Gestures and conceptual integration in mathematical talk

Spontaneous gesture produced in conjunction with speech is considered as both a source of data about mathematical thinking, and as an integral modality in communication and cognition. The analysis draws on a corpus of more than 200 gestures collected during 3 h of interviews with prospective elementary school teachers on the topic of fractions. The analysis examines how gestures express meaning, utilizing the framework of cognitive linguistics to argue that gestures are both composed of, and provide inputs to, conceptual blends for mathematical ideas, and a standard typology drawn from gesture studies is extended to address the function of gestures within mathematics more appropriately. Electronic supplementary material  The online version of the original article (doi:) contains supplementary material, which is available to authorized users.     

Seeing Iconic Gestures While Encoding Events Facilitates Children's Memory of These Events

An experiment with 72 three-year-olds investigated whether encoding events while seeing iconic gestures boosts children's memory representation of these events. The events, shown in videos of actors moving in an unusual manner, were presented with either iconic gestures depicting how the actors performed these actions, interactive gestures, or no gesture. In a recognition memory task, children in the iconic gesture condition remembered actors and actions better than children in the control conditions. Iconic gestures were categorized based on how much of the actors was represented by the hands (feet, legs, or body). Only iconic hand-as-body gestures boosted actor memory. Thus, seeing iconic gestures while encoding events facilitates children's memory of those aspects of events that are schematically highlighted by gesture.     

Differences in problem solving by nonscience majors in introductory chemistry on paired algorithmic-conceptual problems

The purpose of this investigation was to identify and describe the differences in the methods used by faculty teaching introductory chemistry and students enrolled in an introductory chemistry course at the university level to solve paired algorithmic and conceptual problems. Of the 180 students involved, the problem-solving schemas of 20 selected students and 2 professors were evaluated using a graphical method to dissect their think-aloud interviews into episodes indicative of solutions to paired problems on density, stoichiometry, bonding, and gas laws. The interviewed students were classified into four different problem-solving categories (i.e., high algorithmic/high conceptual, high algorithmic/low conceptual, low algorithmic/high conceptual, and low algorithmic/low conceptual), and composite graphs of their problem-solving schemas were compared to those representative of members of the faculty experts' category. Results of these comparisons indicated that as the students' ability to solve both algorithmic and conceptual problems improved, less time and fewer transitions between episodes of the problem-solving schemas were required to complete the problems. Regardless of the students' problem-solving ability, algorithmic-mode problems always required more time and a greater number of transitions for completion than did the paired conceptual-mode problems. However, regardless of topic, all students more frequently correctly solved the algorithmic-mode problems than the corresponding paired conceptual-mode problems. © 1997 John Wiley & Sons, Inc. J Res Sci Teach 34: 905–923, 1997.     

A window into thinking: Using student writing to understand conceptual change in science learning

This study, conducted in an inner-city middle school, followed the conceptual changes shown in 25 students' writing over a 12-week science unit. Conceptual changes for 6 target students are reported. Student understanding was assessed regarding the nature of matter and physical change by paper-and-pencil pretest and posttest. The 6 target students were interviewed about the goal concepts before and after instruction. Students' writing during lesson activities provided qualitative data about their understandings of the goal concepts across the science unit. The researcher constructed concept maps from students' written statements and compared the maps across time to assess changes in the schema of core concepts, complexity, and organization as a result of instruction. Target students' changes were studied in detail to determine patterns of conceptual change. After patterns were located in target students' maps, the remaining 19 students' maps were analyzed for similar patterns. The ideas that students identified in their writing showed changes in central concepts, complexity, and organization as the lessons progressed. When instructional events were analyzed in relation to students' demonstrated ideas, understanding of the goal conceptions appeared in students' writing more often when students had opportunities to explain their new ideas orally and in writing.     

