The Concept of Place Value

Motivation and aim of this paper

An insufficient development of place value understanding is one of the main causes of mathematical weakness. Even though children already need a place value understanding from Grade 1 on (e.g., interpreting the number symbol 14 as 1 bundle of tens and 4 ones), many children in upper primary and junior secondary school still struggle with place value (e.g., with decimal numbers).

Reading research publications indicates that researchers use different terminology when discussing place value, and this can cause misunderstanding for teachers. For example, Ross (1989) states four “properties of our numeration system” that concern place value: (1) the positional property; (2) the base-ten property; (3) the multiplicative property; and (4) the additive property. Houdement and Tempier (2019) indicate that the essence of place value is the juxtaposition of digits, which enables the representation of any quantity, regardless of its size, and that within this representation each individual digit also denotes a quantity. The starting point for Houdement and Tempier is the notion of unit, the foundation of all number systems, where (in the decimal system) ten ones1 form a new unit: one ten... and so on. Bailey (2015) indicates that a fundamental notion of base ten place value is the integration of early experiences of counting by ones and grouping numbers in tens; and later linking these groupings to the corresponding written numeral and how numbers are said.

In our view, any of the existing accounts of what constitutes place value understanding is incomplete in some way and has led us to the point where we feel that there is an important need to clarify the concept of place value. In this regard, the aims of this paper are:

• to clarify the concept of place value;

• to distinguish the overarching concept of place value from prerequisite knowledge and from several sub-concepts of the concept of place value; and

• to propose a way to develop a connected understanding of place value.