Visual‐Spatial Representation,Mathematical Problem Solving,and Students of Varying Abilities

The purpose of this study was to investigate students' use of visual imagery while solving mathematical problems. Students with learning disabilities (LD), average achievers, and gifted students in sixth grade (N= 66) participated in this study. Students were assessed on measures of mathematical problem solving and visual‐spatial representation. Visual‐spatial representations were coded as either primarily schematic representations that encode the spatial relations described in the problem or primarily pictorial representations that encode persons, places, or things described in the problem. Results indicated that gifted students used significantly more visual‐spatial representations than the other two groups. Students with LD used significantly more pictorial representations than their peers. Successful mathematical problem solving was positively correlated with use of schematic representations; conversely, it was negatively correlated with use of pictorial representations.     

Using pictorial mnemonics in the learning of tax: a cognitive load perspective

The scope and complexity of the Australian taxation system (as with other tax regimes) is daunting for many accounting students. This paper documents the implementation of new practices that were initiated in an effort to address some of the challenges faced by undergraduate students studying taxation. Based on the principles of cognitive load theory, summaries of the lecture material became the focus of tutorials. These summaries provided the impetus for teaching staff to experiment with illustrations as a strategic means of delivery. Drawing diagrams and presenting them in the form of pictorial mnemonics proved to be effective tools in helping students understand and synthesize basic taxation concepts, thereby promoting effective deep learning. Both formal and informal feedback was overwhelmingly positive and affirming of this innovative approach to the subject. A selection of the pictorial mnemonics we designed is provided.     

Construction and interference in learning from multiple representation

This paper presents an integrated view of learning from verbal and pictorial representations. Learning from these representations is considered as a task oriented process of constructing multiple mental representations. Construction of these representations includes information selection and information organisation, parsing of symbol structures, mapping of analog structures as well as model construction and model inspection. Based on this theoretical view an experiment was conducted to analyse the effects of different kinds of multiple external representations on the structure of mental models. Sixty university students were randomly assigned to one of the three experimental conditions. The text-only group learned the subject matter with a hypertext, whereas the other two groups learned the subject matter with a hypermedium including this hypertext and different kinds of graphics. The findings indicate that the structure of graphics affects the structure of the mental model. They also indicate that presenting graphics is not always beneficial for the acquisition of knowledge. Whereas task-appropriate graphics may support learning, task-inappropriate graphics may interfere with mental model construction.     

Visual spatial representation in mathematical problem solving by deaf and hearing students

This research examined the use of visual-spatial representation by deaf and hearing students while solving mathematical problems. The connection between spatial skills and success in mathematics performance has long been established in the literature. This study examined the distinction between visual-spatial "schematic" representations that encode the spatial relations described in a problem versus visual-spatial "pictorial" representations that encode only the visual appearance of the objects described in a problem. A total of 305 hearing (n = 156) and deaf (n = 149) participants from middle school, high school, and college participated in this study. At all educational levels, the hearing students performed significantly better in solving the mathematical problems compared to their deaf peers. Although the deaf baccalaureate students exhibited the highest performance of all the deaf participants, they only performed as well as the hearing middle school students who were the lowest scoring hearing group. Deaf students remained flat in their performance on the mathematical problem-solving task from middle school through the college associate degree level. The analysis of the students' problem representations showed that the hearing participants utilized visual-spatial schematic representation to a greater extent than did the deaf participants. However, the use of visual-spatial schematic representations was a stronger positive predictor of mathematical problem-solving performance for the deaf students. When deaf students' problem representation focused simply on the visual-spatial pictorial or iconic aspects of the mathematical problems, there was a negative predictive relationship with their problem-solving performance. On two measures of visual-spatial abilities, the hearing students in high school and college performed significantly better than their deaf peers.     

Spatial visualization, visual imagery, and mathematical problem solving of students with varying abilities

The purpose of this study was to investigate students' use of visual imagery and its relationship to spatial visualization ability while solving mathematical word problems. Students with learning disabilities (LD), average achievers, and gifted students in sixth grade (N = 66) participated in this study. Students were assessed on measures of mathematical problem solving, visual imagery representation, and spatial visualization ability. The results indicated that gifted students performed better on both spatial visualization measures than students with LD and average-achieving students. Use of visual images was positively correlated with higher mathematical word-problem-solving performance. Furthermore, the use of schematic imagery was significantly and positively correlated with higher performance on each spatial visualization measure; conversely, it was negatively correlated with the use of pictorial images.     

