Relevant bibliographies by topics / Algebraic perception

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Algebraic perception'

Author: Grafiati
Published: 4 June 2021
Last updated: 13 February 2022

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Journal articles on the topic "Algebraic perception"

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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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Ji, Jing, Gui Xiong Liu, and Li Ming Wu. "Reachability Analysis of Perception Layer Scheduling for IoT." Applied Mechanics and Materials 385-386 (August 2013): 1689–92. http://dx.doi.org/10.4028/www.scientific.net/amm.385-386.1689.

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In this paper we present a method of reachability analysis for Internet of Things (IoT) perception layer scheduling. First, the model of perception layer information flow and behavior is formed. Because perception network is a system with coexistence of discrete events and successive events, so we use hybrid dynamic logic modeling approach to form the information perception model; Then inequality proving theory, semi-algebraic system and related tools Discoverer soft package are used to give reachability analysis of the model of perceptual system, and the feasibility of this method is verified by the vehicle condition monitoring system application.
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Bishop, Joyce W., Albert D. Otto, and Cheryl A. Lubinski. "Promoting Algebraic Reasoning Using Students' Thinking." Mathematics Teaching in the Middle School 6, no. 9 (May 2001): 508–14. http://dx.doi.org/10.5951/mtms.6.9.0508.

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The changing applications of mathematics have contributed to a shift from the perception that mathematics is a fixed body of arbitrary rules to the realization that the discipline is “a vigorous active science of patterns” (National Research Council 1989, p. 13). NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) recommends using patterns to promote mathematical understanding and, in particular, algebraic reasoning. A number of other mathematics education reform documents make similar recommendations (e.g., AAAS [1989]; National Research Council [1990]; Steen [1990]; NCTM [2000]). Researchers have begun to identify different approaches that students use to reason about patterns (Bishop 1997; MacGregor and Stacey 1993; Orton and Orton 1996; Stacey 1989). Research also shows that using students' thinking about patterns can help them develop a better understanding of mathematical concepts and the representations that reflect those concepts (Carey 1992; Fennema, Carpenter, and Peterson 1989). This article illustrates how students' thinking about geometric patterns can be used to help them develop algebraic reasoning and to make sense of mathematical notation and symbols.
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Heeger, David J., and Allan Jepson. "Visual Perception of Three-Dimensional Motion." Neural Computation 2, no. 2 (June 1990): 129–37. http://dx.doi.org/10.1162/neco.1990.2.2.129.

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As an observer moves and explores the environment, the visual stimulation in his eye is constantly changing. Somehow he is able to perceive the spatial layout of the scene, and to discern his movement through space. Computational vision researchers have been trying to solve this problem for a number of years with only limited success. It is a difficult problem to solve because the relationship between the optical-flow field, the 3D motion parameters, and depth is nonlinear. We have come to understand that this nonlinear equation describing the optical-flow field can be split by an exact algebraic manipulation to yield an equation that relates the image velocities to the translational component of the 3D motion alone. Thus, the depth and the rotational velocity need not be known or estimated prior to solving for the translational velocity. The algorithm applies to the general case of arbitrary motion with respect to an arbitrary scene. It is simple to compute and it is plausible biologically.
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Ranney, Michael. "The role of structural context in perception: Syntax in the recognition of algebraic expressions." Memory & Cognition 15, no. 1 (January 1987): 29–41. http://dx.doi.org/10.3758/bf03197710.

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Booth, David A. "Phenomenology is art, not psychological or neural science." Behavioral and Brain Sciences 26, no. 4 (August 2003): 408–9. http://dx.doi.org/10.1017/s0140525x03220094.

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It is tough to relate visual perception or other achievements to physiological processing in the central nervous system. The diagrammatic, algebraic, and verbal pictures of how sights seem to Lehar do not advance understanding of how we manage to see what is in the world. There are well-known conceptual reasons why no such purely introspective approach can be productive.
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Bragina, O. I. "Problems of Understanding the Text and Symbolic Information in Teaching Mathematics." Psychological-Educational Studies 7, no. 1 (2015): 80–88. http://dx.doi.org/10.17759/psyedu.2015070108.

