Student focusing and noticing, which drive reasoning, are important but under researched aspects of student learning. Quadratic functions representations are perceptually and conceptually complex and thus, offer much for students to focus on and notice. Our study compared a teacher's goals for student focusing and noticing during quadratic…

Online math videos for student learning are abundant; yet they are surprisingly uniform in their monologic, expository mode of presentation and their emphasis on procedural skill. In response, we created an alternative model of online math videos that feature the unscripted dialogue of secondary school students, who convey sources of confusion and…

Teacher-educator and researcher Daniel L. Kohut suggests in "Musical Performance: Learning Theory and Pedagogy" that there are many problems that result from the way music teachers often teach. Most teachers focus on the process, not the goal. The Natural Learning Process that Kohut advocates is the same process that young children use when they…