The “5 E’s” instructional treatment, which is based on the principles of social constructivism, is currently
a very popular method for teaching, especially in school education. A hybrid model is developed in the
present paper for assessing the effectiveness of the “5 E’s” application for teaching mathematics to
engineering students of the University of Peloponnese, Greece. The model uses grey numbers and
neutrosophic sets for evaluating the mean student performance, whereas the quality performance is
assessed by calculating the Grade Point Average index.
Use of ICT for acquiring, practicing and assessing algebraic expertise Christian Bokhove
This document summarizes a research study investigating how ICT can support acquiring, practicing, and assessing algebraic expertise. The study was motivated by signals that students lack algebraic skills and the recognized potential of ICT in mathematics education. The central research question is: In what way can the use of ICT support acquiring, practicing and assessing algebraic expertise? This question is elaborated through sub-questions focusing on criteria for evaluating digital algebra tools, theoretical concepts to understand student behavior in digital environments, improving feedback design, implementing feedback principles in an intervention, and studying the effects of the intervention on algebraic expertise. The goal is to design an online intervention using a suitable digital tool to develop both procedural skills and conceptual understanding in algebra.
Honkela.t leinonen.t lonka.k_raike.a_2000: self-organizing maps and construct...ArchiLab 7
This document discusses using self-organizing maps (SOMs) to model constructive learning. It presents two key ideas:
1) SOMs provide a more realistic model of human learning than traditional computer memory models, as they are dynamic, associative, and adapt existing knowledge rather than just storing facts.
2) SOMs can be used in computer-supported collaborative learning environments to help visualize complex concepts and support inquiry-based learning processes. Two examples of using SOMs for these purposes are described.
EDUC 637
Literature Review InstructionsGeneral Overview
Please read the instructions and rubric for the Literature Review assignment BEFORE you sign-up for a topic. You will want to select a topic wisely so you will be able to identify 5 trends in your research.
For this assignment, you will select a topic in the general area of social studies instruction in middle grade education and examine accompanying literature related to that topic to identify the latest trends and issues. Ultimately, you will compile these results into a PowerPoint presentation of around 10 slides to identify these trends.Learning Objective
You will develop a presentation identifying general trends in middle-grade social studies education associated with a set of articles in the content area.Assignment Process
1. Begin classifying and compiling articles and sub-topics into groups of information for presentation (note 5 trends).
2. You should have scanned at least 30 articles in the process, which then need to be provided as part of this assignment in an attached bibliography list.
3. The final product should be a PowerPoint presentation consisting of:
a. a minimum of 10 but not to exceed 20 slides
b. 5 trends related to your topic (a paragraph or 2 on each trend)
c. identify issues with the type of research and/or writing undertaken
d. identify gaps in the research by identifying areas for further research on the trend
e. bibliography submitted as a Word document of about 30 articles in APA format
4. The final product is to be submitted by 11:59 p.m. (ET) in Sunday of Module 4.
Topic
· Effective Testing Strategies in Social Studies
Literature Review
Integrated Learning in Social Studies Education
Based on the literature reviewed for this assignment, there seems to be a fairly widely-held consensus (though largely anecdotal (see Research Methodology Issues)) among many education professionals that social studies, when integrated with other subjects, increases one's ability to learn more effectively across a broad range of subject matter. Nuthall (1999), for example, analyzed the learning habits of five students in an integrated science and social studies unit on Antarctica. His study concluded that the integration of these two subjects allowed students to acquire new knowledge in each of the disciplines that may not have been similarly acquired had the courses been taught separately. Educators in other areas of study have conveyed similar anecdotal results concerning their respective areas of study as well.
Matheus' (2000) study on using an integrated content social studies class as a means of developing problem-solving skills also cites the validity of integrated social studies curriculum. The author concludes that the integration of social studies curriculum with other subject matter creates connecting pathways between each which can apply across disciplines and even beyond the classroom.
Theodore Kaltsounis (1990) also concludes that, although.
Nature ,Scope,Meaning and Definition of Mathematics pdf 4AngelSophia2
Mathematics is an important subject that helps develop logical thinking and problem solving skills. It is the science of numbers, quantity, and space. Mathematics involves discovering relationships and expressing them symbolically through words, numbers, letters, diagrams, and graphs. While mathematics deals with abstract concepts that are precise and logical, it also has practical applications as a useful tool in many fields. Effective mathematics teaching focuses on developing students' intuition and ability to apply concepts to new situations through discovery learning and making connections between simple and complex ideas.
The document discusses the educational value of using multiple representations when teaching complex scientific concepts. It provides examples of simulation environments that use diagrams, graphs, equations and other representations to teach concepts like forces and motion. The key advantages discussed are that multiple representations:
1) Provide complementary information and support different cognitive processes.
2) Can constrain interpretation by using a familiar representation to help understand a new one.
3) Support deeper understanding by helping learners identify shared concepts across representations and build abstractions.
Multiple representations can benefit learning complex scientific concepts by providing complementary information and supporting different cognitive processes. The document discusses two educational simulations, SimQuest and PAKMA, that use multiple representations like diagrams, graphs, animations and equations to teach forces and motion. These representations complement each other by displaying different relevant information, like showing how values change over time in graphs but providing constant values numerically. They also support different ways of understanding, like seeing patterns in tables or quantitative relationships in equations. However, multiple representations can also overload learners if not implemented carefully.
The current educational research conducted in the context of special education is an attempt to ascertain whether conceptual maps enhance memory and help a child with special learning difficulties in understanding a theoretical lesson, such as the lesson of history. That is why a first-grade Junior high school student diagnosed with special learning difficulties is chosen, who was discouraged by his ineffectual attempt to understand and retrace the lesson of history no longer showed any interest in the lesson. In the framework of this qualitative research, in order to verify the effectiveness of the conceptual maps, a personalized intervention is made in the lesson of history for the student of the first grade, constructing the conceptual maps on the computer with the help of the software program "Inspiration 9". The lessons were based on the book of the history of first-grade Junior high school and refer to the Classical era in Athens. The intervention program lasted five weeks and the student actively participated in this. Upon completion of the intervention, as well as the student's answers to the same test on the 5th and 7th week of intervention, together with the information given to us by the school teacher and the special education teacher in the integration section, verified the valuable help of conceptual charts in this lesson. In particular, their effectiveness in the field of education and in particular of special education was established and the conditions necessary for conceptual charts to help as much as possible in teaching were explored.
The document analyzes how secondary school mathematics textbooks teach the concept of functions between 1953-2010. It categorizes some textbooks using a "hybrid approach" that combines set theory concepts with a focus on graphical representations. This approach presents real-world problems that are then formalized mathematically. However, it is argued that this approach does not fully promote understanding of functions before their formalization and treats problems more as tasks than opportunities for conceptual development. The conceptualization of functions across different representation systems used in textbooks is also examined.
