Using eye-tracking to assess the application of divisibility rules when dividing a multi-digit dividend by a single digit divisor

Potgieter, Pieter; Blignaut, Pieter

doi:10.1145/3129416.3129427

Cited by 3 publications

(1 citation statement)

References 30 publications

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“…The Math-Rule sensemaking category identifies sensemaking of generalizable statements derived from fundamental mathematics principles which are used to guide calculation or decision-making (Baroody et al, 2007;Bing & Redish, 2007;Dixon, Deets, & Bangert, 2001;Haapasalo & Kadijevich, 2000;Hansson et al, 2015;Hiebert & Lefevre, 1986;Moss & Case, 1999;Njini, 2012;Radmehr & Drake, 2019). For example, the knowledge of divisibility rules such as a dividend is divisible by 5 if the last digit is 0 or 5 enables quick decision-making of whether a dividend is divisible (Potgieter & Blignaut, 2017). Rules can be used to guide the step-by-step calculation; however, compared to procedural knowledge, mathematical rules are more generalizable.…”

Section: Math-rule Sensemakingmentioning

confidence: 99%

Development of the Sci-math Sensemaking Framework: categorizing sensemaking of mathematical equations in science

Zhao

Schuchardt

2021

IJ STEM Ed

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Scientific ideas are often expressed as mathematical equations. Understanding the ideas contained within these equations requires making sense of both the embedded mathematics knowledge and scientific knowledge. Students who can engage in this type of blended sensemaking are more successful at solving novel or more complex problems with these equations. However, students often tend to rely on algorithmic/procedural approaches and struggle to make sense of the underlying science. This deficit may partly be the fault of instruction that focuses on superficial connections with the science and mathematics knowledge such as defining variables in the equation and demonstrating step-by-step procedures for solving problems. Research into the types of sensemaking of mathematical equations in science contexts is hindered by the absence of a shared framework. Therefore, a review of the literature was completed to identify themes addressing sensemaking of mathematical equations in science. These themes were compiled into nine categories, four in the science sensemaking dimension and five in the mathematics sensemaking dimension. This framework will allow for comparison across studies on the teaching and learning of mathematical equations in science and thus help to advance our understanding of how students engage in sensemaking when solving quantitative problems as well as how instruction influences this sensemaking.

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