scholarly journals Registros de representação semiótica, relevância e conciliação de metas: uma análise do capítulo Sistemas de equações do 1º grau com duas incógnitas do livro Matemática compreensão e prática de Ênio SilveiraRegisters of semiotic representation, relevance and goal-conciliation: an analysis of the chapter about systems of linear equations with two variables in Ênio Silveira’s book Matemática conpreensão e prática

2018 ◽  
Vol 20 (2) ◽  
Author(s):  
Vanessa Isabel Cataneo ◽  
Fábio José Rauen
Keyword(s):  
Problem Solving ◽  
Natural Language ◽  
Linear Equations ◽  
Intentional Action ◽  
Problem Situations ◽  
Semiotic Representations ◽  
8Th Grade ◽  
Systems Of Linear Equations ◽  
Cognitive Activities

Analisamos neste artigo o capítulo Sistemas de equações do 1º grau com duas incógnitas do livro Matemática Compreensão e Prática: 8º ano, de Ênio Silveira, a partir das noções teóricas de registros de representação semiótica, relevância e conciliação de metas. Assumimos a hipótese de que as atividades cognitivas de formação de representações identificáveis, tratamento e conversão de representações semióticas estão à serviço de conciliações ativas relevantes de um plano de ação intencional do autor que é passível de ser descrito e explicado pelos estágios de formulação de metas e de formulação, execução e checagem de hipóteses abdutivas antefactuais habilitadoras. Os resultados sugerem prevalência de exemplos e atividades que demandam conversão de representações de situações-problema em língua natural para a representação no registro algébrico, pouco desenvolvimento de interpretações gráficas, casos raros de conversões inversas e ausência de propostas de elaboração de problemas.We analyze in this article the chapter about systems of linear equations with two variables in Ênio Silveira’s book Matemática Compreensão e Prática: 8º ano [Mathematics comprehension and practice: 8th grade], using the theoretical notions of registers of semiotic representation, relevance and goal-conciliation. We assume that cognitive activities of formation of identifiable representations, treatment and conversion of semiotic representations are at the service of relevant active conciliations of an author’s plan of intentional action, which we can describe and explain by the stages of formulation of goals and formulation, execution and checking of enabling ante-factual abductive hypotheses. The results suggest prevalence of examples and activities that require conversion of representations of problem/situations in natural language into representations in algebraic register, little development of graphic interpretations, rare cases of reverse conversions and lack of proposals for problem solving.

scholarly journals The Use of BBC (Box, Board, and Comics) Media in The Systems of Linear Equation

2017 ◽  
Vol 2 (1) ◽  
pp. 283
Author(s):  
P D Widyastuti ◽  
M Mardiyana ◽  
D R S Saputro
Keyword(s):  
High School ◽  
Junior High School ◽  
Linear Equations ◽  
High School Senior ◽  
Design Development ◽  
Surrounding Environment ◽  
School Senior ◽  
8Th Grade ◽  
Systems Of Linear Equations ◽  
Analysis Design

<p class="Abstract">Mathematics is one of the lessons in school. Starting from elementary school, junior high school, senior high school, even college. Mathematics is abstract and identic with numbers, so the author guessed that maybe this is the reason why students consider that mathematics is a difficult lesson. In fact, the learners deliver the material step by step. First, the teacher introduced something concrete to the students (related to the surrounding environment). After that, teacher introduced something more abstract to the students. Sometimes, the transition from concrete to abstract become the problem in the learning process. One of the materials that convert concrete to abstract is systems of linear equations in 8th grade because in this stage students are introduced to more coefficients and variables. This article will discuss how to use media in the form of <em>BBC (Box, Board, and Comics)</em> on systems of linear equations. This research is about <em>Research and Development (R &amp;D). </em>The procedures of comics followed the <em>ADDIE </em>model which included analysis, design, development, implementation, and evaluation. This research aims to create a valid media based on the validation by the and students’ responses which can be proven that <em>BBC (Box, Board, and Comics)</em> media are interesting and worthy to use in the classroom.</p>

scholarly journals THE NEWMAN PROCEDURE FOR ANALYZING STUDENTS' ERRORS IN SOLVING SYSTEMS OF LINEAR EQUATIONS

2021 ◽  
Vol 6 (1) ◽  
pp. 31-44
Author(s):  
Veni Saputri ◽  
Rizal Kamsurya
Keyword(s):  
Problem Solving ◽  
Narrative Analysis ◽  
Linear Equations ◽  
Sampling Technique ◽  
High Ability ◽  
Research Subjects ◽  
Learning Content ◽  
Systems Of Linear Equations ◽  
High Ability Students ◽  
Low Ability

This study aimed to analyze students’ errors in problem-solving activities for systems of linear equations. The descriptive qualitative method was adopted and applied to obtain and process the research data. Research subjects were selected using the purposive sampling technique. Three participants were chosen according to their mathematical proficiency levels. Data collection was conducted by tests to measure students’ problem-solving abilities and semi-structural interviews to gather qualitative information about students’ errors in solving systems of linear equations. The interview results were analyzed using narrative analysis to obtain accurate conclusions. The study found that (1) low-ability students tend to perform error at the comprehension stage, (2) medium-ability students are likely to perform error at the transformation stage, and (3) high-ability students tend to perform error at the process skills stage. The solutions based on the ability level are: (1) low-ability students are required to read the question carefully, educators should emphasize the problem-solving procedure, and students should strengthen their understanding of the prerequisite learning content in problem-solving; (2) medium-ability students have to focus on the emphasis and development of their skills in understanding the language of a problem and balance with improving their understanding of learning content and contextual exercising; (3) high-ability students are provided with exercises that can improve their counting speed and accuracy of the subject in resolving a problem.

