scholarly journals Extending a Euclidean Model of Ratio and Proportion

2021 ◽  
Author(s):  
David W. Carraher
Keyword(s):  
Educational Software ◽  
Number Line ◽  
Smooth Transition ◽  
Critical Conditions ◽  
Software Application ◽  
Ratio And Proportion ◽  
Whole Numbers ◽  
Teachers And Students ◽  
Cartesian Plane ◽  
Target Ratio

Abstract This paper is written for mathematics educators and researchers engaged at the elementary and middle school levels and interested in exploring ideas and representations for introducing students to ratio and proportion and for making a smooth transition from multiplication and division by whole numbers to their counterparts with fractions. Book V of Euclid’s Elements offers a scenario for deciding whether two ratios of magnitudes, embodied as a pair of line segments, are equal based on whether the ratios of magnitudes, when multiplied by the same whole numbers, n and m, each yield common products. This test of proportion can be performed using an educational software application where students are presented with a target ratio of commensurable magnitudes, A:B, and challenged to produce a selected ratio, C:D, that behaves like the target ratio under the critical conditions. The selected ratio is automatically constructed such that C:D = m:n, on the basis of a lattice point (n, m) chosen by the student. By adding partitive and Euclidean division to Euclid’s model, five new scenarios with similar goals are proposed. Representations in the Euclidean plane, on a number line, and in the Cartesian plane provide feedback that students may use to help identify a ratio of whole numbers corresponding to the targe ratio of magnitudes. The representations serve to highlight fractions as members of equivalence classes. The model remains to be investigated with teachers and students.

scholarly journals Multimodal Affective Computing to Enhance the User Experience of Educational Software Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Jose Maria Garcia-Garcia ◽  
Víctor M. R. Penichet ◽  
María Dolores Lozano ◽  
Juan Enrique Garrido ◽  
Effie Lai-Chong Law
Keyword(s):  
User Experience ◽  
Affective Computing ◽  
Educational Software ◽  
Control Group ◽  
Emotional States ◽  
Emotion Detection ◽  
Software Application ◽  
Software Applications ◽  
Learning Progress ◽  
The One

Affective computing is becoming more and more important as it enables to extend the possibilities of computing technologies by incorporating emotions. In fact, the detection of users’ emotions has become one of the most important aspects regarding Affective Computing. In this paper, we present an educational software application that incorporates affective computing by detecting the users’ emotional states to adapt its behaviour to the emotions sensed. This way, we aim at increasing users’ engagement to keep them motivated for longer periods of time, thus improving their learning progress. To prove this, the application has been assessed with real users. The performance of a set of users using the proposed system has been compared with a control group that used the same system without implementing emotion detection. The outcomes of this evaluation have shown that our proposed system, incorporating affective computing, produced better results than the one used by the control group.

scholarly journals Bridging Symbolic Computation and Economics: A Dynamic and Interactive Tool to Analyze the Price Elasticity of Supply

2019 ◽  
Vol 24 (4) ◽  
pp. 87 ◽  
Author(s):  
Jorge M. Andraz ◽  
Renato Candeias ◽  
Ana C. Conceição
Keyword(s):  
Digital Technology ◽  
Computer Algebra System ◽  
Educational Software ◽  
Distributed Application ◽  
Student Activity ◽  
Wolfram Mathematica ◽  
Interactive Tool ◽  
Teachers And Students ◽  
Theoretical Results ◽  
Document Format

It is not possible to achieve the objectives and skills of a program in economics, at the secondary and undergraduate levels, without resorting to graphic illustrations. In this way, the use of educational software has been increasingly recognized as a useful tool to promote students’ motivation to deal with, and understand, new economic concepts. Current digital technology allows students to work with a large number and variety of graphics in an interactive way, complementing the theoretical results and the so often used paper and pencil calculations. The computer algebra system Mathematica is a very powerful software that allows the implementation of many interactive visual applications. Thanks to the symbolic and numerical capabilities of Mathematica, these applications allow the user to interact with the graphical and analytical information in real time. However, Mathematica is a commercially distributed application which makes it difficult for teachers and students to access. The main goal of this paper is to present a new dynamic and interactive tool, created with Mathematica and available in the Computable Document Format. This format allows anyone with a computer to use, at no cost, the PES(Linear)-Tool, even without an active Wolfram Mathematica license. The PES(Linear)-Tool can be used as an active learning tool to promote better student activity and engagement in the learning process, among students enrolled in socio-economic programs. This tool is very intuitive to use which makes it suitable for less experienced users.

