Relevant bibliographies by topics / Mathematical perception

Academic literature on the topic 'Mathematical perception'

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Published: 4 June 2021
Last updated: 28 January 2023

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Journal articles on the topic "Mathematical perception"

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Yayuk, Erna, and Dyah Worowirastri Ekowati. "Disposisi Berpikir Kreatif Matematis Pada Siswa Sekolah Dasar." Scholaria: Jurnal Pendidikan dan Kebudayaan 12, no. 2 (May 27, 2022): 89–95. http://dx.doi.org/10.24246/j.js.2022.v12.i2.p89-95.

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The purpose of this research is to find out the creative thinking disposition of elementary school students in mathematics based on their gender group. The research design used is a descriptive qualitative method. Based on the results of the study, it can be concluded that boys have a high mathematical creative thinking disposition and positive perceptions, boys and girls have the same high mathematical creative thinking disposition and moderate perception, in the category of moderate mathematical disposition and moderate perception, students fewer boys than girls. In male students, moderate mathematical creative thinking disposition and negative perceptions have more numbers than in female students. Furthermore, students who have a low creative thinking disposition and moderate perception are only boys. Students who have low mathematical creative thinking disposition and negative perceptions are only female students. The level of disposition and perception is very influential in the process of learning mathematics. Children who have a high mathematical creative thinking disposition and high perception certainly have a better enthusiasm for learning mathematics than other categories,
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Glasko, A. V. "Mathematical model of melody perception." Mathematical Models and Computer Simulations 7, no. 2 (March 2015): 190–201. http://dx.doi.org/10.1134/s2070048215020064.

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Kim, Pan Soo, and Na Ri Kim. "A Study of Mathematically Gifted Student's Perception of Mathematical Creativity." Journal of Gifted/Talented Education 26, no. 4 (December 31, 2016): 747–61. http://dx.doi.org/10.9722/jgte.2016.26.4.747.

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Anggoro, Bambang Sri. "Analisis Persepsi Siswa SMP terhadap Pembelajaran Matematika ditinjau dari Perbedaan Gender dan Disposisi Berpikir Kreatif Matematis." Al-Jabar : Jurnal Pendidikan Matematika 7, no. 2 (December 20, 2016): 153–66. http://dx.doi.org/10.24042/ajpm.v7i2.30.

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This research is a qualitative research with the qualitative descriptive method. The technique of research subject taking in this research use purposive sampling technique. The subjects of this study amounted to 9 students. Data collection techniques used were questionnaire perception and disposition of students' mathematical creative thinking, observation, interview and documentation of mathematics learning. Data analysis techniques, namely data reduction, data presentation, and conclusions. The validity of data in this study using the content validity, construct validity and reliability and triangulation techniques. According to the results of the study and discussion, the conclusion of this study is Based on the gender and disposition of mathematical creative thinking, the perception of mathematics learning that is produced, that is for high DBKM and positive perception is only found in male students, for high DBKM and medium perception, Male and female students, for medium DBKM and medium perception, female students tend to be more than male students, for medium DBKM and negative perceptions of male students tend to be more than female students, for low DBKM and perception is being Only in boys, and for low DBKM and negative perceptions are only found in female students. The disposition of high mathematical creative thinking and positive perception is very influential on learning mathematics because students who have high DBKM and positive perception will be better in learning mathematics than students who have DBKM and perceptions other than high DBKM and positive perceptions of mathematics learning.
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Demange, Dominique. "“…cupiens mathematicam tractare infra radices metaphysice…” Roger Bacon on Mathematical Abstraction." Revista Española de Filosofía Medieval 28, no. 1 (February 24, 2022): 67–98. http://dx.doi.org/10.21071/refime.v28i1.14034.

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In some passages of the Opus maius and the Opus tertium, Roger Bacon holds that mathematical objects are the immediate and adequate objects of human’s intellect: in our sensible life, the intellect develops mostly around quantity itself. We comprehend quantities and bodies by a perception of the intellect because their forms belong to the intellect, namely, an understanding of mathematical truths is almost innate within us. A natural reaction to these sentences is to deduce a strong Pythagorean or Platonic influence in Roger Bacon’s theory of mathematical knowledge. However, Bacon has always followed Aristotle’s view according to which numbers and figures have no real existence apart from the sensible substances, and universal knowledge comes from sensory experience as well. It appears that Bacon’s claim that quantity is the first object of human's intellect comes from an original reading of a passage of Aristotle’s On Memory and Reminiscence. In this paper, we try to clarify Bacon’s views about mathematical abstraction and intellectual perception of mathematical forms in his Parisian questions on Physics and Liber De causis, the Perspectiva, Opus maius, Opus tertium, the Communia mathematica and the Geometria speculativa. We conclude that Bacon considered mathematical abstraction as a mode of perception of the internal structure of the physical world: mathematical abstraction does not mean for Bacon an act of separation of ideal forms from the sensible matter, but a possibility of intuition of the internal structure of the sensible world itself, a faculty which is necessary for human’s perception of space and time.
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Ersoy, Mehmet, and Miray Dağyar. "A MATHEMATICAL PROBLEM-SOLVING PERCEPTION SCALE FOR SECONDARY SCHOOL STUDENTS: A VALIDITY AND RELIABILITY STUDY." Problems of Education in the 21st Century 80, no. 5 (October 25, 2022): 693–707. http://dx.doi.org/10.33225/pec/22.80.693.

