This document describes research into implementing an analytic teaching method within an intelligent tutoring system for solving trigonometry problems.
The researchers developed a protocol for communication between a trigonometry problem solver agent (TRIPS) and a teaching expert agent (TET) within an ITS. TET can apply different teaching methods, including the analytic method, to solutions provided by TRIPS.
The document provides details on how the analytic method was conceptualized for use in this ITS, including: developing analytical reasoning tests based on problem solutions; generating wrong answers to test student understanding; and evaluating student responses. It also discusses the contributions of this work and opportunities for future refinement.
Technological persuasive pedagogy a new way to persuade students in the compu...Alexander Decker
This document introduces a new pedagogical approach called "technological persuasive pedagogy" to more effectively persuade students in computer-based mathematics learning. It discusses prior models and theories of persuasion and identifies 16 principles that can be used to 1) improve negative attitudes, 2) increase positive attitudes, or 3) prevent declines in positive attitudes. The document outlines the content analysis method used to extract these principles from literature on persuasion in education. It describes coding and reliability testing of the principles to develop a codebook for applying them in computer-based mathematics classrooms.
This document describes formative research, a methodology for improving instructional design theories through developmental research or action research. Formative research involves creating an application or instance of a design theory, then formatively evaluating it to identify weaknesses in the application that could reflect weaknesses in the theory and improvements to the application that could reflect improvements to the theory. The key aspects of formative research discussed are: 1) using designed cases, in vivo naturalistic cases, or post facto naturalistic cases; 2) evaluating research based on effectiveness, efficiency, and appeal; and 3) following methodological procedures that involve designing an instance of a theory, collecting formative data, revising the instance, and proposing revisions to the theory.
An Exploration Of Strategies Used By Students To Solve Problems With Multiple...Martha Brown
This document summarizes a study that analyzed how 35 students solved math problems that could be solved in multiple ways. It reviewed relevant literature on problem solving approaches and frameworks. Specifically, it discussed Perkins and Simmons' model of four knowledge frames - content, problem-solving, epistemic, and inquiry - that characterize different types of knowledge used in problem solving. The purpose of the study was to understand the strategies and difficulties students experience when approaching problems with multiple solutions.
Introduction to Computational Thinking.pptxAyodeleOgegbo
This document introduces computational thinking in science classrooms. It defines computational thinking as formulating problems and representing solutions in a way that computers can process. The five key pillars of computational thinking are decomposition, abstraction, pattern recognition, algorithm design, and automation. Computational thinking can be integrated into science through four practices: data practices, modeling and simulation, computational problem-solving, and system thinking.
This document provides an overview of Bloom's Taxonomy, which classifies learning objectives into six levels: Knowledge, Comprehension, Application, Analysis, Synthesis, and Evaluation. Each level is defined and examples of learning objectives for that level are given. The document also discusses using Bloom's Taxonomy to design classroom lectures and assessments that target different cognitive abilities.
A Competence Theory Approach To Problem Solving Method ConstructionRobin Beregovska
The document presents a competence theory approach to analyzing and constructing problem-solving methods (PSMs). It identifies three main steps: 1) specifying an initial competence theory based on the problem statement, 2) conceptually refining the theory by introducing domain vocabulary and assumptions, and 3) operationalizing the refined theory into an executable specification. As an example, it applies this approach to classification problems, defining the problem space, specifying an initial competence theory, and discussing how conceptual refinement and operationalization could proceed.
This document classifies information systems development methodologies into five categories based on the type of problem situation:
1. Well-structured problems with defined requirements - Traditional waterfall methodologies are appropriate.
2. Well-structured problems with unclear requirements - Structured, data-focused, or prototyping methodologies can be used.
3. Unstructured problems with unclear objectives - Soft systems methodologies focus on perspectives of those involved.
4. High user interaction situations - Sociotechnical approaches stressing user needs are most suitable.
5. Complex problems combining aspects of the above - A contingency approach using multiple methodologies is needed.
Technological persuasive pedagogy a new way to persuade students in the compu...Alexander Decker
This document introduces a new pedagogical approach called "technological persuasive pedagogy" to more effectively persuade students in computer-based mathematics learning. It discusses prior models and theories of persuasion and identifies 16 principles that can be used to 1) improve negative attitudes, 2) increase positive attitudes, or 3) prevent declines in positive attitudes. The document outlines the content analysis method used to extract these principles from literature on persuasion in education. It describes coding and reliability testing of the principles to develop a codebook for applying them in computer-based mathematics classrooms.
This document describes formative research, a methodology for improving instructional design theories through developmental research or action research. Formative research involves creating an application or instance of a design theory, then formatively evaluating it to identify weaknesses in the application that could reflect weaknesses in the theory and improvements to the application that could reflect improvements to the theory. The key aspects of formative research discussed are: 1) using designed cases, in vivo naturalistic cases, or post facto naturalistic cases; 2) evaluating research based on effectiveness, efficiency, and appeal; and 3) following methodological procedures that involve designing an instance of a theory, collecting formative data, revising the instance, and proposing revisions to the theory.
An Exploration Of Strategies Used By Students To Solve Problems With Multiple...Martha Brown
This document summarizes a study that analyzed how 35 students solved math problems that could be solved in multiple ways. It reviewed relevant literature on problem solving approaches and frameworks. Specifically, it discussed Perkins and Simmons' model of four knowledge frames - content, problem-solving, epistemic, and inquiry - that characterize different types of knowledge used in problem solving. The purpose of the study was to understand the strategies and difficulties students experience when approaching problems with multiple solutions.
Introduction to Computational Thinking.pptxAyodeleOgegbo
This document introduces computational thinking in science classrooms. It defines computational thinking as formulating problems and representing solutions in a way that computers can process. The five key pillars of computational thinking are decomposition, abstraction, pattern recognition, algorithm design, and automation. Computational thinking can be integrated into science through four practices: data practices, modeling and simulation, computational problem-solving, and system thinking.
This document provides an overview of Bloom's Taxonomy, which classifies learning objectives into six levels: Knowledge, Comprehension, Application, Analysis, Synthesis, and Evaluation. Each level is defined and examples of learning objectives for that level are given. The document also discusses using Bloom's Taxonomy to design classroom lectures and assessments that target different cognitive abilities.
