Design-based research studies are conducted as iterative implementation-analysis-modification cycles, in which emerging theoretical models and pedagogically plausible activities are reciprocally tuned toward each other as a means of investigating conjectures pertaining to mechanisms underlying content teaching and learning. Yet this approach, even when resulting in empirically effective educational products, remains under-conceptualized as long as researchers cannot be explicit about their craft and specifically how data analyses inform design decisions. Consequentially, design decisions may appear arbitrary, design methodology is insufficiently documented for broad dissemination, and design practice is inadequately conversant with learning-sciences perspectives. One reason for this apparent under-theorizing, I propose, is that designers do not have appropriate constructs to formulate and reflect on their own intuitive responses to students’ observed interactions with the media under development. Recent socio-cultural explication of epistemic artifacts as semiotic means for mathematical learners to objectify presymbolic notions (e.g., Radford, Mathematical Thinking and Learning 5(1): 37–70, 2003) may offer design-based researchers intellectual perspectives and analytic tools for theorizing design improvements as responses to participants’ compromised attempts to build and communicate meaning with available media. By explaining these media as potential semiotic means for students to objectify their emerging understandings of mathematical ideas, designers, reciprocally, create semiotic means to objectify their own intuitive design decisions, as they build and improve these media. Examining three case studies of undergraduate students reasoning about a simple probability situation (binomial), I demonstrate how the semiotic approach illuminates the process and content of student reasoning and, so doing, explicates and possibly enhances design-based research methodology.
- RT @MatthewMaddux: Developing mathematical knowledge for teaching teachers: potentials of history of mathematics in teacher educator traini… 5 days ago
- RT @CERME11_2019: In preparation for the conference, we kindly ask you to send questions about ERME research, questions about ERME itself,… 5 days ago
- Developing mathematical knowledge for teaching teachers: potentials of history of mathematics in teacher educator t… twitter.com/i/web/status/1… 6 days ago
- Looking forward to last day (for me) of the EML 2018 with @deborah_ball. What a wonderful opportunity to study, dis… twitter.com/i/web/status/1… 5 months ago
- RT @A2SchoolsSuper: We ❤️ #TreeTown @A2schools #InspireA2 #A2gether Ann Arbor named best place to live in America - again https://t.co/yRrH… 12 months ago