Complex Problem Solving and Worked Examples

2009 ◽  
Vol 23 (2) ◽  
pp. 129-138 ◽  
Author(s):  
Florian Schmidt-Weigand ◽  
Martin Hänze ◽  
Rita Wodzinski
Keyword(s):  
Problem Solving ◽  
Cognitive Load ◽  
Learning Experience ◽  
Worked Examples ◽  
Complex Problem ◽  
Complex Problem Solving ◽  
Strategic Learning ◽  
Learning Behavior ◽  
Worked Example ◽  
8Th Grade

How can worked examples be enhanced to promote complex problem solving? N = 92 students of the 8th grade attended in pairs to a physics problem. Problem solving was supported by (a) a worked example given as a whole, (b) a worked example presented incrementally (i.e. only one solution step at a time), or (c) a worked example presented incrementally and accompanied by strategic prompts. In groups (b) and (c) students self-regulated when to attend to the next solution step. In group (c) each solution step was preceded by a prompt that suggested strategic learning behavior (e.g. note taking, sketching, communicating with the learning partner, etc.). Prompts and solution steps were given on separate sheets. The study revealed that incremental presentation lead to a better learning experience (higher feeling of competence, lower cognitive load) compared to a conventional presentation of the worked example. However, only if additional strategic learning behavior was prompted, students remembered the solution more correctly and reproduced more solution steps.

On Some Properties of Semi-rings

2018 ◽  
pp. 35-50
Author(s):  
A. I. Belousov
Keyword(s):  
Linear Equations ◽  
Oriented Graph ◽  
Theoretical Computer Science ◽  
Alternative Methods ◽  
Main Role ◽  
Cost Matrix ◽  
Sequential Elimination ◽  
The Matrix ◽  
Systems Of Linear Equations ◽  
The Cost

The main objective of this paper is to prove a theorem according to which a method of successive elimination of unknowns in the solution of systems of linear equations in the semi-rings with iteration gives the really smallest solution of the system. The proof is based on the graph interpretation of the system and establishes a relationship between the method of sequential elimination of unknowns and the method for calculating a cost matrix of a labeled oriented graph using the method of sequential calculation of cost matrices following the paths of increasing ranks. Along with that, and in terms of preparing for the proof of the main theorem, we consider the following important properties of the closed semi-rings and semi-rings with iteration.We prove the properties of an infinite sum (a supremum of the sequence in natural ordering of an idempotent semi-ring). In particular, the proof of the continuity of the addition operation is much simpler than in the known issues, which is the basis for the well-known algorithm for solving a linear equation in a semi-ring with iteration.Next, we prove a theorem on the closeness of semi-rings with iteration with respect to solutions of the systems of linear equations. We also give a detailed proof of the theorem of the cost matrix of an oriented graph labeled above a semi-ring as an iteration of the matrix of arc labels.The concept of an automaton over a semi-ring is introduced, which, unlike the usual labeled oriented graph, has a distinguished "final" vertex with a zero out-degree.All of the foregoing provides a basis for the proof of the main theorem, in which the concept of an automaton over a semi-ring plays the main role.The article's results are scientifically and methodologically valuable. The proposed proof of the main theorem allows us to relate two alternative methods for calculating the cost matrix of a labeled oriented graph, and the proposed proofs of already known statements can be useful in presenting the elements of the theory of semi-rings that plays an important role in mathematical studies of students majoring in software technologies and theoretical computer science.

Spoken Natural Language Dialog Systems

1995 ◽  
Author(s):  
Ronnie W. Smith ◽  
D. Richard Hipp
Keyword(s):  
Problem Solving ◽  
Natural Language ◽  
Error Correction ◽  
User Model ◽  
Dialog Systems ◽  
Problem Solving Process ◽  
Processing Architecture ◽  
Dialog Processing

As spoken natural language dialog systems technology continues to make great strides, numerous issues regarding dialog processing still need to be resolved. This book presents an exciting new dialog processing architecture that allows for a number of behaviors required for effective human-machine interactions, including: problem-solving to help the user carry out a task, coherent subdialog movement during the problem-solving process, user model usage, expectation usage for contextual interpretation and error correction, and variable initiative behavior for interacting with users of differing expertise. The book also details how different dialog problems in processing can be handled simultaneously, and provides instructions and in-depth result from pertinent experiments. Researchers and professionals in natural language systems will find this important new book an invaluable addition to their libraries.

scholarly journals A Globally Convergent Parallel SSLE Algorithm for Inequality Constrained Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhijun Luo ◽  
Lirong Wang
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Descent Direction ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Globally Convergent ◽  
Variable Distribution ◽  
Systems Of Linear Equations

A new parallel variable distribution algorithm based on interior point SSLE algorithm is proposed for solving inequality constrained optimization problems under the condition that the constraints are block-separable by the technology of sequential system of linear equation. Each iteration of this algorithm only needs to solve three systems of linear equations with the same coefficient matrix to obtain the descent direction. Furthermore, under certain conditions, the global convergence is achieved.

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