A Competence Theory Approach To Problem Solving Method ConstructionRobin Beregovska
The document presents a competence theory approach to analyzing and constructing problem-solving methods (PSMs). It identifies three main steps: 1) specifying an initial competence theory based on the problem statement, 2) conceptually refining the theory by introducing domain vocabulary and assumptions, and 3) operationalizing the refined theory into an executable specification. As an example, it applies this approach to classification problems, defining the problem space, specifying an initial competence theory, and discussing how conceptual refinement and operationalization could proceed.
This document classifies information systems development methodologies into five categories based on the type of problem situation:
1. Well-structured problems with defined requirements - Traditional waterfall methodologies are appropriate.
2. Well-structured problems with unclear requirements - Structured, data-focused, or prototyping methodologies can be used.
3. Unstructured problems with unclear objectives - Soft systems methodologies focus on perspectives of those involved.
4. High user interaction situations - Sociotechnical approaches stressing user needs are most suitable.
5. Complex problems combining aspects of the above - A contingency approach using multiple methodologies is needed.
Assessing Complex Problem Solving PerformancesRenee Lewis
The document describes an approach to assessing complex problem-solving performances using simulations. It discusses the challenges of multidimensionality and local dependence in extended simulation tasks. The approach uses Evidence-Centered Design to extract features from student performance data, evaluate the features, and make inferences about proficiency. It provides an example of assessing problem-solving with technology using the NAEP Problem-Solving in Technology-Rich Environments study, which measures scientific problem-solving skills through search and simulation modules that keep the content domain constant while varying the computer tools used.
A preliminary survey on optimized multiobjective metaheuristic methods for da...ijcsit
The present survey provides the state-of-the-art of research, copiously devoted to Evolutionary Approach
(EAs) for clustering exemplified with a diversity of evolutionary computations. The Survey provides a
nomenclature that highlights some aspects that are very important in the context of evolutionary data
clustering. The paper missions the clustering trade-offs branched out with wide-ranging Multi Objective
Evolutionary Approaches (MOEAs) methods. Finally, this study addresses the potential challenges of
MOEA design and data clustering, along with conclusions and recommendations for novice and
researchers by positioning most promising paths of future research.
This document provides an overview of the steps involved in quantitative data analysis and applying Partial Least Square Structural Equation Modeling (PLS-SEM). It discusses pretesting questionnaires, preparing raw data through editing and coding, assessing validity through measures like content validity and unidimensionality, and establishing construct validity through convergent and discriminant validity techniques. The goal is to review all the necessary steps for quantitative data analysis using SPSS and applying SEM, from preparing the data to reporting the results.
ActionResearch - Strategies FOR PRACTICE.pptx300272
This document discusses instructional strategies that can be used in action research, including active learning, cooperative learning, experimental inquiry, and graphic organizers. It also provides examples of problems identified in past action research studies, such as students having low scores in problem solving, mathematics, and difficulty comprehending science concepts. The document outlines identifying problems, analyzing problems, considering alternative courses of action, and selecting a probable action, such as using activity cards, assignment sheets, or cooperative learning, to address the issues identified.
The document outlines various aspects of empirical research studies including sampling methods, measures, design, analysis, and conclusions. It discusses sampling procedures, measures of stressors and outcomes, research design types, variables that are controlled for, and issues with determining causality from evidence. Minimum quality criteria for research designs are also presented focusing on randomized controlled trials, experiments, and longitudinal and cross-sectional studies.
Constructing fair tests that give teachers accurate information about students' learning is important. A table of specification helps organize test planning and content validity by determining what content will be covered. Rubrics can also help with validity when used appropriately. Multiple choice tests can be valid for assessing certain cognitive levels like knowledge and comprehension, but other assessment types may better measure skills and higher-level thinking. Teachers should consider cognitive level and learning objectives when choosing assessments.
This document provides an overview of machine learning and case-based reasoning. It begins with an introduction to machine learning that defines the term and discusses common approaches like decision trees, artificial neural networks, genetic algorithms, and reinforcement learning. It then provides a more in-depth discussion of case-based reasoning, covering how it draws from psychological models of human reasoning and problem-solving. The document discusses both the advantages and disadvantages of machine learning approaches.
The document discusses grounded theory as a method for analyzing qualitative data. Grounded theory involves collecting data through interviews or other means, transcribing and coding the data to identify common themes, and developing categories to represent these themes. The researcher then interprets the data within these categories and discusses how the findings relate to the original research aims. Examples are provided of a study analyzing comments from school head teachers about self-evaluation processes and how these link to school improvement goals.
The document discusses grounded theory as a method for analyzing qualitative data. Grounded theory involves collecting data through interviews or other means, transcribing and coding the data to identify common themes, and developing categories to represent these themes. The researcher then interprets the data within these categories and discusses how the findings relate to the original research aims. The example provided examines how school head teachers view self-evaluation as linking to school improvement goals based on quotes from interviews.
The document provides an overview of business research, including defining what research is, the importance of research for managers, and the typical research process. It discusses key concepts like the different types of business research, problem formulation, research design, data collection and analysis, and how to structure a research report. Conducting thorough research is important for managers to solve problems, make informed decisions, understand competition and risks, and invest resources effectively. The scientific process typically involves observation, problem identification, developing a theoretical framework, generating hypotheses, research design, data collection and analysis, interpretation, and implementation.
This document is an assignment on research in mathematics education. It discusses the nature of research in mathematics education compared to mathematics. It notes that while mathematics uses proofs, research in mathematics education uses various forms of evidence to build understanding. It outlines the main purposes of research in mathematics education as understanding mathematical thinking and learning as well as improving instruction. It also discusses standards for evaluating theories and models in mathematics education research, including descriptive power, explanatory power, scope, predictive power, rigor, falsifiability, replicability, and using multiple sources of evidence. The document concludes by emphasizing that mathematics education research is still a young field with progress being made to build robust theory and methods.
Here are some potential responses to your questions:
1. A potential research topic could be "Assessing market demand and identifying target customer segments for a new coffee shop near a university and school."
2. A problem statement could be "It is unclear whether there is sufficient demand in the local area to support a new coffee shop and which customer groups would be most likely to frequent the shop."
3. Objectives could include:
- Determine size and characteristics of potential customer base in the local area
- Identify key customer segments to target with the new coffee shop
- Assess level of demand and spending potential of different customer groups
- Gather customer feedback on preferred shop attributes, products/services, pricing etc.
Blueprinting and drafting questions Liz Norman ANZCVS 2015Liz Norman
The document discusses various concepts related to blueprinting and drafting exam questions, including:
- What a blueprint is and its purpose in documenting content sampling and representativeness.