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Determining students' perceptions of problem-solving is an important step to improve their mathematical problem-solving skills. For this reason, the aim of this study was to develop a scale to determine secondary school students’ perceptions of mathematical problem solving. In the study conducted in a basic research model, a scale application, one of the quantitative research methods, was used. The sample of the study consisted of 325 secondary school students. Validity and reliability analyses were made with the data obtained on the sample. Five sub-dimensions of the scale were determined through exploratory factor analysis. Confirmatory factor analyses were performed for these 5 sub-dimensions, and the fit indices were found to range from acceptable to excellent. The explained variance of the “Mathematical Problem-Solving Perception Scale” was 66.15%, and the Cronbach alpha value for the whole scale was .93. It was concluded that the scale would reveal the perception levels of secondary school students towards mathematical problem solving in a valid and reliable way. Keywords: mathematics, perception, problem solving, scale development, secondary school students
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Astalini, Astalini, Darmaji Darmaji, Dwi Agus Kurniawan, and Auliya Ramadhanti. "Mathematical Physics E-Module : Study of Students’ Perception Based on Gender." Journal of Education Technology 6, no. 1 (March 1, 2022): 91. http://dx.doi.org/10.23887/jet.v6i1.42233.

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Mathematics physics is often considered by students as a very difficult subject to learn, one of the causes that makes this happen is the lack of learning media that supports students. In addition, most of the existing media use foreign languages, so that in this case Indonesian language learning media is needed, namely the mathematical physics e-module on vector material which is then seen from student responses based on gender differences. This study aims to analyze students' perceptions of the mathematics physics e-module and to analyze students' perceptions based on gender differences in the mathematics physics e-module. This type of research is survey-based research with a quantitative approach. The population of this study was physics education students who contracted mathematical physics with a sample of 80 students. The instrument used in this study was a student perception questionnaire with 15 questions and an interview sheet with 10 questions. The data analysis technique used in this research is descriptive statistical analysis and inferential data analysis using t-test. The results showed that overall students had a positive perception with a perception value of 60% in the very good category and 40% in the good category, whereas when viewed from the gender difference, male students had a perception value of 76.6% in the very good category and 23, 3% in the good category, for female students 50% in the very good category and 50% in the good category. That is, students with gender differences have striking differences in perceptions. Student perceptions can be used as a determining factor in the selection of open materials. From the results, it can be seen that gender differences can help in assessing the products made so that they will support the learning process and increase student learning motivation.
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Goldstone, Robert L., Tyler Marghetis, Erik Weitnauer, Erin R. Ottmar, and David Landy. "Adapting Perception, Action, and Technology for Mathematical Reasoning." Current Directions in Psychological Science 26, no. 5 (October 2017): 434–41. http://dx.doi.org/10.1177/0963721417704888.

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Formal mathematical reasoning provides an illuminating test case for understanding how humans can think about things that they did not evolve to comprehend. People engage in algebraic reasoning by (1) creating new assemblies of perception and action routines that evolved originally for other purposes (reuse), (2) adapting those routines to better fit the formal requirements of mathematics (adaptation), and (3) designing cultural tools that mesh well with our perception-action routines to create cognitive systems capable of mathematical reasoning (invention). We describe evidence that a major component of proficiency at algebraic reasoning is Rigged Up Perception-Action Systems (RUPAS), via which originally demanding, strategically controlled cognitive tasks are converted into learned, automatically executed perception and action routines. Informed by RUPAS, we have designed, implemented, and partially assessed a computer-based algebra tutoring system called Graspable Math with an aim toward training learners to develop perception-action routines that are intuitive, efficient, and mathematically valid.
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Tanti, Tanti, Astalini Astalini, Darmaji Darmaji, Dwi Agus Kurniawan, and Riska Fitriani. "Student Perception Review from Gender: Electronic Moduls of Mathematical Physics." JPI (Jurnal Pendidikan Indonesia) 11, no. 1 (February 26, 2022): 125–32. http://dx.doi.org/10.23887/jpiundiksha.v11i1.35107.

