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The article analyzes the problem of assessment of the informativeness (or informational content) and the didactic complexity of various learning material elements (educational concepts, pictures and education texts). The informativeness of learning material elements (LMEs) is considered equal to the number of concepts to be used for its presentation or the description. Under the didactic complexity of LME it is offered to understand the value proportional to the time or amount of the efforts demanded by the 5–class Russian schoolchild for his/her studying this LME. As all educational information is presented in a verbal form, to define the complexity of LME it is necessary to decompose LME into separate concepts, to estimate their separate difficulty, and then to summarize it. The article considers: 1) the estimation of difficulty of experimental and theoretical studying of a concept using the method of paired comparisons; 2) spreading out cards with scientific concepts on them in order of increasing complexity; 3) the calculation of the objects and links in the picture taking into account their abstractness degree; 4) the determination of terms (concepts) number in the text, accounting their complexity. Uniform criteria for estimation of the words (concepts) complexity in educational texts on natural-science disciplines are elaborated and the abstract-ness scale is constructed. The received results can be used to assess the complexity of textbooks in natural sciences. The developed estimation method of didactic complexity of the physics textbooks includes: 1) the estimation of the physics complexity of the textbook summing up the complexity of the physical objects, phenomena, experiments, statements and theories; 2) the measurement of mathematical complexity of the textbook by counting the number of formulas (considering their complexity) and drawings presenting mathematical abstractions (a vector, power lines, graphs); 3) the calculation of the total index of the textbook didactic complexity. With the help of this method 16 Russian physics textbooks for school and university have been analyzed, their distribution within the characteristics
The article analyzes the problem of assessment of the informativeness (or informational content) and the didactic complexity of various learning material elements (educational concepts, pictures and education texts). The informativeness of learning material elements (LMEs) is considered equal to the number of concepts to be used for its presentation or the description. Under the didactic complexity of LME it is offered to understand the value proportional to the time or amount of the efforts demanded by the 5–class Russian schoolchild for his/her studying this LME. As all educational information is presented in a verbal form, to define the complexity of LME it is necessary to decompose LME into separate concepts, to estimate their separate difficulty, and then to summarize it. The article considers: 1) the estimation of difficulty of experimental and theoretical studying of a concept using the method of paired comparisons; 2) spreading out cards with scientific concepts on them in order of increasing complexity; 3) the calculation of the objects and links in the picture taking into account their abstractness degree; 4) the determination of terms (concepts) number in the text, accounting their complexity. Uniform criteria for estimation of the words (concepts) complexity in educational texts on natural-science disciplines are elaborated and the abstract-ness scale is constructed. The received results can be used to assess the complexity of textbooks in natural sciences. The developed estimation method of didactic complexity of the physics textbooks includes: 1) the estimation of the physics complexity of the textbook summing up the complexity of the physical objects, phenomena, experiments, statements and theories; 2) the measurement of mathematical Robert V. Mayer METHODS OF THE INFORMATIVENESS AND DIDACTIC COMPLEXITY ESTIMATION OF EDUCATIONAL CONCEPTS, PICTURES AND TEXTS European Journal of Education Studies-Volume 2 │ Issue 11 │ 2016 2 complexity of the textbook by counting the number of formulas (considering their complexity) and drawings presenting mathematical abstractions (a vector, power lines, graphs); 3) the calculation of the total index of the textbook didactic complexity. With the help of this method 16 Russian physics textbooks for school and university have been analyzed, their distribution within the characteristics space "physical complexity-mathematical complexity" has been studied.
