On Algebraic Expressions of Series-Parallel and Fibonacci Graphs

2003 ◽  
pp. 215-224 ◽  
Author(s):  
Mark Korenblit ◽  
Vadim E. Levit
Keyword(s):  
Algebraic Expressions

scholarly journals Examination of Semantic Structures Used by Teacher Candidates to Transform Algebraic Expressions into Verbal Problems

2021 ◽  
Vol 4 (3) ◽  
Author(s):  
Ayten Pinar Bal ◽  
Keyword(s):  
Teacher Candidates ◽  
Quantitative Research ◽  
Algebraic Expression ◽  
Study Group ◽  
State University ◽  
Algebraic Expressions ◽  
Purposeful Sampling ◽  
Division Problems ◽  
Addition And Subtraction ◽  
Research Types

The aim of this study is to examine the semantic structures used by mathematics teacher candidates to transform algebraic expressions into verbal problems. The research is a descriptive study in the survey model, which is one of the quantitative research types. The study group of the research consists of 165 teacher candidates studying in the primary school mathematics teaching department of a state university in the south of Turkey in the 2019-2020 academic years. 73.2% of the teacher candidates in the study group are female and 26.8% are male. Criterion sampling method, one of the purposeful sampling methods, was used in the selection of teacher candidates in the study group. While the Algebraic Expression Questionnaire Form was used as the data collection tool, the evaluation rubric of verbal problems was used in the analysis of the data. As a result of the research, it has been revealed that pre-service teachers are more successful in transforming algebraic expressions into verbal problems, but they have problems in creating problems with algebraic expressions that make up systems of equations. Again in the study, it was concluded that pre-service teachers used addition and subtraction problems more than multiplication and division problems. On the other hand, when the problems in the type of addition and subtraction are examined in the study, in the type of combining and separating; It has been concluded that the category of equal groups is mostly used in the problems of multiplication and division.

scholarly journals Adaptabilidade de Objetos de Aprendizagem usando Calibragem e Sequenciamento Adaptativo de Exercícios

2018 ◽  
Vol 26 (1) ◽  
pp. 70
Author(s):  
Rômulo César Silva ◽  
Alexandre Ibrahim Direne ◽  
Diego Marczal ◽  
Ana Carla Borille ◽  
Paulo Ricardo Bittencourt Guimarães ◽  
...  
Keyword(s):  
Problem Solving ◽  
Empirical Study ◽  
Cognitive Skills ◽  
Learning Objects ◽  
Skill Level ◽  
Problem Solution ◽  
Algebraic Expressions ◽  
Student Skill ◽  
Definition Of ◽  
Two Parameters

The work approaches theoretical and implementation issues of a framework for creating and executing Learning Objects (LOs) where problem-solving tasks are ordered according to the matching of two parameters, both calculated automatically: (1) student skill level and (2) problem solution difficulty. They are formally defined as algebraic expressions. The definition of skill level is achieved through a rating-based measure that resembles the ones of game mastery scales, while the solution difficulty is based on mistakes and successes of learners to deal with the problem. An empirical study based on existing students data demonstrated the suitability of the formulas. Besides, the motivational aspects of learning are considered in depth. In this sense, it is important to propose activities according to the student’s level of expertise, which is achieved through presenting students with exercises that are compatible with the difficulty degree of their cognitive skills. Also, the results of an experiment conducted with four highschool classes using the framework for the domain of logarithmic properties are presented.

scholarly journals The Estimation of Missing Values in Rectangular Lattice Designs

2019 ◽  
Vol 17 (2) ◽  
pp. 2-23
Author(s):  
Emmanuel Ogochukwu Ossai ◽  
Abimibola Victoria Oladugba
Keyword(s):  
Missing Data ◽  
Missing Values ◽  
Sum Of Squares ◽  
Rectangular Lattice ◽  
Algebraic Expressions

<p>Algebraic expressions for estimating missing data when one or more observation(s) are missing in Rectangular lattice designs with repetition were derived using the method of minimizing the residual sum of squares. Results showed that the estimated value(s) were significantly approximate to that of the actual value(s).</p>

Asymptotic Approximations for Systems Incorporating Fractional Derivative Damping

1996 ◽  
Vol 118 (3) ◽  
pp. 572-579 ◽  
Author(s):  
B. S. Liebst ◽  
P. J. Torvik
Keyword(s):  
Fractional Derivative ◽  
Natural Frequency ◽  
Fractional Derivatives ◽  
Asymptotic Approximations ◽  
Damping Factor ◽  
Polynomial Equations ◽  
Algebraic Expressions ◽  
Dependent Behavior ◽  
Fractional Derivative Damping ◽  
Damping Materials

Viscoelastic constitutive relationships incorporating fractional derivatives have been previously shown to be extremely useful in describing the frequency dependent behavior of common damping materials. However, the implementation of such models in the analysis of damped mechanical systems is somewhat complicated by the fact that polynomial equations with noninteger order exponents must be solved. This paper develops accurate approximations from which the damping factor and damped natural frequency of such systems may be obtained by evaluating relatively simple algebraic expressions.

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