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The role of technology that continues to develop in the era of globalization, especially in the field of education, demands various innovations in the teaching and learning process to improve the quality of learning in the world of education. However, in learning, some students have negative perceptions that can make students not enthusiastic about participating in learning. Students will have difficulty understanding the material and will impact less than optimal learning outcomes of mathematics and physics in learning. This study examines the differences in students' perceptions based on gender in grades A and B in the physics-mathematics e-module. This type of research is quantitative and is conducted by a survey. The data collection instrument is a perception survey using a Likert scale. Data were analyzed descriptively (mean, median, mode, frequency, and percent) and inferential statistics (hypothesis test: normality and homogeneity tests, and hypothesis tests: independent T-test). Technique The sample is a total sample of 80 students from 2 classes. The result of this research is that there is a significant difference between female students' perceptions with a significance level of 0.049 and a significance level of 0.005 for boys. The key is that the average difference in perception between women and men is lower. Men are more rational in inserting something, while women are more emotional. The results of this study are expected to contribute to educators in improving the quality of learning in an educational institution.
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Rosas, Humberto, Watson Vargas, Alexander Cerón, Darío Domínguez, and Adriana Cárdenas. "A Mathematical Expression for Stereoscopic Depth Perception." Photogrammetric Engineering & Remote Sensing 76, no. 3 (March 1, 2010): 301–6. http://dx.doi.org/10.14358/pers.76.3.301.

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Dissertations / Theses on the topic "Mathematical perception"

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Shafarenko, Leila. "Perception-driven automatic segmentation of colour images using mathematical morphology." Thesis, University of Surrey, 1996. http://epubs.surrey.ac.uk/844450/.

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This thesis is a study of perception-driven automatic segmentation of colour images. Despite immediate practical interest for this task, there exist very few reliable algorithms suitable for unsupervised processing. Most of the results presented in this thesis are based on mathematical morphology. This is a relatively new field which explores topological and geometrical properties of images and which has proven to be useful for image processing. The overview of morphological techniques can be found in chapter 2. A brief overview of segmentation methods is presented in, chapter 3. Only a small proportion of the vast number of publications on the subject is reviewed, namely those that are papers directly relevant to the subject of the thesis. Two novel non-parametric algorithms have been developed by the author for processing colour images. The first one is for processing randomly textured images. It uses a bottom-up segmentation algorithm which takes into consideration both colour and texture properties of the image. An "LUV gradient" is introduced which provides both a colour similarity measure and a basis for applying the watershed transform. The patches of watershed mosaic are merged according to their colour contrast until a termination criterion is met. This criterion is based on the topology of a typical processed image. The resulting algorithm does not require any additional information, be it various thresholds, marker extraction rules and suchlike, thus being suitable for automatic processing. The second algorithm deals with non-textured images and takes into consideration the noise that is present during the image acquisition. The watershed algorithm is used to segment either the 2- or 3-dimensional colour histogram of an image. To comply with the way humans perceive colour, this segmentation has to take place in a perceptually uniform colour space such as the Luv space. To avoid over segmentation, the watershed algorithm has to be applied to a smoothed-out histogram. The noise, however, is inhomogeneous in the Luv space and noise analysis for this space based on experimentally justified assumptions is presented. Both algorithms have been extensively tested on real data and were found to give stable results that are in good accord with human perception.
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Tolmie, Julie. "Visualisation, navigation and mathematical perception : a visual notation for rational numbers mod 1." View thesis entry in Australian Digital Theses Program, 2000. http://thesis.anu.edu.au/public/adt-ANU20020313.101505/index.html.

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Tolmie, Julie, and julie tolmie@techbc ca. "Visualisation, navigation and mathematical perception: a visual notation for rational numbers mod1." The Australian National University. School of Mathematical Sciences, 2000. http://thesis.anu.edu.au./public/adt-ANU20020313.101505.

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There are three main results in this dissertation. The first result is the construction of an abstract visual space for rational numbers mod1, based on the visual primitives, colour, and rational radial direction. Mathematics is performed in this visual notation by defining increasingly refined visual objects from these primitives. In particular, the existence of the Farey tree enumeration of rational numbers mod1 is identified in the texture of a two-dimensional animation. ¶ The second result is a new enumeration of the rational numbers mod1, obtained, and expressed, in abstract visual space, as the visual object coset waves of coset fans on the torus. Its geometry is shown to encode a countably infinite tree structure, whose branches are cosets, nZ+m, where n, m (and k) are integers. These cosets are in geometrical 1-1 correspondence with sequences kn+m, (of denominators) of rational numbers, and with visual subobjects of the torus called coset fans. ¶ The third result is an enumeration in time of the visual hierarchy of the discrete buds of the Mandelbrot boundary by coset waves of coset fans. It is constructed by embedding the circular Farey tree geometrically into the empty internal region of the Mandelbrot set. In particular, coset fans attached to points of the (internal) binary tree index countably infinite sequences of buds on the (external) Mandelbrot boundary.
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Bly, Neil M. "Investigating the Influence of Computer Programs on Perception and Application of Mathematical Skills." BYU ScholarsArchive, 2011. https://scholarsarchive.byu.edu/etd/2651.