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We posed the problem of understanding the text and symbol messages by students. We considered the interpretation of the concept of "understanding" in philosophy and psychology, presented psycholinguistic aspect of the concept in detail. We proposed a general classification of problems of perception of speech by students in teaching mathematics. We identified two broad categories of problems of understanding the language statements (direct problematic language codes perception and incorrect perception of the context). We introduce the concept of "reversible language constructs”, discuss the various types of reversible language constructs found in educational materials on math. The analogy is provided to demonstrate the similarity of reversible structures of natural language with constructs of algebraic material. The author presents the classification of reversible constructs. We substantiated the importance of the study of reversible structures decoding by students, identified properties of reversible constructs perception, the conditions for their understanding. We revealed the further ways to study how to create an effective technique for decoding reversible constructs (with the use of educational material on algebra).
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Nicolas, Gandalf, Malena de la Fuente, and Susan T. Fiske. "Mind the overlap in multiple categorization: A review of crossed categorization, intersectionality, and multiracial perception." Group Processes & Intergroup Relations 20, no. 5 (June 25, 2017): 621–31. http://dx.doi.org/10.1177/1368430217708862.

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Research on social categorization continues, with one growth area being multiple categorization. Various approaches study questions that, although different in scope and content, potentially tap the same underlying processes. Current models that aim to understand judgments about targets who belong to multiple social groups include algebraic and nonalgebraic models of crossed categorization, as well as theories related to intersectionality and multiracial categorization. The literature on these models and theories highlights some strengths and limitations. The review discusses potential overlap between models that have mostly advanced independently of each other. Future research can take a more encompassing stance to acknowledge this overlap.
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Berthier, Michel, and Edoardo Provenzi. "The Quantum Nature of Color Perception: Uncertainty Relations for Chromatic Opposition." Journal of Imaging 7, no. 2 (February 22, 2021): 40. http://dx.doi.org/10.3390/jimaging7020040.

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In this paper, we provide an overview on the foundation and first results of a very recent quantum theory of color perception, together with novel results about uncertainty relations for chromatic opposition. The major inspiration for this model is the 1974 remarkable work by H.L. Resnikoff, who had the idea to give up the analysis of the space of perceived colors through metameric classes of spectra in favor of the study of its algebraic properties. This strategy permitted to reveal the importance of hyperbolic geometry in colorimetry. Starting from these premises, we show how Resnikoff’s construction can be extended to a geometrically rich quantum framework, where the concepts of achromatic color, hue and saturation can be rigorously defined. Moreover, the analysis of pure and mixed quantum chromatic states leads to a deep understanding of chromatic opposition and its role in the encoding of visual signals. We complete our paper by proving the existence of uncertainty relations for the degree of chromatic opposition, thus providing a theoretical confirmation of the quantum nature of color perception.
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Hussain, Iqtadar, Tariq Shah, Muhammad Asif Gondal, and Hasan Mahmood. "Analysis of S-box in Image Encryption Using Root Mean Square Error Method." Zeitschrift für Naturforschung A 67, no. 6-7 (July 1, 2012): 327–32. http://dx.doi.org/10.5560/zna.2012-0023.

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The use of substitution boxes (S-boxes) in encryption applications has proven to be an effective nonlinear component in creating confusion and randomness. The S-box is evolving and many variants appear in literature, which include advanced encryption standard (AES) S-box, affine power affine (APA) S-box, Skipjack S-box, Gray S-box, Lui J S-box, residue prime number S-box, Xyi S-box, and S8 S-box. These S-boxes have algebraic and statistical properties which distinguish them from each other in terms of encryption strength. In some circumstances, the parameters from algebraic and statistical analysis yield results which do not provide clear evidence in distinguishing an S-box for an application to a particular set of data. In image encryption applications, the use of S-boxes needs special care because the visual analysis and perception of a viewer can sometimes identify artifacts embedded in the image. In addition to existing algebraic and statistical analysis already used for image encryption applications, we propose an application of root mean square error technique, which further elaborates the results and enables the analyst to vividly distinguish between the performances of various S-boxes. While the use of the root mean square error analysis in statistics has proven to be effective in determining the difference in original data and the processed data, its use in image encryption has shown promising results in estimating the strength of the encryption method. In this paper, we show the application of the root mean square error analysis to S-box image encryption. The parameters from this analysis are used in determining the strength of S-boxes
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Dissertations / Theses on the topic "Algebraic perception"

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Hanselmann, Thomas. "Approximate dynamic programming with adaptive critics and the algebraic perceptron as a fast neural network related to support vector machines." University of Western Australia. School of Electrical, Electronic and Computer Engineering, 2003. http://theses.library.uwa.edu.au/adt-WU2004.0005.