Improving the teaching needs to determine the characteristics of various elements of learning material (ELM). The article considers the problem of measuring didactic complexity of the conceptions, statements and texts, which are used at school. The methodological basis of the research are the works The didactic complexity of ELM is offered to be understood as the characteristic which is proportional to the time needed to assimilate the information presented in this ELM. Uniform criteria for estimation of the scientific conceptions complexity on various natural science subjects are developed and the method of the complexity assessment of the statements (laws, principles, postulates) based on abstraction scale is offered. For an assessment of ELM complexity it is necessary to provide the teacher who, explaining the essence of statement, describes the corresponding situation and gives the definitions to all terms used. The offered method consists in the following: 1) to create the text including the formulation of the law, the description of the situation (the phenomenon, the experiment, etc.) corresponding to this law and the definitions of the science terms used; 2) to compile a dictionary–thesaurus and to estimate the didactic complexity of the conceptions entering it; 3) to start a special computer program which analyzes the text and determines the conceptions quantity and their total complexity. In case of large texts assessment it should be taken into account that the didactic complexity of the issues studied at school is determined by a variety and abstractness of the qualitative and quantitative models used. The developed estimation method of didactic complexity of the physics textbooks includes: 1) the determination of the physics complexity of the textbook summing up the complexity of the physical objects, phenomena, experiments, statements and theories; 2) the measurement of mathematical complexity of the textbook by counting the number of formulas (considering their complexity) and drawings presenting mathematical abstractions (a vector, power lines, graphs); 3) the calculation of the total index of the textbook didactic difficulty. With the help of this method 16 Russian physics textbooks for school and university have been analyzed, their distribution within the characteristics space "physical complexity-mathematical complexity" has been studied. For the determination of the didactic complexity of the textbooks on natural science disciplines the method of pair comparisons of various texts is used. The textbooks are compared according to the following characteristics: 1) the variety and abstractness of qualitative explanations, their isolation from everyday life; 2) the complexity of mathematical methods and models, the variety of solved quantitative tasks. The Russian textbooks on nature study, geography, biology, physics, chemistry (21 textbooks) have been analysed, and their paired comparison with each other has been made. It is found that the chosen characteristics can be considered as independent; the correlation coefficient between them is equal 0,51. On the basis of the obtained data the distribution of school textbooks on physics, chemistry, biology, ecology within space of characteristics "complexity of qualitative models – complexity of quantitative models" is presented, their classification is made.
For assessment of the informativeness and didactic complexity of picture it needs to replace the picture with a full but short description and count the quantity and complexity of the used concepts. It is possible to calculate the objects and links in the picture taking into account their abstractness degree. The results can be used to assess the complexity of textbooks or technique of training.
ICERI2018 Conference, Seville, Spain
ON COMPLEXITY MEASUREMENT OF SOME ISSUES OF THE SCHOOL MATHEMATICS COURSE2018 •
Improvement of teaching technique requires assessment of didactic characteristics of various learning material elements (LME). The problem of the didactic complexity (DC) estimation of various issues of the school mathematics, which can be considered as one of indicators of the pupil's intellectual development, represents a considerable interest. The purpose of the present study is to develop a method for estimating the complexity of various issues of school mathematics. This will answer the question: How does the complexity of the educational material increases during the time of schooling? This problem lays at the intersection of the following scientific areas: the psychology of the educational process (B.M. Velichkovsky, V.M. Krol), the optimization of textbooks (Ya.A. Mikk, V.P. Bespalko), the complexity measurement of the solution of the educational tasks (G.A. Ball, A.V. Gidlevsky), the formation of the cognitive operations in senior classes (N.N. Pospelov, I.N. Pospelov), the application of the content-analysis method to assess the complexity of education texts (R.V. Mayer, A.M. Sokhor), folding and unfolding of knowledge and operations (S.I. Shapiro), the modeling in pedagogy (G.V.Glass, J.C.Stanley, M.V. Yadrovskaya). The complexity of the particular LME is proportional to the time (or number of words) which required for explanation this material to a pupil. It depends on: 1) the volume of the LME, i.e. the minimum quantity of words which necessary to say in order to explain this LME; 2) the level of abstraction, the number of mathematical symbols, formulas and objects shown in the pictures; 3) the degree of the information folding, which is characterized by a share of new concepts expressed through simple concepts. To assess the DC of some LMEs we used: 1) the method of decomposing operations on elementary actions; 2) the method of paired comparisons; 3) the content analysis of the paragraphs of the textbook. It is taken into account: 1) the paragraph volume; 2) the quantity of mathematical symbols in the formulas; 3) the quantity of new concepts that are not included in a given level of knowledge; 4) the information volumes of the new concepts definitions. To measure the information volume V of this LME: 1) we replace the text of the given LME with an equivalent text of minimum length containing the same information; 2) we replace drawings and formulas with their verbal description of the minimum length; 3) we count and summarize up the quantities of words in the texts. To determine the corrected information volume of the LME, it is necessary: 1) to set the level of knowledge (or the system of concepts) relatively to which the DC complexity is determined; 2) to write down definitions of the new concepts used in this LME, which are not known to the pupil, and after that to count the number of their uses; 3) to multiply the quantities of words in the definitions of new concepts by the numbers of their uses and summarize up all these products with information volume V of this LME. As a result of the didactic complexity assessment of the 27 LMEs, it is established that while schooling the mathematics issues complexity increases 150-200 times. It turned out that the LME "Quadratic root and its transformations" is in 3-4 times more complicated than the LME "Multiplication of two-digit natural numbers", and the DC of LME "Properties of a definite integral" is 3.5-5 times larger than the DC of LME "Quadratic function".