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Existing research suggests an intuitive relationship between mathematics and computer programming. These previous studies have focused primarily on the cognitive connection and have ignored the potential impact of programming on an individual's perception and application of mathematical skills. By surveying and interviewing a variety of participants, this study aims to provide a descriptive foundation for the experiential side of cognitive correlations and causalities. These phenomenological accounts, garnered from individual interviews of seven different programmers, indicate four specific areas of interest. First, learning to program provided context for many abstract concepts. Second, programming illustrated the important distinction between understanding the application of math in a specific situation and the execution of a known procedure. Third, programming habits helped participants divide complex problems into more manageable tasks. Finally, the necessity of solving a programming problem provided motivation and eliminated apprehension toward mathematics.
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Franceschiello, Benedetta. "Cortical based mathematical models of geometric optical illusions." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066131/document.

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Cette thèse présente des modèles mathématiques pour la perception visuelle et s'occupe des phénomènes où on reconnait une brèche entre ce qui est représenté et ce qui est perçu. La complétion amodale consiste en percevoir un complètement d'un object qui est partiellement occlus, en opposition avec la complétion modale, dans laquelle on perçoit un object même si ses contours ne sont pas présents dans l'image [Gestalt, 99]. Ces contours, appelés illusoires, sont reconstruits par notre système visuelle et ils sont traités par les cortex visuels primaires (V1/V2) [93]. Des modèles géométriques de l'architecture fonctionnelle de V1 on le retrouve dans le travail de Hoffman [86]. Dans [139] Petitot propose un modèle pour le complètement de contours, équivalent neurale du modèle proposé par Mumford [125]. Dans cet environnement Citti et Sarti introduisent un modèle basé sur l'architecture fonctionnelle de la cortex visuel [28], qui justifie les illusions à un niveau neurale et envisage un modèle neuro-géometrique pour V1. Une autre classe sont les illusions d'optique géométriques (GOI), découvertes dans le XIX siècle [83, 190], qui apparaissent en présence d'une incompatibilité entre ce qui est présent dans l'espace object et le percept. L'idée fondamentale développée ici est que les GOIs se produisent suite à une polarisation de la connectivité de V1/V2, responsable de l'illusion. A partir de [28], où la connectivité qui construit les contours en V1 est modelée avec une métrique sub-Riemannian, on étend cela en disant que pour le GOIs la réponse corticale du stimule initial module la connectivité, en devenant un coefficient pour la métrique. GOIs seront testés avec ce modèle
This thesis presents mathematical models for visual perception and deals with such phenomena in which there is a visible gap between what is represented and what we perceive. A phenomenon which drew the interest most is amodal completion, consisting in perceiving a completion of a partially occluded object, in contrast with the modal completion, where we perceive an object even though its boundaries are not present [Gestalt theory, 99]. Such boundaries reconstructed by our visual system are called illusory contours, and their neural processing is performed by the primary visual cortices (V1/V2), [93]. Geometric models of the functional architecture of primary visual areas date back to Hoffman [86]. In [139] Petitot proposed a model of single boundaries completion through constraint minimization, neural counterpart of the model of Mumford [125]. In this setting Citti and Sarti introduced a cortical based model [28], which justifies the illusions at a neural level and provides a neurogeometrical model for V1. Another class of phenomena are Geometric optical illusions (GOIs), discovered in the XIX century [83, 190], arising in presence of a mismatch of geometrical properties between an item in object space and its associated percept. The fundamental idea developed here is these phenomena arise due to a polarization of the connectivity of V1/V2, responsible for the misperception. Starting from [28] in which the connectivity building contours in V1 is modeled as a sub-Riemannian metric, we extend it claiming that in GOIs the cortical response to the stimulus modulates the connectivity of the cortex, becoming a coefficient for the metric. GOIs will be tested through this model
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Vemulapalli, Smita. "Audio-video based handwritten mathematical content recognition." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/45958.