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[Truncated abstract. Please see the pdf version for the complete text. Also, formulae and special characters can only be approximated here. Please see the pdf version of this abstract for an accurate reproduction.] This thesis treats two aspects of intelligent control: The first part is about long-term optimization by approximating dynamic programming and in the second part a specific class of a fast neural network, related to support vector machines (SVMs), is considered. The first part relates to approximate dynamic programming, especially in the framework of adaptive critic designs (ACDs). Dynamic programming can be used to find an optimal decision or control policy over a long-term period. However, in practice it is difficult, and often impossible, to calculate a dynamic programming solution, due to the 'curse of dimensionality'. The adaptive critic design framework addresses this issue and tries to find a good solution by approximating the dynamic programming process for a stationary environment. In an adaptive critic design there are three modules, the plant or environment to be controlled, a critic to estimate the long-term cost and an action or controller module to produce the decision or control strategy. Even though there have been many publications on the subject over the past two decades, there are some points that have had less attention. While most of the publications address the training of the critic, one of the points that has not received systematic attention is training of the action module.¹ Normally, training starts with an arbitrary, hopefully stable, decision policy and its long-term cost is then estimated by the critic. Often the critic is a neural network that has to be trained, using a temporal difference and Bellman's principle of optimality. Once the critic network has converged, a policy improvement step is carried out by gradient descent to adjust the parameters of the controller network. Then the critic is retrained again to give the new long-term cost estimate. However, it would be preferable to focus more on extremal policies earlier in the training. Therefore, the Calculus of Variations is investigated to discard the idea of using the Euler equations to train the actor. However, an adaptive critic formulation for a continuous plant with a short-term cost as an integral cost density is made and the chain rule is applied to calculate the total derivative of the short-term cost with respect to the actor weights. This is different from the discrete systems, usually used in adaptive critics, which are used in conjunction with total ordered derivatives. This idea is then extended to second order derivatives such that Newton's method can be applied to speed up convergence. Based on this, an almost concurrent actor and critic training was proposed. The equations are developed for any non-linear system and short-term cost density function and these were tested on a linear quadratic regulator (LQR) setup. With this approach the solution to the actor and critic weights can be achieved in only a few actor-critic training cycles. Some other, more minor issues, in the adaptive critic framework are investigated, such as the influence of the discounting factor in the Bellman equation on total ordered derivatives, the target interpretation in backpropagation through time as moving and fixed targets, the relation between simultaneous recurrent networks and dynamic programming is stated and a reinterpretation of the recurrent generalized multilayer perceptron (GMLP) as a recurrent generalized finite impulse MLP (GFIR-MLP) is made. Another subject in this area that is investigated, is that of a hybrid dynamical system, characterized as a continuous plant and a set of basic feedback controllers, which are used to control the plant by finding a switching sequence to select one basic controller at a time. The special but important case is considered when the plant is linear but with some uncertainty in the state space and in the observation vector, and a quadratic cost function. This is a form of robust control, where a dynamic programming solution has to be calculated. ¹Werbos comments that most treatment of action nets or policies either assume enumerative maximization, which is good only for small problems, except for the games of Backgammon or Go [1], or, gradient-based training. The latter is prone to difficulties with local minima due to the non-convex nature of the cost-to-go function. With incremental methods, such as backpropagation through time, calculus of variations and model-predictive control, the dangers of non-convexity of the cost-to-go function with respect to the control is much less than the with respect to the critic parameters, when the sampling times are small. Therefore, getting the critic right has priority. But with larger sampling times, when the control represents a more complex plan, non-convexity becomes more serious.
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Rodrigues, Losada Ricardo J. "Teachers' perceptions of spreadsheet algebra programs as curriculum materials for high school mathematics in Namibia." Thesis, Stellenbosch : Stellenbosch University, 2012. http://hdl.handle.net/10019.1/71846.

