Use Of Multiple Representations Research Articles

Effect of instructional environment on physics students’ representational skills

In a recent study we showed that physics students' problem-solving performance can depend strongly on problem representation, and that giving students a choice of problem representation can have a significant impact on their performance [P. B. Kohl and N. D. Finklestein, Phys. Rev. ST. Phys. Educ. Res. 1, 010104 (2005)] In this paper, we continue that study in an attempt to separate the effect of instructional technique from the effect of content area. We determine that students in a reform-style introductory physics course are learning a broader set of representational skills than those in a more traditional course. We also analyze the representations used in each course studied and find that the reformed course makes use of a richer set of representations than the traditional course and also makes more frequent use of multiple representations. We infer that this difference in instruction is the source of the broader student skills. These results provide insight into how macrolevel features of a course can influence student skills, complementary to the microlevel picture provided by the first study.

'Lesson Rainbow': the use of multiple representations in an Internet-based, discipline-integrated science lesson

This paper presents the development and evaluation of a web-based lesson— Lesson Rainbow. This lesson features multiple representations (MRs), which purposefully deliver concepts in relation to distinctive disciplinary subject areas through story-based animations that are closely related to learners’ life experiences. The researchers selected 58 2nd-year junior high school students as the participants (32 males and 26 females). A quasi-experimental method together with semi-structured interviews was utilised. This research project was intended to investigate students’ conceptual progress, and to evaluate the use of MRs and of situated learning components in the design of Lesson Rainbow. The statistical results indicated that: (1) students’ science concepts significantly increased ( t = 3.84, p < 0.01) through the use of Lesson Rainbow, and (2) students thought that the use of MRs in this web-based lesson was an effective pedagogical tool inasmuch as it allows for the learning of specific theoretical viewpoints in addition to the necessary background information. Lesson Rainbow employing MRs helps learners to understand the meanings of, and interrelationships between, different kinds of external representations. This kind of design facilitates their understanding of the correspondence between abstract symbolic expressions and real-world situations.

High School Students’ Conceptual Coherence of Qualitative Knowledge in the Case of the Force Concept

High School Students’ Conceptual Coherence of Qualitative Knowledge in the Case of the Force Concept

Designing Dynamic Online Lessons with Multimedia Representations

The focus of this paper is on the use of multimedia representations in the online lesson. The information presented here may be of interest to online instructors with varied levels of experience, yet it is geared more toward those who are new to online teaching. A central feature of this paper is the importance of the lesson plan, which can include identification of how multimedia will be used to create instructional messages for the lesson. The potential exists to increase the quality of instruction through the careful use of static and dynamic multimedia representations. Support for the use of multiple representations is documented in the research literature. The Journal of Educators Online, Volume 2, Number 1, January 2005

Conceptual change in learning genetics: an ontological perspective

This article examines conceptual learning of genetics in a Year 10 Australian classroom from an ontological perspective. The study was part of a larger research project about teaching and learning genetics with computer‐based multiple representations. Genetics is an important but difficult topic to teach and learn at school. The study used an interpretive research approach with a case‐study design. Over six weeks, the science teacher taught genetics and engaged his students in computing activities of BioLogica, an interactive program that features multiple representations. Data were collected from multiple sources including classroom observations, interviews and online tests. Data analyses and interpretations indicated that gene conceptions of most students were not sophisticated and that they did not have radical conceptual change that involves a shift across the ontological categories of matter and processes. The findings were largely consistent with students' prior knowledge and the teacher's teaching. The authors highlight the role of the classroom teacher and the use of multiple representations in fostering ontological conceptual change and suggest some directions for further research.