- Factors to consider when blueprinting like breadth across topics, levels of knowledge/skills assessed, and species representation.
- Classifying question difficulty based on familiarity, complexity, abstraction level, and task/response strategies.
- The importance of structuring exams according to subject guidelines and balancing question types and lengths.
The overall message is that blueprinting is crucial for ensuring exams validly represent the intended content domain at appropriate levels of knowledge and skills. Question design factors also impact difficulty levels.
Business research involves systematically studying a problem to find solutions. It is important for managers to make informed decisions. There are two main types of business research: applied research solves current problems, while basic research builds general knowledge. The research process involves defining a problem, developing a theoretical framework, generating hypotheses, collecting and analyzing data, and reporting findings. Proper research design, sampling, measurement, and statistical analysis are crucial for obtaining meaningful results that can help managers address issues and remain competitive.
The document discusses the systems approach in education. It defines the systems approach as a problem-solving process that engages a series of steps to solve an identified educational problem. The systems approach has two major parts: system analysis and system synthesis. System analysis involves breaking down the problem into components, while system synthesis uses the data from system analysis to select and implement solution strategies. The systems approach focuses on all elements of instruction, including the learner, content, experiences, and strategies to ensure the components work as an organic whole to achieve the objectives. Some advantages of the systems approach are that it helps identify suitable resources and allows for continuous improvement. Limitations include resistance to change and that it requires hard work.
TRIZ was invented in the former USSR in 1946 by Genrich Altshuller with his colleagues, and its main purpose at that time was to assist engineers to invent new products in a more efficient manner as oppose to the normal trial and error methodology. TRIZ is a Russian words and it means “Theory of Inventive Problem Solving” or TIPS. It was introduced based on the belief that there are universal principles of invention that are the foundation for creative innovations that help in creating and advancing technology. Even though TRIZ was initially developed to solve inventive problems in engineering-related problem domains, nowadays it has gained popularity in other fields such as in education, business, and other non-technology or non-scientific fields and domains. Several studies have been carried out in the past to investigate and analyze the benefits of teaching TRIZ to students at tertiary or higher level of education, and the results were very encouraging. In this paper, a review of several applications of TRIZ in higher education is performed, and based on the results of the review; a short summary of the findings is presented.
Here are some potential responses to your questions:
1. A potential research topic could be "Determining student and faculty demand for a coffee shop near the university and local schools."
2. A problem statement could be: "There is currently no coffee shop located near the university and local schools to serve the needs of students, faculty and staff during the day. It is unknown whether there is sufficient demand to support a new coffee shop business."
3. Objectives may include:
- Assess the size of potential customer base from the university and schools
- Understand customer preferences for types of coffee, food offerings, atmosphere etc.
- Determine average spending amounts and frequency of visits to a coffee shop
- Identify
A Theory-Based Framework For Assessing Domainl-Specific Problem-Solving AbilityNicole Heredia
1) The document proposes a framework for assessing problem solving ability by decomposing it into its cognitive components, including domain-specific knowledge, metacognition, and motivation.
2) It identifies specific constructs within each component to measure, such as principles, concepts, procedures for domain knowledge, and planning/monitoring for metacognition.
3) Measuring these individual constructs through multiple assessments would provide more valid and useful information than assessing problem solving as a single global construct, and help pinpoint strengths and weaknesses to guide instruction.
The document discusses key concepts in research-based curriculum design including conceptual understandings, research methods, curriculum evaluation, and the relationship between theory, policy, and practice. It poses several discussion questions about the importance of distinguishing scientific research from curriculum development, how social factors influence curriculum research, and how learning theories, evaluation, teacher roles, and knowledge structures affect curriculum validity and scope. The questions also address how terminology, research methodologies, and contextual variables impact research reliability and the application of theory to practice.
STUDENTS’PATTERNS OF INTERACTION WITH A MATHEMATICS INTELLIGENT TUTOR:LEARNIN...IJITE
Purpose: The purpose of this paper is to determine potential identifiers of students’ academic success in
foundation mathematics course by analyzing the data logs of an intelligent tutor.
Design/ methodology/approach: A cross-sectional study design was used. A sample of 58 records was
extracted from the data-logs of the intelligent tutor, ALEKS. This data was triangulated with the data
collected from surveys. Two-step clustering, correlation and regression analysis, Chi-square analysis and
paired sample t-tests were applied to address the research questions.
Findings: The data-logs of ALEKS include information about number of topics practiced and number of
topics mastered by each student. Prior knowledge and derived attribute, which is the ratio of number of
topics mastered to number of topics practiced(denoted by the variable m top in this paper) are found to be
predictors of final marks in the foundation mathematics course with
= 42%.
Students were asked to report their preferred way of selecting topics as either sequential or random.
Results of paired sample t-test demonstrated that the students who selected topics in a sequential manner
were able to retain their mastery of learning after the summative assessment whereas the students who
chose topics randomly were not able to retain their mastery of learning.
Originality and value: This research has established three indicators of academic success in the course of
foundation mathematics which is delivered using the intelligent tutor ALEKS. Instructors can monitor
students’ progress and detect students at-risk who are not able to attain desired pace of learning and guide
them to choose the correct sequence of topics.
I Need Someone To Write My Essay - UK Essay WritingCourtney Esco
This portfolio focuses on analyzing various aspects of media content and how audiences engage with media. It includes sections on communication and semiotics in media, textual analysis of newspapers, narrative analysis of drama series, visual literacy, language and discourse in media. The portfolio aims to understand how signs, narratives, images and language shape audience interpretation and experience of media content.
Do Urgent Essay Writing ,Research Writing ,Summary And Report WritiCourtney Esco
This document provides instructions for students to get essay writing help from HelpWriting.net. It outlines a 5-step process:
1. Create an account with a password and email.
2. Complete a 10-minute order form providing instructions, sources, deadline and sample work.
3. Review bids from writers and choose one based on qualifications. Place a deposit to start.
4. Ensure the paper meets expectations and authorize final payment if pleased. Free revisions are allowed.
5. Multiple revisions can be requested to ensure satisfaction. HelpWriting.net guarantees original, high-quality content or a full refund.
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Assessing Complex Problem Solving PerformancesRenee Lewis
The document describes an approach to assessing complex problem-solving performances using simulations. It discusses the challenges of multidimensionality and local dependence in extended simulation tasks. The approach uses Evidence-Centered Design to extract features from student performance data, evaluate the features, and make inferences about proficiency. It provides an example of assessing problem-solving with technology using the NAEP Problem-Solving in Technology-Rich Environments study, which measures scientific problem-solving skills through search and simulation modules that keep the content domain constant while varying the computer tools used.
