Leveling transparency via situated intermediary learning objectives (SILOs)

When designers set out to create a mathematics learning activity, they have a fair sense of its objectives: students will understand a concept and master relevant procedural skills. In reform-oriented activities, students first engage in concrete situations, wherein they achieve situated, intermediary learning objectives (SILOs), and only then they rearticulate their solutions formally. We define SILOs as heuristics learners devise to accommodate contingencies in an evolving problem space, e.g., monitoring and repairing manipulable structures so that they model with fidelity a source situation. Students achieve SILOs through problem-solving with media, instructors orient toward SILOs via discursive solicitation, and designers articulate SILOs via analyzing implementation data. We describe the emergence of three SILOs in developing the activity Giant Steps for Algebra. Whereas the notion of SILOs emerged spontaneously as a framework to organize a system of practice, i.e. our collaborative design, it aligns with phenomenological theory of knowledge as instrumented action

Exigencies for engaging undergraduates in rhetorical problem solving : insights from engineering managers and A3 report analyses

Undergraduate education has a historical tradition of preparing students to meet the problem-solving challenges they will encounter in work, civic, and personal contexts. This thesis research was conducted to study the role of rhetoric in engineering problem solving and decision making and to pose pedagogical strategies for preparing undergraduate students for workplace problem solving. Exploratory interviews with engineering managers as well as the heuristic analyses of engineering A3 project planning reports suggest that Aristotelian rhetorical principles are critical to the engineer\u27s success: Engineers must ascertain the rhetorical situation surrounding engineering problems; apply and adapt invention heuristics to conduct inquiry; draw from their investigation to find innovative solutions; and influence decision making by navigating workplace decision-making systems and audiences using rhetorically constructed discourse. To prepare undergraduates for workplace problem solving, university educators are challenged to help undergraduates understand the exigence and realize the kairotic potential inherent in rhetorical problem solving. This thesis offers pedagogical strategies that focus on mentoring learning communities in problem-posing experiences that are situated in many disciplinary, work, and civic contexts. Undergraduates build a flexible rhetorical technê for problem solving as they navigate the nuances of relevant problem-solving systems through the lens of rhetorical practice

Cognitive apprenticeship : teaching the craft of reading, writing, and mathtematics

Includes bibliographical references (p. 25-27)This research was supported by the National Institute of Education under Contract no. US-NIE-C-400-81-0030 and the Office of Naval Research under Contract No. N00014-85-C-002

Linking factual and procedural knowledge in solving science problems: A case study in a thermodynamics course

Well-specified problems of the type presented boxed in the introduction to this article are extremely common in science courses. Unfortunately, this does not mean that students find them easy to solve, even when a teacher provides model answers to problems which differ only marginally (in the teacher's eyes) from those put before the students. The central difficulty with such courses is that they do not embody instructional principles that reflect students' need for “direction” in problem solving. In this article, we describe how the necessary heuristics and strategic knowledge were built into the remake of a conventional thermodynamics course. In contrast to mainstream American work on learning problem solving we chose to direct our curriculum reconstruction using the Gal'perin theory of stage-by-stage formation of mental actions and Landa's description of the “through” systematization of knowledge. As indicated by both, we first developed an integrated system of instructional objectives: a programme of actions and methods (PAM) to solve problems in thermodynamics. Then the plan of instruction was designed. This plan indicates which instructional procedures and materials should be used to realize the instructional functions, derived from the learning theory. The evaluation design contained two control and three experimental courses. In discussing our main findings, we consider the generalizability of the procedures we followed in constructing the PAM and the instructional plan

Reinventing discovery learning: a field-wide research program

© 2017, Springer Science+Business Media B.V., part of Springer Nature. Whereas some educational designers believe that students should learn new concepts through explorative problem solving within dedicated environments that constrain key parameters of their search and then support their progressive appropriation of empowering disciplinary forms, others are critical of the ultimate efficacy of this discovery-based pedagogical philosophy, citing an inherent structural challenge of students constructing historically achieved conceptual structures from their ingenuous notions. This special issue presents six educational research projects that, while adhering to principles of discovery-based learning, are motivated by complementary philosophical stances and theoretical constructs. The editorial introduction frames the set of projects as collectively exemplifying the viability and breadth of discovery-based learning, even as these projects: (a) put to work a span of design heuristics, such as productive failure, surfacing implicit know-how, playing epistemic games, problem posing, or participatory simulation activities; (b) vary in their target content and skills, including building electric circuits, solving algebra problems, driving safely in traffic jams, and performing martial-arts maneuvers; and (c) employ different media, such as interactive computer-based modules for constructing models of scientific phenomena or mathematical problem situations, networked classroom collective “video games,” and intercorporeal master–student training practices. The authors of these papers consider the potential generativity of their design heuristics across domains and contexts