Engaging Students through Technology

The use of technology provides an effective way for promoting multiple representations in problem solving and mathematics. Multiple representations allow students to experience different ways of thinking, develop better insights and understandings of problem situations, and increase comprehension about mathematical concepts. Even with all the benefits of multiple representations, however, teachers find it difficult to incorporate open-ended problem solving that capitalizes on these representations because of time constraints and limitations of traditional mathematics teaching. Technology can become a vital and exciting tool in allowing students to explore multiple representations and mathematical situations and relationships (NCTM 2000). Technology empowers students who may have limited mathematical knowledge and limited symbolic and numeric manipulation skills to investigate problem situations. Technology not only frees the students from tedious and repetitive computations but actually encourages the use of multiple representations. Students can easily move from a spreadsheet to a graph or geometry software in their quest for solutions to a given problem. When supported by the teacher, these tools of technology provide students with opportunities to investigate and manipulate mathematical situations to observe, experiment with, and make conjectures about patterns, relationships, tendencies, and generalizations. Teachers should emphasize and encourage the use of multiple representations to support students' thinking and understanding of concepts and problem-solving situations in all areas of mathematics.

A Case Study of Teacher Beliefs on Students' Beliefs about Multiple Representations

The mathematics education community, in its call for reform, underscores the importance of mathematics instruction emphasizing the use of multiple representations in the presentation of concepts. The focus of the study was how teacher beliefs affect their ability to implement a multiple representations curriculum. The novice instructor's attitude remained neutral while the experienced instructor's attitude remained somewhat positive. Of the eight students in the study, six of them showed a more positive attitude towards technology use and multiple representations by the end of the semester. The students increased their calculator use in both classes, particularly in the experienced teacher's class. Implications for further research were that teacher training is essential if reform curricula are to be properly implemented.

Students' Understanding of the Particulate Nature of Matter

The particulate nature of matter is identified in science education standards as one of the fundamental concepts that students should understand at the middle school level. However, science education research in indicates that secondary school students have difficulties understanding the structure of matter. The purpose of the study is to describe how engaging in an extended project‐based unit developed urban middle school students' understanding of the particulate nature of matter. Multiple sources of data were collected, including pre‐ and posttests, interviews, students' drawings, and video recordings of classroom activities. One teacher and her five classes were chosen for an indepth study. Analyses of data show that after experiencing a series of learning activities the majority of students acquired substantial content knowledge. Additionally, the finding indicates that students' understanding of the particulate nature of matter improved over time and that they retained and even reinforced their understanding after applying the concept. Discussions of the design features of curriculum and the teacher's use of multiple representations might provide insights into the effectiveness of learning activities in the unit.

Situational knowledge in physics: The case of electrodynamics

AbstractMajor difficulties for a novice physics problem solver are how to interpret new problems and how to combine information given in the problem with information already known. A domain expert, by contrast, has the knowledge to take full advantage of problem features at a glance. It takes a long period of practice to acquire such situational knowledge, and it would be desirable for this to be taught more effectively. As a first step, this requires information on how situational knowledge differs across individuals of different competence levels. Related research on mental models and problem representations does not give a direct view on the knowledge subjects have of situations before being confronted with the problem. To assess situational knowledge more directly, we asked participants to respond to physics formulas (from the field of electrodynamics) by describing relevant problem situations. We compared physics problem descriptions by experts (n = 6) and by proficient (n = 6) and less proficient (n = 6) novices. We analyzed the situations that were described at the levels of words, sentences, and complete descriptions. Results indicate that competence is related to the structure of problem situations rather than the use of particular concepts, and that the differences in the use of multiple representations are more prominent than differences in the use of one specific kind of representation. Results also indicate that the differences between experts and novices are along different dimensions than the differences between more and less proficient novices. Implications for teaching are discussed. © 2002 Wiley Periodicals, Inc. J Res Sci Teach 39: 928–951, 2002

Frontal brain lesions affect the use of advance information during response planning.

This study examined the nature of the response programming deficit after frontal cortex lesions through the effects of advance information on sequence initiation time. Nine patients with unilateral frontal lesions, 9 patients with temporal lesions, and 9 controls performed a sequential key-press task involving 4 rapid choice responses to a 4-letter stimulus. Three conditions manipulated the number of responses that subjects knew in advance. The frontal group showed slow initiation times in all conditions. Knowing the first response produced an acceleration of initiation time in all 3 groups. However, knowing 3 responses in advance instead of 1 further accelerated initiation time in the control and temporal groups but not in the frontal group. These results indicate that frontal lesions impair the use of multiple representations during programming. This suggests that the attentional control of response selection is an important element of the response planning deficit.