DEVELOPING AN UNDERSTANDING OF IONS IN JUNIOR SECONDARY SCHOOL CHEMISTRY

There is growing research interest in the challenges and opportunities learners face in representing scientific understandings, processes and reasoning. These challenges include integrating verbal, visual and mathematical modes in science discourse to make strong conceptual links between representations and classroom experiences. Our paper reports on a project that aimed to identify practical and theoretical issues entailed in a representation-intensive approach to guiding students’ conceptual learning in science. We focus here on a teacher developing students’ understanding of the formation of ions and molecules. We argue that the representations produced by students in this process met the criteria for representational competence proposed by diSessa (Cognition and Instruction, 22, 293–331, 2004) and Kozma & Russell (2005). The students understood that an effective representation needed to show relevant information, focus on pertinent points, be self-sufficient in its claims about the topic and provide coherent links between different parts of the representation. The final activity showed that their representations reached Kozma & Russell’s (2005) highest level of competence, where the students were able to use specific features of their representations to critique their suitability for explaining bonding and were able to show how their representation linked to the periodic table as a representation. We conclude by considering the implications of these findings.     

An Eye-Tracking Study of Learning From Science Text With Concrete and Abstract Illustrations

This study investigated the online process of reading and the offline learning from an illustrated science text. The authors examined the effects of using a concrete or abstract picture to illustrate a text and adopted eye-tracking methodology to trace text and picture processing. They randomly assigned 59 eleventh-grade students to 3 reading conditions: (a) text only; (b) text with a concrete illustration; and (c) text with an abstract illustration in a pretest, immediate, and delayed posttest design. Results showed that the text illustrated by either the concrete or the abstract picture led to better learning than did the text alone. Eye-fixation data revealed that the abstract illustration promoted more efficient processing of the text. Analyses of the gaze shifts between the 2 types of external representation indicated that the readers of the text with the abstract illustration made a greater effort to integrate verbal and pictorial information. Furthermore, relations between online and offline measures emerged.     

Development and Assessment of a Three-Dimensional Tooth Morphology Quiz for Dental Students

Tooth morphology has a pivotal role in the dental curriculum and provides one of the important foundations of clinical practice. To supplement tooth morphology teaching a three-dimensional (3D) quiz application (app) was developed. The 3D resource enables students to study tooth morphology actively by selecting teeth from an interactive quiz, modify their viewpoint and level of zoom. Additionally, students are able to rotate the tooth to obtain a 3D spatial understanding of the different surfaces of the tooth. A cross-over study was designed to allow comparison of students’ results after studying with the new application or traditionally with extracted/model teeth. Data show that the app provides an efficient learning tool and that students’ scores improve with usage (18% increase over three weeks, P < 0.001). Data also show that student assessment scores were correlated with scores obtained while using the app but were not influenced by the teaching modality initially accessed (r² = 0.175, P < 0.01). Comparison of the 2016 and 2017 class performance shows that the class that had access to the app performed significantly better on their final tooth morphology assessment (68.0% ±15.0 vs. 75.3% ±13.4, P < 0.01). Furthermore, students reported that the 3D application was intuitive, provided useful feedback, presented the key features of the teeth, and assisted in learning tooth morphology. The 3D tooth morphology app thus provides students with a useful adjunct teaching tool for learning dental anatomy. Anat Sci Educ 00: 000–000. © 2018 American Association of Anatomists.     

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.     

Examining the influence of expertise on the effectiveness of diagramming and summarising when studying scientific materials

A 2 (learning strategies: diagram vs. summary) × 2 (levels of expertise: low vs. high) experiment was conducted to compare the effectiveness of using diagrams to writing summaries for students given biological information to learn and who possessed different levels of expertise in that topic area. A main effect of learning strategy used on number of idea units encoded (in diagrams or summaries) was found: drawing diagrams was superior to writing summaries. However, no interaction effect between learning strategies and expertise was found. An examination of students’ subjective ratings of cognitive load revealed that those with low expertise reported higher levels of cognitive load when constructing diagrams. These findings suggest that using diagrams is effective for identifying and encoding important information when learning, but that it would be helpful to provide guidance about diagram use particularly to students who are novices in the topic area to reduce cognitive load.     

