Baruch B. Schwarz

Abstraction in Context: Epistemic Actions

ion in Context: Epistemic Actions Rina Hershkowitz, Weizmann Institute of Science, Rehovot, Israel Baruch B. Schwarz, Hebrew University of Jerusalem, Israel Tommy Dreyfus, Holon Academic Institute of Technology, Israel We propose an approach to the theoretical and empirical identification processes of abstraction in context. Although our outlook is theoretical, our thinking about abstraction emerges from the analysis of interview data. We consider abstraction an activity of vertically reorganizing previously constructed mathematics into a new mathematical structure. We use the term activity to emphasize that abstraction is a process with a history; it may capitalize on tools and other artifacts, and it occurs in a particular social setting. We present the core of a model for the genesis of abstraction. The principal components of the model are three dynamically nested epistemic actions: constructing, recognizing, and building-with. To study abstraction is to identify these epistemic actions of students participating in an activity of abstraction.

Construction of Collective and Individual Knowledge in Argumentative Activity.

In this article, we elaborate methodologies to study construction of knowledge in argumentative activities. For this purpose, we report on a quasi-empirical study on construction of knowledge through successive argumentative activities on a controversial issue. A group of 120 fifth grade students participated in successive argumentative activities; some activities involved individuals and some involved collectives. According to a first methodology, construction of knowledge was measured through arguments/outcomes produced. We developed tools for evaluating changes in individual and collective arguments. In the study, we showed the generally beneficial effect of argumentative activities on collective and individual arguments/outcomes. The significant discrepancies between collective and individual arguments suggested that individual students only partly internalized the collectively constructed arguments. We developed a qualitative methodology to refine this hypothesis as well as other hypotheses concerning the interpretation of the quantitative study. The integration of the quantitative and qualitative methodologies for studying argumentation helped identify several mechanisms of construction of knowledge in argumentative activities. In particular, it brought new light on the mediating role of representational tools such as Argumentative Maps or Pro-Con tables.

The Effects of Monological and Dialogical Argumentation on Concept Learning in Evolutionary Theory

In this study, the effects of argumentation-eliciting interventions on conceptual understanding in evolution were investigated. Two experiments were conducted: In the 1st, 76 undergraduates were randomly assigned to dyads to collaboratively solve and answer items on evolution; half of them were instructed to conduct an argumentative discussion, whereas control dyads were only asked to collaborate. In the 2nd experiment, 42 singletons participated in 1 of 2 conditions: Experimental students engaged in monological argumentation on their own solution and a confederates solution in response to prompts read by the confederate, whereas in the control condition they merely shared their solutions. Conceptual gains were assessed on immediate and delayed posttests. In both experiments, students in the argumentative conditions showed larger learning gains on the delayed posttest than control students. Students in argumentative conditions were able to preserve gains that were obtained immediately following the intervention, whereas control participants either lost immediate gains (dialogical condition) or did not improve their conceptual understanding at any time (monological condition).

Two Wrongs May Make a Right ... If They Argue Together

Several studies have investigated the cognitive development of interacting peers. This study focuses on a phenomenon that has not yet been studied: the cognitive gains of 2 children with low levels of competence who fail to solve a task individually but who improve when working in peer interaction. We show that this phenomenon (which we call the two-wrongs-make-a-right phenomenon) may occur when (a) the 2 wrongs disagree, (b) they have different strategies, and (c) active hypothesis testing is made possible. In a preliminary study, 30 Grade 10 low-achieving students were tested about the rules they use to compare 2 decimal fractions in a questionnaire. The students who were diagnosed as wrongs were invited to solve a task (the 6-cards task) with peers. Three kinds of pairs were formed: 7 W1-W2 pairs in which the 2 wrongs have different conceptual bugs; 4 W1-W1 pairs in which the 2 wrongs have the same conceptual bugs; 4 R-W pairs in which a wrong interacted with a right student. The 6-cards task was designed to create conflicts between students with different conceptual bugs and between wrong and right students. Two days after solving the 6-cards task, the students were asked to answer a similar questionnaire individually. The preliminary study revealed the two-wrongs-make-a-right phenomenon: Among the 7 W1-W2 pairs, at least 1 wrong became right. In contrast, in the 4 R-W pairs, only 1 wrong became right, and in the 3 W1-W1 pairs, no change was detected. In a case study that replicated the phases of the preliminary study, disagreement, argumentative operations (such as challenge and concession), hypothesis testing (with a calculator), and the internalization of social interactions mediated the change of peers from wrongs to rights. We then replicated the initial study with 72 low-achieving Grade 10 and 11 students, confirming the two-wrongs-make-a-right effect.

Argumentation and Learning

This chapter provides multiple perspectives on the intricate relations between argumentation and learning. Different approaches to learning impinge on the way argumentation is conceived of: as a powerful vehicle for reaching shared understanding, as a set of skills pertaining to critical reasoning, or as a tool for social positioning. Each perspective has harvested empirical studies that have stressed the importance of argumentation in learning. Methodological tools that fit the respective perspectives are reviewed. In spite of the pluralistic stance adopted, this chapter attempts to draw connections between the findings obtained in the different perspectives. In a separate part, it considers the specific role of argumentation in learning processes and outcomes for four subjects areas: in mathematics, studies are presented that show deep gaps between argumentation and proof. In science, experimental studies are reviewed to examine whether and how argumentation promotes conceptual change. In history, the chapter considers the role of argumentation in challenging narratives and in claiming a position. At last, we describe the new wave that characterizes civic education programs towards the instillation of argumentative practices in democratic citizenship.

