# Impacts of Representation on Increasing Flexibility in Understanding Number Composition

4-13-2018

4-2018

## Department

Teaching, Learning and Educational Studies

Gina Kling

Christine Browning

Mindy Birzele

## Abstract

Place value is a mathematical concept that young children struggle to understand. A common misconception for children is that the digits that make up multi-digit numbers represent the quantity of that number itself, instead of the number according to its place value (i.e. the 1 in 18 represents 1, instead of 10). The base-ten representation is an efficient way to represent numbers and quantities, but it is not easily learned. One reason children may struggle to fully understand place value is the English language does not make the value of the number known and has hidden base-ten meanings. To contrast, many other languages explicitly give the relation to ten in their numbers. For example, “shi yi” in Chinese translates to “ten one”, which is eleven in English this naming system continues for all numbers. To alleviate this difficulty, place value representations help reinforce what has been learned and present information in a new way, promoting comprehensive content understanding.

In this study we assessed whether using place value representations increase flexibility in understanding number composition in first and second grade students. Students were given identical pre- and post-assessments to measure their growth after small group sessions. The activities used in this research were Finding Neighbors on a Hundreds Chart, Base-Ten Riddles, and Number Grid Puzzles. Analysis of the findings showed that students showed increased flexibility when composing numbers since the total number of ways presented by students more than doubled from pre- to post-assessment; students were able to compose numbers in more complex ways, such as composing 52 as 3 tens and 22 ones rather than 52 ones or 5 tens and 2 ones; more students used a system to compose numbers in as many ways as possible, meaning they had an organized way to determine if all number combinations were found, but there was little improvement in identifying the place-value of numbers in the tens place. We believe that if teachers utilize these activities, students will gain a better understanding of number composition.