Carla van de Sande

Perspectival Understanding of Conceptions and Conceptual Growth in Interaction

Abstract We propose a bridge between cognitive and sociocultural approaches that is anchored on the sociocultural side by distributed cognition and participation, and on the cognitive side by information structures. We interpret information structures as the contents of distributed knowing and interaction in activity systems. Conceptual understanding is considered as achievement of discourse in activity systems, and conceptual growth is change in discourse practice that supports more effective conceptual understanding. We also introduce a concept of perspectival understanding, in which accounts of cognition, including conceptual understanding, include points of view. This concept generalizes the concept of schema by hypothesizing that a perspectival understanding can be constructed by constraint satisfaction when a sufficient schema is not known or recognized. We provide an example in which perspectival understanding was jointly constructed, illustrating an interactional process we call “constructive listening.”

A Framing of Instructional Explanations: Let Us Explain With You

Our goal in this chapter is to merge our understanding of explanations with a perspectival theory of framing. We draw on Leinhardts model of an instructional explanation and show how adding perspective, that is, the way an individual or group understands the kind of activity they are engaged in, together with the way that information is communicated, interpreted, and organized, fits comfortably within Leinhardts analytic framework. We hypothesize that, in a good explanation (according to Leinhardts model), the teacher is sensitive to the resources for framing that students initially have and uses instructional activities to help build a bridge between alternative framings so that s/he is explaining the new material with, rather than to, the students. In order to demonstrate how this merging plays out, we analyze a situation in which the explanation is very focused and involves the solution of a single mathematical exercise on the limit concept by a student and a more experienced other. The emergent learning environment in which the interaction takes place is also a tribute to Leinhardt as a pioneer in the research of free, open, online help forums where students can post queries from coursework and receive help and explanations from anonymous volunteers.

Free, Open, Online, Help Forums: Convenience, Connection, Control, Comfort, and Communication

In contrast to course delivery, help seeking has not advanced with the technological capabilities and preferences of today’s students. Help seeking in higher education remains primarily an individual, private, face-to-face activity. Open, online, help forums have the potential to transform help seeking into a public, social endeavor. These forums connect students with volunteer helpers who have the time, knowledge, and willingness to provide assistance with specific problems from coursework. Although many such forums currently exist and are a popular source of help seeking, they have remained largely off the radar of educational research. In this paper, a calculus help forum is examined for manifestations of convenience, connection, and control, which are commonly used to describe student expectations regarding information technology use. Results indicate that students can receive efficient, accessible, and self-regulated help. Two additional themes for student experience, comfort and communication, are proposed.

Grassroots open, online, calculus help forums

The emergence of free, open, online, help forums has transformed tutoring from a private and individual activity into a public and collective endeavor. These forums support asynchronous exchanges between individuals from around the world. Students visit these forums seeking help on specific queries from coursework and receive help from anonymous others. In contrast to help forums designed and supervised by educational researchers, these forums have a grassroots origin. This paper investigates one such calculus help forum for evidence that forum tutors are scaffolding students to contribute to the successful solution of the exercise they posted. An analysis of 200 exchanges on limit and related rates revealed the presence of effective guided problem solving (marked by leading questions and hints), albeit to a limited extent. This work points to the need for discovering ways to augment constructive interactions in popular help forums that have become part of the student learning experience.

Cognitive load theory meets the real world: worked examples on a popular homework help forum

Open online help forums connect students with volunteer helpers who provide assistance with specific problems from coursework. Cramster, the most popular existing mathematics help forum, is an advocate of cognitive load theory and promotes the provision of worked solutions as the best way to help students. The intent is that students can use these worked solutions as problem-solving models and learn from them. This project investigated this possibility by analysing 194 responses from the Algebra thru pre-Calculus archives from two perspectives: first, student ratings of solution helpfulness were examined; second, a rubric based on the accuracy and construction of the solutions was developed, applied, and compared with student ratings. The results indicate that Cramster helpers provided students with worked solutions that contain steps and sometimes goals, as opposed to final answers only. However, there were also many responses containing errors, and students did not show much discernment in their ratings.