Evaluating the Characteristics of Diagnostic Items for Bridging Errors in Multi-Digit Subtraction

Abstract

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Subtraction errors can inform teachers about students’ mathematical reasoning. Not every subtraction error is informative, it’s implications for students’ mathematical reasoning depends on the item characteristics. Diagnostic items are specifically designed to elicit specific subtraction errors. This study evaluated how the diagnostic capacity of subtraction items is related to their characteristics. The item characteristics being studied are open-ended and multiple-choice (MC) items, bare number, and word problems. As well as various number features, such as the number of digits in the subtrahend and minuend. Diagnostic capacity is defined as the extent to which multi-digit subtraction items that require borrowing (e.g., 1000−680) elicit bridging errors, such as the smaller-from-larger-error. Item response theory (IRT) was used to estimate item properties. Subsequently, the item properties were used in two separate ANOVA analyses to compare the diagnostic capacity of MC versus open-ended items, bare number versus word problems, and number features. As expected, MC items have a higher diagnostic capacity than open-ended items. More interestingly, it was found that the number of digits in the subtrahend and minuend influenced the diagnostic capacity of the items. Items characterized as 3/4n−3n, like 1000−680 had the highest diagnostic capacity, whereas items characterized as 3/4n−2n, such as 1000−20 had the lowest diagnostic capacity. The discussion focuses on the implications of this study for further research into the design of diagnostic items.

Keywords

• diagnostic assessment
• multi-digit subtraction
• multiple-choice items
• item characteristics
• decomposition
• subtraction errors