Long considered central to scientific thinking, this inquiry model is initiated in innovative math programs as well. Moreover, the inquiry model moves the focus from a teacher demonstration at the front of the room to actual hands-on investigation by students. This, in turn, leads to increased use of manipulatives and other concrete models at all levels. Subject matter is treated as an integrated whole rather than as a collection of isolated concepts and procedures, each to be taught and tested individually. This departure from the norm is seen most clearly in innovative secondary mathematics materials, which have changed from the traditional algebra, geometry, and advanced algebra courses to some version of an integrated curriculum.
Innovative programs aim to develop an expanded set of basic skills.
Besides the traditional learning of definitions and procedures, the materials place a strong emphasis on reasoning through complex problems and communicating results. Abstract ideas are developed with a well-defined context. Real-world or even fantasy settings are used to frame investigation and interpret findings, which are eventually generalized as concepts. Use of technology is extensive and varied. In some programs, videotapes introduce problem scenarios.