By Lynsey Gibbons and Kendra Lomax, posted November 23, 2015 –

Counting is an essential building block of mathematics. For the next four entries to the Math Tasks to Talk About blog, we will discuss different aspects of counting. In this first post, we introduce the importance of counting. In subsequent posts, we dig deeper into the important concepts related to counting quantities (part 2) and suggest activities you can do with children in primary grades (part 3) and intermediate grades (part 4) to work on these concepts.

How long are these ropes?

Each autumn I (Lynsey) try to visit my sister and her family in central Pennsylvania. We always have a lovely time attending a Penn State football game, autumn festivals, and Halloween events with my niece and nephew. One evening while we were visiting this past year, Olivia (age 5) decided that she wanted to figure out the length of three different ropes—two jump ropes and a long shoelace. She laid each rope taut on the ground. She then disappeared to find some tape. When she returned, Olivia had a plan. She was going to wrap pieces of tape around each rope, side by side, from one end to the other.

Next, she planned to write a number on each piece to understand its length. After using about five pieces of tape, Olivia realized how laborious this would be and decided to abandon that plan. Instead, she wondered if she could use her feet to count how long each rope was. With my assistance to keep her balance, Olivia put each of her feet end to end to count how many of her foot lengths each rope was. She had some interesting noticings about the three ropes, including which rope was the longest.

Children’s Curiosity and Counting

Children are curious about the world. They want to make sense of what’s going on around them. Like Olivia, children often wonder about questions like what the length of something is, how tall someone is, who has more, how many geese there are, how many armholes are in different clothing items, and how long until we get somewhere. Quantifying stuff is an important part of our everyday lives. Adults have similar wonderings. Those who live in cities with a lot of traffic like we do, are often curious how many cars will make it through each cycle at this stop light, whether it’s worth driving across town to save ten cents per gallon on gasoline, and how much time is needed to drive across town to get that gas before the soccer game starts.

To quantify items, cultures have created different counting systems over time. (To learn more about different counting systems, see this example about the Central Alaskan Yupik.) In many cultures, families help children count their fingers, toys, people at the table, and other sets of objects. Questions concerning who has more and whether we have enough are part of the daily lives of children as young as two or three years old (Van de Walle, Karp, and Bay-Williams 2012). These experiences help children make sense of the important question, “How many?”

By the time children reach kindergarten, they begin to put their counting skills to work in solving simple problems that call for adding, subtracting, multiplying, or dividing amounts (Kilpatrick, Swaford, and Findell 2001). Throughout elementary school, children build on their early ideas of counting and quantity to understand the base-ten structure of our number system and use these understandings to engage in multidigit computation. It is not surprising that many mathematics education policy documents discuss the importance of counting (Kilpatrick, Swaford, and Findell 2001), and that counting standards show up in the early grades in mathematics content standards documents (e.g., Common Core State Standards and NCTM Focal Points). However, in our experience, children in intermediate grades need support with counting as well.

In the next three posts, we will explore important aspects of counting and consider instructional activities that teachers can do in classrooms with children to support their understanding of number. In the meantime, try getting curious about the world around you like Olivia did. Where are there opportunities to count, compare, measure, and wonder? How can these everyday experiences help us learn about counting and quantity?

Your Turn

We want to hear from you. Post your comments below or share your thoughts on Twitter @TCM_at_NCTM using #TCMcounting.

References

Kilpatrick, Jeremy, Jane Swafford, and Bradford Findell, eds. 2001. Adding It Up. Mathematics Learning Study Committee, Center for Education, Washington, DC: National Academies Press.

Van de Walle, John A., Karen S. Karp, and Jennifer M. Bay-Williams. 2012. Elementary and Middle School Mathematics: Teaching Developmentally. Boston, MA: Pearson.

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 around elementary 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.