The role of floor control and of ontology in argumentative activities with discussion-based tools

Argumentative activity has been found beneficial for construction of knowledge and evaluation of information in some conditions. Many theorists in CSCL and some empiricists have suggested that graphical representations may help in this endeavor. In the present study, we examine effects of type of ontology and of synchronicity in students that engage intuitively, without training, in e-discussions. Fifty-four Grade 7 students from two classes participated in the study. We tested the effects of using an informal argumentative ontology and control over turn taking on the average number of claims and arguments relevant to the issue at stake, the average number of different types of references to peers (productive. etc.), and on the number of chat expressions (nicknames, swear words, etc.). We found that when providing both an informal argumentative ontology and control over turn taking, students express less chat expressions and fewer references that are not new relevant claims or arguments to their peers, but express more relevant claims and arguments. These findings suggest the immediate beneficial role of the combination of an informal ontology and control over turn taking in the co-elaboration of knowledge.

The Emergent Perspective in Rich Learning Environments: Some Roles of Tools and Activities in the Construction of Sociomathematical Norms

The emergent perspective (Yackel and Cobb, 1996) is a powerful theory for describing cognitive development within classrooms. Yackel and Cobb have shown that the formation of social and sociomathematical norms, and opportunities for learning are intertwined. The present study is an attempt to extend the range of application of the emergent perspective to middle high school classrooms. The learning environments we consider are rich in the sense that (i) the tasks in which students are engaged are open-ended problem-situations (ii) the activities around the tasks are multiphased, consisting of small group collaboration on problem solving, reporting and reflection in a classroom forum with the teacher (iii) the tools used are multi-representational software. We identify here some practices rooted in such rich environments from which several sociomathematical norms stemmed. The present study shows that socio-mathematical norms do not rise from verbal interactions only, but also from computer manipulations as communicative non-verbal actions.

Computer supported moderation of e-discussions: the ARGUNAUT approach

Despite their potential value for learning purposes, e-discussions do not necessarily lead to desirable results, even when moderated. The study of the moderators role, especially in synchronous, graphical e-discussions, and the development of appropriate tools to assist moderators are the objectives of the ARGUNAUT project. This project aims at unifying awareness and feedback mechanisms in e-discussion environments, presently implemented on two existing platforms. This system is primarily directed to a human moderator and facilitating moderation, but might also help the students monitor their own interactions. At the heart of system are the inter-relations between an off-line AI analysis mechanism and an on-line monitoring module. This is done through a collaboration of technological and pedagogical teams, showing promising preliminary results.

The Blind and the Paralytic: Supporting argumentation in Everyday and Scientific Issues

Traditionally, we define a literate person as somebody who knows how to read, write and calculate. In other words, the literate person is able to handle the signs and symbols used by the society in which she lives. However, this definition is fuzzy. What do we mean by knowing how to read? Do we mean knowing how to decipher the meaning of canonical texts that teachers have themselves constructed or accepted from people who have been invested the authority to give the exact meaning of texts (writers of teaching materials for example)? Indeed, teachers’ written guides often give pedagogical advice how to analyze texts, to extract the main idea: the role of the reader is then to reconstruct a meaning (see Kintsch’s situation model, 1986). Also, when students analyze a text, their objective is generally not more than to comply with the demands of a curriculum, that is (in general) to master skills. However, while literacy definitely involves analytical skills, confining it to a series of skills is far too restricted, and puts aside contextual factors in literacy. As noticed by Olson (1994), in opposition to children’s oral propensity to identify speech acts in conversation, when interpreting written signs they have difficulties to identify their illocutionary force. In other words, children may have difficulties in reading partly because they don’t know for which purpose the texts with which they are presented with were written. The approach to literacy we adopt here conveys the versatility that any literate human must exhibit, to be able to communicate actions through different modes and to negotiate them. This practically means that the literate human should express actions in various modes such as reading or writing, with flexible motives such as clarifying an issue, presenting, demonstrating, defending, or convincing.

Online moderation of synchronous e-argumentation

In this paper, we present findings on moderation of synchronous, small-group argumentation in blended, co-located learning environments. Drawing on findings from the literature on human facilitation of dialogue in face-to-face settings, we first elaborate on the potential promise of this new practice. However, little is known about what constitutes effective human facilitation in synchronous e-discussions. A multi-method exploratory approach was then adopted to provide first insights into some of the difficulties and characteristics of moderation in these settings. To this end, we focused on (1) students’ perspectives on what constitutes effective e-moderation of synchronous peer argumentation in classrooms and (2) the relations between characteristics of actual and perceived moderation effectiveness. The analyses presented in this paper reveal that the role of the e-moderator in synchronous peer discussions is a complex one and that expectations from e-moderators seem at times even contradictory. Also, comparisons with findings on moderation in other communication formats (e.g., asynchronous, face-to-face) show that insights on effective instructional practices in these formats cannot be simply transferred to synchronous communication formats. We close this paper by briefly describing a tool that provides real-time support for e-moderators of synchronous group discussions, and whose development had been sparked by these findings in a further cycle of our design research program. Several questions and hypotheses are articulated to be investigated in future research, both with these new tools and in general.