Design Patterns for the Use of Technology in Introductory Mathematics Tutorials

Abstract

Abstract. Learning mathematics actively, oriented at mathematical processes, in a technology-enhanced learning environment differs widely from learning in traditional mathematics courses. The traditional lecture -an expert presents the knowledge the learners have to acquire -usually doesn't activate the students' thinking. This article introduces three didactical design patterns which describe how university students can be enabled to use technology in order to explore and solve mathematical problems in open learning scenarios: TECHNOLOGY ON DEMAND, HELP ON DEMAND, and FEEDBACK ON DEMAND.

On an Architectural Concept for Didactics in the Context of Constructive Alignment

“…The Play Projects described by (Yakovleva & Yakovlev, 2014) require several steps: i) selecting and fixing a research problem, ii) splitting students into (two) groups, iii) asking students to craft solutions, and finally iv) organizing a meeting where students then present and defend their solutions. (Bescherer & Spannagel, 2009) introduce -among several other patterns -the Technology on Demand Pattern. Implementation of this pattern requires the selection of an appropriate problem that has to meet given requirements, the design of appropriate questions, tasks and hints to guide students through a solution process requiring software tools.…”

Adding intelligent assessment: a Java framework for integrating dynamic mathematical software components into interactive learning activities

“…The learning environment MoveIt!-M implements the assessment according to the principles of the feedback on demand pattern (Bescherer and Spannagel 2009). The student can ask for feedback by pressing a button.…”