Use of ICT for acquiring, practicing and assessing algebraic expertise Christian Bokhove
This document summarizes a research study investigating how ICT can support acquiring, practicing, and assessing algebraic expertise. The study was motivated by signals that students lack algebraic skills and the recognized potential of ICT in mathematics education. The central research question is: In what way can the use of ICT support acquiring, practicing and assessing algebraic expertise? This question is elaborated through sub-questions focusing on criteria for evaluating digital algebra tools, theoretical concepts to understand student behavior in digital environments, improving feedback design, implementing feedback principles in an intervention, and studying the effects of the intervention on algebraic expertise. The goal is to design an online intervention using a suitable digital tool to develop both procedural skills and conceptual understanding in algebra.
Honkela.t leinonen.t lonka.k_raike.a_2000: self-organizing maps and construct...ArchiLab 7
This document discusses using self-organizing maps (SOMs) to model constructive learning. It presents two key ideas:
1) SOMs provide a more realistic model of human learning than traditional computer memory models, as they are dynamic, associative, and adapt existing knowledge rather than just storing facts.
2) SOMs can be used in computer-supported collaborative learning environments to help visualize complex concepts and support inquiry-based learning processes. Two examples of using SOMs for these purposes are described.
EDUC 637
Literature Review InstructionsGeneral Overview
Please read the instructions and rubric for the Literature Review assignment BEFORE you sign-up for a topic. You will want to select a topic wisely so you will be able to identify 5 trends in your research.
For this assignment, you will select a topic in the general area of social studies instruction in middle grade education and examine accompanying literature related to that topic to identify the latest trends and issues. Ultimately, you will compile these results into a PowerPoint presentation of around 10 slides to identify these trends.Learning Objective
You will develop a presentation identifying general trends in middle-grade social studies education associated with a set of articles in the content area.Assignment Process
1. Begin classifying and compiling articles and sub-topics into groups of information for presentation (note 5 trends).
2. You should have scanned at least 30 articles in the process, which then need to be provided as part of this assignment in an attached bibliography list.
3. The final product should be a PowerPoint presentation consisting of:
a. a minimum of 10 but not to exceed 20 slides
b. 5 trends related to your topic (a paragraph or 2 on each trend)
c. identify issues with the type of research and/or writing undertaken
d. identify gaps in the research by identifying areas for further research on the trend
e. bibliography submitted as a Word document of about 30 articles in APA format
4. The final product is to be submitted by 11:59 p.m. (ET) in Sunday of Module 4.
Topic
· Effective Testing Strategies in Social Studies
Literature Review
Integrated Learning in Social Studies Education
Based on the literature reviewed for this assignment, there seems to be a fairly widely-held consensus (though largely anecdotal (see Research Methodology Issues)) among many education professionals that social studies, when integrated with other subjects, increases one's ability to learn more effectively across a broad range of subject matter. Nuthall (1999), for example, analyzed the learning habits of five students in an integrated science and social studies unit on Antarctica. His study concluded that the integration of these two subjects allowed students to acquire new knowledge in each of the disciplines that may not have been similarly acquired had the courses been taught separately. Educators in other areas of study have conveyed similar anecdotal results concerning their respective areas of study as well.
Matheus' (2000) study on using an integrated content social studies class as a means of developing problem-solving skills also cites the validity of integrated social studies curriculum. The author concludes that the integration of social studies curriculum with other subject matter creates connecting pathways between each which can apply across disciplines and even beyond the classroom.
Theodore Kaltsounis (1990) also concludes that, although.
Nature ,Scope,Meaning and Definition of Mathematics pdf 4AngelSophia2
Mathematics is an important subject that helps develop logical thinking and problem solving skills. It is the science of numbers, quantity, and space. Mathematics involves discovering relationships and expressing them symbolically through words, numbers, letters, diagrams, and graphs. While mathematics deals with abstract concepts that are precise and logical, it also has practical applications as a useful tool in many fields. Effective mathematics teaching focuses on developing students' intuition and ability to apply concepts to new situations through discovery learning and making connections between simple and complex ideas.
The document discusses the educational value of using multiple representations when teaching complex scientific concepts. It provides examples of simulation environments that use diagrams, graphs, equations and other representations to teach concepts like forces and motion. The key advantages discussed are that multiple representations:
1) Provide complementary information and support different cognitive processes.
2) Can constrain interpretation by using a familiar representation to help understand a new one.
3) Support deeper understanding by helping learners identify shared concepts across representations and build abstractions.
Multiple representations can benefit learning complex scientific concepts by providing complementary information and supporting different cognitive processes. The document discusses two educational simulations, SimQuest and PAKMA, that use multiple representations like diagrams, graphs, animations and equations to teach forces and motion. These representations complement each other by displaying different relevant information, like showing how values change over time in graphs but providing constant values numerically. They also support different ways of understanding, like seeing patterns in tables or quantitative relationships in equations. However, multiple representations can also overload learners if not implemented carefully.
The current educational research conducted in the context of special education is an attempt to ascertain whether conceptual maps enhance memory and help a child with special learning difficulties in understanding a theoretical lesson, such as the lesson of history. That is why a first-grade Junior high school student diagnosed with special learning difficulties is chosen, who was discouraged by his ineffectual attempt to understand and retrace the lesson of history no longer showed any interest in the lesson. In the framework of this qualitative research, in order to verify the effectiveness of the conceptual maps, a personalized intervention is made in the lesson of history for the student of the first grade, constructing the conceptual maps on the computer with the help of the software program "Inspiration 9". The lessons were based on the book of the history of first-grade Junior high school and refer to the Classical era in Athens. The intervention program lasted five weeks and the student actively participated in this. Upon completion of the intervention, as well as the student's answers to the same test on the 5th and 7th week of intervention, together with the information given to us by the school teacher and the special education teacher in the integration section, verified the valuable help of conceptual charts in this lesson. In particular, their effectiveness in the field of education and in particular of special education was established and the conditions necessary for conceptual charts to help as much as possible in teaching were explored.
The document analyzes how secondary school mathematics textbooks teach the concept of functions between 1953-2010. It categorizes some textbooks using a "hybrid approach" that combines set theory concepts with a focus on graphical representations. This approach presents real-world problems that are then formalized mathematically. However, it is argued that this approach does not fully promote understanding of functions before their formalization and treats problems more as tasks than opportunities for conceptual development. The conceptualization of functions across different representation systems used in textbooks is also examined.
Nature ,Scope,Meaning and Definition of Mathematics AngelSophia2
This document provides an overview of mathematics as a subject. It discusses how mathematics plays an important role in social and economic development. It also examines definitions of mathematics from different sources, describing it as a systematic, organized science that deals with quantities, measurements, and spatial relationships. The document outlines key characteristics of mathematics, including that it is a science of discovery, an intellectual game, and a tool subject. It also discusses the abstract nature of mathematical concepts and how mathematics requires logical sequencing and applying concepts to new situations.
