The Emergence of the “FlexTech” Orchestration of Inferential Reasoning on Pattern Generalization

The purpose of this study is to further our understanding of orchestrating math-talk with digital technology. The technology used is common in Swedish mathematics classrooms and involves personal computers, a projector directed towards a whiteboard at the front of the class and software programs for facilitating communication and collective exploration. We use the construct of instrumental orchestration to conceptualize a teacher’s intentional and systematic organization and use of digital technology to guide math-talk in terms of a collective instrumental genesis. We consider math-talk as a matter of inferential reasoning, taking place in the Game of Giving and Asking for Reasons (GoGAR).The combination of instrumental orchestration and inferential reasoning laid the foundation of a design experiment that addressed the research question: How can collective inferential reasoning be orchestrated in a technology-enhanced learning environment? The design experiment was conducted in lower-secondary school (students 14–16 years old) and consisted of three lessons on pattern generalization. Each lesson was tested and refined twice by the research team. The design experiment resulted in the emergence of the FlexTech orchestration, which provided teachers and students with opportunities to utilize the flexibility to construct, switch and mark in the orchestration of an instrumental math-GoGAR.

Triangulating Multi-Method Assessments of Parental Support for Early Math Skills

Past research has examined parental support for math during early childhood using parent-report surveys and observational measures of math talk. However, since most studies only present findings from one of these methods, the construct (parental support for early math) and the method are inextricably linked, and we know little about whether these methods provide similar or unique information about children’s exposure to math concepts. This study directly addresses the mono-operation bias operating in past research by collecting and comparing multiple measures of support for number and spatial skills, including math talk during semi-structured observations of parent–child interactions, parent reports on a home math activities questionnaire, and time diaries. Findings from 128 parents of 4-year-old children reveal substantial within-measure variability across all three data sources in the frequency of number and spatial activities and the type and content of parent talk about number and spatial concepts. Convergence in parental math support measures was evident among parent reports from the questionnaire and time diaries, such that scale composites about monthly number activities were related to number activities on the previous work day, and monthly spatial activities were correlated with spatial activities the prior non-work days. However, few parent report measures from the survey or time diary were significantly correlated with observed quantity or type of math talk in the semi-structured observations. Future research implications of these findings are discussed.

Fostering Parent–Child Math Talk with the 4Cs

Research shows that frequent, high-quality mathematics talk that is shared between parents and children can increase mathematics achievement. This article describes ways in which teachers can support parents in increasing the frequency and quality of parent–child mathematics interactions, leading to better outcomes for students.