The curriculum resources used for teaching secondary mathematics vary considerably from school to school. Some schools base their teaching largely on a single published scheme, while others design their own schemes of learning, curating their resources from a range of (often free) online sources. Both approaches seem problematic from the…

In-class example problems that students work out on their own using active problem-solving are typically well received and help the students better learn the material; however, they are difficult to enact in large classes with limited resources due to the number of questions received and the speed at which different students work through the…

This study compared students' learning in troubleshooting and problem solving activities. The troubleshooting activities provided students with solutions to conceptual problems in the form of refutation texts; namely, solutions that portray common misconceptions, refute them, and then present the accepted scientific ideas. They required students…

In the present chapter, we review the evidence for several principles that are especially promising for improving mathematics instruction. Using the classification scheme proposed by Koedinger et al. (2013), we begin with principles that focus on improving memory and fluency: scaffolding, distributed practice, and feedback. We then move to worked…

This article presents findings from a case study that explored creative persistence through a reconceptualization of what it means to "fail" within an educational setting. Participants included in-service teachers enrolled in a semester-long graduate level educational technology course who reflected that they were able to view their…

"Self-diagnosis tasks" are aimed at fostering diagnostic behavior by explicitly requiring students to present diagnosis as part of the activity of reviewing their problem solutions. Recitation groups in an introductory physics class of about 200 college students were distributed into a control group and three intervention groups in which different…

"Self-diagnosis tasks" aim at fostering students' learning in an examination context by requiring students to present diagnoses of their solutions to quiz problems. We examined the relationship between students' learning from self-diagnosis and the typicality of the problem situation. Four recitation groups in an introductory physics class…