Implementation of Abstract Data Types in Dynamic Sketches for Learning Geometry
Informatics in Education. An International Journal
A long-term observation of students' usage of a dynamic geometry in a classroom at all grade levels has challenged to develop an approach for learning and understanding mathematics in an easier way for both students and teachers. The paper deals with the results of a study that investigates the process and outcomes of the implementation of abstract data types in dynamic sketches (by composing scripts) for learning geometry. Four abstract data types have been developed and defined using
... specifications. The development of a dynamic sketch scenario with the implementation of these abstract data types is presented in detail. An example of creating an interactive microworld, using abstract data types, is presented and discussed as well. Keywords: abstract data type, ADT, learning geometry, dynamic sketch, interactive microworld. Definition 2. ADT specification is a representation-independent formal definition of each operation of a data type. Thus, the complete design of a single data type would proceed by first giving its specification, followed by an (efficient) implementation which agrees with the specification. Definition 3. Algebraic specification is defined as a set of three elements (S, 0P, E): a set S of values, a set OP of operation symbols, and a set E of equations or axioms. Definition 4. Implementation of data abstraction is an assignment of meaning to the values and operations in terms of the values and operations of another data type or set of data types. A correct implementation is an implementation that satisfies the axioms. Definition 5. A generating function is a function that generates the value of a type.