Bridging scientific reasoning and conceptual change through adaptive web‐based learning

This study reports an adaptive digital learning project, Scientific Concept Construction and Reconstruction (SCCR), and examines its effects on 108 8th grade students' scientific reasoning and conceptual change through mixed methods. A one‐group pre‐, post‐, and retention quasi‐experimental design was used in the study. All students received tests for Atomic Achievement, Scientific Reasoning, and Atomic Dependent Reasoning before, 1 week after, and 8 weeks after learning. A total of 18 students, six from each class, were each interviewed for 1 hour before, immediately after, and 2 months after learning. A flow map was used to provide a sequential representation of the flow of students' scientific narrative elicited from the interviews, and to further analyze the level of scientific reasoning and conceptual change. Results show students' concepts of atoms, scientific reasoning, and conceptual change made progress, which is consistent with the interviewing results regarding the level of scientific reasoning and quantity of conceptual change. This study demonstrated that students' conceptual change and scientific reasoning could be improved through the SCCR learning project. Moreover, regression results indicated students' scientific reasoning contributed more to their conceptual change than to the concepts students held immediately after learning. It implies that scientific reasoning was pivotal for conceptual change and prompted students to make associations among new mental sets and existing hierarchical structure‐based memory. © 2009 Wiley Periodicals, Inc. J Res Sci Teach 47: 91–119, 2010     

Two hands and a tale: When gestures benefit adult narrative comprehension

It is well established that observing and producing gesture by a learner can enhance comprehension of verbal messages, including narratives. What is less well understood, however, is under which conditions gestures benefit comprehension most. This study examined the role of gesture observation and production in adult narrative comprehension, through investigating whether gesture production moderates the effect of gesture observation. Crucially, observing typical gestures, but not atypical gestures, significantly benefited narrative comprehension. Furthermore, no significant benefit of producing gestures was found, and there was no evidence that gesture production moderated the differential effects of observing typical and atypical gestures on narrative comprehension. Overall, the current study not only provides evidence that iconic gestures can benefit adult narrative comprehension, but also highlights under which conditions gestures are likely to be of benefit.     

Influence of text structure on learning counterintuitive physics concepts

The purpose of this study was to explore the influences of text structure on students' conceptual change. Case studies were conducted of three sections of physics (Physical World, Physics, and Honors Physics) for 8 months of an academic year. Qualitative data (including observation field notes, interviews, videotapes, audiotapes, and questionnaires) were analyzed from the perspective of grounded theory by constant comparison through the framework of social constructivism. Results showed that individuals used refutational text to change their alternative conceptions, find support for their scientific preconceptions, gain the language necessary to discuss their ideas, and acquire new concepts. We also found instances, however, when students ignored the text and persisted with their alternative conception, or when students found support for their nonscientific ideas from refutational text. In these cases, we found that either the refutation was not direct enough to be effective, or students' reading strategies were insufficient to facilitate conceptual change. In investigating the power of refutational text, we found that refutational text does cause cognitive conflict. We also discovered that while cognitive conflict may be necessary for conceptual change to occur, it is not sufficient. Although refutational text is effective on the average for groups of students, it will need to be supplemented by discussion for individuals. J Res Sci Teach 34: 701–719, 1997.     

Sometimes more is better: Agent gestures,procedural knowledge and the foreign language learner

Pedagogical agents in multimedia learning environments have frequently been designed to produce pointing gestures (deictic) to direct spatial awareness. Although this might be beneficial for native English-speaking students who possess high levels of comprehension, only using pointing gestures with foreign language students learning English is problematic because these students need more assistance with language comprehension than just directing spatial awareness. The purpose of this study was to explore how gesture type and gesture frequency help foreign language students perceive the agent’s persona and the ability to recall procedural information. The results found one significant interaction between average gestures and no gesture in terms of facilitation, but all other conditions and persona subscales were not significant. For learning outcomes, the enhanced gesture condition significantly recalled more information than the no gesture condition (p = 0.017), and was approaching significance with the conversational gesture condition (p = 0.059). The findings suggest that when the learning population consists of foreign language students, pedagogical agents should use representational and beat gestures to help students comprehend more of the language, and the gesture frequency needs to be increased to account for the lack of verbal listening skills with this population.     

Developing strategic readers: a multimodal analysis of a primary school teacher's use of speech,gesture and artefacts

Research on implementing reading strategy instruction has primarily focused on teachers' verbal communication with limited attention to other semiotic resources such as gesture and artefacts. In this paper, we construct a ‘telling case’ on the basis of how one primary teacher from the United States used speech, gesture and artefacts as a means of communication while instructing her students in reasons to predict when reading. Data sources for this case study consisted of field notes, artefacts and digital video. We analysed the teacher's use of gesture, speech and artefacts from a social semiotic multimodal perspective. Findings indicate that the teacher created meaning by interweaving multiple modes in the communicative contexts of strategy instruction using speech, deictic gestures, metaphoric gestures and artefacts. These findings are important to reading strategy instruction because much of the research and discussion of practice to date has centred on the instruction of reading strategies using teacher and student speech and not attending to the use of semiotic resources beyond speech.     