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Thesis (MEd)--Stellenbosch University, 2012
Includes bibliography
ENGLISH ABSTRACT: The use of information and communications technologies (ICTs) in the form of spreadsheet algebra programmes (SAPs) is important in the professional development of high school mathematics teachers. This is in line with The Namibian government‟s Vision 2030 in which ICT skills and competencies are regarded as core elements of living and participating in the 21st century. ICTs are also considered to be fundamental to the development of a dynamic knowledge-based economy (KBE) through the Education and Training Sector Improvement Program (ETSIP). ETSIP‟s aim is to embed ICT at all levels of the education system. It also aims to integrate the use of ICTs as tools in the delivery of curriculum and learning and in so doing, lead to a marked improvement in the quality of the learning and teaching process across all levels. Education has a key role in achieving Vision 2030. The aim of this research was to investigate mathematics teachers‟ perceptions of SAPs as curriculum materials in selected Namibian secondary (high) schools. This research adopted a qualitative methodology, which in this instance was a case study. The sample population consisted of five teachers from Okamu (pseudonym) secondary school in the Ohangwena Region of Namibia. Four of them had been teaching mathematics at different levels in the mentioned school for a period of four years, and one of them was teaching physical science. Three methods of data collection were used. The first two were semi-structured interviews and focus group interviews based on teachers‟ experiences using SAPs. The third method was an audio taped observation of a lesson taught by one of the teachers,. This research provides evidence about teachers‟ perceptions regarding time concerns and constraints with regards to the SAPs and the use of the SAPs. The teachers showed willingness and enthusiasm to use SAPs on linear and quadratic functions in their teaching. Some of the teachers became more aware of the epistemic dimensions associated with mathematical and algebraic symbols. Interview data reveal that the teachers had not considered these dimensions when teaching with the usual paper-and-pen format. The research also provides evidence of a teacher‟s early vision about the use of spreadsheets as an instrument to teach linear functions. This teacher did not consider any epistemic value for the instrumented spreadsheets techniques, or that they might contribute to a deeper understanding of the linear functions. His concern was focused more on getting the learners to acquire computer skills, such as learning how to use spreadsheets. It is recommended that in-service professional development about ICT integration into mathematics teaching be offered. This might help teachers to learn how their knowledge and skills could be used in the classroom more effectively in order to save time. It is also suggested that professional development programmes be designed to stimulate and promote teachers‟ willingness to develop an understanding of the characteristics of ICTs such as SAPs and their uses. Lastly, it is recommended that new SAPs be designed in order to deepen the understanding of algebra at the secondary level.
AFRIKAANSE OPSOMMING: Die gebruik van inligting- en kommunikasietegnologieë (IKT's) in die vorm van sigblad-algebra-programme (SAP's) is belangrik vir die professionele ontwikkeling van hoërskoolwiskunde-onderwysers. Dit is in pas met die Namibiese regering se visie vir 2030, Vision 2030, waarin IKT-vaardighede en -bevoegdhede beskou word as kernelemente van die lewe in en deelname aan die 21ste eeu. IKT's word ook beskou as grondliggend aan die ontwikkeling van ‟n dinamiese kennisekonomie (KE) deur middel van die Verbeteringsprogram vir die Onderwys- en Opleidingsektore (ETSIP). ETSIP het as oogmerk om IKT op alle vlakke van die onderwysstelsel vas te lê. Dit het ook ten doel om die gebruik van IKT's as hulpmiddele te integreer in die lewering van kurrikulum en leer en sodoende ‟n duidelike verbetering in die gehalte van die onderrig-en-leerproses oor alle vlakke heen tot gevolg te hê. Onderwys het ‟n sleutelrol te speel by die bereiking van Vision 2030. Die doel van hierdie navorsing was om wiskundeonderwysers se persepsies van SAP's as kurrikulummateriaal in geselekteerde Namibiese sekondêre (hoër-) skole te ondersoek. Hierdie navorsing het ‟n kwalitatiewe metode gevolg, in hierdie geval ‟n gevallestudie. Die proefgroep het bestaan uit vyf onderwysers van die sekondêre skool Okamu (skuilnaam) in die Ohangwena-streek van Namibië. Vier van hulle het reeds vier jaar lank wiskunde op verskillende vlakke in die betrokke skool gegee en een van hulle het fisiese wetenskap gegee. Drie metodes is ingespan om data in te samel. Die eerste twee was semigestruktureerde onderhoude en fokusgroeponderhoude gebaseer op onderwysers se ervaringe ten opsigte van die gebruik van SAP's. Die derde metode was ‟n klankopname van ‟n waarnemingsessie van ‟n les wat deur een van die onderwysers gegee is. Hierdie navorsing getuig van onderwysers se persepsies ten opsigte van tydskwessies en -beperkinge met betrekking tot die SAP's en die gebruik van die SAP's. Die onderwysers het ‟n gewilligheid en geesdrif geopenbaar om by lineêre en kwadratiese funksies SAP's in hul onderrig te gebruik. Party onderwysers het meer bewus geraak van die epistemiese dimensies in verband met wiskundige en algebraïese simbole. Onderhouddata onthul dat die onderwysers nie hierdie dimensies in ag geneem het toe hulle met die gewone papier-en-pen-formaat klasgegee het nie. Die navorsing bevestig ook ‟n onderwyser se aanvanklike insig oor die gebruik van sigblaaie as 'n instrument om lineêre funksies te onderrig. Hierdie onderwyser het nie die epistemiese waarde vir die geïnstrumenteerde sigbladtegnieke in ag geneem nie, of dat hulle sou kon bydra tot ‟n grondiger begrip van die lineêre funksies nie. Sy belangstelling was eerder daarop gefokus om die leerders sover te kry om rekenaarvaardighede, soos om sigblaaie te kan gebruik, te verwerf. Daar word aanbeveel dat indiens- professionele ontwikkeling oor IKT-integrasie in wiskundeonderrig aangebied word. Dit sal onderwysers moontlik help om te leer hoe hulle kennis en vaardighede meer doeltreffend in die klaskamer gebruik kan word om tyd te bespaar. Daar word ook voorgestel dat professionele ontwikkelingsprogramme ontwerp word, ter stimulering en bevordering van onderwysers se bereidwilligheid om ‟n begrip te ontwikkel van die kenmerke en gebruike van IKT's soos SAP's. Laastens word daar aanbeveel dat nuwe SAP's ontwerp word om die verstaan van algebra op sekondêre vlak te verdiep.
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Stuve, Claire E. "A Study of Student Perceptions on Adaptive Learning Systems in College Algebra and Their Effect on Learning Outcomes." University of Toledo / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1430233337.