Soft Computing: Contents, Techniques and ApplicationCSEIJJournal
Soft Computing is a relatively new branch of Computer Science that deals with approximate reasoning. The
techniques of Soft Computing are used successfully nowadays in many domestic, commercial and industrial
applications becoming a major research object in automatic control engineering. The present paper
reviews the contents of Soft Computing, which include probabilistic and in particular Bayesian reasoning,
fuzzy logic, artificial neural networks and genetic algorithms. These topics are complementary to each
other and can be used simultaneously for solving complex real-life problems, which cannot or it is too
difficult be modelled mathematically. The paper also explores the main techniques used in Soft Computing
and discusses their advantages with respect to the traditional techniques of hard computing.
Soft Computing: Contents, Techniques and ApplicationCSEIJJournal
Soft Computing is a relatively new branch of Computer Science that deals with approximate reasoning. The
techniques of Soft Computing are used successfully nowadays in many domestic, commercial and industrial
applications becoming a major research object in automatic control engineering. The present paper
reviews the contents of Soft Computing, which include probabilistic and in particular Bayesian reasoning,
fuzzy logic, artificial neural networks and genetic algorithms. These topics are complementary to each
other and can be used simultaneously for solving complex real-life problems, which cannot or it is too
difficult be modelled mathematically. The paper also explores the main techniques used in Soft Computing
and discusses their advantages with respect to the traditional techniques of hard computing
Outline of a Multidimensional Theory of Learning by Competences: An Essay abo...inventionjournals
There are several possibilities for understanding complex and polysemic terms such as Education and Learning. In this sense, over the last 30 years a theory of learning in particular has gained enough scientific status and reliability to serve as support for the implementation and regulation of education systems around the world: it is the Theory of Learning by Competencies. This theory, however, is subject to refinements and modifications, especially when confronted with scientific models such as Metaciência Social (created by Pablo Bispo dos Santos) and Unified Field Theory (created by Albert Einstein). This paper presents an essay to discuss the possibility of creating and applying (to several objects of study) a new methodology of educational evaluation called: Holospheric Learning System.
An Analysis Of Science Textbooks For Grade 6 The Electric Circuit LessonLisa Cain
The document analyzes and compares how electric circuits are presented in 6th grade science textbooks in Finland and Thailand. It finds that:
1) The Thai textbook emphasized procedural knowledge, while the Finnish textbook emphasized conceptual knowledge to a greater extent.
2) Both textbooks introduced physics concepts by describing their relation to other concepts introduced earlier.
3) Representations used included diagrams, pictures, and tables to clarify concepts, employing traditional contexts like technical applications and how technology relates to society.
Dr. M.THIRUNAVUKKARASU
Research Associate
Department of Education
Bharathidasan University,
Tiruchirappalli - 620 024, Tamil Nadu, India
E-mail: edutechthiru@gmail.com
Accommodation in the formal world of mathematical thinkingjohn Magginas
Today we started Galois Theory. Professor
Schmidt reviewed normal field extensions and then
defined Galois extensions. He stated the theorem that
characterizes Galois extensions as normal and separable.
He then went over some easy consequences of this.
Towards the end, he explained the basic principle of
Galois Theory - the correspondence between groups and
fields, and how this allows one to study fields using group
theory. I'm still a bit confused about the details, but I
think I understand the overall idea now. I'm interested to
see how this theory develops and connects to group theory
like he mentioned earlier in the semester.
fundamental theorem yet, but the basic ideas were now in place
A Structural Model Related To The Understanding Of The Concept Of Function D...Cheryl Brown
1) The document discusses a study that examines secondary students' understanding of the concept of function across three dimensions: definition, representation (recognition and interpretation), and problem solving.
2) Confirmatory factor analysis confirmed these four dimensions comprise the conceptual understanding of functions. The ability to define the concept was found to influence performance on the other dimensions.
3) The study aims to verify the proposed theoretical structure of conceptual understanding of functions and examine how the dimensions are interrelated, as well as identify differences in student performance at different grade levels.
Ontological Model of Educational Programs in Computer Science (Bachelor and M...ijsrd.com
In this work there is illustrated an ontological model of educational programs in computer science for bachelor and master degrees in Computer science and for master educational program “Computer science as second competence†by Tempus project PROMIS.
1) The purpose of this study was to examine the relationship between visual static models and students' written solutions to fraction problems using a large sample of student work.
2) The results indicate that common student errors relate to how students interpret the given model or their own model of the situation. Students' flexibility with visual models is related to successful written solutions.
3) Researchers hypothesize that exposure to varied mathematical representations influences students' ability to flexibly use static visual representations. Students need a solid understanding of real-world situations to successfully create and interpret visual models.
Hooke’s LawName Abstract;Include instead of these .docxwellesleyterresa
Hooke’s Law
Name
Abstract;
Include instead of these lines the objectives of the lab (what you investigated), the short description of how you did it and the conclusions formulated based on the obtained results.
It should be ½ to 1 page long.
Picture of the experimental set up
Read the Instructions and Procedure from the HOL lab manual.
Record the cumulative stretch ( elongation) for one spring . Make sure you don’t stretch the spring beyond the elasticity limits.
Force (N)
Accumulated (cm) Elongation (stretch)
Accumulated (m) Elongation (stretch)
Data Point 1
Data Point 2
Data Point 3
Data Point 4
Data Point 5
Data Point 6
Data Point 7
Data Point 8
Data Point 9
Data Point 10
Hooke’s Law
1
Calculations and Analysis
1. Plot the Force (y-axis) vs elongation (x-axis) on a computer spreadsheet or on piece of paper. Insert the graph (Excel or picture) in the space below:
2. Find the spring constant for the spring in Newton/meters from the slopethe graph. (Refer to the Excel tutorial in the Introduction section or/and read ecampus instructions.
k=
3. A student measured 15s for the 20 complete oscillations for an object of 200g attached at the free end of a spring. Calculate the period of oscillation (T) and the spring constant (k).
Write the equation used and then the numerical values.
Al-Saadi 5
Al-Saadi, Ahmed
COM 1101 -13 – Composition & Rhetoric
November 6, 2017
Dr. J. Parla Palumbo
Essay three – Definition
Education
Education is the instructive process geared towards facilitating an individual to acquire knowledge (Smith). According to Smith, education is different from schooling in the approach that each takes towards the learners. In schooling, the leaners are objects for the teacher to work on, while in education, the learners are considered as human beings with whom the teachers should interact. Individuals can also acquire a belief system or develop constructive habits through the process of education. The essential nature of these benefits has led international communities to promote the agenda of education as a necessity and even recognize it as a fundamental human right under the World Health Organisation (WHO). Education takes many forms, but it is primarily any instruction that is geared towards the betterment of the human condition through the development of the learning capacity of man.
Education is an instructive process. This definition implies that there is an object and a subject in the education process. The subject is a more knowledgeable, or skilled individual while the object is the person that is being trained on how to acquire the values, knowledge or skill. Hence, the subject is generally acknowledged as the teacher or instructor while the object of the educational process is always the student. Education affects the thought process ...
