Graph Interpretation Research Articles

Some New Graph Interpretations of Padovan Numbers

Padovan numbers and Perrin numbers belong to the family of numbers of the Fibonacci type and they are well described in the literature. In this paper, by studying independent (1,2)-dominating sets in paths and cycles, we obtain new binomial formulas for Padovan and Perrin numbers. As a consequence of graph interpretation, we propose a new dependence between Padovan and Perrin numbers. By studying special independent (1,2)-dominating sets in a composition of two graphs, we define Padovan polynomials of graphs. By the fact that every independent (1,2)-dominating set includes the set of leaves as a subset, in some cases a symmetric structure of the independent (1,2)-dominating set can be used.

Extraction of logical networks during decompiling transistor-level CMOS circuit descriptions

Objectives. The problem of restoring the functional description of digital VLSI devices presented at the transistor level is considered. The objective of the work is to develop means for extraction of blocks representing logical networks from two-level descriptions of CMOS circuits at the transistor level, which were obtained as a result of recognition (extraction) of subcircuits that implement logic elements.Methods. Graph based methods and software tools are proposed for extracting a connected blocks representing a logical network from two-level descriptions of a transistor circuits in SPICE format. In the graph interpretation, the task is reduced to constructing a labeled directed graph of a logical network based on a labeled undirected bipartite graph specifying a two-level description of the transistor circuit.Results. The proposed method makes it possible to identify lexicographically ranked logical networks, from which a transition is made to logical equations that specify the functions implemented at the outputs of the resulting networks. Software tools have been developed that provide the generation of a hierarchical description in SPICE format that implements the original circuit at the transistor level, as well as descriptions of found logical networks in the SF language of hierarchical structural and functional descriptions of discrete devices and in high-level languages (VHDL and Verilog).Conclusion. The developed methods are implemented in C++, included in the program for decompiling transistor CMOS circuits and tested within it on practical examples of transistor-level circuits. The paper provides examples of reverse engineering of some practical transistor circuits.

Analysis of Kinematics Graph Interpretation Skills Using RapidMiner

This study explores the application of data mining techniques in physics education research, focusing on the analysis of kinematics graph interpretation skills. The research had two main objectives: to demonstrate the utility of RapidMiner, a data mining tool, in analyzing educational data, and to compare its effectiveness with traditional item analysis methods. Fifty-nine Grade-10 students at Chiang Mai University Demonstration School completed the Test of Understanding Graphs in Kinematics (TUG-K) before and after participating in a problem-based learning module integrating high-speed video analysis. Traditional statistical analysis revealed significant improvement in student performance (p<0.001, effect size 0.76). Association rule mining, conducted using RapidMiner, uncovered key relationships between test items that were not apparent through traditional analysis. These relationships provided insights into common student misconceptions and areas requiring targeted instruction. The study demonstrates the potential of advanced data mining techniques to reveal deeper patterns in educational data compared to conventional item analysis methods. This novel application of RapidMiner in physics education research offers a promising approach for more detailed analysis of student understanding, potentially informing more effective teaching strategies and curriculum design in physics education.

PELATIHAN PENGGUNAAN APLIKASI GEOGEBRA PADA MATERI PERSAMAAN GARIS LURUS

The background for this community service activity is Pakis Islamic Middle School, which is one of the schools that has not yet implemented too many ICT-based learning models. This is due to the lack of projector facilities provided in each class as a medium for implementing ICT-based learning models. One learning model that is suitable to be applied based on the material being studied is to use the Geogebra application. Students can see the interpretation of graphs through the application. This service activity is carried out using the training method for trainees who are studying straight line equations. During the activity, monitoring was also carried out by the service team and evaluation through the results of test scores and questionnaires. The result of this community service activity is that the test results of the trainees found an average of 83.2. From this average, the training can be said to be successful because it is above the KKM standard in mathematics. While the value of the questionnaire was found that 92% of the training participants gave a positive response to using the Geogebra application on straight line equations. The advantages that trainees find are graphs that can be generated quickly, the GeoGebra application can provide a clearer visual experience to trainees in understanding mathematical concepts, can be used as an evaluation to ensure that the graphs that have been made are correct.

