Counting

CountingCounting is an extremely important aspect of

early number instruction.There are various levels in mathematical

sophistication of the ways children use counting.Knowing these levels helps teaches be better

able to develop instruction approaches focused on developing more sophisticated strategies.

What is Emergent Counting?Diagnosis: A child is at the emergent counting

stage if s/he is beginning to think about number and attempting to determine the quantity of objects. This child is unable to count a collection of visible items, say 12 to 15 counters. S/he either does not know the number word sequence or cannot coordinate the number words with items.

Prescription: This child needs practice saying the number words to ten forward and backward; saying the number words for written numerals 1-10; and counting small collections of objects.

Things to TryPractice saying number words forward and

backward in the range 1—10. Have the child start at different numbers other than 1 or 10. Ask a child what comes before various numbers and what comes after. Extend beyond 10 as the child is ready.

Things to TryShow a child written numerals 1—10 and

ask him/her to say the number word for each symbol. Say the correct number word if the child does not know.

Ask a child to show quantities on his/her fingers. Notice if the child builds the quantity from one or is able to show the fingers simultaneously. Show quantities on your fingers and ask the child to tell how many.

Wright, Stanger, Stafford, and Martland (2006)

What is Perceptual Counting?Diagnosis: “[T]he child at the perceptual stage

is able to count a collection of counters” (Wright, et. al., p. 110). The items to be counted are available for the child to see, hear, or feel (i.e., but cannot be concealed/screened).

Prescription: This child needs practice saying the number words to 20 and beyond, both forward and backward; saying the number words for written numerals 1-20; counting two separate collections and adding quantities that are screened or flashed.

Get me eight counters, please

Wright, Stanger, Stafford, and Martland (2006)

Things to TryAlternate with the child saying number words

1—20, forward and backward, sometimes starting at 1 and sometimes starting at other numbers. Ask the child what comes before a given number and what comes after.

Things to TryNaming written numerals in the teens can

be especially problematic because the pattern is backward and the words do not necessarily match the symbols (e.g., 19 – ‘nine’ ‘teen’ but written with the ‘1’ first); 12 – 21)

Play some version of “Where do I go?” (see picture next page).

Wright, Stanger, Stafford, and Martland (2006)

ResourcesSee the online activities for early

numeracy from Count Me in Too, the Australian version of Math Recovery Add+Vantage for the classroom. http://www.curriculumsupport.education.nsw.gov.au/countmein/children.html

Make a numeral track (and/or numeral cards) with doors that open and close over the numerals http://kymath.org/resources/docs/2008/numeraltrack%201-120.doc

What is Figurative Counting?A perceptual counter’s focus of attention is on

saying the number names and matching them one-to-one with physical objects and then taking the last number they say as the answer to the question: “How many?”

Diagnosis: In contrast, a figurative counter has a different focus of attention. His/her attention is focused on trying to imagine hidden objects that s/he cannot see, and then counting those hidden objects (i.e., objects are concealed/screened).

What is Figurative Counting?Because this is a hard task for them, they are most

likely to use a physical stand-in for the hidden objects.Commonly these physical stand-ins are fingers. As they

become more efficient, figurative counters will often use body movements such as tapping, jaw movements, or raising eyebrows, as stand-ins for imagined objects. A figurative counter then physically counts these stand-ins.

Gradually, figurative counters begin to imagine a certain number of hidden objects, without yet knowing what that number is, but knowing they can work it out using physical stand-ins. They still begin counting from one.

Things to TryPlay “Bunny Ears”

Ask the child to put a hand on his/her head and show fingers for 1 through 5.

Tell a child to put 5 on one bunny ear and put some more on the other to make sums of 6 through 10.

Then ask the child to use two hands on his/her head to make numbers to 10. See if s/he can show the numbers 2 through 10 in different ways using two hands.

Flash your own bunny ears and see if a child can tell how many.

ResourcesSee the online activities for early numeracy

from Count Me in Too, the Australian version of Math Recovery Add+Vantage for the classroomhttp://www.curriculumsupport.education.nsw.gov.au/countmein/children.html

Make a numeral track (and/or numeral cards) with doors that open and close over the numerals http://kymath.org/resources/docs/2008/numeraltrack%201-120.doc

ResourcesSee “The Classroom Kit,” specfically:http://www.theclassroomkit.com/stages-of-

learning-numeracy.htmlhttp://www.theclassroomkit.com/maths-

games.htmlhttp://www.theclassroomkit.com/

numeracy-worksheets.htmlhttp://www.theclassroomkit.com/

numeracy-resources.html

ResourcesFosnot and Cameron. (2008). Games for Early

Number Sense. Heinemann .Interactive Ten Frame from the National

Council of Teachers of Mathematics. http://illuminations.nctm.org/ActivityDetail.aspx?ID=75

Dots-Fingers, one of the many free printable Early Years Mathematics Activities and Games from Manitoba Education and Literacy, http://www.edu.gov.mb.ca/k12/cur/math/games/index.html

ReferencesWright, Martland, Stafford, Stanger.

(2007). Teaching Number; Advancing children’s skills and strategies, 2nd edition. Paul Chapman Publishing

Wright, Stanger, Stafford, and Martland. (2006). Teaching Number in the Classroom with 4-8 year-olds. Paul Chapman Publishing.

http://mathrecovery.org