CSMP is an exciting K-6 math program, designated as an "exemplary educational program that works" by the U.S. Department of Education, which funded its development, evaluation, and dissemination. Its spiral, problem solving approach uses picture languages, abaci, and technically challenging games. Simple problems subtly introduce sophisticated concepts. While class and teacher-student interactions are fundamental to CSMP, its graphical and manipulative portions are obvious candidates for computerization. We have already built template prototypes for Venn diagrams (computationally difficult) and arrow relations (graphically complex),which allow individual exercises (interactive graphics and grading) to be automatically generated. Because our software now works only under the Unix operating system, we propose to investigate the feasibility of implementing it under Windows 95/NT on PC's expected to be typical of the prospective user-base. Conundrum will enhance CSMP's flexibility to address special needs, including at-risk, low achievers, bilingual, compensatory education, gifted and talented, and special education. Feedback will be immediate and accurate. Conundrum can make the nontraditional CSMP materials and the advanced mathematics for which they form the foundation, less intimidating to many elementary school teachers. Student and teacher tutoring, tools for constructing new exercises, and automated troubleshooting of a student's individual weaknesses are planned extensions.Summary Of Anticipated Results And Implications:Our project's goal is to implement the exercises and tools of CSMP on computer hardware expected to be reasonably affordable in two years. Markets for Conundrum will besought in schools; in home schooling-, and in the over-the-counter market (where we foresee interest among parents seeking more challenges for their children). Our development is two-tiered - first, we build a software template for a type of tool from which we then generate particular exercise software "instantiations.' We have already constructed a template for Venn diagram involving integers. From this template, we have within minutes generated several particular Venn exercises, including action graphics and automatic grading. The Venn template, and a template for arrow diagrams involving function composition that has also been completed, were implemented under the Unix operating system (OS) with X-Windows graphics. Unix, OS of choice for science and math in academic research, is the environment in which we can prototype graphical applications most quickly. Elementary schools, however, use DOS/Windows and Mac OS's. All of the C++ math algorithms we have already constructed are expected to port seamlessly to Windows 95/NT, but, although many of our graphical approaches are OS-independent, our widgets (buttons, tokens, menus, etc.) will probably have to be redone. In Phase I we will investigate the feasibility of implementing our prototype templates under W95/NT on a P75-P100 PC with SVGA graphics, at an adequate speed. If these prototypes can be satisfactorily ported, then in Phase II we will extend Conundum to other types of problems. Our initial focus will be the 4th grade templates and exercises, so that with early on-site testing, we will have a marketable product as soon as possible. Later in Phase II we will create the relatively few additional templates needed for grades 5 and 6. We will secure investors by Phase II, and finalize our marketing plan. During Phase II we will determine whether the software should be made to run on less expensive PC's and on Macs, will continue to make extensions to various levels of sophistication, and will implement tutoring, troubleshooting, and tool-making enhancements.