M-Distance-regular graphs and their relation to multivariate P-polynomial association schemes

An association scheme is P-polynomial if and only if it consists of the distance matrices of a distance-regular graph. Recently, bivariate P-polynomial association schemes of type (α,β) were introduced by Bernard et al., and multivariate P-polynomial association schemes were later defined by Bannai et al. In this paper, the notion of m-distance-regular graph is defined and shown to give a graph interpretation of the multivariate P-polynomial association schemes. Various examples are provided. Refined structures and additional constraints for multivariate P-polynomial association schemes and m-distance-regular graphs are also considered. In particular, bivariate P-polynomial schemes of type (α,β) are discussed, and their connection to 2-distance-regular graphs is established.

ALTMAN: A Novel Method for Cell Cycle Analysis.

Accurate analysis of S-phase fraction is crucial for the assessment of cell proliferation levels, tumor malignancy and prognostic effects of treatment. Most of the currently developed methods for S-phase cell analysis rely on flow cytometric analysis of DNA content determination. However, the lack of standardized procedures for sample analysis and interpretation of cell cycle fitting graphs poses a significant limitation in clinical practice for utilizing flow cytometry to measure the cell cycle based on DNA content. Herein, we developed an approach for analyzing S-phase cells based on telomerase activity determination. Briefly, this approach distinguishes S-phase cells in cell populations via direct fluorescence tracking of telomerase activity within individual cells. The dynamic analysis of telomerase activity in different cell cycles was made possible by the ALTMAN strategy developed in our previous studies, which has been successfully employed to distinguish S-phase cells in cultured cells. This method offers a novel avenue for the assessment of cell cycle status and the evaluation of the proliferation status of tumor cells and the prognosis effect of tumor patients via analyzing the differences in telomerase activity during different cell cycle processes.

Analysis of Differences in Graph Interpretation Understanding of Grade X Students of Madrasah Aliyah Negeri (MAN) 1 Malang on Kinematics Topic Based on Gender

This study aims to analyze the conception profile of MAN 1 Malang students on the subject matter of kinematics based on gender using multiple choice tests. The type of research used is quantitative descriptive research. This research was conducted on 94 students (47 male and 47 female students) of MAN 1 Malang. Quantitative data was obtained from the score of correct answers from students when answering questions. The method used was survey method. After the validation test and reliability test, there were 20 questions categorized as valid and could be used for research. The questions that passed the test were then given to students to do in the form of a written test. The results showed that students' understanding of the concept of kinematics was categorized as very low. This is due to the average student concept understanding score of 24.04. Based on the data analysis that has been done, it is concluded that there is no difference in concept understanding between male students and female students.

Practice rehearsal pairs with dynamic video media: Improving students' kinematics graph interpretation skills

Practice rehearsal pairs with dynamic video media: Improving students' kinematics graph interpretation skills

A New Approach to Detect Hand-Drawn Dashed Lines in Engineering Sketches

Sketched drawings sometimes include non-solid lines drawn as sets of consecutive strokes. They represent dashed lines, which are useful for various purposes. Recognizing such dashed lines while parsing drawings is reasonably straightforward if they are outlined with a ruler and compass but becomes challenging when they are hand-drawn. The problem is manageable if the strokes are drawn consecutively so we can leverage the entire sequence. However, it becomes more challenging if they are drawn unordered, and/or we do not have access to the sequence (like in batch vectorization). In this paper, we describe a new approach to identify groups of strokes as depicting single hand-drawn dashed lines. The approach does not use sequence information and is tolerant with irregularities and imprecisions of the strokes. Our goal is to identify hidden lines of sketched engineering line-drawings, which would enable the interpretation of line-drawings with hidden edges, which currently cannot be efficiently vectorized. We speculate that other fields like hand-drawn graph interpretation may also benefit from our approach.

Students’ preparation in IELTS Writing Task 1: How to write a summary of visual information