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Schroeder, Darin Craig. "A look at attitude and achievement as a result of self-regulated learning in the Algebra I classroom." Lexington, Ky. : [University of Kentucky Libraries], 2007. http://lib.uky.edu/ETD/ukyinam2007d00620/DarinCraigSchroeder.pdf.

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Thesis (Ph. D.)--University of Kentucky, 2007.
Title from document title page (viewed on September 4, 2007). Document formatted into pages; contains: viii, 132 p. : ill. (some col.). Includes abstract and vita. Includes bibliographical references (p. 100-105).
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Matika, Richard S. "STUDENT AND INSTRUCTOR PERCEPTIONS OF FACTORS IMPORTANT FOR STUDENT SUCCESS IN ONLINE AND IN-PERSON ALGEBRA CLASSES AT SOMERSET COMMUNITY COLLEGE." UKnowledge, 2012. http://uknowledge.uky.edu/epe_etds/4.

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Online mathematics courses at Somerset Community College (SCC) have traditionally had a lower retention rate than their in-person counterparts. This study looked at online and in-person students at SCC in the courses Intermediate Algebra and College Algebra. Beginning of semester student demographics were considered to determine whether or not the online and in-person student populations were comparable. End of semester student demographics, retention rates, and grades on the final exams were examined to determine whether or not there were patterns among completer students. Finally, a survey was administered to students and instructors to determine their perceptions of several factors thought to influence student success and to determine areas of agreement and disagreement among these factors. Follow-up telephone interviews were given to instructors and students in order to identify areas that were not covered in the survey. The results indicated that although online courses tended to attract older students, the online and in-person student groups were similar in terms of make-up. This was true both at the beginning and at the end of the semester. The in-person sections showed better results, both in terms of retention and grades on the final exams. The survey results were analyzed using Rasch analysis. This showed differences between students and instructors, most importantly in the areas of student self-efficacy behaviors and communication between instructor and student. These differences between students and instructors were generally exacerbated in the online sections indicating that these areas might have had an impact on the lower retention and grades of the online sections.
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Fassett, David R. "Academic standards alignment with essential work skills : perceptions from Indiana guidance counselors and employers." Virtual Press, 2006. http://liblink.bsu.edu/uhtbin/catkey/1354645.

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The purpose of this exploratory study was to look at the importance of Indiana's Algebra I academic standards in relationship with essential, entry-level work skills as perceived by employers and guidance counselors in northern and northeastern Indiana. Counselors and employers were sent electronic (e-mail and web-based) or hard (paper) copies of a survey instrument. Section II of the survey asked for demographic data, (age, race, gender) as well as information related to the size of the business or school, type of business, and years in current position. Respondents were also asked to rate their knowledge of the Indiana academic standards, the Americans with disabilities Act and Section 504 of the Vocational Rehabilitation Act. In Section III, respondents were presented with the nine Indiana Algebra I standards, along with examples to illustrate and further explain each standard. Employers rated each standard, and the standards combined, on its importance to skills required from people seeking jobs immediately after leaving high school using a Likert scale. Guidance counselors rated the importance of the standards based on what they knew of the labor market within school district and surrounding areas using the same Likert scale. Comments were solicited at the end of the survey instruments. Employers disagreed with the importance of any of the Algebra I standards, or the standards as whole, as entry-level work skills. Their highest mean rating was 2.4. Counselors also disagreed, although on two standards their mean rating was above the Neutral rating. Sample size was deemed too low for generalization, but study does supply a framework for future research.
Department of Special Education
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Samson, Duncan Alistair. "An analysis of the influence of question design on pupils' approaches to number pattern generalisation tasks." Thesis, Rhodes University, 2008. http://hdl.handle.net/10962/d1003302.

