Twenty years ago when the author was student teaching, he quickly learned what geometry teachers and researchers (e.g., Senk 1985) have long known: High school geometry students struggle with proof. Throughout his career, he has tried to create instructional materials to make proof more accessible to his students. From field-testing materials with…

This paper describes an emerging approach to the design of task sequences and the theory that undergirds it. The approach aims at promoting particular mathematical concepts, understood as the result of reflective abstraction. Central to this approach is the identification of available student activities from which students can abstract the…

Presents a developmental approach to teaching programing at all educational levels which stresses concepts rather than syntax; provides motivation, relevant examples, and activities; proceeds from concrete to pictorial to abstract according to age and experience of learners; and utilizes increasingly complex activities building upon and extending…

This article describes methods for teaching higher level thinking skills to children. A four-step teaching plan utilizing Beyer's Taxonomy of thinking skills provides a sequential technique for teaching these skills as do increased verbal interaction, skillful questioning, and use of knowledge organizers. The I PLAN strategy can aid decision…

This article presents 10 practical teaching procedures to encourage students to develop formal reasoning skills. A twelfth-grade English course is used as an example. Procedures include pretesting, sequencing instruction, providing students with concrete experiences, discussing reasoning patterns and forms of argumentation, assigning argumentative…