The International English Language Testing System (IELTS) Writing Task 1 is used to test participants' ability to select and report main ideas, describe and compare data, identify trends in factual information, or describe a process. This research describes the types of questions in IELTS Writing Task 1 and how to write a summary of visual information usually in the form of a graph, chart, or diagram in IELTS Writing Task 1. This research uses a descriptive qualitative approach. The analysis shows that IELTS Academic Writing Task 1 emphasizes graph interpretation and analysis. In this activity, verbal proficiency must be multiplied by the ability to comprehend and represent information as graphs (graphicacy). The provided information may be directly reflective of what we see (as in pictures or drawings) or more abstract, such as spatial (maps, plans, and diagrams) or numerical (charts, graphs, and tables) information (as in tables and graphs. There are several types of IELTS Writing Task 1, for example, pie charts, bar charts, bar graphs, line graphs, tables, maps, diagram processes, line and bar charts, also pie and bar charts. Each form of data visualization has its way of describing it. To complete the IELTS Writing Task 1, participants are required to write a minimum of 150 words of writing or an essay. We can divide the number of words into 3 paragraphs (introduction, body, and conclusion) to make it easier to write an essay according to the data presented. The IELTS Writing Task 1 can be fairly challenging, particularly if we have not prepared. Overcoming these challenges requires good preparation, consistent practice, and a deep understanding of the IELTS format, structure, and requirements.

Improved Metacognition Reviewed Based on Mathematical Resilience through Flipped Classroom

This study investigates students’ interpretation of kinematics graphs. A total of 121 students taking a physics class were selected to solve problems involving the analysis of graphs depicting position, velocity, and acceleration versus time. Conducting interviews aimed to uncover students’ difficulties while solving kinematics problems. The result emphasizes that students were able to determine velocity (if given positiontime graph) and acceleration (if given velocity-time graph). However, students faced difficulty in selecting textual descriptions and choosing the corresponding graph when given a kinematics graph. These findings suggest that in learning physics, there should be an increased emphasis on deep analysis of kinematics graphs. Keywords: flipped classroom, mathematical resilience, metacognition

Mathematical Connection of Prospective Mathematics Teachers in Constructing Graph-Based Real-life Problem

Mathematical connection ability is one of the important abilities that students should have. Connecting real-world problems to mathematical concepts can make learning mathematics more meaningful for students. In everyday life, there is a lot of information presented in graphs. Graphing competence consists of graph interpretation and graph construction. Even though graph construction is a crucial yet neglected skill. From the previous explanation, the purpose of this study is to describe the ability of students to construct a graph based on a real-life problem. This descriptive qualitative study is collected from 37 prospective mathematics teachers in a university. All students had to answer one question about constructing a graph based on a real-life situation given. The result of this study, students’ mathematical connection between everyday life and mathematics itself was still low. Using indicators in this study: 10.81% of the students could not represent the real-life situation in the graph that they constructed; 75.68% of the students made graphs but many features of the graphs did not represent the situation well; and 13.51% of the students made more representing graph but some features of the graph did not relevant. Therefore, in mathematics learning the teacher should give more experience to the students to explore everyday life situations using mathematics and encourage students to write their thoughts down so that mathematics becomes meaningful for students. Keywords: constructing graph-based real-life problem, mathematical connection, prospective mathematics teachers

How Students Understand Graphical Patterns: Fine-Grained, Intuitive Knowledge Used in Graphical Thinking

Engaging in the construction and interpretation of graphs is a complex process involving concerted activation of context-specific cognitive resources. As students engage in this process, they apply fine-grained, intuitive ideas to graphical patterns: graphical forms. Using data involving pairs of students constructing and interpreting graphs, we expand on the current knowledge base on graphical forms to contribute an empirically based catalog. We also situate our cognitively oriented work in relation to research that has emphasized (a) misconceptions and (b) social practices. In addition, we draw connections to the research on covariational reasoning. We end with implications regarding how graphical forms contribute to our understanding of students’ graphical reasoning and how instructors can support students.

Graph Out Loud: Pre-Service Teachers' Data Decisions and Interpretations of CBM Progress Graphs.

Data-based instruction (DBI) is a process in which teachers use progress data to make ongoing instructional decisions for students with learning disabilities. Curriculum-based measurement (CBM) is a common form of progress monitoring, and CBM data are placed on a graph to guide decision-making. Despite the central role that graph interpretation plays in the successful implementation of DBI, relatively little attention has been devoted to investigating this skill among special education teachers. In the present study, we examined the data decisions of 32 pre-service special education teachers (29 females and 3 males). Participants viewed data presented sequentially on CBM progress graphs and used a think-aloud procedure to explain their reasoning each time they indicated they would make instructional changes. We also asked participants to make the same type of decisions in response to static CBM progress graphs depicting 10 weeks of data. Overall, there was inconsistency in pre-service teachers' responses related to when or why they would make an instructional change. Decisions were often influenced by graph-related features, such as variability in the data. Furthermore, responses suggested misunderstandings that led to premature instructional change decisions and reliance on individual data points.

