DEVELOPMENT OF COUNTING AND CARDINALITY SKILLS: HOW TO INDIVIDUALIZE SUPPORT FOR YOUR GROWING LEARNERS

A few weeks ago, we shared some suggestions for strategies you can use to support students’ growing understanding of counting and cardinality (link here). This week, we’re going to focus on how these skills develop and how you can individualize your support for growing learners who are developing skills at different rates.

How Do Counting and Cardinality Skills Typically Develop?

Around age four, we see students’ skills developing in both counting and cardinality, and they’re working hand in hand. Preschoolers can typically count to 10, and can count up to 5 objects arranged in a line. And, when they’re finished counting and asked how many there are, they can say 5 without having to recount. Not only can four-year-olds count a group of given objects, but they can also produce a group of up to 5 objects. Producing the correct number of objects is a complex skill because it requires coordinating both counting and cardinality! In order to arrive at the correct amount, students must use one-to-one correspondence and understand the significance of the counting as it relates to producing the correct quantity of objects (cardinality).

Source: EMAS Ginsburg

As students reach age five and head into kindergarten, their counting and cardinality skills continue to grow. They can often count to twenty and can produce a group of up to 10 objects. Some students can do these things with as many as 30 objects!  Most 5-year-olds have also developed some strategies to keep track of what objects have and have not been counted, like moving objects from one pile into another as they count.

As students move into first grade, they can count up to 200, and count backwards from 20. They can also “count on”, which means they can start counting at a number other than one. They can provide the “neighboring” number, which is the number that comes immediately before or after a given number (like knowing that fourteen comes before fifteen). And, they can count in groups rather than one-by-one (like counting a group of 10 objects by groups of 2 or by groups of 5).

Individualizing Supports for Students’ Counting and Cardinality Skills

The information shared above outlines the typical development of students’ counting and cardinality skills. However, not all students develop at the same rate and in the same ways. Here we focus on one of the counting skills students are developing: knowing number names and the counting sequence.

Students who are having difficulty learning the counting sequence may make several different types of errors including: saying the sequence out of order, skipping numbers, or using the same number more than once. Below we show examples of each of these types of errors along with strategies to support students’ understanding of the counting sequence.

Type of Counting Error Examples Remedy
SEQUENCE ERROR
Saying the number sequence out of order, skipping numbers, or using the same number more than once.

 

Struggling with the count sequence past twelve

“1, 2, 3, 6, 10” Practice reciting (or singing) the single-digit sequence, first focusing on one to ten, then later moving on to numbers greater than ten.
Skips 15:
“1…13, 14, 16, 17, 18.”
Highlight and practice exceptions, such as fif + teen. Fifteen and thirteen are commonly skipped because they are irregular.
Uses incorrect words:
“1…13, 14, fiveteen”
“1…18, 19, 10-teen” or
“1…29, 20-ten, 20-eleven”
Recognize that a nine signals the end of a series and that a new one needs to begin (e.g., nineteen marks the end of the teens.)

 

Recognize that each new series (decade) involves combining a decade and the single-digit sequence, such as twenty, twenty plus one, twenty plus two, etc.

Stops at a certain number:
“1…20” (stops)
“1…20” (starts from 1 again). Click here to see a video example of this type of counting error where a student stops at twenty-nine.
Recognize the decade term that begins each new series (e.g., twenty follows nineteen, thirty follows twenty-nine, and so forth). This involves both memorizing terms such as ten, twenty, and thirty by rote and recognizing a pattern: “add –ty to the the single-digit sequence” (e.g., six + ty, seven + ty, eight + ty, nine + ty).
Table Reproduced from D. Frye, A. J. Baroody, M. Burchinal, S. M. Carver, N. C. Jordan and J. McDowell, Teaching Math to Young Children, A Practice Guide (NCEE 2014-4005) (Washington DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education, 2013).

Click here for a more complete table that includes other common counting errors, and strategies for scaffolding learners who might need more support with the development of their counting and cardinality skills.

Knowing what students’ typical development of counting and cardinality skills looks like, and signs that a student might be struggling with their development of these skills, will help you provide appropriate supports for all learners.


More questions? VKRP provides support via the online chat feature when you are in the system, via email vkrp@virginia.edu, and via toll free 866-301-8278 ext.

Reading, Writing, Arithmetic, and RELATIONSHIPS!

In the hustle and bustle of busy school days it’s easy to lose focus on what decades of research reveals is a critical component of the recipe for a child’s success in school—a strong teacher-child relationship.  A student who is connected to a teacher who is supportive, accepting, and sensitive gets more out of school each day. In fact, research shows that a child’s relationship with their kindergarten teacher can have a lasting impact on their school success many years later, particularly for children who may struggle academically and/or socially. In this article, written by Tes, Bridget Hamre, an Associate Professor at UVA, talks about the importance of teacher-child relationships.

teacher and child working together
Source: istock/dolgachov

As you know, a strong teacher-student relationship doesn’t happen overnight.  It is built over time through multiple, moment to moment interactions.  Some children naturally form positive relationships with their teachers. Think about the students in your classroom: which students take initiative in starting conversations with you, ask you for help, tell you about their lives?

boy looking confused
Source: iStock/michaeljung

Some children, however, need extra support to connect. Think again about your students: which students become frustrated in the classroom but don’t seek your support, which students do you have to frequently redirect or give constructive feedback to, which student’s drain your energy during the day? These are the students who most need to be strongly connected to their teachers and who are most likely not to have the strong connection they need.

What can you do to help a student connect to you?  One effective strategy is Banking Time. Banking Time is a simple intervention where you spend short regular intervals (10 minutes, 2-3 times a week for 6 weeks) interacting with a student so that you and the child can learn about each other outside of the busy demands of the school day. Research has shown that spending this time with children who struggle to regulate their behavior (i.e., students who are very active and impulsive, become frustrated easily, and are sometimes argumentative) improved their behavior as reported by teachers and parents, and improved the stress students experienced as part of the school day (as measured by the hormone cortisol).

teacher and child playing together
Source: iStock/kate_sept2004

In Banking Time, teachers let the student lead the interactions and use specific techniques such as observing and commenting on the student’s behaviors and feelings. You can learn more about Banking Time in this short summary document and if you think this might be something you want to try, you can download the Banking Time Manual.

When teachers are responsive and sensitive to a child’s needs, it sends the message that their teacher values and respects them, they are safe with their teacher, and they can rely on their teacher when they need help.


More questions? VKRP provides support via the online chat feature when you are in the system, via email vkrp@virginia.edu, and via toll free 866-301-8278 ext.