Artefacts Teach-Math. The Meaning Construction Of Trigonometric FunctionsBryce Nelson
This document describes a teaching approach for building students' understanding of trigonometric functions with technological artifacts. It involves three phases: 1) posing an initial question about measuring a tree's height, 2) returning to this question after research on clinometers, and 3) having students use a dynamic geometry software to model the situation and determine the tree's height and whether it can be safely cut down. The approach is grounded in theoretical frameworks of instrumental genesis and semiotic mediation to support students' meaningful learning of trigonometric concepts through active problem-solving with digital tools.
Analysis Of Two-Variable Function Graphing ActivitiesLisa Cain
This document discusses a study analyzing activities designed to help university students understand and graph two-variable functions. The activities were designed using APOS theory and analyzed using the moments of study from the Anthropological Theory of Didactics to evaluate their effectiveness and institutional viability. The study aims to determine if the activities help students develop the conceptual understanding of two-variable functions and if their organization is conducive for use in an instructional setting.
Understanding knowledge network, learning and connectivismAlaa Al Dahdouh
Behaviorism, Cognitivism, Constructivism and other growing theories such as Actor-Network and Connectivism are circulating in the educational field. For each, there are allies who stand behind research evidence and consistency of observation. Meantime, those existing theories dominate the field until the background is changed or new concrete evidence proves their insufficiencies. Connectivists claim that the background or the general climate has recently changed: a new generation of researchers, connectivists propose a new way of conceiving knowledge. According to them, knowledge is a network and learning is a process of exploring this network. Other researchers find this notion either not clear or not new and probably, with no effect in the education field. This paper addresses a foggy understanding of knowledge defined as a network and the lack of resources talking about this topic. Therefore, it tries to clarify what it means to define knowledge as a network and in what way it can affect teaching and learning.
The document summarizes and analyzes several research papers on using visualization as a learning tool in mathematics education. It discusses how the papers investigate visualization from an epistemological perspective. Key findings include: 1) Visual representations like number lines are open to various interpretations by students and benefit from social interaction; 2) Technology allows dynamic visualization that reveals multiple meanings; 3) Visual metaphors can be overgeneralized if not addressed by teachers. The analysis highlights the importance of considering individual differences in visualization preferences and avoiding claims about universal efficacy of visual tools.
The problem of effective computation is discussed. Short historical analysis of this problem and basic ways of its development in culture and science, including computer science, are represented. Place the problem of the creation effective calculation in modern science is discussed. Necessity of creation “computation metascience” as system with variable hierarchy (open system) is observed. Polymetric analysis as example of this metascience is represented and discussed.
Application Of Systemic Approach In Initial Teaching Of Chemistry Learning T...Sabrina Ball
This document discusses a study on applying a systemic approach to teach 7th grade students the mole concept in chemistry. Students had difficulties learning the mole concept due to its abstract nature. The study divided students into "excellent", "good", and "acceptable" groups based on a pre-test, with experimental and control subgroups. Students in the experimental subgroup learned using systemics (graphical concept maps), while controls used traditional methods. Results showed systemics helped "excellent" and "acceptable" students, but not "good" students. Further research is needed on larger samples to statistically confirm these findings.
This study investigated teachers' preferences for using visualization methods in teaching absolute value concepts. Researchers observed one 9th grade math class and teacher in Erzurum, Turkey. They found that visualization had a positive effect in the preliminary phases of instruction but did not stimulate problem solving later. This may be due to an emphasis on analytical problem solving in exams. The study concluded that visualization helps understanding at first but other methods are needed to develop problem solving skills.
Topic “Without application in the world, the value of knowledge is greatly diminished. Consider this claim with respect to two areas of knowledge". Academic level: Undergraduate, Citation style: Harvard, Number of sources: 1.
This document analyzes a single student learning episode using two theoretical lenses: the instrumental genesis perspective and the onto-semiotic approach. The instrumental genesis perspective focuses on how students develop techniques for using tools or artifacts to solve mathematical tasks, and the relationships between thinking and gestures. The onto-semiotic approach views mathematical knowledge and learning as involving systems of practices within social and institutional contexts. Analyzing the same episode from both perspectives provides complementary insights and a richer understanding of the phenomena, while also helping to identify the strengths and limitations of each theoretical approach. Networking the two theories in this way contributes to theoretical development in mathematics education.
HMM Classifier for Human Activity RecognitionCSEIJJournal
The rapid improvement in technology causes more attention towards to Recognizing of human activities
from video. These new technological growth has made vision-based research much more interesting and
efficient than ever before. This paper present novel HMM (Hidden Markov Model) based approach for
Human activity recognition from video. There are different approaches of HMM to recognize action of
human from video. Like threshold and voting to automatically and effectively segment and recognize
complex activities, segment and recognize complex activities and for simple activities we use Elman
Network (EN) and two hybrids of Neural Network (NN) and HMM, i.e. HMM-NN and NN-HMM.
IOT SOLUTIONS FOR SMART PARKING- SIGFOX TECHNOLOGYCSEIJJournal
Sigfox technology has emerged as a competitive product in the communication service provider market for
approximately a decade. Widely implemented for smart parking solutions across various European
countries, it has now gained traction in Germany as well. The technology's successful track record and
reputation in the market demonstrate its effectiveness and reliability in addressing the communication
needs of IoT applications, particularly in the context of vehicle parking systems. This is noted in terms of a
city like Berlin-Germany, for on which the study is conducted. The major challenge being on how to relate
the parking techniques in a more user friendly, cost effective and less energy consumpmti0n mode where
the questions had at the beginning of the paper, relatively at the end the answers are sought to it via Sigfox
and its comparison with other related technologies like LoRA WAN and weightless. But more so future
areas of research study is also pointed out on areas which are not clearly identified in this particular
research area.
This paper entails the pros, cons adaptive, emerging and existing technology study in terms of cloud, big
data, Data analytics are all discussed in tandem to Sigfox.
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Nature ,Scope,Meaning and Definition of Mathematics AngelSophia2
This document provides an overview of mathematics as a subject. It discusses how mathematics plays an important role in social and economic development. It also examines definitions of mathematics from different sources, describing it as a systematic, organized science that deals with quantities, measurements, and spatial relationships. The document outlines key characteristics of mathematics, including that it is a science of discovery, an intellectual game, and a tool subject. It also discusses the abstract nature of mathematical concepts and how mathematics requires logical sequencing and applying concepts to new situations.
Soft Computing: Contents, Techniques and ApplicationCSEIJJournal
Soft Computing is a relatively new branch of Computer Science that deals with approximate reasoning. The
techniques of Soft Computing are used successfully nowadays in many domestic, commercial and industrial
applications becoming a major research object in automatic control engineering. The present paper
reviews the contents of Soft Computing, which include probabilistic and in particular Bayesian reasoning,
fuzzy logic, artificial neural networks and genetic algorithms. These topics are complementary to each
other and can be used simultaneously for solving complex real-life problems, which cannot or it is too
difficult be modelled mathematically. The paper also explores the main techniques used in Soft Computing
and discusses their advantages with respect to the traditional techniques of hard computing.
