This qualitative, instrumental case study examined how a mentor inquiry community can serve as a space for mentors to articulate their knowledge and what about the inquiry community, its characteristics, might harm or help that development. Using Design-Based Research as the methodology, a mentor inquiry community, composed of three…

These problems and activities have been used to demonstrate the uses of multiple representations as well as provide opportunities for students to practice using multiple representations in solving problems. (Contains 3 figures and 2 tables.)

External representations (ERs), such as diagrams, animations, and dynamic models are vital tools for communicating and constructing knowledge in biochemistry. To build a meaningful understanding of structure, function, and process, it is essential that students become visually literate by mastering key cognitive skills that are essential for…

Including gesture in instruction facilitates learning. Why? One possibility is that gesture points out objects in the immediate context and thus helps ground the words learners hear in the world they see. Previous work on gesture's role in instruction has used gestures that either point to or trace paths on objects, thus providing support for this…

Before the advent of symbolism, i.e. before the end of the 16th Century, algebraic calculations were made using natural language. Through a kind of metaphorical process, a few terms from everyday life (e.g. thing, root) acquired a technical mathematical status and constituted the specialized language of algebra. The introduction of letters and…

The possible use of a calendar algorithm was assessed in DBC, an autistic "savant" of normal measured intelligence. Testing of all the dates in a year revealed a random distribution of errors. Re-testing DBC on the same dates one year later shows that his errors were not stable across time. Finally, DBC was able to answer "reversed" questions that…