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Explaining new ideas to oneself can promote transfer, but how and when such self-explanation is effective is unclear. This study evaluated whether self-explanation leads to lasting improvements in transfer success and whether it is more effective in combination with direct instruction or invention. Third- through fifth-grade children (ages 8-11; n=85)(More)
Comparing and contrasting examples is a core cognitive process that supports learning in children and adults across a variety of topics. In this experimental study, we evaluated the benefits of supporting comparison in a classroom context for children learning about computational estimation. Fifth- and sixth-grade students (N=157) learned about estimation(More)
Explaining new ideas to oneself can promote learning and transfer, but questions remain about how to maximize the pedagogical value of self-explanations. This study investigated how type of instruction affected self-explanation quality and subsequent learning outcomes for second- through fifth-grade children learning to solve mathematical equivalence(More)
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 contex-tual, conceptual, or procedural knowledge each improved students' ability to add and subtract fractions.(More)
Cognitive modeling can be used to compare alternative instructional strategies and to guide the design of curriculum materials. We modeled two alternative strategies for fraction division, and the models led to specific empirical predictions of the benefits and drawbacks of each strategy. These insights provided concrete suggestions for developing lessons(More)
Competence in many domains rests on children developing conceptual and procedural knowledge, as well as procedural flexibility. However, research on the developmental relations between these different types of knowledge has yielded unclear results, in part because little attention has been paid to the validity of the measures or to the effects of prior(More)
This paper reports on a study of learning with erroneous examples, mathematical problems presented to students in which one or more of the steps are incorrect. It is hypothesized that such examples can deepen student understanding of mathematics content, yet very few empirical studies have tested this in classrooms settings. In a classroom study, 255 6th,(More)
BACKGROUND Knowledge of concepts and procedures seems to develop in an iterative fashion, with increases in one type of knowledge leading to increases in the other type of knowledge. This suggests that iterating between lessons on concepts and procedures may improve learning. AIMS The purpose of the current study was to evaluate the instructional benefits(More)
This study examines whether asking students to critique incorrect solutions to decimal problems based on common misconceptions can help them learn about decimals better than asking them to solve the same problems and receive feedback. In a web-based tutoring system, 208 middle school students either had to identify, explain, and correct errors made by a(More)
(2012). To err is human, to explain and correct is divine: A study of interactive erroneous examples with middle school math students. In: A. Abstract. Erroneous examples are an instructional technique that hold promise to help children learn. In the study reported in this paper, sixth and seventh grade math students were presented with erroneous examples(More)