A preliminary survey on optimized multiobjective metaheuristic methods for da...ijcsit
The present survey provides the state-of-the-art of research, copiously devoted to Evolutionary Approach
(EAs) for clustering exemplified with a diversity of evolutionary computations. The Survey provides a
nomenclature that highlights some aspects that are very important in the context of evolutionary data
clustering. The paper missions the clustering trade-offs branched out with wide-ranging Multi Objective
Evolutionary Approaches (MOEAs) methods. Finally, this study addresses the potential challenges of
MOEA design and data clustering, along with conclusions and recommendations for novice and
researchers by positioning most promising paths of future research.
This document provides an overview of the steps involved in quantitative data analysis and applying Partial Least Square Structural Equation Modeling (PLS-SEM). It discusses pretesting questionnaires, preparing raw data through editing and coding, assessing validity through measures like content validity and unidimensionality, and establishing construct validity through convergent and discriminant validity techniques. The goal is to review all the necessary steps for quantitative data analysis using SPSS and applying SEM, from preparing the data to reporting the results.
ActionResearch - Strategies FOR PRACTICE.pptx300272
This document discusses instructional strategies that can be used in action research, including active learning, cooperative learning, experimental inquiry, and graphic organizers. It also provides examples of problems identified in past action research studies, such as students having low scores in problem solving, mathematics, and difficulty comprehending science concepts. The document outlines identifying problems, analyzing problems, considering alternative courses of action, and selecting a probable action, such as using activity cards, assignment sheets, or cooperative learning, to address the issues identified.
The document outlines various aspects of empirical research studies including sampling methods, measures, design, analysis, and conclusions. It discusses sampling procedures, measures of stressors and outcomes, research design types, variables that are controlled for, and issues with determining causality from evidence. Minimum quality criteria for research designs are also presented focusing on randomized controlled trials, experiments, and longitudinal and cross-sectional studies.
Constructing fair tests that give teachers accurate information about students' learning is important. A table of specification helps organize test planning and content validity by determining what content will be covered. Rubrics can also help with validity when used appropriately. Multiple choice tests can be valid for assessing certain cognitive levels like knowledge and comprehension, but other assessment types may better measure skills and higher-level thinking. Teachers should consider cognitive level and learning objectives when choosing assessments.
This document provides an overview of machine learning and case-based reasoning. It begins with an introduction to machine learning that defines the term and discusses common approaches like decision trees, artificial neural networks, genetic algorithms, and reinforcement learning. It then provides a more in-depth discussion of case-based reasoning, covering how it draws from psychological models of human reasoning and problem-solving. The document discusses both the advantages and disadvantages of machine learning approaches.
The document discusses grounded theory as a method for analyzing qualitative data. Grounded theory involves collecting data through interviews or other means, transcribing and coding the data to identify common themes, and developing categories to represent these themes. The researcher then interprets the data within these categories and discusses how the findings relate to the original research aims. Examples are provided of a study analyzing comments from school head teachers about self-evaluation processes and how these link to school improvement goals.
The document discusses grounded theory as a method for analyzing qualitative data. Grounded theory involves collecting data through interviews or other means, transcribing and coding the data to identify common themes, and developing categories to represent these themes. The researcher then interprets the data within these categories and discusses how the findings relate to the original research aims. The example provided examines how school head teachers view self-evaluation as linking to school improvement goals based on quotes from interviews.
The document provides an overview of business research, including defining what research is, the importance of research for managers, and the typical research process. It discusses key concepts like the different types of business research, problem formulation, research design, data collection and analysis, and how to structure a research report. Conducting thorough research is important for managers to solve problems, make informed decisions, understand competition and risks, and invest resources effectively. The scientific process typically involves observation, problem identification, developing a theoretical framework, generating hypotheses, research design, data collection and analysis, interpretation, and implementation.
This document is an assignment on research in mathematics education. It discusses the nature of research in mathematics education compared to mathematics. It notes that while mathematics uses proofs, research in mathematics education uses various forms of evidence to build understanding. It outlines the main purposes of research in mathematics education as understanding mathematical thinking and learning as well as improving instruction. It also discusses standards for evaluating theories and models in mathematics education research, including descriptive power, explanatory power, scope, predictive power, rigor, falsifiability, replicability, and using multiple sources of evidence. The document concludes by emphasizing that mathematics education research is still a young field with progress being made to build robust theory and methods.
Here are some potential responses to your questions:
1. A potential research topic could be "Assessing market demand and identifying target customer segments for a new coffee shop near a university and school."
2. A problem statement could be "It is unclear whether there is sufficient demand in the local area to support a new coffee shop and which customer groups would be most likely to frequent the shop."
3. Objectives could include:
- Determine size and characteristics of potential customer base in the local area
- Identify key customer segments to target with the new coffee shop
- Assess level of demand and spending potential of different customer groups
- Gather customer feedback on preferred shop attributes, products/services, pricing etc.
Blueprinting and drafting questions Liz Norman ANZCVS 2015Liz Norman
The document discusses various concepts related to blueprinting and drafting exam questions, including:
- What a blueprint is and its purpose in documenting content sampling and representativeness.
- Factors to consider when blueprinting like breadth across topics, levels of knowledge/skills assessed, and species representation.
- Classifying question difficulty based on familiarity, complexity, abstraction level, and task/response strategies.
- The importance of structuring exams according to subject guidelines and balancing question types and lengths.
The overall message is that blueprinting is crucial for ensuring exams validly represent the intended content domain at appropriate levels of knowledge and skills. Question design factors also impact difficulty levels.
Business research involves systematically studying a problem to find solutions. It is important for managers to make informed decisions. There are two main types of business research: applied research solves current problems, while basic research builds general knowledge. The research process involves defining a problem, developing a theoretical framework, generating hypotheses, collecting and analyzing data, and reporting findings. Proper research design, sampling, measurement, and statistical analysis are crucial for obtaining meaningful results that can help managers address issues and remain competitive.
The document discusses the systems approach in education. It defines the systems approach as a problem-solving process that engages a series of steps to solve an identified educational problem. The systems approach has two major parts: system analysis and system synthesis. System analysis involves breaking down the problem into components, while system synthesis uses the data from system analysis to select and implement solution strategies. The systems approach focuses on all elements of instruction, including the learner, content, experiences, and strategies to ensure the components work as an organic whole to achieve the objectives. Some advantages of the systems approach are that it helps identify suitable resources and allows for continuous improvement. Limitations include resistance to change and that it requires hard work.