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This study is based on a qualitative investigation framed within an interpretive paradigm, and aims to investigate the extent to which question design affects the solution strategies adopted by children when solving linear number pattern generalisation tasks presented in pictorial and numeric contexts. The research tool comprised a series of 22 pencil and paper exercises based on linear generalisation tasks set in both numeric and 2-dimensional pictorial contexts. The responses to these linear generalisation questions were classified by means of stage descriptors as well as stage modifiers. The method or strategy adopted was carefully analysed and classified into one of seven categories. A meta-analysis focused on the formula derived for the nth term in conjunction with its justification. The process of justification proved to be a critical factor in being able to accurately interpret the origin of the sub-structure evident in many of these responses. From a theoretical perspective, the central role of justification/proof within the context of this study is seen as communication of mathematical understanding, and the process of justification/proof proved to be highly successful in providing a window of understanding into each pupil’s cognitive reasoning. The results of this study strongly support the notion that question design can play a critical role in influencing pupils’ choice of strategy and level of attainment when solving pattern generalisation tasks. Furthermore, this study identified a diverse range of visually motivated strategies and mechanisms of visualisation. An awareness and appreciation for such a diversity of visualisation strategies, as well as an understanding of the importance of appropriate question design, has direct pedagogical application within the context of the mathematics classroom.
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Samson, Duncan Alistair. "An analysis of the influence of question design on pupils' approaches to number pattern generalisation tasks /." 2007. http://eprints.ru.ac.za/1121/.

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Vilakazi, Aubrey Sifiso. "An exploration of mathematical literacy teachers' perceptions of, and performance in mathematical literacy tasks based on algebra." Thesis, 2010. http://hdl.handle.net/10413/6211.

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Mathematical Literacy (ML) has only recently been introduced to learners, and research in South Africa concerning learners’ conceptual understanding in ML is not widely available. However an important predictor of learners’ success or difficulties in concepts is the success or difficulties that in-service teachers experience themselves. It is therefore important for us as mathematics educators to identify areas in Mathematical Literacy that teachers are struggling to learn and apply. With this in mind, the study sets to explore teachers’ perceptions about, and performance in Mathematical Literacy tasks based on algebraic concepts. This study is located within the principles of the qualitative research case study approach. The combination of data collection techniques has allowed me to identify broad trends across the group as a whole as well as differences within the participants of the group itself. The participants of the study were a class of 17 students who were completing the ACEML programme at UKZN. Four sources of data were used. Firstly, data was generated from teachers’ reflections about certain tasks, the solution of which required the use of algebra. A second data collection instrument was an open-form questionnaire and the third instrument was two unstructured interviews with two teachers. The final instrument was the analysis of the teachers’ examination scripts. For this study, teachers from this group were classified along the lines of whether they were qualified to teach mathematics or not. The theoretical framework for the study was derived from the OECD/PISA (2003) cycle of mathematisation which specifies 5 aspects of mathematisation, together with the theory of reification. For the purpose of this research, a participant was considered as a “mathematics specialist” if s/he studied mathematics up to tertiary level, while a participant was considered as “non-mathematics teacher” if s/he studied mathematics only up to Grade 12 level. The findings reveal that although the teachers conveyed varying understandings of the ML curriculum, they believed that knowledge of basic algebra was necessary and adequate for them to deal with ML problems. Furthermore the teachers believed mathematical teaching experience contributes to improved problem solving in ML and that ‘practice and familiarity’ helped teachers improve their problem solving skills in ML. They also voiced a concern that the pace of the programme constituted a barrier to their success. Within the group, it was found that Mathematics specialist teachers performed better than the non-Mathematics teachers. All teachers found the mathematisation aspects of solving the mathematical problem and of reinterpreting the mathematical solution to make sense of the real-life problems, challenging, while the non-Mathematics teachers experienced problems with all five aspects of mathematisation. The findings of the study suggest that teachers need help in moving from lower levels to higher levels of mathematisation. Opportunities for mathematical modeling experiences need to be incorporated in the part-time in-service contact courses like ACEML. Further research is needed to inform education authorities about whether the use of teachers with only grade 12 mathematical knowledge to teach ML is advisable.
Thesis (M.Ed.)-University of KwaZulu-Natal, Edgewood, 2010.
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Abrego, Patricia C. "Perceptions of Campus Administrators, Teachers, and Students on Use of Interactive Videoconferencing for the Delivery of High School Algebra in Selected Rural Public HIgh Schools in South Texas." 2009. http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7628.

