By Lynsey Gibbons and Kendra Lomax, posted December 21, 2015 –

Our second post in this series described the big ideas about learning to count. The Common Core State Standards in Mathematics propose that kindergarten students should learn the counting sequence through 100; develop principles of counting, such as one-to-one correspondence and cardinality; and represent amounts by writing numerals. First graders expand their counting sequence to 120 and begin to consider place-value ideas. In our experiences, children in these early grades can count well beyond 120 with great success, suggesting that these benchmarks should not limit our expectations for what students can do. Many young children are ready to explore larger numbers; therefore, we give them opportunities to count increasingly larger amounts.

Count Everything

Our go-to advice for parents who ask about how to support their young mathematicians is to have children “count everything!” This can begin at home in informal situations and be extended into school with more formal situations. The opportunities to work on ideas of number and quantity are endless: Count the stairs as you walk up, decide which bowl of cherries contains more, organize beads into groups of ten, guess how many Legos^® you have and then find out! The Talking Math with Your Kids blog by Christopher Danielson describes some informal conversations with children ages 1–9. This is a great resource for everyday mathematical conversations you could have with children.

Counting Collections: Connecting Quantity, Verbal Counting, and Symbolic Notation

Another way to support children in developing these important counting ideas is by offering many opportunities for them to count items. Counting Collections is a structured counting activity in which children work with a partner to count how many items are in a collection and then record their count on paper. By working together, students develop social skills—like sharing decisions about how to count and what to do if you disagree—as well as mathematical skills—like strategies for keeping track, learning the counting sequence, and ideas about place value.  Counting Collections is a wonderful opportunity for children to develop their sense of quantity and expand their facility with the forward number sequence. Encouraging students to record their count gives them practice with representing quantity, an important skill in modeling and solving problems. As children gain experience with counting objects and counting increasingly larger collections, they can explore ways to make their counting more efficient, such as counting groups of items, arranging the items in rows and columns, and using cups to keep track of groups of 2s, 5s, or 10s. These strategies lend themselves to developing ideas about place value, skip counting, and multiplication. See Counting Collections (Schwerdtfeger and Chan 2007) for further description of the activity, including images and student work.

Choral Counting: Developing Verbal Counting Sequences and Symbolic Notation

Different from other oral counting activities, Choral Counting includes both the verbal and written notation for numbers and asks students to analyze patterns in our number system. Examining number patterns in the count gives students opportunities to consider place-value ideas and computation strategies. Choral Counting can also be used to work on counting backward, an important skill in learning to solve subtraction situations in the early years. Students typically have many more experiences with counting forward than they do backward, and choral counting provides a meaningful opportunity to connect and build on these patterns.

Quick Images: Exploring Quantity through Subitizing, Composing, and Decomposing Number

In a Quick Images activity, children are quickly shown pictures displaying groups of objects or symbols, viewing each for only a few seconds. The image is shown a couple of times, and then children discuss how many objects they saw and how they saw them. This activity, which  in curricula like Investigations in Number, Space, and Data by TERC, is one of our favorite activities because it is fun, easy for teachers or parents to learn how to do, accessible to a wide range of learners, and allows children to work on rich mathematical ideas.

Beginning in their early years, children develop the ability to subitize, or quickly perceive the cardinality of a small number of objects or symbols. For example, when reading the numbers on a die, eventually we won’t count the dots, or pips, one by one. Rather, we will identify the X shape on dice as having five dots. We learn to perceive other formations of small quantities without counting. By showing an image for only a few seconds, the Quick Images activity supports children in using subitizing to determine the total number of dots, rather than counting by ones. This activity offers a context in which to practice composing and decomposing numbers, which is an important skill that will later support students in using strategies that are more efficient to add or subtract quantities.

In our fourth, and final, blog post, we will share counting activities for intermediate grades that help students continue to develop their understanding of our number system, connect their learning about number from earlier grades to the larger quantities they will encounter, and develop understanding of place value. Happy counting!

Your Turn

We want to hear from you. Please let us know which activities you try and what you learn; comment below or share your thoughts on Twitter @TCM_at_NCTM using #TCMcounting.

Resources

Number Talks by Sherry Parrish is a great resource for K–grade 1 Quick Image tasks. More information on subitizing can be found in a 1999 TCM article by Doug Clements.

You can find planning tools and sample tasks for Counting Collections, Choral Counting, and Quick Images at Teacher Education by Design (TEDD). For videos of these activities, search for each activity on the Teaching Channel.

References

TERC. 2008. Investigations in Number, Data, and Space Series. Pearson Scott Foresman.

Parrish, Sherry. 2010. Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K–5. Math Solutions.

---

 

Lynsey Gibbons, @lynseymathed, is an assistant professor in mathematics education at Boston University in Massachusetts.  She is a former elementary school teacher and mathematics coach. Her current scholarly work seeks to understand how we can reorganize schools to support the learning of children and adults. Kendra Lomax, @kendralomax, is a math educator at the University of Washington in Seattle. She designs and facilitates professional learning opportunities about elementary school mathematics through projects like TEDD.org. Curiosity about children’s mathematical thinking is at the heart of her work. The authors would like to note that they are continually learning about children and counting. They have learned a great deal from their colleagues, reading the mathematics education literature, and interacting with children about counting. The following colleagues have greatly informed their thinking about how to support children in finding the joy in mathematics and in counting in particular: Ruth Balf, Adrian Cunard, Megan Franke, Allison Hintz, Elham Kazemi, Becca Lewis, Teresa Lind, Angela Chan Turrou, and many teachers in the Seattle, Washington, area.