Proceedings of ICERI2020 Conference 9th-10th November 2020
THE COGNITIVE COMPLEXITY ESTIMATION OF THE BASIC STATEMENTS OF THE SCHOOL MATH COURSE (ENG)2020 •
The most important condition for successful learning is understanding of educational texts (ET) or teacher's explanations. The main difficulty when working with ET is to decode the meaning of the terms used and the thoughts expressed. The result depends on the text cognitive complexity, on the concentration degree of semantic information in its constituent sentences and mathematical statements. The article is devoted to the actual problem of measuring the educational information density in the theoretical component of mathematics textbooks in various classes of Russian schools. The aim of the research is: 1) to develop objective methods for assessing the cognitive complexity of educational texts by measuring the amount of semantic information in them; 2) to determine the information density in theoretical arguments (definitions, theorems, conclusions, etc.) carried out in school mathematics textbooks. Here the information density is considered to be equal to the average coefficient of knowledge folding, i.e. the ratio of the information amount to the text volume. The methodological basis of this research is the works by E. G. Gel'fman, M. A. Kholodnaya (psihodidactics); Ya. A. Mikk (textbook theory); A. V. Gidlevsky, T. A. Zdrikovskaya, I. S. Naumov, V. S. Vykhovanets (difficulty and complexity of educational texts); N. K. Krioni, A. D. Nikin, A. V. Fillipova, Ch.Ch. Chang, S.M. Silalahi (content analysis of texts); N.V. Lukashevich, Val. A. Lukov, Vl. A. Lukov (thesaurus approach); N. B. Samsonov, E. V. Chmyhova, D. G. Davydov, Yu. A. Tomina (cognitive complexity of scientific and educational text). The applied method requires creating a sample of typical textual and mathematical statements that characterize the study of mathematics in given grades, and counting the number of terms that occur, taking into account their complexity. The dictionary-thesaurus of applied terms is created; their complexity is determined by the method of the complex concepts decomposition into simple ones and by the pair-comparison method. A special computer program is used to evaluate the text complexity. It addresses to the text file dictionary.txt, which contains a list of more than 200 mathematical terms with the specified complexity, and the file F.txt with the text being analyzed. The program takes a term from the dictionary and analyzes the file with the text line by line, counting the number of the given term in it. The difficulty of the text understanding depends on the average complexity of the sentences forming it. With the method of automated calculation of terms in the text and accounting of their complexity, text files are analyzed, their information content is measured, and average values of the information density in various classes are estimated. More than 15 different math textbooks are analyzed, from which the most typical theoretical statements and formulas are selected. As an evaluation result of the theoretical information density in school courses of mathematics (5 th-6 th grades) and algebra (7 th-11 th grades), it was found that in the 1 st-9 th grades the cognitive complexity increases slowly, and in the 10 th-11 th grades it grows rapidly. Having estimation of the theoretical information density and information volume for 1 st-11 th grades, we can determine the total amount of educational information received by students at math lessons.
Proceedings of ICERI2020 Conference 9th-10th November 2020
THE METAPHOR "STUDENT'S BRAIN AS MESSAGE DECODER" AND USING IT WHILE DIDACTIC SYSTEMS MODELLING (ENG)2020 •
Metaphorical transfer helps to establish a connection between the more developed knowledge field, from which terms are borrowed, and the semantically poor field of knowledge. Various metaphor-models allow to model the learning process and to understand its essence better. From positions of the information-cybernetic approach the following metaphors are of great interest: 1) "the teacher and the student are an information system of the type: the source => the communication channel => the receiver"; 2) "the brain is the decoder of messages" or "the brain is the communication channel between the sense organs and the pupil's memory". The creation and improvement of new metaphors, their use for building qualitative and mathematical models are an actual problem of the education theory. The purpose of this research is as follows: 1) to analyze the features of the quantitative modelling of didactic system (DS); 2) to develop and deepen the metaphors "the brain is the message decoder" or "the brain is the communication channel"; 3) to define the concept "the complexity profile of the message (text)", 4) to create the mathematical and computer models of the student's understanding of the teacher's message. The methodological basis of the research is the works on theoretical pedagogy and didactics (E. G. Gel'fman, M. A. Kholodnaya, B. M. Velichkovsky, V. I. Zagvyazinsky, T. P. Zinchenko), mathematical theory of learning (R. Atkinson, G. Bauer, R. Bush, E. Crothers, O. G. Gokhman, L. P. Leontiev, V. V. Mayer, F. Mosteller, F. S. Roberts), simulation modelling (R. Shannon), processing of semantic information (I. P. Kuznetsov), cognitive