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Campus administrators from rural public school districts are continuously looking for creative innovative ways to respond to the educational challenges placed upon them by federal and state-legislated accountability requirements. Advances in interactive videoconferencing (ITVC) technologies provide a way to address these challenges. However, these advancements sometimes lack needed resources to make a network of this magnitude work. The Mid-Rio Collaborative was established to share educational resources and knowledge between Texas A&M International University in Laredo, Texas, and surrounding rural public school districts in South Texas. The established collaborative provided the backdrop for the study while meeting the educational needs of this region. The purpose of this study was to examine the use of interactive videoconferencing as a viable alternative for the delivery of high school Algebra. A mixed methods case study of four campuses explored the perceptions of administrators teachers, and students in the use of interactive videoconferencing. The sampled population included 4 administrators, 4 teachers, 35 students (12 experimental and 23 control) from selected rural districts. Qualitative and quantitative research methodologies were utilized in identifying perceptions of participating principals, teachers, and students. Major findings of this study included (a) campus administrators’ values and beliefs influence teacher use of interactive videoconferencing; (b) a difference exists in experienced and novice teacher perceptions regarding the impact of ITVC, (c) perceptions are dependent upon the Teacher Partner role in the teaching and learning process; (d) increased interaction between students, teacher, content, other learners, and technology exists with instruction delivered through ITVC; (e) perceptions of cognitive and classroom conditions differed between students receiving instruction via face-to-face and interactive videoconferencing; finally, (f) students receiving instruction through ITVC did not demonstrate academic gains in state-mandated tests (TAKS). Study results support the current body of research that contends there is no significant difference between instruction delivered face-to-face and instruction being delivered via interactive videoconferencing.
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Books on the topic "Algebraic perception"

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Sommer, Gerald, and Yehoshua Y. Zeevi, eds. Algebraic Frames for the Perception-Action Cycle. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/10722492.

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Sommer, Gerald, and Jan J. Koenderink, eds. Algebraic Frames for the Perception-Action Cycle. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0017857.

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1945-, Sommer Gerald, and Koenderink Jan J, eds. Algebraic frames for the perception-action cycle: International workshop, AFPAC '97, Kiel, Germany, September 8-9, 1997 : proceedings. Berlin: Springer, 1997.

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Patrizio, Frosini, Landi Claudia, Cerri Andrea, Fabio Barbara, and SpringerLink (Online service), eds. Computational Topology in Image Context: 4th International Workshop, CTIC 2012, Bertinoro, Italy, May 28-30, 2012. Proceedings. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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Froats, Stephanie. That's a wrap!: Patterning and algebra, and geometry : an integrated unit for grade 2/3. [Ontario: s.n.], 2001.

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McGinn, Vicki. The great cover up: Patterning and algebra : an integrated unit for grade 3/4. [Ontario: s.n.], 2001.

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Algebraic Frames for the Perception-Action Cycle: International Workshop, AFPAC'97, Kiel, Germany, September 8-9, 1997, Proceedings (Lecture Notes in Computer Science). Springer, 1997.

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(Editor), Gerald Sommer, and Yehoshua Y. Zeevi (Editor), eds. Algebraic Frames for the Perception-Action Cycle: Second International Workshop, AFPAC 2000, Kiel, Germany, September 10-11, 2000 Proceedings (Lecture Notes in Computer Science). Springer, 2000.

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Pryce, Paula. Sanctuary. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780190680589.003.0007.

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Highlighting the interconnected roles of agency, habitus, and ambiguity, this chapter describes the book’s core thesis: the variability and interdependence of three culturally specific knowledge types (performative knowledge, unknowing, and unitive being), which result from practitioners’ differing capacities to “evoke the divine.” Expressed as an algebraic formula, this new epistemological theory of differential knowledge adds to classic studies of ritual and perception by detailing the diversity and fluidity with which “communitas” or phenomenological intersubjectivity actually occurs in a particular ethnographic context. It offers an anthropology of knowledge that can assist in the analysis of complex pluralistic societies. The chapter’s extensive use of ethnographic narrative and poetic language conveys how the three variable knowledge types arise in people’s ritualized lives and demonstrates how the ethnographer used intersubjective fieldwork methods to gain insights to contemplative experience even in environments of silence and interiority.
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Morphing: A Guide to Mathematical Transformations for Architects and Designers. King Publishing, Laurence, 2015.

