Assessment for Learning in the Calculus Classroom: A Proactive Approach to Engage Students in Active Learning

Abstract

We describe FROG, an integrated environment for authoring and run-ning collaborative learning scenarios, called Orchestration Graphs. We describe the pedagogical background and the technical architecture, and present a case study of a teacher using FROG to experiment with a variation of a jigsaw script. 1 Pedagogical background This paper presents FROG, an integrated environment with tools implementing Orches-tration Graphs (OG) [2]. OG model teaching and learning scenarios as a structured network of learning activities devoted to a set of learning objectives. FROG1, one of several possible implementations of OG, allows educators to design in advance, teachers to orchestrate in real time, and researchers to study afterwards what students actually do while learning. Orchestration Graphs depict the structure (what is done when by whom), the ped-agogical rationale behind the activity flow, and the work flow created by data transfor-mations and student groupings (" social structure "). An " Orchestration Graph Engine " allows the teacher to run educational scenarios with her students following the activities as specified in the OG – or as modified real-time by her as she monitors their work – to provide input data and obtain output products. Finally, products and traces of the learning process are collected and processed; a stochastic model of the scenario uses these traces to predict (or confirm) learner states [2, p 95-100]. OG constitute a useful modelling language for any form of organized education (e-learning, large auditorium, MOOC, seminar, elementary school classroom) independent of learning theory and pedagogical paradigm. FROG is a tool for the action researcher and the design researcher. By translating educational scenarios into computational struc-tures and providing an environment to test and run them, the modelling formalism (OG) provides a formal model for education. The implementing tool (FROG) takes care of the 'algorithmic' aspects of teaching – a significant part of a much broader whole. They do not constrict towards a specific learning theory and the ensuing pedagogical practice; OG are pedagogically neutral, but certainly more useful when the pedagogy and the social interactions among students are rich.