PRESERVICE ELEMENTARY TEACHERS’ MENTAL COMPUTATION STRATEGY USE IN MULTIPLICATION ON ONE-AND TWO-DIGIT NATURAL NUMBERS

Oct 15, 2026

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The study examines whether mental computation strategies reported in the research literature sufficiently account for how preservice elementary teachers use strategies when multiplying one- and two-digit natural numbers. Strategy use is measured through a written questionnaire administered to preservice elementary teachers. Results show few genuinely new strategies compared with existing literature. The findings also indicate a theoretical need to clarify strategy definitions and identify valuable multiplication strategies not present in current research classifications.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages10

Reading Time25 min

AccessFree to download

Introduction

Mental computation

What is mental computation?

What is a mental computation strategy?

Why learn mental computation strategies?

Why should preservice elementary teachers study mental computation strategies?

PRESERVICE ELEMENTARY TEACHERS’ MENTAL COMPUTATION STRATEGY USE IN MULTIPLICATION ON ONE-AND TWO-DIGIT NATURAL NUMBERS Anders MÅNSSON Abstract: It is investigated if the mental computation strategies in the research literature are enough to satisfactorily categorize the mental computation strategy use by preservice elementary teachers in multiplication on one-and two-digit natural numbers. The preservice elementary teachers use of mental computation strategies is measured operationally with a written questionnaire. The paper indicates that there are few new strategies used by preservice elementary teachers which are not already contained in the research literature. However, the paper indicates that there is a theoretical need to clarify the strategy definitions, and that there several useful and valuable strategies on multiplication that do not occur in the research literature on mental computation. Key words: mental computation strategy, multiplication, preservice elementary teacher, written questionnaire. 1. Introduction Mental computation is part of the elementary school curricular content globally, and in recent years there have in many countries been an increased focus on mental computation in elementary schoolteacher education (Csíkos, 2016; Hartnett, 2007; Lemonidis et al, 2014) . There are many advantages of becoming better at mental computation, for example that it improves number sense (Hajra & Kofman, 2017; Heirdsfield et al, 2002, 2011), it gives a better understanding of the place value system and elementary calculation rules (Gürbüz & Erdem, 2016; Maclellan, 2001; Reys, 1984, 1992; Sowder, 1990, 1992, 1994), and it is often involved in everyday use of mathematics (Baranyai et al, 2019a; Thompson, 2010) . Mental computation strategies in connection to elementary school pupils have been well researched, but less so in connection to preservice elementary teachers (PETs) . In this article the latter group’s strategy use will be investigated. A brief background to mental computation is given in sections 2.1−2.4 before stating the research question in section 3.1. 2. Mental computation 2. 1. What is mental computation? One can in the research literature find different definitions of mental computation, or synonyms such as mental calculation, mental math, and mental arithmetic (Lemonidis, 2016; Sowder, 1988; Thompson, 1999) . An overarching trait among the definitions, and the one that will be used in this paper, is calculating without use of any equipment (Baranyai et al, 2019b; Lopez, 2014 ; McIntosh & Dole, 2000; Reys et al, 1995) . 2. 2. What is a mental computation strategy? Mental computation strategies are different ways that arithmetic problems are solved mentally (Hartnett, 2007; Threlfall, 2000, 2002) . For example, one can calculate 6 × 23 as 6 × 20 + 6 × 3 = 120 + 18 = 138, which is a mental computation strategy commonly referred to as “the distributive rule”. Some strategies are more general like this, and others are more dependent on the numbers involved in the calculation such that multiplication by 2, 4, 8,…can be done by repeated doubling. Mental computation strategies elementary school pupils use to calculate with natural numbers up to 100 have been well researched and documented for addition and subtraction (Beishuizen, 1993; Blöte et al, 2000; Heirdsfield, 1997, 2001; Klein et al, 1998) . Some of these strategies have official names, such as SA (standard algorithm done mentally) , 1010 (separately adding tens and ones), N10 (stringing), N10C (stringing with compensation), A10 (bridging through multiples often), and B (balancing) . There exist variants of these definitions and their names, but generally there is consensus on what they should mean (Heirdsfield, 2004; Varol & Farran, 2007) . Elementary school pupils’ use of mental computation strategies for multiplication and division has been researched to a lesser degree (Callingham, 2005; Heirdsfield et al, 1999; Murray et al,

FAQs

What question does the paper investigate?

It investigates whether research literature provides enough mental computation strategy categories to describe preservice elementary teachers’ strategy use in multiplication of one- and two-digit natural numbers.

How is the teachers’ strategy use measured?

Strategy use is measured operationally using a written questionnaire completed by preservice elementary teachers.

What do the results suggest about the strategies found?

The study indicates few new strategies are used that are not already in the research literature, but it also suggests theoretical clarification of strategy definitions and highlights useful multiplication strategies missing from the literature.

Oct 15, 2026

Uploaded by Aditya