Seeing Iconic Gesture Promotes First- and Second-Order Verb Generalization in Preschoolers

This study investigated whether seeing iconic gestures depicting verb referents promotes two types of generalization. We taught 3- to 4-year-olds novel locomotion verbs. Children who saw iconic manner gestures during training generalized more verbs to novel events (first-order generalization) than children who saw interactive gestures (Experiment 1, N = 48; Experiment 2, N = 48) and path-tracing gestures (Experiment 3, N = 48). Furthermore, immediately (Experiments 1 and 3) and after 1 week (Experiment 2), the iconic manner gesture group outperformed the control groups in subsequent generalization trials with different novel verbs (second-order generalization), although all groups saw interactive gestures. Thus, seeing iconic gestures that depict verb referents helps children (a) generalize individual verb meanings to novel events and (b) learn more verbs from the same subcategory.     

Co-development of Conceptual Understanding and Critical Attitude: Analyzing texts on radiocarbon dating

This research documents the impact of a teaching interview aimed at developing a critical attitude in students, and focused on a particular topic: radiocarbon dating. This teaching interview is designed to observe students' reaction to limited written explanations of the phenomenon under study, and their possible frustration or intellectual satisfaction in relation to these texts. We aim to document the possible link between students’ developing conceptual understanding of a topic and their ability to express their frustration when presented with very incomplete explanations, or their intellectual satisfaction when presented with complete explanation. As a side product, we intend to observe some of their a priori ideas concerning this topic. Ten teaching interviews conducted with fourth-year University students were recorded, transcribed and coded. Beyond a series of results concerning students’ a priori understanding of the domain, the analysis of the interviews suggests that, when students are presented with texts of increasing completeness and discuss these with the interviewer, their critical reactions evolve in time in a very specific way. We propose a tentative model for this co-evolution of student conceptual command and critical stance. The discussion bears on possible interpretations for the ‘anesthesia of judgment’ observed in most students at the beginning of the interview, and for a few of them throughout the discussion. Keeping in mind the ‘competence vs concepts’ current alternative, the conditions that seem to free students’ critical potential are analyzed in relation to their evolving command of the topic and their degree of intellectual satisfaction.     

Speech and Gesture Production Provide Unique Insights Into Young Children’s Spatial Reasoning

This study took a novel approach to understanding the role of language in spatial development by combining approaches from spatial language and gesture research. It analyzed forty-three 4.5- to 6-year-old’s speech and gesture production during explanations of reasoning behind performance on Spatial Analogies and Children’s Mental Transformation Tasks. Results showed that speech and gesture relevant for solving the trials (disambiguating correct choices) predicted spatial performance when controlling for age, gender, and spatial words and gestures produced. Children performed the spatial tasks well if they produced relevant information either verbally through speech or nonverbally through gesture. These results highlight the importance of not only focusing on concepts children can reference but also on how such concepts are used in spatial tasks.     

Scientific investigations,metaphorical gestures,and the emergence of abstract scientific concepts

Where anthropological and psychological studies have shown that gestures are a central feature of communication and cognition, little is known about the role of gesture in learning and instruction. Drawing from a large database on student learning, we show that when students engage in conversations in the presence of material objects, these objects provide a phenomenal ground against which students can enact metaphorical gestures that embody (give a body to) entities that are conceptual and abstract. In such instances, gestures are often subsequently replaced by an increasing reliance upon the verbal mode of communication. If gestures constitute a bridge between experiences in the physical world and abstract conceptual language, as we conjecture here, our study has significant implications for both learning and instruction.     

