This paper examines the foundational concepts of place value notation and the base ten number system as they relate to early childhood mathematics education. It explains what place value and number sense are, why they matter, and what essential ideas must be taught to young learners. The paper also identifies common misconceptions children develop — such as misreading teen numbers, miswriting numbers above 100, and misjudging digit magnitude — and suggests practical, interactive teaching strategies, including the use of physical objects and grouping activities, to help children build a strong and lasting understanding of positional arithmetic.
This study guide is drawn from PaperDue's library of 130,000+ paper examples across 47 subjects.
The paper demonstrates the use of worked examples as explanatory evidence. Rather than simply asserting that children struggle with place value, the author constructs step-by-step numerical illustrations (e.g., the addition decomposition table, the hundreds/tens/ones grouping model) that make the argument tangible and verifiable. This technique bridges theoretical claims from cited sources with observable classroom phenomena.
The paper opens with three definitional sections establishing shared vocabulary (place value, base ten, number sense). It then pivots to pedagogy with a section on essential teaching content, followed by a diagnostic section cataloguing common misconceptions. A strategies section offers solutions before the conclusion synthesizes key takeaways. This problem–solution arc gives the paper a clear and purposeful shape suitable for an education audience.
Place value notation, also known as positional notation, is a system of encoding numbers that simplifies arithmetic. It is the basis for understanding arithmetic and is essential to the way we read, write, speak, and use whole numbers. Another important function of place value notation is that it allows us to string together and make sense of a sequence of whole numbers. Quite simply, the place value system allows us to interpret a sequence of digits that would otherwise appear random.
The base ten number system uses digits zero through nine to represent all number values, no matter how small or large. The digit in each position has a value ten times greater than that of the digit to its right, while zero serves as the placeholder. The position of each digit denotes the quantity it represents — ones, tens, hundreds, thousands, ten thousands, and so on. Thus, the value of a digit multiplied by the power of its position gives us the quantity that digit represents (Kennedy, Tipps, & Johnson, 2008).
Number sense refers to a person's understanding of the numerical system, including their ability to make numerical judgments and solve complex mathematical problems. It is the way we visualize number patterns and develop an understanding of their positional hierarchy as values move from tens toward the thousands. For students of mathematics, it is important not only to learn the magnitude of every quantity and place in the system, but also to understand the relationship that exists between each place (Sue Willis, Jacob, Powell, Tomazos, & Treacy, 2004).
A heightened place value sense allows students to effectively group numbers together and understand their significance. It also makes it easier to divide numbers into parts in order to perform calculations. Consider the following example:
257 + 312 = ?
200 + 300 = 500
50 + 10 = 60
7 + 2 = 9
500 + 60 + 9 = 569
A well-developed number sense can also help students achieve a wide range of calculation possibilities, including the ability to:
Count, read, write, recognize, order, and understand number sequences; solve problems involving addition, subtraction, multiplication, and division; link, arrange, and convert between decimals and fractions; solve complex calculations involving fractions and decimals; understand and use the properties of odd and even numbers; and develop both mental and written problem-solving strategies, using digital technology where appropriate.
As noted above, the value of each place increases by a power of ten as we move from right to left. It is therefore important that children learning the number system are taught that numbers are grouped into tens, hundreds, and thousands, so that it becomes clear that numbers are not an endless, undifferentiated continuum.
Secondly, in order to help children develop a thorough understanding of the place value system, teachers must recognize that this is a slow and gradual process and treat it accordingly. Children should begin by counting using small numbers, naming those numbers, and performing simple additions and subtractions. It is vital that they understand the importance of counting in groups, as this skill proves useful when counting a large number of objects. Gradually, they can work their way up to counting in twos, fives, hundreds, and thousands as they progress (Liedtke, 2010).
The use of physical objects such as rubber bands, pebbles, or poker chips can also be a very effective way of teaching children about the numeric system.
When working with children, teachers should be prepared for the many misconceptions children will develop about the number system; these children will need time to adjust. When making the transition from counting small numbers to handling larger, more complex numbers, they often come unstuck.
Ryan, J., & Williams, J. (2007). Children's mathematics. Maidenhead: McGraw-Hill/Open University Press.
Shumway, J. F. (2011). Number sense routines. Portland, ME: Stenhouse Publishers.
Sue Willis, W. D., Jacob, L., Powell, B., Tomazos, D., & Treacy, K. (2004). First steps in mathematics. Melbourne: Harcourt Education Australia.
You’re 48% through this paper. Sign up to read the remaining 2 sections.
Sign Up Now — Instant Access Already a member? Log inAlways verify citation format against your institution’s current style guide requirements.