Adapting the mathematical task framework to design online didactic objects

Abstract

Designing didactic objects involves imagining how students can conceive of specific mathematical topics and then imagining what types of classroom discussions could support these mental constructions. This study investigated whether it was possible to design Java applets that might serve as didactic objects to support online learning where 'discussions' are broadly defined as the conversations students have with themselves as they interact with the dynamic mathematical representations on the screen. Eighty-four pre-service elementary teachers enrolled in hybrid mathematics courses were asked to interact with a series of applets designed to support their understanding of qualitative graphing. The results of the surveys indicate that various design features of the applets did in fact cause perturbations and opportunities for resolutions that enabled the users to 'discuss' their learning by reflecting on their in-class discussions and online activities. The discussion includes four design features for guiding future applet creation.

Students’ Activity in an Online Learning Environment for Mathematics: The Role of Thinking Levels

“…Indeed, mathematical applets can support higher order thinking by letting students interact with (and manipulate) visual representations and engage with concrete examples of abstract constructs (Dimitriou-Hadjichristou & Ogbonnaya, 2015; Gadanidis et al., 2003). Of course, applets should be designed in a way that facilitates this kind of platform (Bowers et al., 2011).…”

iPads in the Mathematics Classroom: Developing Criteria for Selecting Appropriate Learning Apps

“…Apps for learning mathematics should be cognitively demanding (Bowers, Bezuk, & Aguilar, 2011;Dick & Hollebrands, 2011;Underwood et al, 2005). That is, they should require higher-level thinking rather than simple memorization or application of procedures.…”

“…Note that perceived task difficulty is not necessarily correlated with cognitive demand. In algebra, for example, memorizing and using the quadratic formula may be difficult for some students, but an app that simply requires the application of the quadratic formula to several equations in the form Ax 2 + Bx + C = 0 is not cognitively demanding (Bowers et al, 2011). The app should evoke critical thinking from the user.…”