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Book chapters on the topic "Algebraic perception"

1

Sommer, Gerald. "Algebraic aspects of designing behavior based systems." In Algebraic Frames for the Perception-Action Cycle, 1–28. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0017858.

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Heyden, Anders, Gunnar Sparr, and Kalle Åström. "Perception and action using multilinear forms." In Algebraic Frames for the Perception-Action Cycle, 54–65. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0017860.

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Marchand, Éric, and François Chaumette. "Visual perception strategies for 3D reconstruction." In Algebraic Frames for the Perception-Action Cycle, 290–305. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0017874.

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Ritter, Helge. "Neural network approaches for perception and action." In Algebraic Frames for the Perception-Action Cycle, 356–78. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0017878.

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Rundblad, Ekaterina, Valeri Labunets, Jaakko Astola, and Karen Egiazarian. "Algebraic Frames for Commutative Hyperharmonic Analysis of Signals and Images." In Algebraic Frames for the Perception-Action Cycle, 294–308. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/10722492_23.

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Csurka, Gabriella, and Olivier Faugeras. "Algebraic and geometric tools to compute projective and permutation invariants." In Algebraic Frames for the Perception-Action Cycle, 207–18. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0017869.

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Aloimonos, Y., and C. Fermüller. "Analyzing Action Representations." In Algebraic Frames for the Perception-Action Cycle, 1–21. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/10722492_1.

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Chernov, Vladimir M. "Hurwitzion Algebra and its Application to the FFT Synthesis." In Algebraic Frames for the Perception-Action Cycle, 154–63. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/10722492_10.

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Cremers, Daniel, Christoph Schnörr, Joachim Weickert, and Christian Schellewald. "Diffusion–Snakes Using Statistical Shape Knowledge." In Algebraic Frames for the Perception-Action Cycle, 164–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/10722492_11.

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Felsberg, Michael, and Gerald Sommer. "The Multidimensional Isotropic Generalization of Quadrature Filters in Geometric Algebra." In Algebraic Frames for the Perception-Action Cycle, 175–85. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/10722492_12.

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Conference papers on the topic "Algebraic perception"

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Hanselmann, T., and L. Noakes. "A decomposition algorithm based on the algebraic perceptron." In ANZIIS 2001. Proceedings of the Seventh Australian and New Zealand Intelligent Information Systems Conference. IEEE, 2001. http://dx.doi.org/10.1109/anziis.2001.974088.

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Suarez Araujo, Carmen P., and Gerhard X. Ritter. "Morphological neural networks and image algebra in artificial perception systems." In San Diego '92, edited by Paul D. Gader, Edward R. Dougherty, and Jean C. Serra. SPIE, 1992. http://dx.doi.org/10.1117/12.60638.

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Mateycik, Fran, Zdeslav Hrepic, David Jonassen, N. Sanjay Rebello, Leon Hsu, Charles Henderson, and Laura McCullough. "Students' Perceptions of Case-Reuse Based Problem Solving in Algebra-Based Physics." In 2007 PHYSICS EDUCATION RESEARCH CONFERENCE. AIP, 2007. http://dx.doi.org/10.1063/1.2820917.

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Van Heerden, Leanri, and Nicolaas Luwes. "Addressing engineering threshold concepts in an African university of technology." In Sixth International Conference on Higher Education Advances. Valencia: Universitat Politècnica de València, 2020. http://dx.doi.org/10.4995/head20.2020.11187.

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Learning new skills isn’t only for the benefit of passing the exam but being able to apply those skills in a productive way. One cannot learn before one understands which is why student understanding is a priority for facilitators. This becomes especially important in threshold concepts where a student will be unable to progress to the next stage before the threshold concept is mastered, but facilitators do not focus on pedagogy as they rely on the support of instructional designers. This explorative paper looks at student perceptions of their understanding of the threshold concept in electrical engineering, logic gates, after completing a lesson designed using the proposed ten-step activity plan. The activity plan is derived from the learning theories of Gagne, Biggs, Vygotsky and Gibson. A sample of 18 students completed an online survey that focused on their acquiring of skills relating to logic gates, truth tables and Boolean algebra. Results showed a positive experience with 88.89% of participants indicating that they left the lesson with a good understanding of the threshold concept. This ten-step activity plan can assist to close the gap between instructional designer and facilitator to design threshold concept lessons based on sound learning theory.
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