Mathematical reasoning with algebraic and geometric representations is essential for success in upperdivision and graduate-level physics courses. Complex algebra requires student to fluently move between algebraic and geometric representations. By designing a task for middle-division physics students to translate a geometric representation to…

Preservice preparation courses for elementary teachers of science can provide opportunities to build pedagogical content knowledge. One common concern of preservice teachers is how to cope with a preplanned lesson that does not proceed as planned. Providing opportunities for preservice teachers to experience the unexpected actually immerses them…