Soft Computing: Contents, Techniques and ApplicationCSEIJJournal
Soft Computing is a relatively new branch of Computer Science that deals with approximate reasoning. The
techniques of Soft Computing are used successfully nowadays in many domestic, commercial and industrial
applications becoming a major research object in automatic control engineering. The present paper
reviews the contents of Soft Computing, which include probabilistic and in particular Bayesian reasoning,
fuzzy logic, artificial neural networks and genetic algorithms. These topics are complementary to each
other and can be used simultaneously for solving complex real-life problems, which cannot or it is too
difficult be modelled mathematically. The paper also explores the main techniques used in Soft Computing
and discusses their advantages with respect to the traditional techniques of hard computing
Outline of a Multidimensional Theory of Learning by Competences: An Essay abo...inventionjournals
There are several possibilities for understanding complex and polysemic terms such as Education and Learning. In this sense, over the last 30 years a theory of learning in particular has gained enough scientific status and reliability to serve as support for the implementation and regulation of education systems around the world: it is the Theory of Learning by Competencies. This theory, however, is subject to refinements and modifications, especially when confronted with scientific models such as Metaciência Social (created by Pablo Bispo dos Santos) and Unified Field Theory (created by Albert Einstein). This paper presents an essay to discuss the possibility of creating and applying (to several objects of study) a new methodology of educational evaluation called: Holospheric Learning System.
An Analysis Of Science Textbooks For Grade 6 The Electric Circuit LessonLisa Cain
The document analyzes and compares how electric circuits are presented in 6th grade science textbooks in Finland and Thailand. It finds that:
1) The Thai textbook emphasized procedural knowledge, while the Finnish textbook emphasized conceptual knowledge to a greater extent.
2) Both textbooks introduced physics concepts by describing their relation to other concepts introduced earlier.
3) Representations used included diagrams, pictures, and tables to clarify concepts, employing traditional contexts like technical applications and how technology relates to society.
Dr. M.THIRUNAVUKKARASU
Research Associate
Department of Education
Bharathidasan University,
Tiruchirappalli - 620 024, Tamil Nadu, India
E-mail: edutechthiru@gmail.com
Accommodation in the formal world of mathematical thinkingjohn Magginas
Today we started Galois Theory. Professor
Schmidt reviewed normal field extensions and then
defined Galois extensions. He stated the theorem that
characterizes Galois extensions as normal and separable.
He then went over some easy consequences of this.
Towards the end, he explained the basic principle of
Galois Theory - the correspondence between groups and
fields, and how this allows one to study fields using group
theory. I'm still a bit confused about the details, but I
think I understand the overall idea now. I'm interested to
see how this theory develops and connects to group theory
like he mentioned earlier in the semester.
fundamental theorem yet, but the basic ideas were now in place
A Structural Model Related To The Understanding Of The Concept Of Function D...Cheryl Brown
1) The document discusses a study that examines secondary students' understanding of the concept of function across three dimensions: definition, representation (recognition and interpretation), and problem solving.
2) Confirmatory factor analysis confirmed these four dimensions comprise the conceptual understanding of functions. The ability to define the concept was found to influence performance on the other dimensions.
3) The study aims to verify the proposed theoretical structure of conceptual understanding of functions and examine how the dimensions are interrelated, as well as identify differences in student performance at different grade levels.
Ontological Model of Educational Programs in Computer Science (Bachelor and M...ijsrd.com
In this work there is illustrated an ontological model of educational programs in computer science for bachelor and master degrees in Computer science and for master educational program “Computer science as second competence†by Tempus project PROMIS.
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2) The results indicate that common student errors relate to how students interpret the given model or their own model of the situation. Students' flexibility with visual models is related to successful written solutions.
3) Researchers hypothesize that exposure to varied mathematical representations influences students' ability to flexibly use static visual representations. Students need a solid understanding of real-world situations to successfully create and interpret visual models.
Hooke’s LawName Abstract;Include instead of these .docxwellesleyterresa
Hooke’s Law
Name
Abstract;
Include instead of these lines the objectives of the lab (what you investigated), the short description of how you did it and the conclusions formulated based on the obtained results.
It should be ½ to 1 page long.
Picture of the experimental set up
Read the Instructions and Procedure from the HOL lab manual.
Record the cumulative stretch ( elongation) for one spring . Make sure you don’t stretch the spring beyond the elasticity limits.
Force (N)
Accumulated (cm) Elongation (stretch)
Accumulated (m) Elongation (stretch)
Data Point 1
Data Point 2
Data Point 3
Data Point 4
Data Point 5
Data Point 6
Data Point 7
Data Point 8
Data Point 9
Data Point 10
Hooke’s Law
1
Calculations and Analysis
1. Plot the Force (y-axis) vs elongation (x-axis) on a computer spreadsheet or on piece of paper. Insert the graph (Excel or picture) in the space below:
2. Find the spring constant for the spring in Newton/meters from the slopethe graph. (Refer to the Excel tutorial in the Introduction section or/and read ecampus instructions.
k=
3. A student measured 15s for the 20 complete oscillations for an object of 200g attached at the free end of a spring. Calculate the period of oscillation (T) and the spring constant (k).
Write the equation used and then the numerical values.
Al-Saadi 5
Al-Saadi, Ahmed
COM 1101 -13 – Composition & Rhetoric
November 6, 2017
Dr. J. Parla Palumbo
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Education is an instructive process. This definition implies that there is an object and a subject in the education process. The subject is a more knowledgeable, or skilled individual while the object is the person that is being trained on how to acquire the values, knowledge or skill. Hence, the subject is generally acknowledged as the teacher or instructor while the object of the educational process is always the student. Education affects the thought process ...
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FUZZY ASSESSMENT OF THE “5 E’S” INSTRUCTIONAL TREATMENT FOR TEACHING MATHEMATICS TO ENGINEERING STUDENTS
1. Computer Science & Engineering: An International Journal (CSEIJ), Vol 13, No 2, April 2023
DOI:10.5121/cseij.2023.13201 1
FUZZY ASSESSMENT OF THE “5 E’S”
INSTRUCTIONAL TREATMENT FOR TEACHING
MATHEMATICS TO ENGINEERING STUDENTS
Michael Gr. Voskoglou
Department of Mathematical Sciences, University of Peloponnese,
Patras, Greece
ABSTRACT
The “5 E’s” instructional treatment, which is based on the principles of social constructivism, is currently
a very popular method for teaching, especially in school education. A hybrid model is developed in the
present paper for assessing the effectiveness of the “5 E’s” application for teaching mathematics to
engineering students of the University of Peloponnese, Greece. The model uses grey numbers and
neutrosophic sets for evaluating the mean student performance, whereas the quality performance is
assessed by calculating the Grade Point Average index.