TRIZ was invented in the former USSR in 1946 by Genrich Altshuller with his colleagues, and its main purpose at that time was to assist engineers to invent new products in a more efficient manner as oppose to the normal trial and error methodology. TRIZ is a Russian words and it means “Theory of Inventive Problem Solving” or TIPS. It was introduced based on the belief that there are universal principles of invention that are the foundation for creative innovations that help in creating and advancing technology. Even though TRIZ was initially developed to solve inventive problems in engineering-related problem domains, nowadays it has gained popularity in other fields such as in education, business, and other non-technology or non-scientific fields and domains. Several studies have been carried out in the past to investigate and analyze the benefits of teaching TRIZ to students at tertiary or higher level of education, and the results were very encouraging. In this paper, a review of several applications of TRIZ in higher education is performed, and based on the results of the review; a short summary of the findings is presented.
Here are some potential responses to your questions:
1. A potential research topic could be "Determining student and faculty demand for a coffee shop near the university and local schools."
2. A problem statement could be: "There is currently no coffee shop located near the university and local schools to serve the needs of students, faculty and staff during the day. It is unknown whether there is sufficient demand to support a new coffee shop business."
3. Objectives may include:
- Assess the size of potential customer base from the university and schools
- Understand customer preferences for types of coffee, food offerings, atmosphere etc.
- Determine average spending amounts and frequency of visits to a coffee shop
- Identify
A Theory-Based Framework For Assessing Domainl-Specific Problem-Solving AbilityNicole Heredia
1) The document proposes a framework for assessing problem solving ability by decomposing it into its cognitive components, including domain-specific knowledge, metacognition, and motivation.
2) It identifies specific constructs within each component to measure, such as principles, concepts, procedures for domain knowledge, and planning/monitoring for metacognition.
3) Measuring these individual constructs through multiple assessments would provide more valid and useful information than assessing problem solving as a single global construct, and help pinpoint strengths and weaknesses to guide instruction.
The document discusses key concepts in research-based curriculum design including conceptual understandings, research methods, curriculum evaluation, and the relationship between theory, policy, and practice. It poses several discussion questions about the importance of distinguishing scientific research from curriculum development, how social factors influence curriculum research, and how learning theories, evaluation, teacher roles, and knowledge structures affect curriculum validity and scope. The questions also address how terminology, research methodologies, and contextual variables impact research reliability and the application of theory to practice.
STUDENTS’PATTERNS OF INTERACTION WITH A MATHEMATICS INTELLIGENT TUTOR:LEARNIN...IJITE
Purpose: The purpose of this paper is to determine potential identifiers of students’ academic success in
foundation mathematics course by analyzing the data logs of an intelligent tutor.
Design/ methodology/approach: A cross-sectional study design was used. A sample of 58 records was
extracted from the data-logs of the intelligent tutor, ALEKS. This data was triangulated with the data
collected from surveys. Two-step clustering, correlation and regression analysis, Chi-square analysis and
paired sample t-tests were applied to address the research questions.
Findings: The data-logs of ALEKS include information about number of topics practiced and number of
topics mastered by each student. Prior knowledge and derived attribute, which is the ratio of number of
topics mastered to number of topics practiced(denoted by the variable m top in this paper) are found to be
predictors of final marks in the foundation mathematics course with
= 42%.
Students were asked to report their preferred way of selecting topics as either sequential or random.
Results of paired sample t-test demonstrated that the students who selected topics in a sequential manner
were able to retain their mastery of learning after the summative assessment whereas the students who
chose topics randomly were not able to retain their mastery of learning.
Originality and value: This research has established three indicators of academic success in the course of
foundation mathematics which is delivered using the intelligent tutor ALEKS. Instructors can monitor
students’ progress and detect students at-risk who are not able to attain desired pace of learning and guide
them to choose the correct sequence of topics.
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This portfolio focuses on analyzing various aspects of media content and how audiences engage with media. It includes sections on communication and semiotics in media, textual analysis of newspapers, narrative analysis of drama series, visual literacy, language and discourse in media. The portfolio aims to understand how signs, narratives, images and language shape audience interpretation and experience of media content.
Do Urgent Essay Writing ,Research Writing ,Summary And Report WritiCourtney Esco
This document provides instructions for students to get essay writing help from HelpWriting.net. It outlines a 5-step process:
1. Create an account with a password and email.
2. Complete a 10-minute order form providing instructions, sources, deadline and sample work.
3. Review bids from writers and choose one based on qualifications. Place a deposit to start.
4. Ensure the paper meets expectations and authorize final payment if pleased. Free revisions are allowed.
5. Multiple revisions can be requested to ensure satisfaction. HelpWriting.net guarantees original, high-quality content or a full refund.
003 Compare And Contrast Essay Intro Example FresCourtney Esco
This document discusses the evolution of allergies in humans. It notes that approximately 25% of people in developed countries suffer from allergic disorders such as hay fever, asthma, eczema, and anaphylaxis. The rates are even higher among school-aged children at 40-50% suffering from one or more allergies. While medications can help manage allergies, it often takes years to find an effective treatment regimen. The document questions why humans evolved to have allergic disorders given their prevalence and disruptive nature, noting that while the biological mechanisms of allergies are understood, the evolutionary reasons are still debated among researchers.
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ANALYTIC METHOD IMPLEMENTATION WITH A TRIGONOMETRY PROBLEM SOLVER
1.
2. SERDICA — Bulgaricae
mathematicae publicationes
20 (1994) 208-218
ANALYTIC METHOD IMPLEMENTATION WITH A
TRIGONOMETRY PROBLEM SOLVER
HRISTO PETKOV, DANAIL DOCHEV
Abstract. One of the most important aspects when developing a problem solving
machine for the purposes of ITS is that the different teaching methods should be
fully compatible with the solutions the problem solver provides and should be
applicable to them. This paper examines the possibility of implementing a specific
teaching method (the Analytic Method) with a specific problem domain (a class
of mathematical knowledge - High School Trigonometry).
A simple and convenient control regime is presented along with a set of conven-
tions for applying the analytic method with TRIPS, avoiding most of the pitfalls.
As an illustration an ongoing example working within this control regime is pro-
vided.
The main objectives of this paper are to consider the potential formalization of
the theoretically developed teaching methods and learning tools for the purposes
of ITS and to describe an experimental prototype implementation of a specific
teaching method, illustrating these ideas.
