Students Learning Progression through Instrumental Decoding of Mathematical Ideas
The current study aims to focus on mathematical tasks for students’ mathematical literacy and problem solving literacy. Excerpts are presented from dynamic hypothetical learning paths [DHLP]s and students’ learning progression. The excerpts center around activities aimed to develop the students’ geometrical thinking through the development of their ability to solve real-world problems. The students cooperated in class or worked individually to represent the images using their static or dynamic means and tools (e.g. compass and ruler, a computing environment, interactive boards, dynamic geometry software). My further aim was the students to utilize transformation processes for representations by instrumentally decoding their ideas on static and dynamic objects. An important role for the students’ cognitive development was the design of propositions and theorems (e.g the Pythagorean Theorem), through Linking Visual Active Representations (LVAR). Especially for the latter option an essential role has played the dynamic geometry software, Geometer’s Sketchpad. Furthermore, the paper provides examples that contain rich mathematical material; therefore, student’s mathematical modeling through instrumental decoding of mathematical ideas is the means of reinforcing students’ conceptual knowledge.
