. A S S E S S I N G E A R LY N U M E R A C Y The assessment and instructional resources focus on four key aspects of numeracy: ● Number Skills—the basic tools of numerate thinking, including counting, reading and writing numerals, and recognizing visual-spatial quantities without counting. ● 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. ● 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: ● building a solid foundation of understanding rather than focusing on speed or memory ● recognizing and supporting differences in developmental stage and learning style ● understanding how children learn mathematics and typical learning patterns for mathematics ● recognizing visual-spatial strengths and the scaffolding that visual-spatial thinking provides for making sense of number ● 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. B C E A R LY N U M E R A C Y P R O J E C T ( K – 1 ) 5 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: ● the purpose of the item ● sample results, if available ● instructions for scoring the item according to the framework ● what to look for when using the item ● materials needed ● 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 1 very unrealistic estimate and incorrect count 3 ● In field testing of roughly 200 kindergarten ● counts in unsystematic ways ● (considered reasonable estimates) ● ● 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 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 ● Estimation ● 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 ● 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 ● ● 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. 30 6 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 A S S E S S I N G P R O J E C T E A R LY ( K – 1 ) N U M E R A C Y 31 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 B C E A R LY N U M E R AC Y P R O J E C T 55 ( 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. 56 B C E A R LY A S S E S S I N G N U M E R A C Y E A R LY N U M E R A C Y P R O J E C T B C ( K – 1 ) E A R LY N U M E R AC Y P R O J E C T ( K – 1 ) 57 7 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 : 56 A S S E S S I N G E A R LY N U M E R A C Y 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 58 B C 8 E A R LY N U M E R AC Y P R O J E C T ( K – 1 ) A S S E S S I N G A S S E S S I N G E A R LY N U M E R A C Y 59 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. B C E A R LY N U M E R A C Y P R O J E C T ( K – 1 ) 9 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 E A R LY 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. B C E A R LY N U M E R A C Y P R O J E C T ( K – 1 ) 11 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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