KEYWORDS
Fuzzy Sets, Neutrosophic Sets, Grey Numbers, Fizzy Assessment, “5 E’s” Instructional Treatmen, Grade
Point Average (GPA) index.
1. INTRODUCTION
The idea that knowledge is a human construction supported by the experience, which was first
stated by Vico in the 18th
century and was further extended by Kant, affected greatly the
epistemology of Piaget, who is considered to be the forerunner of the theory of constructivism for
the process of learning. Constructivism introduced formally by von Clasersfeld in Piaget’s
foundation of the USA in 1975 [1]. The constructivist approach is based on the following two
principles:
Knowledge is not passively received from the environment, but it is actively constructed
by synthesizing past knowledge and experience with the new information.
The “coming to know” is a process of adaptation based on and constantly modified by
the individual’s experience of the world.
On the other hand, the socio-cultural theory for learning is based on Vygotsky’s ideas claiming
that knowledge is a product of culture and social interaction. Learning takes place when the
individuals engage socially to talk and act about shared problems or interests [2-4].
The combination of the principles of constructivism with the socio-cultural ideas created the
theory of social constructivism for learning [3, 5]. The “5 E’s” is an instructional model for
teaching based on the principles of social constructivism, which has become very popular
recently, especially in school education. Each of the “5 E's” describes a phase of learning which
begins with the letter "E" [6].
2. Computer Science & Engineering: An International Journal (CSEIJ), Vol 13, No 2, April 2023
2
In this paper a fuzzy assessment method is developed for evaluating the effectiveness of the “5
E's” instruction for teaching mathematics to engineering students, which uses grey numbers
(GNs) and neutrosophic sets (NSs) as tools. In particular, this method is very useful when the
instructor is not sure about the grades assigned to each student for evaluating his/her individual
performance.
The rest of the paper is organized as follows: Section 2 includes a brief description of the “5 E's”
instructional treatment. Section 3 introduces the mathematical background about GNs and NSs
being necessary for the understanding of the paper. The assessment method with GNs and NSs is
developed in Section 4 and it is applied for evaluating the effectiveness of the “5 E's”
instructional treatment in Section 5. The article closes with the final conclusions and a brief
discussion for further research, which are presented in Section 6.
2. THE “5 E’S INSTRUCTIONAL TREATMENT
The consecutive phases of the “5 E’s instructional treatment are the following:
Engage (E1): This is the starting phase which connects the past with the present learning
experiences and focuses student thinking on the learning outcomes of the current
activities.
Explore (E2): During this phase students explore their environment to create a common
base of experiences by identifying and developing concepts, processes and skills.
Explain (E3): In this phase students explain and verbalize the concepts that they have
been explored and they develop new skills. The teacher has the opportunity to introduce
formal terms, definitions and explanations for the new concepts and processes and to
demonstrate new skills or behaviors.
Elaborate (E4): In this phase students develop a deeper and broader conceptual
understanding and obtain more information about areas of interest by practicing on their
new skills and behaviors.
Evaluate (E5): This is the final step of the “5E’s” instructional model, where learners are
encouraged to assess their understanding and abilities and teachers evaluate student skills
on the new knowledge.
Depending on the student reactions, there are forward or backward transitions between the three
middle phases (explore, explain, elaborate) of the 5E’s model during the teaching process (see
Figure 1).
Figure 1: The flow diagram of the “5 E’s instructional treatment
The “5 E's” model allows students and teachers to experience common activities, to use and build
on prior knowledge and experience and to assess their understanding of a concept. Although it
has been mainly applied in school education [7], it can be used with students of all ages,
including adults [8].
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3. MATHEMATICAL BACKGROUND
3.1. Fuzzy Sets and Logic
The development of human science and civilization owes a lot to Aristotle’s (384-322 BC)
bivalent logic (BL), which was in the center of human reasoning for centuries. BL is based on the
“Principle of the Excluded Middle”, according to which each proposition is either true or false.
Opposite views, however, appeared also early in the human history supporting the existence of a
third area between true and false, where these two notions can exist together; e.g. by Buddha
Siddhartha Gautama (India, around 500 BC), by Plato (427-377 BC), more recently by the
Marxist philosophers, etc. Integrated propositions of multi-valued logics reported, however, only
during the early 1900’s, mainly by Lukasiewicz and Tarski [9, Section 2]. According to the
Lukasiewicz’s “Principle of Valence” propositions are not only either true or false, but they may
have intermediate truth-values too.
Zadeh, replacing the characteristic function of a crisp subset of the universe U with the
membership function m: U→ [0, 1], introduced in 1965 the concept of fuzzy set (FS) [10], in
which each element x of U has a membership degree m(x) in the unit interval. The closer m(x) to
1, the better x satisfies the characteristic property of the corresponding FS. For example, if A is
the FS of the tall men of a country and m(x) = 0.8, then x is a rather tall man. On the contrary, if
m(x) = 0.4, then x is a rather short man. Formally, a FS A in U can be written as a set of ordered
pairs in the form
F = {(x, m(x)): xU} (1)
As an example, Figure 2 represents the graph of the FS T of “tall people”. People with heights
less than 1.50 m are considered of having membership degree 0 in T. The membership degree is
continuously increasing for heights greater than 1.50m, taking its maximal value 1 for heights
equal or greater than 1.80 m. Therefore, the “fuzzy part” of the graph - which is conventionally
represented in Figure 2 by the straight line segment AC, but its exact form depends upon the way
in which the membership function has been defined - lies in the area of the rectangle ABCD
defined by the OX axis, its parallel through the point E and the two perpendicular to it lines at the
points A and B.
Figure 2: Graphical representation of the FS of “tall people”
Zadeh also introduced, with the help of FS, the infinite-valued in the unit interval fuzzy logic
(FL) [11], on the purpose of dealing with the existing in the everyday life partial truths. FL, in
which truth values are modelled by numbers in the unit interval, embodies the Lukasiewicz’s
“Principle of Valence”.
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Uncertainty can be defined as the shortage of precise knowledge or complete information on the
data that describe the state of a situation. It was only in a second moment that FS theory and FL
were used to embrace uncertainty modelling. This happened when membership functions were
reinterpreted as possibility distributions [12, 13]. Zadeh [12] articulated the relationship between
possibility and probability, noticing that what is probable must preliminarily be possible.
Probability theory used to be for a long period the unique tool in hands of the specialists for
dealing with problems connected to uncertainty. Probability, however, was proved to be
sufficient only for tackling the cases of uncertainty which are due to randomness [14].
Randomness characterizes events with known outcomes which, however, cannot be predicted in
advance, e.g. the games of chance. FSs, apart from randomness, tackle also successfully the
uncertainty due to vagueness, which is created when one is unable to distinguish between two
properties, such as “a good player” and “a mediocre player”. For general facts on FSs and the
connected to them uncertainty we refer to the book [15].
