Human-Computer Interaction in 3D Object Manipulation in Virtual Environments: a Cognitive Ergonomics Contribution Sarwan Abbasi
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Representing Exact Number Visually Using Mental Abacus
Journal of Experimental Psychology: General © 2011 American Psychological Association 2011, Vol. ●●, No. ●, 000–000 0096-3445/11/$12.00 DOI: 10.1037/a0024427 Representing Exact Number Visually Using Mental Abacus Michael C. Frank David Barner Stanford University University of California, San Diego Mental abacus (MA) is a system for performing rapid and precise arithmetic by manipulating a mental representation of an abacus, a physical calculation device. Previous work has speculated that MA is based on visual imagery, suggesting that it might be a method of representing exact number nonlinguistically, but given the limitations on visual working memory, it is unknown how MA structures could be stored. We investigated the structure of the representations underlying MA in a group of children in India. Our results suggest that MA is represented in visual working memory by splitting the abacus into a series of columns, each of which is independently stored as a unit with its own detailed substructure. In addition, we show that the computations of practiced MA users (but not those of control participants) are relatively insensitive to verbal interference, consistent with the hypothesis that MA is a nonlinguistic format for exact numerical computation. Keywords: abacus, mental arithmetic, number, visual cognition Human adults, unlike other animals, have the capacity to per- Previous work, reviewed below, has described the MA phenom- form exact numerical computations. Although other creatures are enon and has provided suggestive evidence that MA is represented sensitive to precise differences between small quantities and can nonlinguistically, in a visual format. However, this proposal re- represent the approximate magnitude of large sets, no nonhuman mains tentative for two reasons. -
Project Design: Tetris
Project Design: Tetris Prof. Stephen Edwards Spring 2020 Arsalaan Ansari (aaa2325) Kevin Rayfeng Li (krl2134) Sooyeon Jo (sj2801) Josh Learn (jrl2196) Introduction The purpose of this project is to build a Tetris video game system using System Verilog and C language on a FPGA board. Our Tetris game will be a single player game where the computer randomly generates tetromino blocks (in the shapes of O, J, L, Z, S, I) that the user can rotate using their keyboard. Tetrominoes can be stacked to create lines that will be cleared by the computer and be counted as points that will be tracked. Once a tetromino passes the boundary of the screen the user will lose. Fig 1: Screenshot from an online implementation of Tetris User input will come through key inputs from a keyboard, and the Tetris sprite based output will be displayed using a VGA display. The System Verilog code will create the sprite based imagery for the VGA display and will communicate with the C language game logic to change what is displayed. Additionally, the System Verilog code will generate accompanying audio that will supplement the game in the form of sound effects. The C game logic will generate random tetromino blocks to drop, translate key inputs to rotation of blocks, detect and clear lines, determine what sound effects to be played, keep track of the score, and determine when the game has ended. Architecture The figure below is the architecture for our project Fig 2: Proposed architecture Hardware Implementation VGA Block The Tetris game will have 3 layers of graphics. -
A Review of Research on Addition and Subtraction. Working Paper No
DOCADIENIIRESUME ED 223 447 SE 039, 613 AUTHOR' Carpenter, Thomas P.; And Others TITLE A Review of Re'search on Addition andSubtraction. Working Paper No. 330.-Report from the Program on Student Diversity and Classroom Processes. -INSTITUTION Wisconsin Center for Education Research, Madison. SPONS AGENCY National Inst. of Education (ED), Washington, DC. PUB DATE Sep 82 GRANT NIE-G-81-0009 NOTE 186p. PUB TYPE Information Analyses (070) EDRS PRICE MF01/PC08 Plus Postage. DESCRIPTORS *Addition; *Basic Skills; Cognitive Processes; Computation; Educational Research; Elementary Education; *Elementary School Mathematics; *Learning Theories; Literature Reviews; Mathematical Concepts; Mathematics Instructioh; Problem Solving; *SubtraCtion IDENTIFIERS *Mathematics Education Research; Word PrOblems ABSTRACT This material is designed to examine the research on how children acquire basic addition and subtractionconcepts and skills. Two major lines of theories of the development ofbasic number concepts, called logical concept and quantificationskill approaches, are identified. Mjcir recurring issues in thedevelopment of early number concepts are also discussed.This is followed by examination of studies specifically related to addition and subtraction: It is noted that by kindergarten mostchildren understand the rudiments of these operations, but a complete understanding develops over a protracted span of years.The direction 4of initial and ongoing ,research is discussed,and word problem studies and investigations on children's Solutions ofsymbolic -