1. Main Objectives. The presented research serves two goals which are the
main objectives of the paper. The obvious objective is to experiment with the well
known analytic method, theoretically developed in education for the purposes of learn-
ing, and to try to adapt and implement it as a teaching method, suitable for computer
formalization. The final goal of this is aiming at the automation of the teaching pro-
cess. However there is a second and equally important objective, which is to explore the
flexibility and the explicitness of a problem solving machine developed for the purposes
of ITS. All this is done under the assumption that a domain problem solver will be
suitable for the purposes of ITS to the extent it involves flexibility and explicitness.
Explicitness demands stating something in details, clearly and fully expressed. Ex-
plicitness includes also the requirement for the solution to be self-evident on the basis
of being comprehensible for the user. It should provide suitable explanations as well.
The flexibility of the Domain Expert implies multiple reasonable solutions and different
3. Analytic Method Implementation with a Trigonometry Problem Solver 209
teaching strategies implementation. By developing a specific teaching method we have
tried to assign some context of the above stated general requirements.
2. Architectural Issues for Applying the Analytic Method. The basic
architectural presupposition for experimenting the analytic method is the architecture
of an overall ITS (Intelligent Tutoring System), details of which are provided in [1] and
[2]. Actually this paper would be followed and assessed much more easily if [2] is read
first.
The analytic method is viewed in the context of TET (Teaching Expert for
Trigonometry problem solving) experimented with TRIPS (TRIgonometry Problem
Solver), both of which are agents of a multiexpert ITS.
TET uses the inferences of TRIPS (called solutions) and applies different teach-
ing strategies to them.
Besides making decisions for applying a specific teaching method, TET uses the
solutions of TRIPS to generate appropriate tests, supporting the teaching process.
The teaching expert contains different teaching methods (analytic method,
brain attack, successive refinement, discovery learning and assessment, cognitive ap-
prenticeship, goal-directed asking etc.) that are chosen by the Cognitive Expert (not
described here) and applied by TET. A similar approach for experimenting multiple
teaching strategies has been used by Spensley et. al. (1990) in [3]. The current presen-
tation is constrained to the application of only one of the enumerated teaching methods
- the analytic one.
At present the teaching methods are not fully implemented on a computer sys-
tem, but they are rather theoretical devices mainly because of some computer memory
problems with the logical environment.
These methods have been conceptualized chiefly to prove that TRIPS is appro-
priate for use in an ITS.
3. Description of the Analytic Method. The analytic method (AM) is one
of the oldest methods, used in teaching and learning. The task of this method is to
decompose the problems into subproblems so as to explore and examine the elemen-
tary principles these problems are based on. Thus the reasoning acquires a validating
character (for more details see [4] and [5]).
The reason of exploring the analytic method with TRIPS is that this teaching
method is characterized by strong syllogism and all the reasoning is based on logical
inferences, conclusions and deductions.
The analytic method implementation to teaching is based on the confidence that
the whole task could be followed, understood and accepted much more comprehensively
and could be processed more precisely and directly through its intermediate composite
subproblems [6].
The method of analytical reasoning focuses on its ability to analyze and criticize
the task argumentation by understanding, estimating and evaluating the relationships
4. 210 Hristo Petkov, Danail Dochev
among the arguments and the cases of reasoning or parts of them.
Usually when solving a certain problem the usage and the application of the
analytic approach is coupled with other methods of teaching and learning. But for the
sake of research experiments this approach is isolated and detached by using analytic
reasoning tests for example. In the general case sets of questions, provoking analytic
reasoning, are used. The purpose of this inquiring in the conventional analytic checks
is to test the ability of the subject to understand a given structure of arbitrary re-
lationships among fictitious things or events and to deduce or infer new information
from the relationships given. However our case was slightly different, for the ITS is not
going to check the analytic skills of the student, but it would rather apply the user’s
analytic and logical reasoning abilities for teaching purposes. So it would be appro-
priate to modify a bit the classical framework of the analytic method by introducing
a feedback for the sake of tutoring. An example of a teaching feedback, which is not
very complex, is the straightforward evaluation of the answers the student gives to the
test questions. The most simple feedback is with YES/NO evaluation of the answers,
but a smarter solution is to introduce analysis into the feedback again, thus interposing
depth at several levels of the teaching process. We shall impose a constraint to the first
level of depth by cutting it with YES/NO feedback.
4. Analytical Reasoning Tests. The analytical reasoning tests as a rule
involve a set of questions which measure and examine the ability to understand a given
structure of relationships ([7], [8]). Each analytical reasoning group consists of:
• a set of about 3 – 7 mutually related statements or conditions (often some
other explanatory material is added as well);
• three or more questions which test the degree of understanding the structure,
its implications and inklings.
Though each question of a group is based on the same set of conditions, the
questions are independent of one another. Answering a question of a group does not
influence the answers of the remaining questions.
Each group of questions for analytical reasoning testing is based on a definite
set of conditions establishing the interconnections among things and/or the events, [9].
The links are rather ordinary, plain and common, such as:
• Temporal order: (X happened before Y but after Z);
• Spatial order: (X is nearer to Y and Z);
• Cause and effect: (The application of the transformation X causes the possi-
bility of applying the transformation Y).
Some of the relationships may be fixed or constant (at any step only one trans-
formation is to be implemented). Other relationships are variable: (At that step either
the transformation X or the trans formation Y should be applied).
A certain number of interrelations and interdependences not provided in the
assignment can easily be inferred from the data. When presenting the conditions for
5. Analytic Method Implementation with a Trigonometry Problem Solver 211
the analytical reasoning they must be stated clearly and should be distinct, transparent
and obvious [10]. This requirement is imposed because the student should be assisted
and facilitated in determining the exact nature of the relationship or relationships
involved.
5. Theoretical Application of the Analytic Method. The assignment
for applying the analytic method is: First to set up the arguments of a task and to
decompose it into subproblems; Second to discuss the results and to observe what
inference, based on the solution of the subproblems, can be made.
The phases of theoretical application of the analytical method in problem solv-
ing are as follows:
• confronting the problem and encountering the difficulties and the conflicts
(set up by TRIPS);
• supplying the required information (data, facts and knowledge), necessary
and essential to eliminate the confrontation (TRIPS);
• clarifying and elucidating the essence, the nature and the core of the problem
(TRIPS);
• decomposing and disintegrating the problem into subproblems (TRIPS);
• searching for, discovering, and implementing alternative solutions (creative,
constructive analytical thinking •to achieve various solutions), (TRIPS & TET);
• evaluating the alternatives and checking up the choices and the options,
(TRIPS & TET).