The case for a more universal number-line model of subtraction

1973 ◽  
Vol 20 (1) ◽  
pp. 61-64
Author(s):  
Sister Marijane Werner
Keyword(s):  
Elementary School ◽  
Elementary School Teachers ◽  
Teaching Strategy ◽  
Number Line ◽  
School Teachers ◽  
Guided Discovery ◽  
Elementary School Mathematics ◽  
Whole Numbers ◽  
Single Exception ◽  
Mathematics Program

The use of a number line as a model for the four fundamental operations of mathematics has become a fairly common and effective teaching strategy. The number line has been the means to guided discovery for many pupils in the elementary school mathematics program. However, the model of subtraction of whole numbers on the number line that authors and editors of textbooks for teachers and pupils have commonly used has severe limitations. The single exception to this observation is the thirtieth yearbook of the NCTM, More Topics in Mathematics for Elementary School Teachers (1969), but the approach used there has not caught fire. Perhaps we need to rekindle the fire.

Technology-Enhanced Learning

2013 ◽  
pp. 963-978
Author(s):  
Adrian F. Ashman
Keyword(s):  
Rural Communities ◽  
Educational Software ◽  
Universal Design For Learning ◽  
Technology Enhanced Learning ◽  
Special Schools ◽  
Use Of Technology ◽  
Design For Learning ◽  
Teachers And Students ◽  
Information And Communication ◽  
Enhanced Learning

Small, modestly funded and resourced schools can be disadvantaged by limited access to information and communication technology (ICT). This chapter outlines a two-year project conducted in six small special schools located in metropolitan and rural communities. The project was designed to increase the participating schools’ ICT capabilities and promote the use of technology to deliver the curriculum in efficient and appealing ways to their students with a diversity of intellectual and behavioral difficulties. An ICT specialist supported the schools over the course of the project and promoted the introduction of Universal Design for Learning. At the conclusion of the project all schools had made notable gains in acquiring state-of-the-art technology. Teachers and students had become capable and enthusiastic users of hardware and a range of operating and educational software.

scholarly journals Evaluation of an educational technology regarding clinical evaluation of preterm newborns

2013 ◽  
Vol 21 (1) ◽  
pp. 363-370 ◽  
Author(s):  
Luciana Mara Monti Fonseca ◽  
Natália Del'Angelo Aredes ◽  
Adriana Moraes Leite ◽  
Claudia Benedita dos Santos ◽  
Regina Aparecida Garcia de Lima ◽  
...  
Keyword(s):  
Nursing Students ◽  
Educational Software ◽  
Point Of View ◽  
Undergraduate Nursing Students ◽  
Neonatal Nursing ◽  
Undergraduate Nursing ◽  
Teachers And Students ◽  
Examination Techniques ◽  
Nursing Courses ◽  
Preterm Newborns

AIM: To evaluate, from the students' point of view, educational software developed as a tool to help teachers and students in neonatal nursing. METHOD: The study evaluates the contents and simulations addressed in the software. A total of 57 undergraduate nursing students affiliated with five Brazilian public colleges participated. RESULTS: The general assessment of the software was highly satisfactory: 82.4% of the sample characterized the software as quite effective as a teaching tool. Most components were assessed as good or very good. The participants' suggestions and comments are being considered in the improvement and adaptation of the new software version. CONCLUSION: The results show that the product is adequate for use in neonatal nursing courses and nursing training on the physical examination techniques and semiology of preterm newborns, falling within the pedagogical framework of active methods.

Rapid Communication: Understanding the Real Value of Fractions and Decimals

2011 ◽  
Vol 64 (11) ◽  
pp. 2088-2098 ◽  
Author(s):  
Teresa Iuculano ◽  
Brian Butterworth
Keyword(s):  
Linear Representation ◽  
Number Line ◽  
Target Number ◽  
The Real ◽  
Rapid Communication ◽  
Whole Numbers ◽  
Whole Number ◽  
Adults And Children ◽  
Real Value

Understanding fractions and decimals is difficult because whole numbers are the most frequently and earliest experienced type of number, and learners must avoid conceptualizing fractions and decimals in terms of their whole-number components (the “whole-number bias”). We explored the understanding of fractions, decimals, two-digit integers, and money in adults and 10-year-olds using two number line tasks: marking the line to indicate the target number, and estimating the numerical value of a mark on the line. Results were very similar for decimals, integers, and money in both tasks for both groups, demonstrating that the linear representation previously shown for integers is also evident for decimals already by the age of 10. Fractions seem to be “task dependent” so that when asked to place a fractional value on a line, both adults and children displayed a linear representation, while this pattern did not occur in the reverse task.

scholarly journals Estratégias didático-metodológicas com GeoGebra para o ensino e a aprendizagem de quadrantes no plano cartesianoDidactic-methodological strategies for teaching and learning Cartesian quadrants using GeoGebra

