The understanding of arithmetic concepts across grades
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The development of a firm grasp of arithmetic principles follows a conceptual understanding of the concepts in question, which helps in simplifying computation and eliminating errors that may occur during calculation. The goal of this study was to expand on the understanding of the arithmetic principles of inversion (a + b - b), associativity (a + b - c), and equivalence (a + b + c = a + _). Participants were grade 2, 3, and 4 children from two elementary schools. Participants were presented with 12 three-term arithmetic problems, containing four from each category of concepts. Participants replied with their answers followed by a verbal report of steps employed for each question. Accuracy and strategy were immediately recorded after each question. Two 3 by 3 mixed-model ANOVAs and a correlational analysis on grade, accuracy, and shortcut-use were performed. The results showed an increase in the use and accuracy of the inversion and equivalence shortcut across grades, with the concept of inversion being the most used and the inversion problems having the highest overall accuracy. The associativity shortcut was the least likely to be used, and the equivalence problems had the lowest accuracy overall.