When applying the analytic method for teaching purposes it is assumed, that
the student is acquainted with the solutions and has the knowledge and skills to perform
them until the opposite is proved.
The general principles used in implementing the analytical method for teaching
purposes in problem solving are listed below:
The student’s learning and knowledge acquisition is shift from:
• the simple to the more complex;
• from the tangible and the explicit to the intangible and the more abstract;
• from the general and the generic to the specific, the particular and the indi-
vidual;
• from the known, told and experienced to the unknown, the unfamiliar and
the unidentified.
6. Implementation of the Analytic Method. For the purposes of applying
the teaching methods of TET with TRIPS a communication protocol has been devel-
oped. The solution provided by TRIPS to TET consists of a set of lines and a set of
justifications. The set of lines for solving a problem is called a solution printout. The
set of the list data structures, dynamically gen erated at each step in the process of
problem solving is called justification. All the derivations made over the justifications
are called an explanation. The set of a specific solution printout of a problem with the
6. 212 Hristo Petkov, Danail Dochev
specific justifications and explanations to it is called a variant of that problem. The
finite set of all the variants of a given problem (all the alternative solutions) is called a
case.
Every case is conveyed to TET. TET selects a variant and uses analytical tests
that matches it. In the general case matching is accomplished by unifying the con-
straints of the test with the justifications of the variant. On success this test is acti-
vated and presented to the student.The answers of the student are evaluated by TET
with Yes/No or Right/Wrong. The general algorithm for applying the analytic method
is given on Fig.1, where A1 and A2 are standard measures for the test samples and R1
and R2 are the values of the results, obtained by testing the student. The test samples
from the algorithm are presented in the Appendix. When the tests over a given vari-
ant or variants are exhausted, cognitive expertise is used so as to make a decision on
whether to continue the application of the selected teaching method, whether to choose
another teaching method, or to end up the teaching session. The application of the
analytic method is terminated also when the justifications of the variant do not match
the constraints of any of the tests in a test sample. A test sample is a set of analytic
tests applied successively at a given step of the general algorithm.
One of the implementation problems is that every test for analytical reasoning
is specific and it is formalized in a particular way. For example the constraints in the
assumption of the Test Sample No.1 are general for all trigonometric problems, so it
can be applied always, no matter what the discussed problem is, but the tests from
the Test Sample 2 are quite different and it is difficult or even impossible to develop
general specifications for applying them, so we shall restrict to a specific application.
Let us consider Test Sample No.1. Following the protocol TRIPS generates a
variant and passes down this variant to TET. It is interesting to investigate how the
wrong answers of that test (solution printouts) should be generated by TET. The wrong
answers are derived from the right answers by violating one or more than one of the
constraints. The most ”natural thing to do” is to skip some lines of the solution.
The first constraint may be violated by dropping out any one of the solution
lines except for the first and the last one. The second constraint may be violated by
repeating some of the lines in the solution. The 3rd constraint is set up on the basis of
the assigned list from the justifications of a variant. The 4th constraint may be violated
by skipping a line from the solution printout at random. The 5th constraint is checked
out or violated on the basis of the contradictory lists of the justifications of a variant.
The 6th constraint may be violated by applying two opposite transformations, taken
from the contradictory list, successively. And the 8th constraint may be violated by
cutting off the solution printout before the first simplifying transformation (TS or AS),
is applied (it can be read from the list of the corresponding justification).
The techniques used for implementing the analytic tests are quite simple, but
the more simple the techniques are the more efficient its computer program realization is.
8. 214 Hristo Petkov, Danail Dochev
7. Contributions. As a part of an ITS, TET is an attempt to design and
implement an operational Domain Expert-Teaching Expert protocol in a real world
environment. The contributions of TET are:
• integrating different types of knowledge into one model by building up com-
patibility techniques;
• conceptualizing of detached teaching expert methods;
• developing an approach for computer implementation of purely theoretical
teaching methods;
Since the analytic method of TET considered here is well-known and very old
one (probably one of the oldest methods for learning) the specific contributions, related
to that method are:
• formalizing the method;
• making the analytical method and its implementation compatible with specific
domain knowledge;
• developing knowledge bases for representing the conceptualized knowledge in
a logic programming environment (PROLOG);
The implementation of formalized teaching methods to a specific problem do-
main is a thankless research work, taking out a lot of time and efforts with minimal
results. This research with TRIPS is forthcoming and its objective is to bridge the gap
between AI, Cognitive science and Education in ITS.
Conclusion. The the proposed analytic algorithm is a pathological case of
analysis and does not pretend to cover the theoretical method. But the algorithm is
rather flexible and provides opportunities to experiment with various types of analytic
tests.
The computer formalization is still somewhat primitive, although it captures
the style and the essence of the teaching method it is intended to represent.
Refinement and sophistication of this method, along with the extension of the
test procedures is among the major goals of future research work.
APPENDIX
Test Sample Type 1
A problem for trigonometric simplification is subjected to the following con-
straints:
•1• The solution of the problem must be written down LINE by LINE;
•2• The transition from one line to another is made by transformations;
•3• The following transformations are allowed: [AS,AD,TS,TD,SB,CD];
•4• For the transition from line to line EXACTLY one transformation should
be used;
•5• Some of the transformations are opposite of others e.g. [AS,AD], [TS,TD];
9. Analytic Method Implementation with a Trigonometry Problem Solver 215
•6• Two opposite transformations cannot be applied successively;
•7• The simplification of the expression is evaluated in terms of:
• Number of monomials
• Complexity of the trigonometric functions
• Number of different subterms
•8• At least one simplification transformation should be applied in the solution.
?1? Which of the following examples satisfies the above stated constraints?