Toward a new conception of conceptions: Interplay of talk,gestures, and structures in the setting

Most studies about students' conceptions and conceptual change are based exclusively on the analysis language, which is treated as a tool to make private contents of the mind public to researchers. Following recent studies that focused on (a) language and discursive practice and (b) the pragmatics of communication that draws on talk, gestures, and semiotic resources in the setting, we propose a redefinition of the nature of conception. Conceptions are understood as the dialectical relation of simultaneously available speech, gestures, and contextual structures that cannot be reduced to verbal rendering because gestures and contextual structures constitute different modalities in the communication. Drawing on data collected during a physics unit about gas taught in French tenth grade classrooms, we show why an appropriate account of conceptions requires: (a) gestures simultaneously produced with talk; and (b) identification of the relevant structures in the setting used by the participants as meaning‐making (semiotic) resources. We propose to: (a) reconceptualize the notion of conception as consisting of a dialectical unit of all relevant semiotic (meaning‐making) resources publicly made available by a speaker (talk, gesture, context); and (b) consider conceptual change through the temporal evolution of the dialectical unit defined in this manner. © 2006 Wiley Periodicals, Inc. J Res Sci Teach 43: 1086–1109, 2006     

Designed and Spontaneous Gestures in Elementary Astronomy Education

We make a case for using gestures and actions to understand and convey spatial and dynamic properties of systems. Problems in learning elementary astronomy are analysed in the context of demands of spatial thinking, in a system which is not amenable to direct perception, namely, the sun–earth–moon (SEM) system. We describe a pedagogy which uses gestures (most often in combination with concrete models and diagrams) to facilitate the visualisation and simulation required in elementary astronomy. These gestures are presented in terms of their purpose in pedagogy: to internalise a natural phenomenon, or an astronomical model, or general properties of space. In terms of design these pedagogical gestures mediate between concrete models of the SEM system and related spatial configurations on the one hand, and their corresponding abstract diagrammatic representations on the other: called here the model–gesture–diagram pedagogical link. Next we present some video data on students’ gestures observed during collaborative problem‐solving which took place in the course of our pedagogic intervention. Implications of these results are drawn for embodiment and multimodality of thought.     

How students reason about matter flows and accumulations in complex biological phenomena: An emerging learning progression for mass balance

In recent years, there has been a strong push to transform STEM education at K-12 and collegiate levels to help students learn to think like scientists. One aspect of this transformation involves redesigning instruction and curricula around fundamental scientific ideas that serve as conceptual scaffolds students can use to build cohesive knowledge structures. In this study, we investigated how students use mass balance reasoning as a conceptual scaffold to gain a deeper understanding of how matter moves through biological systems. Our aim was to lay the groundwork for a mass balance learning progression in physiology. We drew on a general models framework from biology and a covariational reasoning framework from math education to interpret students' mass balance ideas. We used a constant comparative method to identify students' reasoning patterns from 73 interviews conducted with undergraduate biology students. We helped validate the reasoning patterns identified with >8000 written responses collected from students at multiple institutions. From our analyses, we identified two related progress variables that describe key elements of students' performances: the first describes how students identify and use matter flows in biology phenomena; the second characterizes how students use net rate-of-change to predict how matter accumulates in, or disperses from, a compartment. We also present a case study of how we used our emerging mass balance learning progression to inform instructional practices to support students' mass balance reasoning. Our progress variables describe one way students engage in three dimensional learning by showing how student performances associated with the practice of mathematical thinking reveal their understanding of the core concept of matter flows as governed by the crosscutting concept of matter conservation. Though our work is situated in physiology, it extends previous work in climate change education and is applicable to other scientific fields, such as physics, engineering, and geochemistry.     

Students' Visualization of Diagrams Representing the Human Circulatory System: The use of spatial isomorphism and representational conventions

This study investigated students' interpretation of diagrams representing the human circulatory system. We conducted an interview study with three students aged 14–15 (Year 10) who were studying biology in a Hong Kong school. During the interviews, students were asked to interpret diagrams and relationships between diagrams that represented aspects of the circulatory system. All diagrams used in the interviews had been used by their teacher when teaching the topic. Students' interpretations were expressed by their verbal response and their drawing. Dual coding theory was used to interpret students' responses. There was evidence that one student relied on verbal recall as a strategy in interpreting diagrams. It was found that students might have relied unduly on similarities in spatial features, rather than on deeper meanings represented by conventions, of diagrams when they associated diagrams that represented different aspects of the circulatory system. A pattern of students' understanding of structure–behaviour–function relationship of the biological system was observed. This study suggests the importance of a consistent diagrammatic and verbal representation in communicating scientific ideas. Implications for teaching practice that facilitates learning with diagrams and address students' undue focus on spatial features of diagrams are discussed.