3.2. Neutrosophic Sets
Several generalizations and extensions of the theory of FSs have been developed during the last
years for the purpose of tackling more effectively all the forms of the existing in real world
uncertainty. The most important among them are briefly reviewed in [16].
Atanassov in 1986, considered, in addition to Zadeh’s membership degree, the degree of non-
membership and extended FS to the notion of intuitionistic FS (IFS) [17]. Smarandache in 1995,
inspired by the frequently appearing in real life neutralities - like <friend, neutral, enemy>, <win,
draw, defeat>, <high, medium, short>, etc. - generalized IFS to the concept of neutrosophic set
(NS) by adding the degree of indeterminacy or neutrality [18]. The word “neutrosophy” is a
synthesis of the word “neutral´ and the Greek word “sophia” (wisdom) and means “the
knowledge of the neutral thought”. The simplest form of a NS is defined as follows:
Definition 1: A single valued NS (SVNS) A in the universe U is of the form
A = {(x,T(x),I(x),F(x)): xU, T(x),I(x),F(x)[0,1], 0T(x)+I(x)+F(x)3} (2)
In equation (2) T(x), I(x), F(x) are the degrees of truth (or membership), indeterminacy (or
neutrality) and falsity (or non-membership) of x in A respectively, called the neutrosophic
components of x. For simplicity, we write A<T, I, F>. Indeterminacy is defined to be in general
everything that exists between the opposites of truth and falsity [19].
Example 1: Let U be the set of the players of a soccer club and let A be the SVNS of the good
players of the club. Then each player x is characterized by a neutrosophic triplet (t, i, f) with
respect to A, with t, i, f in [0, 1]. For example, x(0.7, 0.1, 0.4) ∈ A means that there exists a 70%
belief that x is a good player, but at the same time there exist a 10% doubt about it and a 40%
belief that x is not a good player. In particular, x (0, 1, 0) ∈ A means that we do not know
absolutely nothing about the quality of player x (new player).
If the sum T(x) + I(x) + F(x) < 1, then it leaves room for incomplete information about x, if it is
equal to 1 for complete information and if it is >1 for inconsistent (i.e. contradiction tolerant)
information about x. A SVNS may contain simultaneously elements leaving room to all the
previous types of information. All notions and operations defined on FSs are naturally extended
to SVNSs [20].
Summation of neutrosophic triplets is equivalent to the union of NSs. That is why the
neutrosophic summation and implicitly its extension to neutrosophic scalar multiplication can be
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defined in many ways, equivalently to the known in the literature neutrosophic union operators
[21]. For the needs of the present work, writing the elements of a SVNS A in the form of
neutrosophic triplets and considering them simply as ordered triplets we define addition and
scalar product as follows:
Definition 2: Let (t1, i1, f1), (t2, i2, f2) be in A and let k be a positive number. Then:
The sum (t1, i1, f1) + (t2, i2, f2) = (t1+ t2, i1+ i2, f1+ f2) (2)
The scalar product k(t1, i1, f1) = (kt1, k i1, kf1) (3)
Remark 1: Summation and scalar product of the elements of a SVNS A with respect to
Definition 2 need not be closed operations in A, since it may happen that (t1+ t2)+(i1+ i2)+(f1+
f2)>3 or kt1+k i1 + kf1>3. With the help of Definition 2, however, one can define in A the mean
value of a finite number of elements of A as follows:
Definition 3: Let A be a SVNS and let (t1, i1, f1), (t2, i2, f2), …., (tk, ik, fk) be a finite number of
elements of A. Assume that (ti, ii, fi) appears ni times in an application, i = 1,2,…., k. Set n =
n1+n2+….+nk. Then the mean value of all these elements of A is defined to be the element
(tm,im,fm) of A calculated by
1
n
[n1(t1, i1,f1)+n2(t2,i2,f2)+….+nk(tk,ik, fk)] (4)
3.3. Grey Numbers
The theory of grey systems [22] introduces an alternative way for managing the uncertainty in
case of approximate data. A grey system is understood to be any system which lacks information,
such as structure message, operation mechanism or/and behavior document.
Closed real intervals are used for performing the necessary calculations in grey systems. In fact, a
closed real interval [x, y] could be considered as representing a real number T, termed as a GN,
whose exact value in [x, y] is unknown. We write then T ∈ [x, y]. A GN T, however, is
frequently accompanied by a whitenization function f: [x, y] → [0, 1], such that, if f(a)
approaches 1, then a in [x, y] approaches the unknown value of T. If no whitenization function is
defined, it is logical to consider as a representative crisp approximation of the GN T the real
number
V(T) =
x+y
2
(3)
The arithmetic operations on GNs are introduced with the help of the known arithmetic of the
real intervals [23]. In this work we are going to make use only of the addition of GNs and of the
scalar multiplication of a GN with a positive number, which are defined as follows:
Definition 2: Let A ∈ [x1, y1], B ∈ [x2, y2] be two GNs and let k be a positive number. Then:
The sum: A+B is the GN A+B ∈ [x1+y1, x2+y2] (4)
The scalar product kA is the GN kA ∈ [kx1, ky1] (5)
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4. FUZZY ASSESSMENT METHODS WITH QUALITATIVE GRADES
In many cases it is a common practice to assess the student performance by using qualitative
(linguistic) instead of numerical grades. A widely accepted scale of such grades is the following:
A=excellent, B=very good, C=good, D=mediocre and F=unsatisfactory. Here we present three
fuzzy assessment methods that we are going to use in this work for assessing the overall
performance of a student group.
4.1. Mean Performance
In case of using qualitative grades the mean performance of a student group cannot be evaluated
with the classical method of calculating the mean value of the student individual grades. To
overcome this difficulty, we assign to each grade a GN, denoted for simplicity with the same
letter, as follows: A = [85, 100], B = [75, 84], C = [60, 74], D = [50, 59], F = [0, 49]. The choice
of the above GNs, although it corresponds to generally accepted standards, is not unique. For
example, for a more strict assessment, one may choose A= [90, 100], B = [80, 89], C= [70, 79], D
= [60, 69], F = [0, 59], etc. Such changes, however, does not affect the generality of our method
Assume now that, from the n in total students of the group, nX obtained the grade X=A, B, C, D,
F. It is logical then to accept that the crisp approximationV(M) of the GN
M = A B C D F
1
(n n B n
A C n D )
+ + n F
n
(5)
Can be used for estimating the mean performance of the student group.
4.2. Quality Performance
A very popular in the USA and other countries method for evaluating the quality performance of
a group is the use of the Grade Point Average (GPA) index [24, p.125], which is calculated by
the formula
GPA = F D C B A
0n +n +2n +3n +4n
n
(6)
In other words, the GPA index is a weighted average in which greater coefficients (weights) are
assigned to the higher grades. Note that, since in the worst case (n=nF) is GPA=0 and in the ideal
case (n=nA) is GPA=4, we have in general that
0≤GPA≤4 (7)
When two groups have the same GPA index, however, this method is not sufficient to show
which of them performs better. In such cases the Rectangular Fuzzy Assessment Model (RFAM),
which is based on the Center of Gravity (COG) defuzzification technique can be used [24, pp.