Example 1:
1. 2 − sin 2
(α) + cos 2(α) + cos (α) ∗ (tg (α) + cos (α))
2. 1 + 1 − sin 2
(α) + cos 2(α) + cos (α) ∗ (tg (α) + cos (α))
3. 1 + cos 2(α) + cos 2(α) + cos (α) ∗ (tg (α) + cos (α))
4. 1 + 2 ∗ cos 2(α) + cos (α) ∗ (tg (α) + cos (α))
5. 1 + 2 ∗ cos 2(α) + cos (α) ∗ tg (α) + cos (α)2
6. 1 + 3 ∗ cos 2(α) + cos (α) ∗ tg (α) + cos (α)2
7. 1 + 3 ∗ cos 2(α) + cos (α) ∗ tg (α) + cos (α)2
Example 2:
1. 2 − sin 2
(α) + cos 2(α) + cos (α) ∗ (tg (α) + cos (α))
2. 1 + cos 2(α) + cos 2(α) + cos (α) ∗ (tg (α) + cos (α))
3. 1 + 2 ∗ cos 2(α) + cos (α) ∗ (tg (α) + cos (α))
4. 1 + 3 ∗ cos 2(α) + cos (α) ∗ tg (α) + cos (α)2
5. 1 + 3 ∗ cos 2(α) + cos (α) ∗ tg (α) + cos (α)2
. . .
TRIPS can be used to generate solutions violating 0, 1 or more than one of the
constraints. In the considered Example 1 none of the constraints is violated, though
the solution itself is somewhat difficult to handle.
?2? Which of the following sequences of transformations CANNOT be imple-
mented in solving problems for trigonometric simplification?
A) AS,AD,TS,SB,TD
B) AS,TS,AD,TS,AS
C) AS,AS,AS,AS
D) AD,TD,AD
E) TS,AS,TS,AS
F) SB,AS,SB
TRIPS could be used to generate alternative real world examples over the pre-
sented set of operators. These examples are chosen from the already solved problems.
?3? If we know that AS and TS reduce V2 and SB,TD, and AD increase it, which
of the following sequences could have completed the simplification of the expression?
10. 216 Hristo Petkov, Danail Dochev
A) AS,TS,AS,TS
B) AD,SB,AS,TD
. . .
The sequence of the operators chosen by the student is to be verified by TRIPS
in terms of plausibility.
?4? Let us have the following solution:
1. 2 − sin 2
(α) + cos 2(α) + cos (α) ∗ (tg (α) + cos (α))
2. 1 + 1 − sin 2
(α) + cos 2(α) + cos (α) ∗ (tg (α) + cos (α))
3. 1 + cos 2(α) + cos 2(α) + cos (α) ∗ (tg (α) + cos (α))
4. 1 + 2 ∗ cos 2(α) + cos (α) ∗ (tg (α) + cos (α))
5. 1 + 2 ∗ cos 2(α) + cos (α) ∗ tg (α) + cos (α)2
6. 1 + 3 ∗ cos 2(α) + cos (α) ∗ tg (α) + cos (α)2
7. 1 + 3 ∗ cos 2(α) + cos (α) ∗ tg (α) + cos (α)2
Without using evaluations, choose a couple of successive steps which result in
simplifying the expression?
A) 1-2 & 2-3
B) 2-3 & 5-6
. . .
TRIPS can be used to explore wrong answers by applying analysis recursively
as a feed-back.
Test Sample Type 2
A certain trigonometric problem is solved in five steps: S1, S2, S3, S4 and S5.
For solving the problem all the five transformations – Op1, Op2, Op3, Op4, Op5 –
must be used. The solution is subjected to the following restrictions:
1) In the solution Op1 must be applied earlier than Op4 and Op5
2) Op2 must be applied earlier than Op3 and earlier than Op4
3) It is not allowed to apply more than one transformation at a given step
?1? Which of the following sequences is an acceptable solution path, where the
transformations are listed as applied in the sequence from step S1 to S5?
A) Op1, Op2, Op3, Op4, Op5
A) Op2, Op3, Op4, Op3, Op2
. . .
TRIPS could be used either to generate solutions over these sets of operators
or to generate an appropriate question and choices over a given problem. This is done
by matching a readily available test with the currently solved domain problem.
11. Analytic Method Implementation with a Trigonometry Problem Solver 217
?2? Which of the following couples of transformations can be executed at step
S1 and step S2 respectively in some of the solutions?
A) Op1 and Op4
B) Op2 and Op5
. . .
?3? If Op5 is applied earlier than Op1 in the solution, which of the following
choices must be true for that solution as well?
A) Op1 is applied earlier than Op2
B) Op3 is applied earlier than Op2
. . .
With TRIPS the student, would be able to check the answers.
?4? The step in the solution, subjected to the constraints of the assignment,
which allows the application of each of the five transformations and at the same time
provides the opportunity to apply the rest of the four transformations at the next steps
is:
A) S1
B) S2
. . .
R E F E R E N C E S
[1] Petkov, H., D. Dochev, Z. Markov, G. Agre. Analysis and Formalization
of a class of Mathematical Knowledge. Technological Report for the Ministry of
Science and Education, Bulgaria, 1992.
[2] Petkov, H. and D. Dochev. Flexible Problem Solving for ITS with TRIPS.
Serdica, 20 (1994), 120-132.
[3] Spensley, F., M. Elsom-Cook, P. Byerley, P. Brooks, M. Federici and
C. Scaroni. Using Multiple Teaching Strategies in an ITS, Intelligent Tutoring
Systems: At the Crossroad of Artificial Intelligence and Education, C. Frasson &
G.Gauthier (Eds.), Ablex Publishing Corporation, Norwood, New Jersey, 1990.
[4] The Official Guide for GMAT Review. Graduate Management Admission Council.
Educational Testing Service, Princeton, NJ, 1992.
[5] The Official Software for GMAT Review. Graduate Management Admission Coun-
cil. Educational Testing Service, Princeton, NJ, 1992, Version 4.0, Completely Re-
vised.
12. 218 Hristo Petkov, Danail Dochev
[6] The Official Guide to MBE Programs. Graduate Management Admission Council.
Educational Testing Service, Princeton, NJ, 1992.
[7] Practicing to Take the GRE General Test No.7. Graduate Management Admission
Council. Educational Testing Service, Princeton, NJ, 1992.
[8] Practicing to Take the GRE General Test No.7. Software Editions. Graduate Man-
agement Admission Council. Educational Testing Service, Princeton, NJ, 1992.
[9] Graduate Record Examinations Registration & Information Bulletin – 1992-93,
Published for the Graduate Record Examinations Board by Educational Testing
Service, 1992, 30-32 and 43-45.
[10] The Graduate Management Admission Test 92-93, Bulletin of Information and
Registration Form. Published for the Graduate Record Examinations Board by
Educational Testing Service, 1992, 17-19.
Institute of Informatics,
Bulgarian Academy of Science,
Acad. G. Bonchev St., Bl. 29A,
1113 Sofia, BULGARIA
Received 23.12.1992
Revised 29.04.1993