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Recognizing handwritten mathematical content is a challenging problem, and more so when such content appears in classroom videos. However, given the fact that in such videos the handwritten text and the accompanying audio refer to the same content, a combination of video and audio based recognizer has the potential to significantly improve the content recognition accuracy. This dissertation, using a combination of video and audio based recognizers, focuses on improving the recognition accuracy associated with handwritten mathematical content in such videos. Our approach makes use of a video recognizer as the primary recognizer and a multi-stage assembly, developed as part of this research, is used to facilitate effective combination with an audio recognizer. Specifically, we address the following challenges related to audio-video based handwritten mathematical content recognition: (1) Video Preprocessing - generates a timestamped sequence of segmented characters from the classroom video in the face of occlusions and shadows caused by the instructor, (2) Ambiguity Detection - determines the subset of input characters that may have been incorrectly recognized by the video based recognizer and forwards this subset for disambiguation, (3) A/V Synchronization - establishes correspondence between the handwritten character and the spoken content, (4) A/V Combination - combines the synchronized outputs from the video and audio based recognizers and generates the final recognized character, and (5) Grammar Assisted A/V Based Mathematical Content Recognition - utilizes a base mathematical speech grammar for both character and structure disambiguation. Experiments conducted using videos recorded in a classroom-like environment demonstrate the significant improvements in recognition accuracy that can be achieved using our techniques.
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Jie, Li 1976. "An eye movement dependent visual attention model and its application /." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=115910.

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In this dissertation, we study the relationship between eye movements and visual attention. Different types of eye movements are investigated including microsaccades, eye fixation, and eye pursuit. First, we demonstrate that microsaccades occur during pursuit and they are linked to covert attention shifts. Employing a psychophysical task that involves covert attention shifts to a peripheral square, we detect if microsaccades occur during eye pursuit, and, if so, whether, and in what way, microsaccades are related to attention shifts. Microsaccades are found to occur during pursuit and they present in similar patterns as those occurring during eye fixation. We discover that microsaccades tend to be biased towards the same direction as pursuit and the bias increases with increases of pursuit velocities. Through the analysis of microsaccade orientation and latency, we argue that microsaccades occurring during pursuit, rather than being randomly distributed, have a link with covert attention shifts. This is consistent with what has been reported for microsaccades occurring during fixation. Further analysis of microsaccade amplitude supports this argument. The potential attention mechanisms for the characteristics of microsaccades are discussed. We suggest that the attention allocation during pursuit is responsible for the characteristics of microsaccades. Our analyses of microsaccades also enforce the argument that microsaccades may be the suppressed saccades.
In addition to microsaccades, the attention allocation during eye fixation and eye pursuit are considered as well. We demonstrate that, during eye fixation, the local image content around the area of a fixation point is a significant factor to influence the fixation duration. However, during pursuit, the pursuit direction, rather than image contents, is important to decide attention allocation. According to these results, a top-down attention model based on types of eye movements is built. Three types of eye movements are considered separately in the model. They are eye fixation, eye pursuit, and saccadic eye movements (including microsaccades). The model is applied to the design of an interactive 2D video game. We demonstrate that the game is successfully designed in different difficulty levels through the analysis of attention allocation by our attention model. Our results imply that the attention modeling can be used to alter the game play so as to provide varying difficulty levels and it is also promising to take advantage of eye tracking data for broader applications, such as for navigation, intelligent map searching, augmented reality, and others.
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Fry, Carol Jean. "Eye fixation patterns in the solution of mathematical word problems by young adults : relation to cognitive style and spatial ability /." The Ohio State University, 1987. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487584612164575.

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Flores, John Robert. "The effects of cross-age tutoring on underachieving fifth-grade students in the areas of mathematical achievement and self-perception." Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184709.

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The purpose of this study was to investigate the effects of cross-age tutoring on underachieving fifth grade students in the areas of mathematical achievement and self-perception. Although much remains to be examined and discovered relative to the rationale and theories that serve as bases for cross-age tutoring, there is mounting evidence that tutoring may increase academic achievement and self-perception. There was a need for such a study because the research on tutoring is contradictory. Some studies show that tutoring is beneficial for students, while other studies indicate that tutoring does not make a difference. Although there is a belief that tutoring is beneficial, the effects of participating in a cross-age tutoring program have yet to be answered by the research community. A one-group pretest/posttest design was utilized. The population consisted of 20 underachieving fifth grade students tutoring 20 underachieving first grade students. Three self-perception subscale measures and two mathematical achievement subscale measures were given to the underachieving fifth grade students before and after the intervention. Significant results beyond the.05 level of confidence were obtained on three of the five hypotheses. The three self-perception subscale measures changed significantly, but decreased over time. The two mathematical achievement subscale measures did not change significantly over time. These findings do not support the intervention of cross-age tutoring as an effective influence on mathematical achievement or self-perception.
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Favali, Marta. "Formal models of visual perception based on cortical architectures." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066094/document.