DO THE SPATIAL FEATURES OF AN ADJUNCT DISPLAY THAT READERS COMPLETE WHILE READING AFFECT THEIR UNDERSTANDING OF A COMPLEX SYSTEM?

We varied the spatial features of adjunct displays that depicted a complex scientific system (i.e. human circulatory system). University students (n = 47), who were assigned randomly to a display condition before reading, selected relevant information from the text and wrote it (a) next to a list of definitions (list condition), (b) inside boxes organized to coincide with the sequence of blood flow (chart condition), or (c) on a picture of the heart (pictorial condition). Students in the chart and pictorial conditions had higher scores on 2 learning tests. Results supported the nonequivalence hypothesis, which states that a spatial display can promote learning more effectively than a list because a display’s nonverbal (e.g. spatial) features explicitly depict relationships among a system’s components. The results have implications for science educators.     

Examining the Effects of Different Multiple Representational Systems in Learning Primary Mathematics

Multi-representational learning environments are now commonplace in schools and homes. Research that has evaluated the effectiveness of such environments shows that learners can benefit from multiple representations once they have mastered a number of complex tasks. One of the key tasks for learning with multiple representations is successful translation between representations. In order to explore the factors that influence learners' translation between representations, this article presents 2 experiments with a multi-representational environment where the difficulty of translating between representations was manipulated. Pairs of pictorial, mathematical, or mixed pictorial and mathematical representations were used to teach children in 1 of 3 experimental conditions aspects of computational estimation. In Experiment 1, all children learned to become more accurate estimators. Children in the pictorial and the mathematical conditions improved in their ability to judge the accuracy of their estimates, but children in the mixed condition did not. Experiment 2 explored if the mixed condition's difficulties with translation were temporary by requiring additional time to be spent on the system. It was found that children in all the experimental conditions improved in their judgments of estimation accuracy. It is argued that the mixed condition's failure to improve in Experiment 1 was due to the difficulties they experienced in translating information between disparate types of representation. Their success in Experiment 2 was explained not by learning to translate between representations, but through the adoption of a single representation that contained all the necessary information. This strategy was only effective because of the way that information was distributed across representations.     

Variability in Reading Scores on a Given Level of Intelligence Test Scores

ABSTRACT

Previous studies have shown that several key variables influence student achievement in geometry, but no research has been conducted to determine how these variables interact. A model of achievement in geometry was tested on a sample of 102 high school students. Structural equation modeling was used to test hypothesized relationships among variables linked to successful problem solving in geometry. These variables, including motivation, achievement emotions, pictorial representation, and categorization skills, were examined for their influence on geometry achievement. Results indicated that the model fit well. Achievement emotions, specifically boredom and enjoyment, had a significant influence on student motivation. Student motivation influenced students’ use of pictorial representations and achievement. Pictorial representation also directly influenced achievement. Categorization skills had a significant influence on pictorial representations and student achievement. The implications of these findings for geometry instruction and for future research are discussed.     

Understanding pictorial information in biology: students’ cognitive activities and visual reading strategies

ABSTRACT

In classroom, scientific contents are increasingly communicated through visual forms of representations. Students’ learning outcomes rely on their ability to read and understand pictorial information. Understanding pictorial information in biology requires cognitive effort and can be challenging to students. Yet evidence-based knowledge about students’ visual reading strategies during the process of understanding pictorial information is pending. Therefore, 42 students at the age of 14–15 were asked to think aloud while trying to understand visual representations of the blood circulatory system and the patellar reflex. A category system was developed differentiating 16 categories of cognitive activities. A Principal Component Analysis revealed two underlying patterns of activities that can be interpreted as visual reading strategies: 1. Inferences predominated by using a problem-solving schema; 2. Inferences predominated by recall of prior content knowledge. Each pattern consists of a specific set of cognitive activities that reflect selection, organisation and integration of pictorial information as well as different levels of expertise. The results give detailed insights into cognitive activities of students who were required to understand the pictorial information of complex organ systems. They provide an evidence-based foundation to derive instructional aids that can promote students pictorial-information-based learning on different levels of expertise.     

