© 2008-2014 Stephanie Z. Smith and Marvin E. Smith

Counting Proficiency Assessment

Student Name: ______________________ Grade Level: _____ Date: ____________

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 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

Record of student’s oral counting of a set of objects: (Actual number of objects: 43 or ____) Mark skips (/) in the sequence of number names. Circle the ending number. Record deviations from the

standard sequence and other notes in this space:

Evaluation of student’s counting of a set of objects:  Sequence of Number Names: Did the student use the correct sequence of number names?

 Correct sequence to the number of objects  Correct sequence to _________  Errors in sequence of number names  Unstable order

 One-to-One Correspondence: Did the student match one number name to one object?  Exactly  Sloppily  Erratically

 Keeping Track: Was the student deliberate and careful?  Consistently deliberate and careful  Occasionally not deliberate or careful  Typically not deliberate or careful

 Accuracy: Was the student accurate?  Accurate  Minor errors (within 3; final count ___________)  Major errors (more than 3; final count ___________)

 Cardinality: Did the student understand the last number counted identifies how many?  Solid understanding (without additional prompt  or with additional prompt )  Uncertain that the last number name used tells the number of objects counted

 Counting By Groups: Did the student count by groups or by ones?  Skip-counted or counted by groups (group size ______)  Counted by ones

 Quantity: Did the student attach units to the number of objects? (e.g., “There are 43 tiles”)  Number and unit  Number only

 Order Irrelevance: The student showed some evidence of understanding order irrelevance? 

Counting Profile Rating:  Exemplary  Proficient

 Emerging  Limited

© 2008-2014 Stephanie Z. Smith and Marvin E. Smith

Classroom Counting Profile Teacher Name: ______________________ Grade Level: _____ Date: ____________

Profile Level

Profile Criteria Student Names

E xe

m p

la ry

Number Names: No errors to 43 or more One-To-One Correspondence: Exact Keeping Track: Consistently deliberate and careful Accuracy: Consistently accurate Cardinality: Solid understanding Counting by Groups: Counted by groups larger than one (includes skip-counting) Quantity: Usually attends to number and unit Order Irrelevance: May show some evidence

P ro

fi ci

en t

Number Names: No errors to 43 or more One-To-One Correspondence: Exact Keeping Track: Consistently deliberate and careful Accuracy: Usually accurate Cardinality: Solid understanding Counting by Groups: Counted by ones Quantity: Attends to number; may attend to unit Order Irrelevance: May show some evidence

E m

er g

in g

Number Names: Stable order and accurate names to at least 20; may have sequence errors beyond 20 One-To-One Correspondence: Exact or sloppy Keeping Track: Occasionally not deliberate and careful Accuracy: Minor errors or decade skips/repeats Cardinality: Solid understanding Counting by Groups: Counted by ones Quantity: Attends only to number Order Irrelevance: May show some evidence

L im

it ed

Number Names: Unstable order, major sequence errors, or correct sequence to less than 20 One-To-One Correspondence: Erratic (rote count often does not match object count) Keeping Track: Typically not deliberate and careful Accuracy: Frequent major errors Cardinality: Uncertain that the last number name used tells the number of objects counted Counting by Groups: Counted by ones Quantity: Attends only to number Order Irrelevance: May show some evidence

Criteria shown in bold are REQUIRED to for that particular level.

Task for conducting the assessment:

1. How many tiles are in this pile? [If needed: Please count out loud so I can hear you.] 2. Please recount the tiles for me.

© 2008-2014 Stephanie Z. Smith and Marvin E. Smith

Pre-Operational Concepts and Counting Processes Definitions:

attribute: an inherent characteristic quantity: a number and a unit, indicating how many (discrete units) or how much

(continuous units) of some attribute that can be represented with the specified unit

quantify: to determine, express, or measure the quantity count: to determine the number of objects or units in some quantity by matching a

number name with each object or unit rote counting: counting from memory or by unthinking routine rational counting: counting for a reason and with understanding one-to-one correspondence: associating one and only one number name with each

object or unit being counted number names: the speech sound that defines and conveys the meaning of a number stable order: the number name list has a fixed order that must be used every time to

maintain meaning cardinal numbers: numbers (e.g., one, two, three, etc.) used in counting to indicate

how many (objects in a collection; or units of an attribute; or elements in a set) cardinality: recognizing that the last number name used tells the number of objects

counted order irrelevance: the order in which objects are counted does not matter (the resulting

cardinality is the same) counting patterns: the repetitive features of cardinal number names, words, and

symbols subitize: immediately recognize the number in a collection (i.e., identify the cardinal

value of a collection without counting) representation: an image, form, or symbol number words: combinations of letter symbols that represent number names numerals: symbols that represent number names

Four Principles of Counting:

stable order one-to-one correspondence cardinality order irrelevance

Sources:

Reys, R. E., Lindquist, M. M., Lambdin, D. V., & Smith, N. L. (2007). Helping children learn mathematics (8th ed.). Boston, MA: John Wiley and Sons.

Baroody, A. J., & Wilkins, J. L. M. (1999). The development of informal counting, number, and arithmetic skills and concepts. In J. V. Copley (Ed.), Mathematics in the early years (pp. 48-65). Reston, VA: National Council of Teachers of Mathematics and National Association for the Education of Young Children.

Riedesel, C. A., Schwartz, J. E., & Clements, D. H. (1996). Teaching elementary school mathematics. Boston, MA: Allyn and Bacon.