Roles of Semantic Structure of Arithmetic Word Problems on Pupils’ Ability to Identify the Correct Operation
ROLES OF SEMANTIC STRUCTURE OF ARITHMETIC WORD PROBLEMS ON PUPILS’ ABILITY TO IDENTIFY THE CORRECT OPERATION J ustin D. V ale nt in and Dr Lim Chap Sam (University of Science Malaysia) December,Dec em ber , 20042 004 Abstract This paper draws on findings from a study conducted in seven primary schools in Seychelles about pupils’ proficiency in one-step arithmetic word problems to discuss the roles of semantic structures of the problems on the pupils’ ability to identify the operation required to solve them. A sample of 530 pupils drawn from Primary 4, 5 and 6 responded to a 52 multiple choice item test in which they were to read a problem and select the operation that is required to solve it. The results showed some consistencies with other international studies in which pupil related better to additive than to multiplicative problems. Moreover, they could solve better those problems that do not involve relational statements. The general picture indicated that there is an overall increase in performance with an increase in grade level yet, when individual schools are considered this increase in performance in significant in only one school. In the other results there were many cases of homogenous pairs of means. Analysis of distractors conducted on the pupils’ responses to the seventeen most difficult items reveal that in most cases when an item required the operation indicating an additive or multiplicative structure, the most popular wrong answer would be one of the same semantic structure. Otherwise there is a strong tendency for the pupils to select the operation of addition when they could not identify the correct operation for a particular problem. -
Strategy Use and Basic Arithmetic Cognition in Adults
STRATEGY USE AND BASIC ARITHMETIC COGNITION IN ADULTS A Thesis Submitted to the College of Graduate Studies and Research in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in the Department of Psychology University of Saskatchewan Saskatoon By Arron W. S. Metcalfe ©Copyright Arron W. Metcalfe, October 2010. All Rights Reserved. PERMISSION TO USE In presenting this dissertation in partial fulfillment of the requirements for a Postgraduate degree from the University of Saskatchewan, I agree that the Libraries of this University may make it freely available for inspection. I further agree that permission for copying of this dissertation in any manner, in whole or in part, for scholarly purposes may be granted by the professor or professors who supervised my dissertation work or, in their absence, by the Head of the Department or the Dean of the College in which my thesis work was done. It is understood that any copying or publication or use of this dissertation or parts thereof for financial gain shall not be allowed without my written permission. It is also understood that due recognition shall be given to me and to the University of Saskatchewan in any scholarly use which may be made of any material in my thesis/dissertation. Requests for permission to copy or to make other uses of materials in this dissertation in whole or part should be addressed to: Head of the Department of Psychology University of Saskatchewan Saskatoon, Saskatchewan S7N 5A5 Canada i ABSTRACT Arithmetic cognition research was at one time concerned mostly with the representation and retrieval of arithmetic facts in memory. -
Homework 4: Tetronimoes
CS 371M Homework 4: Tetronimoes Submission: All submissions should be done via git. Refer to the git setup, and submission documents for the correct procedure. The root directory of your repository should contain your README file, and your Android Studio project directory. Overview: “If Tetris has taught me anything, it’s that errors pile up and accomplishments disappear.” – Some guy on Reddit In this and the next homework, you will be implementing a simple game of Tetris. For those who have never played Tetris, definitely try it out. Below is a link to a free online tetris game. Use the “up” arrow key to rotate the blocks. https://www.freetetris.org/game.php On the following page is a screenshot of the game as it should look for this class. For previous assignments, layout and quality of appearance have not been major factors in grading. However, appearance will be considered for this assignment. Your app should look at least as polished as the example app. API: We have defined several framework classes for your use. TCell: A class that represents a singe square. Each TCell has a color and (x,y) coordinates. TGrid: A class that creates a grid of cells. Use this to represent the main grid of cells in your game. This class also provides several utility functions that help you to detect and delete full rows of cells. Tetromino: A class that represents a Tetris Tetromino. This class can be inserted into a TGrid, moved, and rotated. All Tetromino movement functions return a Boolean value depending on whether the movement succeeded or not. -
The Posing of Division Problems by Preservice Elementary School Teachers: Conceptual Knowledge and Contextual Connections