Frontal brain lesions affect the use of advance information during response planning.

This study examined the nature of the response programming deficit after frontal cortex lesions through the effects of advance information on sequence initiation time. Nine patients with unilateral frontal lesions, 9 patients with temporal lesions, and 9 controls performed a sequential key-press task involving 4 rapid choice responses to a 4-letter stimulus. Three conditions manipulated the number of responses that subjects knew in advance. The frontal group showed slow initiation times in all conditions. Knowing the first response produced an acceleration of initiation time in all 3 groups. However, knowing 3 responses in advance instead of 1 further accelerated initiation time in the control and temporal groups but not in the frontal group. These results indicate that frontal lesions impair the use of multiple representations during programming. This suggests that the attentional control of response selection is an important element of the response planning deficit.

Cross-National Comparison of Representational Competence

Flexible use of multiple representations has been described as a key component of competent mathematical thinking and problem solving. In this study, 6th-grade American students are compared to 3 samples of Asian (Chinese, Japanese, and Taiwanese) 6th graders to determine if the well-documented mathematical achievement of students from these Asian nations may be due in part to a greater understanding of mathematical representations. The results show that, among all groups, Chinese students generally scored highest on the representation tasks and, except on items about the visual representations of fractions, all Asian samples scored significantly higher than the American sample. The results are discussed in terms of possible instructional antecedents and textbook differences.

Preservice Teachers' Use of Multiple Representations In Solving Arithmetic Mean Problems

The development of preservice teachers' views of various mathematical concepts involves building a repertoire of flexible representations of the concepts they teach. In this study, science and mathematics preservice teachers (n = 19) were asked to solve graphical and numerical problems involving the arithmetic mean and to provide two different solutions for each problem. Background information about the preservice teachers was obtained, including subject area specialty, type of statistics courses previously taken, type of science laboratory courses previously taken, and prior experience with real data outside the classroom. In solving the problems, some participants presented two different methods: algorithmic computation and balancing deviations about the mean. A significant difference was found between science and mathematics preservice teachers in the use of balancing deviations to solve the problems but not in the use of the computational algorithm.

Robust speech recognition using the modulation spectrogram

The performance of present-day automatic speech recognition (ASR) systems is seriously compromised by levels of acoustic interference (such as additive noise and room reverberation) representative of real-world speaking conditions. Studies on the perception of speech by human listeners suggest that recognizer robustness might be improved by focusing on temporal structure in the speech signal that appears as low-frequency (below 16 Hz) amplitude modulations in subband channels following critical-band frequency analysis. A speech representation that emphasizes this temporal structure, the “modulation spectrogram”, has been developed. Visual displays of speech produced with the modulation spectrogram are relatively stable in the presence of high levels of background noise and reverberation. Using the modulation spectrogram as a front end for ASR provides a significant improvement in performance on highly reverberant speech. When the modulation spectrogram is used in combination with log-RASTA-PLP (log RelAtive SpecTrAl Perceptual Linear Predictive analysis) performance over a range of noisy and reverberant conditions is significantly improved, suggesting that the use of multiple representations is another promising method for improving the robustness of ASR systems.

Supporting Innovation: The Impact of a Teacher's Conceptions of Functions on His Implementation of a Reform Curriculum

In this study we investigate the content conceptions of an experienced high school mathematics teacher and link those conceptions to their role in the teacher's first implementation of reform-oriented curricular materials during a 6-week unit on functions. The teacher communicated deep and integrated conceptions of functions, dominated by graphical representations and covariation notions. These themes played crucial roles in the teacher's practice when he emphasized the use of multiple representations to understand dependence patterns in data. The teacher's well-articulated ideas about features of a variety of relationships in different representations supported meaningful discussions with students during the implementation of an unfamiliar classroom approach to functions.

Supporting Innovation: The Impact of a Teacher's Conceptions of Functions on His Implementation of a Reform Curriculum

In this study we investigate the content conceptions of an experienced high school mathematics teacher and link those conceptions to their role in the teacher's first implementation of reform-oriented curricular materials during a 6-week unit on functions. The teacher communicated deep and integrated conceptions of functions, dominated by graphical representations and covariation notions. These themes played crucial roles in the teacher's practice when he emphasized the use of multiple representations to understand dependence patterns in data. The teacher's well-articulated ideas about features of a variety of relationships in different representations supported meaningful discussions with students during the implementation of an unfamiliar classroom approach to functions.

