APL-generated teaching and testing items to enhance a student's ability to discover functional relationships

摘要

Ideas and designs for programs to generate teaching examples are introduced. Some of these ideas are tested and demonstrated by a prototype APL program. Descriptions of the internal structure and requirements of the example generators are presented. The examples produced by the program are designed to motivate students to discover rules or relationships capable of mapping the in-domain inputs to correct outputs. Experimental examples used for demonstrating typical concepts and mathematical processes include the functions ρ, , x, +, ÷, | and with their intrinsic APL definitions. Initially, the types of arguments for these examples will be kept simple at first to promote learning such mathematical functions by permitting only single scalar arguments. Later, for discovery learning, the functions may be selected to permit or require arguments that are vector or array objects. An important component in the design of this system is parameter specification. Parameters determine the number of examples and their perspicuity. A student using the system may request additional examples that are easy to comprehend before the function is discovered from the program generated examples provided. The example-generating program also facilitates checking that establishes that a student's response is operationally equivalent to a correct one.