An introductory review on the application of principal component analysis in the data exploration of the chemical analysis of food samples.

Principal component analysis (PCA) is currently one of the most used multivariate data analysis techniques for evaluating information from food analysis. In this review, a brief introduction to the theoretical principles that underlie PCA will be given, in addition to presenting the most commonly used computer programs. An example from the literature was discussed to illustrate the use of this chemometric tool and interpretation of graphs and parameters obtained. A list of recently published articles will also be presented, in order to show the applicability and potential of the technique in the food analysis field.

Understanding and overcoming students’ difficulties in interpreting graphs: insights from a racing car problem

The study investigates university students’ difficulties in interpreting graphs through the analysis of their responses to the modified PISA racing car problem. The impact of adding a distractor that is appealing to students and supplementary questions to enhance students’ graph understanding is explored. Eye-tracking technology was used to capture participants’ visual attention during the task. The findings highlight the challenges of treating graphs as pictures and the benefits of incorporating additional questions to improve students’ comprehension. The study emphasizes the need for instructional strategies that address intuitive reasoning and promote reflective thinking in graph interpretation.

Developing statistical literacy in high school through real data and exponential functions: an educational evaluation

The use of real data for the interpretation of statistical graphs encompassing exponential function was investigated. The goal was to develop, apply and assess an educational product composed of a website that simulates exponential functions, using real data for the interpretation of statistical graphs. The issue of how to develop statistical literacy for the interpretation of graphs involving exponential function in high school students using real data was addressed. The theoretical basis of Vygotsky's socio-interactionism was used. The application of the product, which was contextualized in a didactic sequence, was carried out in a class of the first year of high school. The collected data were treated qualitatively, based on the presuppositions of Bardin's content analysis; texts resulting from the application of the didactic sequence served as sources of analysis. Four categories were generated from the analysis of the texts: students' difficulty, students' protagonist, mathematics and exponential functions, and educational product and didactic sequence.

‘But, is it supposed to be a straight line?’ Scaffolding students’ experiences with pressure sensors and material resistance in a high school biology classroom

ABSTRACT This case study examines how material resistance (limitations posed by the physical world) and graph interpretation intersected during a high school biology investigation using digital sensors. We use an extended episode from a small group to illustrate how, in an inquiry-based unit, measuring near the resolution limit of a sensor caused scaling issues in graphs. Qualitative videotape analysis focuses on both the students’ attempts to make sense of a perceived lack of variation in the collected data and the teacher's and classroom researchers’ misinterpretation of the students’ difficulties with graph interpretation. We suggest that these educators, though experienced, could have benefited from additional strategies to help them recognise and respond to graph interpretation issues introduced by digital representations of real-world data, and that the students could have benefited from explicit prompts to discuss the limitations of their equipment. We describe several implications for researchers, teachers, and curriculum developers interested in implementing inquiry-based biology investigations using sensor data. We argue that students should be supported to recognise that encountering unexpected results from their investigations and working to understand what these results have to say about the real world is an important and valid part of the practice of real science.

Study of graphs mediated by learning object: a discussion based on initial teacher training

This article presents a study that analyzes a Learning Object (LO) of graph interpretation, conduced with teachers in initial training in the Institutional Program of Scholarships for Teaching Initiation — PIBID. The qualitative empirical study aimed to analyze and discuss pedagogical and exploratory conditions of the LO built in the GeoGebra software. Data were collected from the participants through activities created and shared in the LO, field notebook annotations, observations, records and description of representations. In the organization and analysis of data, the categorization was used. The theoretical framework encompasses reflections on policies for Initial Teacher Training, in interaction with digital alternatives, study of graphs and mathematical visualization. The results suggest that LO, mediated by digital technologies in Mathematics Degree, promotes discussions and reflections regarding future pedagogical possibilities of representation, creativity and construction of mathematical thinking.

Zero-divisor graphs and zero-divisor functors

Inspired by a very recent work of A. Đurić, S. Jevđenić and N. Stopar, we introduce a new definition of zero-divisor graphs attached to rings that includes all of the classical definitions already known in the literature. We provide an interpretation of such graphs by means of a functor that we call zero-divisor functor and which is associated with a family of special equivalence relations fixed beforehand. We thus recover and generalize many known results for zero-divisor graphs and provide a framework which might be useful for further investigations on this topic.