Are Manipulatives Necessary for Assessing Early Operations?

Tangible manipulatives are commonly used to teach mathematics and assess the mathematics understanding of young learners. However, manipulatives have drawbacks during assessment. To evaluate the utility and necessity of manipulatives during assessment of mathematical operations, examiners administered addition and subtraction problems with concrete manipulatives or pictorial supports to 2,390 children aged 2.8 to 6.7 years. We compared the impacts of test format (presentation of concrete manipulatives versus pictorial supports) and operation (addition versus subtraction) on test items’ abilities to capture young learners’ early operations abilities and on items’ difficulties. Preliminary findings indicate both test formats and both mathematical operations equally well captured children’s latent operations abilities. Students found addition items with pictorial supports easier than addition items presented with manipulatives, and they responded more quickly to test items presented with pictorial supports. Implications for assessment in early mathematics and future research are discussed.