A Kindergarten Q&A: Numbers Represent Quantities

As we said in the original post, our ideas for our blog are wide-ranging. We are excited to have a space that offers us the opportunity to answer common questions from the field. This Q&A is the first of that type of blog post. Have questions you’d like to see answered? Email us.

Question: How do Kindergarteners learn to write the numbers, and use them to represent quantities?

Answer: We are frequently asked about how Investigations supports young students in the development of numeral writing. One thing it’s important to remember is that learning to write the numbers is intricately connected with students’ developing understanding that a number —whether the spoken word “three”, a group with 3 objects, or the written number “3”—describes a quantity. Consider this excerpt from the Teacher Note: Observing Kindergarteners as They Count:

“In Kindergarten, students come to understand that a quantity can be represented in a variety of ways. Many activities ask students to use numbers, pictures and/or words to show how many, or to count out a set when given a number, orally or in writing. Students need many opportunities to see how numbers are used to record, and in this context they practice correct numeral formation. Recording mathematical information such as the number of students in school today or objects in the Counting Jar provides such opportunities. Tools such as the calendar and number line provide a model of numerals in their natural order. While recognizing numerals and knowing how to write numerals are important skills in communicating math ideas, they are not directly related to counting and understanding quantity. Whereas young students who are learning how to write numerals frequently reverse certain ones, this is not a mathematical problem but often a matter of experience. Like letter formation, number formation and practice writing numerals should be part of handwriting instruction rather than mathematics.” (KU2, p. 157)

Using numbers to record across KU2

In addition to providing many opportunities for students to see and use numbers as they solve problems and show their work, the curriculum encourages teachers to model number formation as they record:

KU2, p. 45

Finally, the curriculum includes activities explicitly aimed at providing practice with writing the numbers across the year. Roll and Record is one such activity. In Unit 2, students roll a 1-6 dot cube and record the number, as a numeral, in the appropriate column. In Unit 4, the game shifts and involves rolling two dot cubes (1-6, 1-3), and recording the total.

KU4, p. 74

In Unit 6, students roll two 0-5 dot cubes, and in Unit 8, students play variations of this game, now called Race to the Top, on gameboards that provide practice writing the numbers to 20.

(Note that, while these games provide explicit practice with writing the numbers, they are also engaging students in other, significant mathematical work (e.g. subitizing amounts to 6, connecting counting and combining, developing an understanding of the teen numbers as ten ones and some number of ones) at the same time.

Being able to accurately write the numbers is one aspect of the Kindergarten curriculum. But it’s important to remember that, “just as saying the alphabet does not indicate that a student can read, being able to say” or write 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 “does not necessarily indicate that students know what those counting words” and numerals mean. (KU2, Teacher Note: Counting is More Than 1, 2, 3, p. 156) What’s critical in Kindergarten, and what the Investigations curriculum takes seriously, is that students can use numbers to communicate mathematical information and ideas.