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L’objectif de cette thèse est de développer des modèles mathématiques de perception visuelle basés sur des architectures corticales et de les appliquer pour reproduire des expériences phénoménologiques ainsi que pour traiter des images naturelles. Nous nous concentrons sur les tâches de vision de bas niveau et nous sommes intéressés par le problème du groupement et de l’individuation des unités perceptives. Nous ferons face au problème de la reconstruction des figures illusoires et de la détection des vaisseaux rétiniens dans les images optiques. Ensuite, nous considérerons le problème du codage et du décodage de l’activité cérébrale du cortex visuel obtenue par Imagerie par Résonance Magnétique fonctionnelle (IRMf). Ceci permet d’estimer la structure du cortex d’un patient spécifique et éventuellement de reconstruire le stimulus visuel de l’activité IRMf, dans une stratégie “de lecture du cerveau”. La distinction entre notre approche et l’état de la littérature consiste à utiliser des modèles neuromathématiques du cortex comme connaissance a priori pour régulariser la structure estimée. Même si c’est un objectif à long terme, nous proposons une première approche pour améliorer les résultats dans ce domaine. L’ensemble du travail de cette thèse a été développé en tenant compte des résultats de la phénoménologie de la perception et des résultats de la neurophysiologie. Dans le domaine de la phénoménologie de la perception, au début du siècle dernier, la théorie de la psychologie de la Gestalt a défini l’intégration des contours et en particulier Wertheimer [1938], Kohler [1947], Kofka [1935] ont défini le regroupement des lois de perception. Celles-ci sont cruciales dans la construction d’objets visuels : les éléments avec des caractéristiques en commun peuvent être regroupés pour former un nouvel objet visuel plus grand. Des expériences psychophysiques ont été proposées pour mesurer les paramètres quantitatifs de ces lois. Un intérêt particulier de cette thèse est le concept de champ d’association introduit par Field et al. [1993] lequel code différents principes de la Gestalt (dont la bonne continuation et la proximité).Ces auteurs ont montré que la co-linéarité de stimulus et la co-circularité jouent un rôle important dans la caractéristique du groupement. Leur étude a montré comment les chances de percevoir un chemin curviligne étaient élevées si l’orientation de ses éléments était tangente à ce chemin. D’autre part, en neurophysiologie, une grande quantité d’expériences confirment que le problème du groupement et de détection des contours est effectué par le cortex visuel primaire (V1) [Hubel, 1995]. Un cadre mathématique, basé sur les instruments différentiels, a été introduit pour formaliser ces résultats. Les premiers modèles géométriques sont dus à Koenderink and van Doorn
The objective of this thesis is to develop mathematical models of visual perception based on cortical architectures and to apply them to reproduce phenomenological experiments and to process natural images. We primarly focus on low level vision tasks and in particular we are interested in the problem of grouping and of individuation of perceptual units. In this setting we will face the problem of the reconstruction of illusory figures and the detection of retinal vessels in optical images. Then we consider the problem of encoding and decoding of the fMRI signal from in vivo acquired brain activity of visual cortex. This allows to estimate the structure of the cortex of a specific human patient and eventually to reconstruct the visual stimulus from fMRI activity, in a so called “brain reading” strategy. The difference between our approach and the state of the art literature consists in using previously defined neuromathematical models of the cortices as a-priori knowledge to regularise in vivo estimated structure. Even if it is a long term objective, we propose a first approach to improve the results in this field. The entire work of this thesis has been developed taking into account results from phenomenology of perception and results of neurophysiology.In the field of the phenomenology of perception, at the beginning of the last century, the theory of the Gestalt psychology [Wertheimer, 1938, Kohler, 1947, Kofka, 1935] defined the integration of contours and in particular they defined grouping laws underlying perception. These are crucial in the construction of visual objects: points with characteristics in common can be grouped together to form a new visual object. Many psychophysical experiments have been proposed to measure the quantitative parameters of these laws. A particular interest of this thesis is the concept of association fields introduced by Field et al. [1993] which encodes different Gestalt principles (as good continuation, proximity). They showed that stimulus co-linearity and co-circularity play an important role for the feature of grouping. Their study showed how chances of perceiving the curvilinear path were high if the orientation of its features was the one tangent at that point and collapsed as their relative orientation deviated from being tangent
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Books on the topic "Mathematical perception"

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Pentland, Alexander. The parts of perception. Menlo Park, CA: Center for the Study of Language and Information/SRI International, 1987.

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Music: A mathematical offering. Cambridge, UK: Cambridge University Press, 2007.

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1932-, Dutta Majumder D., ed. Fuzzy mathematical approach to pattern recognition. New York: Wiley, 1986.

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Berendt, Bettina. Representation and processing of knowledge about distances in environmental spaces: A computational model of inferred route distances investigating their qualitative and quantitiative determinants. Frankfurt am Main: Infix, 1999.

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Tsotsos, John Konstantine. The complexity of perceptual search tasks. Toronto: University of Toronto, Dept. of Computer Science, 1989.