2021 ◽  
Vol 23 (1) ◽  
pp. 355-390
Author(s):  
Sarah Souto dos Santos ◽  
Aleandra Da Silva Figueira-Sampaio ◽  
Eliane Elias Ferreira dos Santos
Keyword(s):  
Middle School ◽  
Public Schools ◽  
Elementary Education ◽  
Middle School Teachers ◽  
Teaching And Learning ◽  
School Teachers ◽  
9Th Grade ◽  
Teachers And Students ◽  
Cartesian Plane ◽  
Investigación Cualitativa

ResumoNa educação básica, as primeiras noções sobre o plano cartesiano iniciam com a identificação dos eixos coordenados e com a compreensão de que estes dividem o plano em quatro regiões chamadas de quadrantes. Esse entendimento se estende com a compreensão das noções relativas à posição, localização de figuras e deslocamentos no plano cartesiano. O objetivo do trabalho foi propor estratégias didático-metodológicas com o GeoGebra na abordagem matemática de quadrantes no plano cartesiano. Trata-se de uma pesquisa qualitativa, de caráter exploratório, desenvolvida com professores de matemática do ensino fundamental II (do 6º ao 9º ano) de escolas públicas. A escolha do GeoGebra foi pelas funcionalidades que podem contribuir para o entendimento da temática. As estratégias didático-metodológicas foram elaboradas em fichas padronizadas e detalhadas para que professores e alunos tenham um roteiro de orientação durante a atividade.Palavras-chave: Software gratuito, Ensino fundamental (6º ao 9º ano), Educação matemática.AbstractIn elementary education, initial notions of the Cartesian plane start with identification of coordinate axes and the recognition that these divide planes into four quadrants.  This initial understanding extends to notions related to position, location, and displacement in the Cartesian plane. Our objective was to propose didactic-methodological strategies to introduce Cartesian quadrants using GeoGebra.  This qualitative study had an exploratory nature and was developed with middle-school teachers (6th to 9th grades) from public schools. GeoGebra was chosen because of features that contribute to building an understanding of the topic. The didactic-methodological strategies were standardised and detailed so that teachers and students would be guided throughout the activity.Keywords: Free software, Middle school (6th to 9th grade), Mathematics education.ResumenEn la educación básica, las primeras nociones sobre el plano cartesiano comienzan con la identificación de los ejes coordinados y con la comprensión de que dividen el plano en cuatro regiones llamadas cuadrantes. Ese entendimiento se extiende con la comprensión de nociones relativas de posición, ubicación de figuras y desplazamientos en el plano cartesiano. El objetivo del trabajo fue proponer estrategias didáctico-metodológicas con el GeoGebra para el enfoque matemático de cuadrantes en el plano cartesiano. Trátase de una investigación cualitativa, de carácter exploratoria, desarrollada con maestros de matemáticas del liceo (del 6º al 9º grado) de la enseñanza pública. La elección del GeoGebra fue por sus funcionalidades poder contribuir para la comprensión del tema. Las estrategias didáctico-metodológicas fueron elaboradas en formularios estándares y detallados para que profesores y alumnos tengan una guía de orientación durante la actividad.Palabras clave: Software libre, Liceo (6º al 9º grado), Educación matemática.

scholarly journals Carbohydrates Through Animation: Preliminary Step

2004 ◽  
Vol 2 (2) ◽  
pp. 4
Author(s):  
J.K. Sugai ◽  
M.S.R. Figueiredo ◽  
R.V. Antônio ◽  
P.M Oliveira ◽  
V.A Cardoso ◽  
...  
Keyword(s):  
Learning Process ◽  
Concept Maps ◽  
Educational Software ◽  
New Technology ◽  
Educational Tools ◽  
Preliminary Step ◽  
Modern Education ◽  
Teachers And Students ◽  
Information And Communication ◽  
Education Needs

Methods of education are changing, so the educational tools must change too. The developmentof the systems of information and communication gave the opportunity to bring new technology tothe learning process. Modern education needs interactive programs that may be available to theacademic community, in order to ease the learning process and sharing of the knowledge. Then,an educational software on Carbohydrates is being developed using concept maps and FLASH-MXanimations program, and approached through six modules. The introduction of Carbohydrates wasmade by the module Carbohydrates on Nature, which shows the animations gures of a teacher andstudents, visiting a farm, identifying the carbohydrates found in vegetables, animals, and microor-ganisms, integrated by links containing short texts to help understanding the structure and functionof carbohydrates. This module was presented, as pilot experiment, to teachers and students, whichdemonstrated satisfaction, and high receptivity, by using animation and interactivitys program asstrategy to biochemistrys education. The present work is part of the project Biochemistry throughanimation, which is having continuity.

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