Exploring the learning and teaching of multiplicative reasoning through measures: a design-based research project

This study explores the learning and teaching of multiplicative reasoning through measurement contexts with Year 2 learners, aged 6 and 7, in a primary school in South Wales, through the design and evaluation of learning tasks. Typically, in the UK, the multiplicative relationship is introduced as an extension of counting, in which counting in composite units (units with a value greater than one) is developed using visual and concrete resources with discrete quantities. A contrasting approach, developed in the 1960s in Russia, by Davydov and Elkonin, involves the introduction of the concept of number, and later the multiplicative relationship, through contexts involving measures with continuous quantities. It is not common for a measures approach to be used to introduce the multiplicative relationship when counting, and number operations as an extension of counting, is the predominant approach within a curriculum. This study explores the teaching and learning of the multiplicative relationship through measures contexts, in a situation where learners have typically been introduced to number through discrete quantities. A design-based research (design research) approach was adopted. Using research informed design principles, and applying a socio-constructivist theoretical framework, tasks were designed, implemented, evaluated and developed through two cycles of research, with Year 2 learners. Observation and interviews, with learners (n=21) and practitioners (n=5), were used to inform task development and evaluation. The tasks with the learners, led by the researcher, were audio recorded, transcribed and coded. Through analysis of the data from both cycles, themes were constructed. Data collected support the assertion that measures tasks offer rich opportunities for multiplicative reasoning. A key theme from analysis is the construction of the equality relationship, and this study offers new insight into how this might be perceived in measures contexts.

Name dc:type.qualificationname

phd

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

University of Wales Trinity Saint David

Year dc:date.issued

2024

Author dc:creator

• Wallis, Rachel

• L Addysg (Cyffredinol)
• LB1501 Addysg Gynradd

Dc Identifier Grantnumber

UWTSD

OAI identifier oai:identifier

oai:repository.uwtsd.ac.uk:3066