DOCUMENT RESUME ED 381 348 SE 056 020 AUTHOR Silver, Edward A.; Burkett, Mary Lee TITLE The Posing of Divis;nn Problems by Preservice Elementary School Teachers: Conceptual Knowledge and Contextual Connections. SPONS AGENCY National Science Foundation, Washington, D.C. PUB DATE May 94 CONTRACT NSF-MDR-8850580 NOTE 32p.; Paper presented at the Annual Meeting of the American Educational Research Association (New Orleans, LA, April 1994). PUB TYPE Reports Research/Technical (143) Speeches /Conference Papers (150) EDRS PRICE MF01/PCO2 Plus Postage. DESCRIPTORS Arithmetic; *Division; Elementary Education; *Elementary School Teachers; Higher Education; 'Mathematics Instruction; Preservice Teacher Education; *Questioning Techniques IDENTIFIERS Mathematics Education Research; *Preservice Teachers; Problem Posing; Situated Lep.rning; *Subject Content Knowledge ABSTRACT Previous research has suggested that many elementary school teachers have a firmer understanding of addition and subtraction concepts than they have of more complex topics in elementary mathematics, such as division. In this study, (n=24) prospective elementary teachers' understanding of aspects of division involving remainders was explored by examining the problems they posed. The tea-:hers' responses revealed a clear preference for posing problems associated with real world contexts, suggesting that the term "story problem" had that particular meaning for this group. Although the vast majority of problems were situated in contexts, the problems and solutions frequently did not represent a solid connection between the mathematical and situational aspects of the problem. About two-thirds of the subjects spontaneously posed problems and proposed solutions that reflected their understanding of the relationship between the given computation and at least one member of its family of associated computations. -
Arithmetical Development: Commentary on Chapters 9 Through 15 and Future Directions
ARITHMETICAL DEVELOPMENT: COMMENTARY ON CHAPTERS 9 THROUGH 15 AND FUTURE DIRECTIONS David C. Geary University of Missouri at Columbia The second half of this book focuses on the important issues of arithmetical instruction and arithmetical learning in special populations. The former repre- sents an area of considerable debate in the United States, and the outcome of this debate could affect the mathematics education of millions of American children (Hirsch, 1996; Loveless, 2001). At one of the end points of this debate are those who advocate an educational approach based on a constructivist philosophy, whereby teachers provide materials and problems to solve but allow students leeway to discover for themselves the associated concepts and problem-solving procedures. At the other end are those who advocate direct instruction, whereby teachers provide explicit instruction on basic skills and concepts and children are required to practice these basic skills. In the first section of my commentary, I briefly address this debate, as it relates to chapters 9, 10, and 11 (by Dowker; Fuson and Burghardt; and Ambrose; Baek, and Carpenter respectively). Chapters 12 to 15 (by Donlan; Jordan, Hanich, and Uberti; and Delazer; and Heavey respectively) focus on the important issue of arithmetical learning in special populations, a topic that has been largely neglected, at least in relation to research on reading competencies in special populations. I discuss these chapters and related issues in the second section of my commentary. In the third, I briefly consider future directions. Instructional Research (Chapters 9 to 11) Constructivism is an instructional approach based on the developmental theories of Piaget and Vygotsky (e.g., Cobb, Yackel, & Wood, 1992). -
Tetromino Reptiles
Mathigon – Lesson Plan Tetromino Reptiles Standards Prior knowledge NC Key Stage 3: Use scale factors, scale diagrams and maps It will help if students have some familiarity with expressing relationships CCSS 7.G.A.1: Solve problems involving scale drawings of using ratio, and with square numbers. geometric figures Lesson outline This task uses Polypad’s tetrominoes as a context for exploring enlargements (dilations) and scale factors. Tetrominoes are shapes which can be made from 4 individual squares, and will be instantly recognisable to any student who has played the classic game Tetris. Lesson objective: Understand how the area of a shape changes when it is enlarged. Lesson activity Warm-up Show students this Polypad canvas. Explain that two of the tetrominoes have been enlarged (dilated) correctly, but two of them have mistakes. Invite students to work out the scale factor by which the two correct enlargements have been drawn, and to use the pen tool (or copy the diagrams onto squared paper) to correct the mistakes in the Canvas Link incorrect enlargements. Solution: The square has been correctly enlarged by a scale factor of 3, and the L tetromino has been correctly enlarged by a scale factor of 5. The T tetromino and the Z tetromino have not been enlarged correctly. If students haven’t seen tetrominoes before, and you think they could benefit from additional scaffolding before the warm up above, you could challenge them to find all the different arrangements of four 1-square tiles. They can use this canvas as a starting point. Main Activity Some shapes can be used to tile an enlargement of themselves – this is sometimes called a rep-tile. -