126-130].
4.3. Neutrosophic Assessment
Frequently in practice the instructor has doubts about the grades assigned to some students, either
because he/she had not the opportunity to evaluate their skills explicitly during a course, or
because they didn’t clarify their answers properly in a written test. In such cases, the most
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suitable method for assessing the overall performance of a student group is to use NSs as tools.
Considering, for example, the NS of the good students of the group, one introduces neutrosophic
triplets characterizing the individual performance of each student and then calculates the mean
value of all these triplets with the help of equation (4) in order to obtain the proper conclusions
about the group’s overall performance. In order to have complete information for each student’s
performance, the sum of the component of each triplet must be equal to 1.
5. THE CLASSROOM APPLICATION
The purpose of the following classroom application was to evaluate the effectiveness of the “5
E’s” instructional treatment for teaching mathematics to engineering students. The subjects were
the first term students of two departments of the School of Engineering of the University of
Peloponnese during the teaching of the course “Higher Mathematics I”, which includes Complex
Numbers, Differential and Integral Calculus in one variable and elements from Linear Algebra.
According to the grades obtained in the PanHellenic examination for entrance in Higher
Education, the potential of the two departments in mathematics was about the same. The course’s
instructor was also the same person, but the teaching methods followed were different. Namely,
the “5 E’s” approach was applied for teaching the course to the 60 students of the first department
(experimental group), whereas the classical method with lectures and exercises on the board was
applied for the 60 students of the second department (control group).
The results of the final examination, after the end of the course, were the following:
Department I: A: 9 students, B: 15, C: 18, D: 12, F: 6
Department II: A: 12, B: 15, C: 9, D: 12, F: 12
Therefore, applying the assessment methods of Section 4, we evaluated the performance of the
two departments as follows:
Mean performance
By equation (5) one finds that
MI =
1
60
+15[75,84]+18[60,74]+
( 1
9[85,1 2[5
00] 0,59] +6[0,49]) =
1
60
[3570,4994]≈[59.5,83.23].
Therefore, equation (3) gives that V(MI)≈71.36, which shows that the experimental group
demonstrated a good (C) mean performance.
In the same way one finds that V(MII)≈62.56, which shows that the control group also
demonstrated a good (C) mean performance, which, however, was 8.8% worse than that of the
experimental group.
Quality performance
Equation (6) gives that
GPAI=
12+2*18+3*15+4*9
60
=2.12 and similarly GPAII=2.05, which shows that the
experimental group demonstrated a slightly better quality performance. In fact, with the help of
equation (7) it is easy to check that the superiority of the experimental group in this case is only
0.07*25=1.75%.
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Note that, some of the student answers in the final examination were not clearly presented or well
justified. As a result, the instructor was not quite sure for the accuracy of the grades assigned to
them. For this reason, we decided to apply the neutrosophic method of section 4.3 for the
assessment of the two departments’ overall performance. For this, starting from the students with
the higher grades, let us denote by Si, i=1,2,….,60, the students of each department. Considering
the NS of the good students, we assigned neutrosophic triplets to all
students of the two departments as follows:
Department I: S1-S32: (1,0,0), S33-S38: (0.8,0.1,0.1), S39-S42: (0.7,0.2,0.1), S43-S46:
(0.4,0.2,0.4), S47-S50: (0.3,0.2,0.5), S51-S53: (0.2,0.2,0.6), S54-S55: (0.1,0.2,0.7), S56-S57:
(0,0.2,0.0.8), , S578-S60: (0,0,1).
Department II: S1-S31: (1,0,0), S32-S35: (0.8,0.1,0.1), S36: (0.7,0.1,0.2), S35-S43:
(0.4,0.1,0.5), S44-S46: (0.3,0.2,0.5), S47-S50: (0.2,0.2,0.6), S51-S52: (0.1,0.2,0.7), S53-S58:
(0,0.3,.0.7), , S59-S60: (0,0,1).
Then, by equation (4), the mean value of the neutrosophic triplets of Department I is equal to
1
60
[32(1,0,0)+6 (0.8,0.1,0.1)+ 4(0.7,0.2,0.1)+4 (0.4, 0.2,0.4)+ 4(0.3,0.2,0.5)+3(0.2,0.2,0.6)+
2(0.1,0.2, 0.7)+2(0,0.2,0.0.8)+3 (0,0,1)≈(0.72, 0.07, 0.21). In the same way one finds that the
mean value of the neutrosophic triplets of Department II is equal to (0.65, 0.08, 0.27).
Thus, the probability for a random student of Department I to be a good student is 72%, but at the
same time there exists a 7% doubt about it and a 21% probability to be not a good student. Also,
the probability for a random student of Department II to be a good student is 65%, with a 8%
doubt about it and a 27% probability to be not a good student. Consequently, the experimental
group, despites the doubts of the instructor for the grades assigned to the students, demonstrated a
better overall performance.
6. CONCLUSION
The classroom application presented in this work demonstrated a superiority of the experimental
group with respect to the control group. This superiority was significant concerning the two
groups’ mean and overall (in terms of the neutrosophic assessment) performance, but rather
negligible concerning their quality performance. This gives a strong indication that the
application of the “5 E’s” method benefits more the mediocre and the weak in mathematics
students, but less the good students. Much more experimental research is needed, however, for
obtaining safer conclusions. Other applications of FSs and their extensions is of course another
interesting topic for future research, e.g. see {25, 26], etc.
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AUTHOR
Michael Gr. Voskoglou (B.Sc., M.Sc., Ph.D.. in Mathematics) is an Emeritus
Professor of Mathematical Sciences of the Graduate Technological Educational
Institute of Western Greece. He worked as a Visiting Researcher at the Institute of
Mathematics and Informatics of the Bulgarian Academy of Sciences in Sofia for
three years (1997-2000), under sabbatical. He has lectured as a Visiting Professor in
postgraduate courses of the School of Management at the University of Warsaw
(2009), at the Department of Operational Mathematics of the University of Applied
Sciences in Berlin (2010) and at the Mathematics Department of the National
Institute of Technology of Durgapur (2016) under a grand of the Indian Government. He is the
author/editor of 18 books and of more than 600 papers published in international journals and Proceedings
of conferences of about 30 countries, with more than 2000 citations from other researchers. He is also a
reviewer of the American Mathematical Society and Editor in many reputed mathematical journals. He has
supervised many student dissertations and he used to be external examiner of Ph.D. dissertations at
universities of Egypt, India and Saudi Arabia. He is the recipient of many scholarships, distinctions and
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honorary awards and member of many scientific associations (AMS, HMS, ICTMA, IETI, etc.) His
research interests include Algebra, Fuzzy Logic, Markov Chains, Artificial Intelligence and Mathematics
Education.