FLEXIBLE USE AND UNDERSTANDING OF PLACE VALUE VIA TRADITIONAL AND DIGITAL TOOLS

Oct 12, 2026

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Place value is an early mathematics concept central to building flexible arithmetic strategies and successful algorithmic computation. The study examines typical mistakes and misconceptions among 3rd graders in German elementary school and analyzes the individual actions involved when manipulating numbers in place value charts. A follow-up quantitative study compares real and virtual manipulatives and evaluates their effects on students’ place value understanding and learning.

LanguageEnglish

CategoryPresentations

FormatPDF

Pages8

Reading Time3 min

AccessFree to download

Introduction

Place value and number systems

Decimal partitions and place value charts

Research design and quantitative follow-up

FLEXIBLE USE AND UNDERSTANDING OF PLACE VALUE VIA TRADITIONAL AND DIGITAL TOOLS Ulrich Kortenkamp 1 , Silke Ladel2 1Martin-Luther-University Halle-Wittenberg, 2University of Saarland Germany Place value is a key concept for numbers that is introduced in early mathematics. It is necessary to have a flexible understanding of place value for efficient arithmetic strategies and success in written algorithmic arithmetic. In our research we explore typical mistakes and misconceptions that occur with 3rd graders in German elementary school and investigate the various underlying actions when manipulating numbers in a place value chart. We also report on a follow-up quantitative study that compares real and virtual manipulatives for place value and their effect on learning of place value. INTRODUCTION As demonstrated in the PME 36 plenary by Mariotti (2012), it is helpful to analyse artefacts from a semiotic perspective for their semiotic potential. The Theory of Semiotic Mediation (TSM) can be used to analyze teaching experiments at all school levels and with artefacts of any type. This latter is particularly important when we want to find out whether and how new artefacts, in particular digital ones, can improve the teaching and learning process. In our research about place value and flexible interpretation of place value charts we realized that instead of focusing on sign productions it was more helpful to look at the individual actions that can be observed when children work with a place value chart. Using Artefact-Centric-Activity-Theory (ACAT, Ladel & Kortenkamp 2013) we designed a digital artefact as an alternative to traditional paper-and-pencil place value charts. This paper will report about the necessity of teaching place value, will analyze typical tasks found in textbooks, and show how these tasks correspond (or not) to certain actions with either artefact, the traditional and the electronic one. Finally, it will elaborate on a pre-study that helped to design an experiment that is currently conducted with 3rd graders (N > 300) in a quantitative study that shall contribute to the research for designing learning environments for place value that has been started by Hiebert and Wearne (1992), who conclude: The data reported here suggest that understanding, as measured by the place-value tasks, does not translate directly into procedures but that it does interact with procedures to yield increased flexibility and power. However, this interaction is influenced by the in-structional environment and, in this case, flourished more when instruction attempted to facilitate students’ understanding rather than procedural proficiency. (p. 121) 2014. In Liljedahl, P., Oesterle, S., Nicol, C., & Allan, D. (Eds.) Proceedings of the Joint Meeting 4-33 of PME 38 and PME-NA 36,Vol. 4, pp. 33-40. Vancouver, Canada: PME. Kortenkamp, Ladel PLACE VALUE AND NUMBER SYSTEMS The decimal number system (in fact, any positional system) is a powerful tool for writing mathematics and doing arithmetic. Any number 1 can be written using only 10 different digits in a unique way using a finite number of places . It is easily possible to compare, add, subtract and –a bit harder– multiply or divide two numbers when we are given the numbers of bundles in the maximal bundling. The underlying idea of the number system carries the proof for this non-obvious fact: By creating bundles of ten objects, bundles, bundles of bundles, etc. repeatedly until there are less than 10 objects of any same bundle size available we end up with a unique maximal bundling of objects. Creating bundles of objects is a basic task in many exercises in early mathematics learning, as it constitutes the basic operation for working with larger numbers. Another key concept besides bundling is the part-whole-concept that concerns the fact that each number can be partitioned into smaller parts that add up to whole. While this is trivial for most of us, it is still an i

FAQs

Why is flexible understanding of place value important for arithmetic?

It supports efficient arithmetic strategies and helps students succeed with written algorithmic arithmetic.

What kinds of learning problems does the research focus on?

Typical mistakes and misconceptions that occur with 3rd graders, together with the underlying actions children perform when working with place value charts.

How does the study compare traditional and digital tools?

It designs a digital artefact as an alternative to traditional paper-and-pencil charts and reports a quantitative follow-up comparing real and virtual manipulatives.

Oct 12, 2026

Upload by asda1da