Diagnosing misconceptions: Revealing changing decimal fraction knowledge

• We created a measurement instrument to diagnose decimal misconceptions.
• These measures were reliable and valid.
• Accuracy improved due to a decrease in low, but not high, confidence errors.
• Two misconception types decreased and one misconception type increased over time.

Conceptual change is a gradual process that occurs as students integrate new information into their existing conceptions. Throughout this process, assessing learning requires measures to diagnose misconceptions and understand how knowledge is changing. We developed three measures of misconceptions to assess students' knowledge early in instruction on decimals that measured the: 1) prevalence of misconception errors based on response patterns, 2) existence of misconceptions in a more abstract context, and 3) strength of misconceptions using confidence ratings. Students ages 9–11 (N = 297) completed the assessment at three time points. These measures revealed that whole number and role of zero misconceptions decreased and fraction misconceptions increased over time. The current measures also differentiated between weaker misconceptions that were changed after brief instruction and strongly held misconceptions. The current measures can create a more complete picture of knowledge than only measuring students' accuracy, providing a window into the conceptual change process.