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General pattern theory: A mathematical study of regular structures. Oxford: Clarendon, 1993.

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Norwich, Kenneth H. Information, sensation, and perception. San Diego, CA: Academic Press, 1993.

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D, Hoffman Donald, and Prakash Chetan, eds. Observer mechanics: A formal theory of perception. San Diego: Academic Press, 1989.

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9

Alwar, M. A. Pratyaksam: Bharatiyadarsana-ganakayantravijnanayordrstya samiksa. Tirupatih: Rastriyasamskrtavidyapitham, 2010.

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Pratyaksam: Bharatiyadarsana-ganakayantravijnanayordrstya samiksa. Tirupatih: Rastriyasamskrtavidyapitham, 2010.

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Book chapters on the topic "Mathematical perception"

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Tieszen, Richard L. "Perception." In Mathematical Intuition, 48–65. Dordrecht: Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-2293-8_3.

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Corrochano, Eduardo Bayro. "Mathematical Preliminaries." In Geometric Computing for Perception Action Systems, 3–17. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0177-6_1.

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Vogt, Robert C. "Review of Mathematical Morphology." In Springer Series in Perception Engineering, 31–85. New York, NY: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4613-9652-9_2.

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Dolev, Yuval. "Three remarks on mathematical perception." In The New Yearbook for Phenomenology and Phenomenological Philosophy, 546–60. London: Routledge, 2021. http://dx.doi.org/10.4324/9781003131250-24.

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Pierantoni, Ruggero. "Anatomical and Mathematical Tools in the Visual Pathways Studies: An Historical Overview." In Human and Machine Perception, 43–54. Boston, MA: Springer US, 1997. http://dx.doi.org/10.1007/978-1-4615-5965-8_4.

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Riede, Adolf J. I. "Modeling the Sensorial Perception in the Classroom." In Modeling Students' Mathematical Modeling Competencies, 201–12. Boston, MA: Springer US, 2009. http://dx.doi.org/10.1007/978-1-4419-0561-1_17.

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Favali, Marta, Giovanna Citti, and Alessandro Sarti. "Mathematical Models of Visual Perception Based on Cortical Architectures." In Mathematical and Theoretical Neuroscience, 123–33. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-68297-6_8.

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Saniga, M. "Mathematical Approaches to the Concept of Time." In The Nature of Time: Geometry, Physics and Perception, 129–30. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-010-0155-7_13.

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Prasad, Rai Gyan Narain. "Concept of Perception in Vedanta Darsana and modern Mathematical Sciences." In History of the Mathematical Sciences, 109–17. Gurgaon: Hindustan Book Agency, 2004. http://dx.doi.org/10.1007/978-93-86279-16-3_9.

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Wong, A. S. W., Y. Li, and E. Newton. "Mathematical Simulation of Human Psychological Perception of Moisture Sensation." In Computational Textile, 265–73. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-70658-8_17.

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Conference papers on the topic "Mathematical perception"

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Vanrell, Maria, and Jordi M. Vitria. "Mathematical morphology, granulometries, and texture perception." In SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, edited by Edward R. Dougherty, Paul D. Gader, and Jean C. Serra. SPIE, 1993. http://dx.doi.org/10.1117/12.146655.

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Srivastava, Megha, Hoda Heidari, and Andreas Krause. "Mathematical Notions vs. Human Perception of Fairness." In KDD '19: The 25th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. New York, NY, USA: ACM, 2019. http://dx.doi.org/10.1145/3292500.3330664.

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Pandya, Aalok, and Aman S. Mathur. "Mathematical Derivation for New Holographic Display Method." In 3D Image Acquisition and Display: Technology, Perception and Applications. Washington, D.C.: OSA, 2017. http://dx.doi.org/10.1364/3d.2017.dw3f.4.

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Mumford, David. "Mathematical theories of shape: do they model perception?" In San Diego, '91, San Diego, CA, edited by Baba C. Vemuri. SPIE, 1991. http://dx.doi.org/10.1117/12.49981.

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Misnon, Fauzan Amin, Yeoh Siong Hu, Irman Abd Rahman, and Muhamad Samudi Yasir. "Malaysian public perception towards nuclear power energy-related issues." In MATHEMATICAL SCIENCES AND ITS APPLICATIONS. Author(s), 2017. http://dx.doi.org/10.1063/1.4972904.

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Barchilon Ben-Av, Mercedes, and Irina Gurevich. "STUDENTS' PERCEPTION OF THE MATHEMATICAL CLASSROOM WHEN INTEGRATING DIGITAL TECHNOLOGIES." In 10th International Conference on Education and New Learning Technologies. IATED, 2018. http://dx.doi.org/10.21125/edulearn.2018.0894.

