We examined the development of the ability to differentiate logically determinate from logically indeterminate problems. The results indicated that a) young children tend to reduce the number of empirical possibilities via "cutting" the second half of less informative propositions, b) these errors do not stem from encoding or recall errors, c) from elementary to middle school, children tend to increase their understanding of logical form, and d) this increase corresponds to a decrease in the rate of cuts.

Typical mathematics instruction involves blocked practiceacross a set of conceptually similar problems. Interleaving, orpractice across a set of conceptually dissimilar problems,improves learning and transfer by repeatedly reloadinginformation and increasing discrimination of problemfeatures. Similarly, comparing problems across differentcontexts highlights relevant and irrelevant knowledge. Ourexperiment is the first to investigate the relative effects ofinterleaving geometry problems and interleaving contexts.Thirty-three fourth-grade students received the same practiceproblems but were randomly assigned to one of threeconditions: interleaved by math skill, interleaved by context,and interleaved by math skill and by context (i.e., hyper-interleaved). Afterward, each participant was exposed to testsassessing declarative and procedural knowledge. The resultssuggest that interleaving math skill within varying contextsenhances the acquisition of mathematical procedures.