CaMeRa: A computational model of multiple representations

This research aims to clarify, by constructing and testing a computer simulation, the use of multiple representations in problem solving, focusing on their role in visual reasoning. The model is motivated by extensive experimental evidence in the literature for the features it incorporates, but this article focuses on the system's structure. We illustrate the model's behavior by simulating the cognitive and perceptual processes of an economics expert as he teaches some well-learned economics principles while drawing a graph on a blackboard. Data in the experimental literature and concurrent verbal protocols were used to guide construction of a linked production system and parallel network, CaMeRa (Computation with Multiple Representations), that employs a “Mind's Eye” representation for pictorial information, consisting of a bitmap and associated node-link structures. Propositional list structures are used to represent verbal information and reasoning. Small individual pieces from the different representations are linked on a sequential and temporary basis to form a reasoning and inferencing chain, using visually encoded information recalled to the Mind's Eye from long-term memory and from cues recognized on an external display. CaMeRa, like the expert, uses the diagrammatic and verbal representations to complement one another, thus exploiting the unique advantages of each.

CaMeRa: A Computational Model of Multiple Representations

This research aims to clarify, by constructing and testing a computer simulation, the use of multiple representations in problem solving, focusing on their role in visual reasoning. The model is motivated by extensive experimental evidence in the literature for the features it incorporates, but this article focuses on the system's structure. We illustrate the model's behavior by simulating the cognitive and perceptual processes of an economics expert as he teaches some well‐learned economics principles while drawing a graph on a blackboard. Data in the experimental literature and concurrent verbal protocols were used to guide construction of a linked production system and parallel network, CaMeRa (Computation with Multiple Representations), that employs a “Mind's Eye” representation for pictorial information, consisting of a bitmap and associated node‐link structures. Propositional list structures are used to represent verbal information and reasoning. Small individual pieces from the different representations are linked on a sequential and temporary basis to form a reasoning and inferencing chain, using visually encoded information recalled to the Mind's Eye from long‐term memory and from cues recognized on an external display. CaMeRa, like the expert, uses the diagrammatic and verbal representations to complement one another, thus exploiting the unique advantages of each.

Multiple Representations—Using Different Perspectives to Form a Clearer Picture

The concept of function is central to the study of precalculus and calculus. As educators explore ways to improve and invigorate the teaching of mathematics at the secondary and undergraduate levels, and as technology becomes more common in the classroom, the use of multiple representations to study functions and other concepts is gaining more attention in the curriculum. Because each representation emphasizes and suppresses various aspects of a concept, we believe that students gain a more thorough understanding of a function if it is explored using numerical, graphical, and analytical methods.

Detecting Framing Effects in Financial Statements*

Abstract. In this study, we address the question of what kinds of cognitive representations auditors use in a situation of potential financial statement fraud. We divide the problem of detecting fraud into two parts: detecting the frame management has constructed to mask the fraud, and detecting the fraud. We examine two ways proposed by Kahneman and Tversky (1986) for detecting a frame: (1) use of multiple representations that provide alternative interpretations of data in the financial statements; and (2) use of a procedure that transforms financial statement data into a standard representation.Twenty‐four audit partners served as participants in the study. Each partner conducted a simulation of a concurring partner review. All auditors reviewed four cases in which management had created a misleading description of the company (a frame) and a financial statement fraud.The results support Kahneman and Tversky's proposal that frames can be detected by transforming a problem into a standard representation. Auditors who used a standard representation successfully detected management's frame, aggregated the items, and detected fraud in all four cases. Auditors who used a standard representation followed a procedure specified by generally accepted auditing standards (Canadian Institute of Chartered Accountants 1988, American Institute of Certified Public Accountants 1984) for aggregating items. Auditors who used multiple representations detected management's frame on all four cases. These auditors, however, did not use the aggregation procedure specified by auditing standards and failed to detect the fraud on all four cases.