A Speech Therapy Game for Children with Speech Sound Disorders
Apraxia World: A Speech Therapy Game for Children with Speech Sound Disorders Adam Hair* Penelope Monroe* Beena Ahmed Texas A&M University University of Sydney University of New South Wales College Station, TX, USA Sydney, NSW, Australia Sydney, NSW, Australia [email protected] [email protected] Texas A&M University at Qatar Doha, Qatar [email protected] Kirrie J. Ballard Ricardo Gutierrez-Osuna University of Sydney Texas A&M University Sydney, NSW, Australia College Station, TX, USA [email protected] [email protected] ABSTRACT INTRODUCTION This paper presents Apraxia World, a remote therapy tool Speech sound disorders (SSDs) can affect language for speech sound disorders that integrates speech exercises production and speech articulation in children, leading to into an engaging platformer-style game. In Apraxia World, serious communicative disabilities [4]. Estimates for the the player controls the avatar with virtual buttons/joystick, prevalence of SSDs in children vary; some suggest between whereas speech input is associated with assets needed to 2% and 25% of children aged 5-7 years may be affected advance from one level to the next. We tested performance [21], while others estimate values closer to 1% of the and child preference of two strategies for delivering speech primary-school-aged population [26]. Regardless of their exercises: during each level, and after it. Most children exact prevalence, SSDs can have potentially devastating indicated that doing exercises after completing each level effects on a child’s communication development [10]. was less disruptive and preferable to doing exercises Fortunately, children can reduce symptoms and improve scattered through the level. -
Developing a Pedagogical Domain Theory of Early Algebra Problem Solving Kenneth R
Developing a Pedagogical Domain Theory of Early Algebra Problem Solving Kenneth R. Koedinger Benjamin A. MacLaren March 2002 CMU-CS-02-119 CMU-HCII-02-100 School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 Abstract We describe a theory of quantitative representations and processes that makes novel predictions about student problem-solving and learning during the transition from arithmetic to algebraic competence or "early algebra". Our Early Algebra Problem Solving (EAPS) theory comes in the form of a cognitive model within the ACT-R cognitive architecture. As a "pedagogical domain theory", our EAPS theory can be used to make sense of the pattern of difficulties and successes students experience in early algebra problem solving and learning. In particular, the theory provides an explanation for the surprising result that algebra students perform better on certain word problems than on equivalent equations (Koedinger & Nathan, 2000; Nathan & Koedinger, 2000). It also makes explicit the knowledge and knowledge selection processes behind student strategies and errors and provides a theoretical tool for psychologists and mathematics educators to both productively generate and accurately evaluate hypotheses about early algebra learning and instruction. We have abstracted our development process into six model-building constraints that may be appropriate for creating cognitive models of problem solving in other domains. This research was supported by a grant from the James S. McDonnell Foundation program in Cognitive Studies for Educational Practice, grant #95-11. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the McDonnell Foundation. -
BOOK the Tetris Effect: the Game That Hypnotized the World
Notes by Steve Carr [www.houseofcarr.com/thread] BOOK The Tetris Effect: The Game That Hypnotized the World AUTHOR Dan Ackerman PUBLISHER Public Affairs PUBLICATION DATE September 2016 SYNOPSIS [From the publisher] In this fast-paced business story, reporter Dan Ackerman reveals how Tetris became one of the world's first viral hits, passed from player to player, eventually breaking through the Iron Curtain into the West. British, American, and Japanese moguls waged a bitter fight over the rights, sending their fixers racing around the globe to secure backroom deals, while a secretive Soviet organization named ELORG chased down the game's growing global profits. The Tetris Effect is an homage to both creator and creation, and a must-read for anyone who's ever played the game-which is to say everyone. “Henk Rogers flew on February 21, 1989. He was one of three competing Westerners descending on Moscow nearly simultaneously. Each was chasing the same prize, an important government-controlled technology that was having a profound impact on people around the world . That technology was perhaps the greatest cultural export in the history of the USSR, and it was called Tetris . Tetris was the most important technology to come out of that country since Sputnik.” “Tetris was different. It didn’t rely on low-fi imitations of cartoon characters. In fact, its curious animations didn’t imitate anything at all. The game was purely abstract, geometry in real time. It wasn’t just a game, it was an uncrackable code puzzle that appealed equally to moms and mathematicians.” “Tetris was the first video game played in space, by cosmonaut Aleksandr A.