Many U.S. students possess only a weak knowledge of fraction arithmetic. I hypothesize that textbooks are a critical reason for students' poor performance on fraction arithmetic. This is not because of what textbooks contain but rather because of what they lack. Distributions of fraction arithmetic problems in textbooks are imbalanced, with…

This study compares the effects of a concrete-representational-abstract (CRA) intervention against a modified CRA-Integrated (CRA-I) intervention using a pretest-posttest design with random assignment of matched pairs to intervention conditions. The researchers designed both interventions to improve participants' understanding of and ability to…

The regression discontinuity design (RDD) has the potential to yield findings with causal validity approaching that of the randomized controlled trial (RCT). However, Schochet (2008a) estimated that, on average, an RDD study of an education intervention would need to include three to four times as many schools or students as an RCT to produce…

Young adolescents should be able to write organized multi-paragraph compositions that develop a central idea and unfold in logical and sequential order, unified through the use of transitional words and phrases. In other words, the compositions should not just consist of a string of related sentences, but represent a dynamic text that has…

We present a methodology for designing better learning environments. In Phase 1, 6th-grade students' (n = 223) prior knowledge was assessed using a difficulty factors assessment (DFA). The assessment revealed that scaffolds designed to elicit contextual, conceptual, or procedural knowledge each improved students' ability to add and subtract…