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Johor, Hanisah, Shamsul Rijal Muhammad Sabri, and Firdaus Mohd Hamzah. "Students’ perception on application of calculus in civil engineering courses." In PROCEEDINGS OF THE 21ST NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM21): Germination of Mathematical Sciences Education and Research towards Global Sustainability. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4887678.

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Othman, Zarith Sofiah, Nor Habibah Tarmuji, and Zulkifli Ab Ghani Hilmi. "Students perception on the usage of PowerPoint in learning calculus." In THE 4TH INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES: Mathematical Sciences: Championing the Way in a Problem Based and Data Driven Society. Author(s), 2017. http://dx.doi.org/10.1063/1.4980942.

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Hassan, Suriani, Nur Amira Abdol Rahman, Khadizah Ghazali, Norlita Ismail, and Kamsia Budin. "Perception on obesity among university students: A case study using factor analysis." In PROCEEDINGS OF THE 21ST NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM21): Germination of Mathematical Sciences Education and Research towards Global Sustainability. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4887722.

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Paisan, Norfaizah, and Hajar Sulaiman. "Students’ performance and perception in solving sentence-form mathematical problems through multimedia usage in Google classroom." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2020 (MATHTECH 2020): Sustainable Development of Mathematics & Mathematics in Sustainability Revolution. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0075317.

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Reports on the topic "Mathematical perception"

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Grissett, James D. Mathematical Model for Interaction of Canals and Otoliths in Perception of Orientation, Translation, and Rotation. Fort Belvoir, VA: Defense Technical Information Center, December 1993. http://dx.doi.org/10.21236/ada280897.

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Raychev, Nikolay. Mathematical foundations of neural networks. Implementing a perceptron from scratch. Web of Open Science, August 2020. http://dx.doi.org/10.37686/nsr.v1i1.74.

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Tucker Blackmon, Angelicque. Formative External Evaluation and Data Analysis Report Year Three: Building Opportunities for STEM Success. Innovative Learning Center, LLC, August 2020. http://dx.doi.org/10.52012/mlfk2041.

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Tucker-Blackmon, Angelicque. Engagement in Engineering Pathways “E-PATH” An Initiative to Retain Non-Traditional Students in Engineering Year Three Summative External Evaluation Report. Innovative Learning Center, LLC, July 2020. http://dx.doi.org/10.52012/tyob9090.

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Abstract:
The summative external evaluation report described the program's impact on faculty and students participating in recitation sessions and active teaching professional development sessions over two years. Student persistence and retention in engineering courses continue to be a challenge in undergraduate education, especially for students underrepresented in engineering disciplines. The program's goal was to use peer-facilitated instruction in core engineering courses known to have high attrition rates to retain underrepresented students, especially women, in engineering to diversify and broaden engineering participation. Knowledge generated around using peer-facilitated instruction at two-year colleges can improve underrepresented students' success and participation in engineering across a broad range of institutions. Students in the program participated in peer-facilitated recitation sessions linked to fundamental engineering courses, such as engineering analysis, statics, and dynamics. These courses have the highest failure rate among women and underrepresented minority students. As a mixed-methods evaluation study, student engagement was measured as students' comfort with asking questions, collaboration with peers, and applying mathematics concepts. SPSS was used to analyze pre-and post-surveys for statistical significance. Qualitative data were collected through classroom observations and focus group sessions with recitation leaders. Semi-structured interviews were conducted with faculty members and students to understand their experiences in the program. Findings revealed that women students had marginalization and intimidation perceptions primarily from courses with significantly more men than women. However, they shared numerous strategies that could support them towards success through the engineering pathway. Women and underrepresented students perceived that they did not have a network of peers and faculty as role models to identify within engineering disciplines. The recitation sessions had a positive social impact on Hispanic women. As opportunities to collaborate increased, Hispanic womens' social engagement was expected to increase. This social engagement level has already been predicted to increase women students' persistence and retention in engineering and result in them not leaving the engineering pathway. An analysis of quantitative survey data from students in the three engineering courses revealed a significant effect of race and ethnicity for comfort in asking questions in class, collaborating with peers outside the classroom, and applying mathematical concepts. Further examination of this effect for comfort with asking questions in class revealed that comfort asking questions was driven by one or two extreme post-test scores of Asian students. A follow-up ANOVA for this item revealed that Asian women reported feeling excluded in the classroom. However, it was difficult to determine whether these differences are stable given the small sample size for students identifying as Asian. Furthermore, gender differences were significant for comfort in communicating with professors and peers. Overall, women reported less comfort communicating with their professors than men. Results from student metrics will inform faculty professional development efforts to increase faculty support and maximize student engagement, persistence, and retention in engineering courses at community colleges. Summative results from this project could inform the national STEM community about recitation support to further improve undergraduate engineering learning and educational research.
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