When learning about fractions, teaching usually follows certain topics -- e.g. part of the whole, fraction equivalence, and size comparison. Not yet answered is whether students' conceptual and procedural knowledge of fractions is coherent between those topics. To answer this question, we performed a latent profile analysis of data from N = 1005…

This article investigates how students with mathematical difficulties (MD) differ from typically developing (TD) students in enumeration processes of small sets of objects (of 1 up to 9 dots). We present a study with 20 fifth-grade students of which ten were found to have MD in initial diagnostics. The students were supposed to exactly enumerate…

Quantity recognition in whole number representations is a fundamental skill children need to acquire in their mathematical development. Despite the observed correlation to mathematics achievement, however, the ability to recognize quantities in structured whole number representations has not been studied extensively. In this article, we…

Educational research assumes that error reflections are efficient if they include the rationale behind the own error instead of just correcting the error. However, thus far there is a lack of empirical evidence regarding this aspect. Thus, we conducted a field experiment with pre-post-follow-up design and with 7th and 8th grade students (N = 174).…

Thus far, it is unclear how students can learn most effectively from their own errors. In this study, reflections on the rationale behind self-made errors are assumed to enhance knowledge acquisition. In a field experiment with pre/post/follow-up design, the authors practiced fractions with 174 seventh- and eighth-grade students who were randomly…

Constructive error handling is considered an important factor for individual learning processes. In a quasi-experimental study with Grades 6 to 9 students, we investigate effects on students' attitudes towards errors as learning opportunities in two conditions: an error-tolerant classroom culture, and the first condition along with additional…