Pictorial presentation and review strategies in science learning

To test the effects of pictorial presentation and a pictorial review task on science learning, all-verbal or verbal-pictorial presentation conditions were followed by either pictorial practice or a control task. The 96 undergraduate participants were randomly assigned to one of the four conditions presented on a computer-assisted instruction terminal. The groups differed significantly on a pictorial recognition test but not on a verbal posttest. The results favored the pictorial presentation with review condition. Experiment Two tested the effectiveness of the pictorial review task compared to a read-twice control. The same all-verbal presentation condition was given to 50 undergraduates who were then randomly assigned to the pictorial review task or to the re-read condition. The pictorial review condition facilitated performance on the pictorial posttest relative to the re-read condition and produced more favorable attitudes as well.     

Effects of representation sequences and spatial ability on students’ scientific understandings about the mechanism of breathing

The purpose of this study was to investigate the effects of representation sequences and spatial ability on students’ scientific understandings about the mechanism of breathing in human beings. 130 seventh graders were assigned to two groups with different sequential combinations of static and dynamic representations: SD group (i.e., viewing static representations and then dynamic ones), and DS group (i.e., viewing dynamic representations and then static ones). Among them, 16 students (8 from each group) with different levels of prior knowledge and spatial ability were interviewed. Data sources included a spatial ability test, pre- and post-tests of scientific understandings (involving factual, conceptual, and spatial knowledge), and semi-structured interviews. The statistical results indicated that the SD sequence helped students gain significantly more factual knowledge. The significant interaction effects further suggested that while the representation sequences had no effect on students with low spatial ability, high spatial ability students in the SD group outperformed than their counterparts in DS group on the items of the conceptual and spatial knowledge. Additionally, the analysis of interviews indicated that the representation sequences could affect the foci of students’ explanations and shape their perceptions about the representations. The results suggested interplays among representation sequences, spatial ability, and students’ understandings, and provided insight into the design and arrangement of multiple representations for science learning.     

Students’ Learning Activities While Studying Biological Process Diagrams

Process diagrams describe how a system functions (e.g. photosynthesis) and are an important type of representation in Biology education. In the present study, we examined students’ learning activities while studying process diagrams, related to their resulting comprehension of these diagrams. Each student completed three learning tasks. Verbal data and eye-tracking data were collected as indications of students’ learning activities. For the verbal data, we applied a fine-grained coding scheme to optimally describe students’ learning activities. For the eye-tracking data, we used fixation time and transitions between areas of interest in the process diagrams as indices of learning activities. Various learning activities while studying process diagrams were found that distinguished between more and less successful students. Results showed that between-student variance in comprehension score was highly predicted by meaning making of the process arrows (80%) and fixation time in the main area (65%). Students employed successful learning activities consistently across learning tasks. Furthermore, compared to unsuccessful students, successful students used a more coherent approach of interrelated learning activities for comprehending process diagrams.     

The Effect of Two-dimensional and Stereoscopic Presentation on Middle School Students’ Performance of Spatial Cognition Tasks

We investigated whether and how student performance on three types of spatial cognition tasks differs when worked with two-dimensional or stereoscopic representations. We recruited nineteen middle school students visiting a planetarium in a large Midwestern American city and analyzed their performance on a series of spatial cognition tasks in terms of response accuracy and task completion time. Results show that response accuracy did not differ between the two types of representations while task completion time was significantly greater with the stereoscopic representations. The completion time increased as the number of mental manipulations of 3D objects increased in the tasks. Post-interviews provide evidence that some students continued to think of stereoscopic representations as two-dimensional. Based on cognitive load and cue theories, we interpret that, in the absence of pictorial depth cues, students may need more time to be familiar with stereoscopic representations for optimal performance. In light of these results, we discuss potential uses of stereoscopic representations for science learning.     

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.