Technology-Immune/Technology-Enabled Problem Solving as Agency of Design-Based Mathematics Education

Abstract

The paper is written as a reflection on the author’s online teaching of a graduate elementary mathematics content and methods course through the asynchronous modality. The need for developing skills in posing problems that integrate non-technological and technological problem-solving strategies is emphasized. Such problems are considered agency of design-based mathematics education. The importance of revealing hidden mathematical ideas stemming from teacher candidates’ willingness to explore self-posed problems within the forum components of the course is discussed. Using these hidden ideas, the paper demonstrates connectivity among different mathematical concepts including historical connections. Teacher candidates’ reflections on the course have been included and reviewed.

Exploring Polygonal Number Sieves through Computational Triangulation

“…Using the threedimensional table provided by Wolfram Alpha, the first three elements of the Cullen-type sieves of the second order were identified, located within the corresponding spreadsheets, and connections between two types of modeling were mathematically explained. In that way, the paper, emphasizing the value of the notion of computational triangulation [4], can serve as a bridge to earlier writings on the TITE framework [24,25] by offering a new domain for using technology in mathematics education.…”