models of the brain information processing (D. Broadbent, A. Deutsch, D. Deutsch, D. Norman, E. Traisman), speech communication (O. Ya. Gokhman, T. M. Nadeina). We use the "black box" method, when the DS is divided into separate blocks (internal structure and mechanism of functioning of this blocks are not discussed) and their reactions to external influences are analyzed. This allows to build qualitative and mathematical models of the DS, based on the facts that: 1) the teacher and student form an informational semantic system; 2) learning сan be considered as perceiving (listening or reading) a sequence of educational texts of increasing complexity; 3) as the student learns more complex material elements, the "brain decoder" throughput capacity increases due to the "zone of proximal development". For study of the mathematical model of DS the spreadsheet MS Excel is used. The article defines the concepts of "brain decoder transfer coefficient", "volume and information comprehension coefficients", "dependence of the transfer coefficient on the complexity of elementary statements". It is shown that the message transmitted from the teacher (textbook) to the student we can decompose into elementary phrases and evaluate their complexity. This allows to create a complexity text profile, i.e. the dependence graph of the number of elementary phrases on their complexity. The student's "brain decoder" is considered as a communication channel with limited bandwidth; its transfer coefficient depends on the complexity of incoming phrases and the degree of the student's training. The article contains six figures that help to understand the dependence of the knowledge acquired by the student on the bandwidth of his/her "brain decoder" and the complexity profile of the text, as well as to explain the phenomenon of partial understanding of the educational text.
Summary: It is offered a method of measurement of quantity of different types of information and their complexity by means of computer. The applied computer program, uses the dictionary thesaurus, which counts frequencies of a mention of various physical and mathematical terms in the text file, and considers their complexity. The expert defines quantity of mathematical symbols and complexity of formulas. Considering all this, the program counts the volume and complexity of empirical, theoretical and mathematical information, total volume of scientific information, total volume of the paragraph, a share of scientific information, specific quantity of E–, T – M–knowledge. Also the profile of the text consisting of a vector of most often meeting words and a vector of frequencies is created. Results of the content analysis of several paragraphs of various textbooks of physics are presented in article, the comparative analysis of them is carried out. It is established that educational texts strongly differ by number of empirical and mathematical information therefore these two characteristics have to be considered at their classification. Keywords: didactics of physics, content analysis, textbook, information measurement, empirical and theoretical knowledge.
2017 •
The technique and results of an assessment of Abstractness of more than 20 modern school textbooks on biology, geography, physics and chemistry are considered by method of pair comparisons. Thus it is assumed that didactic complexity of the textbook is mainly determined by the level of Abstractness of the material stated in it and depends on: the variety and Abstractness of qualitative explanations, their isolation from everyday life (i); the complexity of mathematical methods and models, variety of the solved quantitative problems (ii). The levels of Abstractness of each textbook are determined, their distribution in two-dimensional space of attributes (i) and (ii) is studied. The received results allow to range textbooks on their didactic complexity.
Procedia - Social and Behavioral Sciences
Students’ Interpretations of the 6th Grade Science Textbook Design2014 •
This study was aimed at exploring the processes involved and the results attained by undergraduates in understanding information from multiple sources on two different tasks: reading/reading and writing a synthesis. The participants were 161 undergraduates –females and males- in Psychology. All of them were asked to read three texts about intelligence, and to answer a prior knowledge questionnaire –before reading- and a comprehension test –after reading-. The experiment was designed based on two different conditions: task (reading/reading&synthesis) and media (performing the task on paper or computer). Three ANOVAs were conducted with task and media as independent variables and global, superficial and deep comprehension as dependent variables. No significant differences were found between tasks. Significant differences were found on deep comprehension for media condition in favor of the students who did the task on paper.
STAGING KNOWLEDGE AND EXPERIENCE: HOW TO TAKE ADVANTAGE OF REPRESENTATIONAL TECHNOLOGIES IN EDUCATION AND TRAINING?
On-Line Assessment of Students’ Global Reading Strategies through Triple Task Technique2012 •
STAGING KNOWLEDGE AND EXPERIENCE: HOW TO TAKE ADVANTAGE OF REPRESENTATIONAL TECHNOLOGIES IN EDUCATION AND TRAINING?
Automated Analysis of Pupils’ Self-Explanations of a Narrative Text2012 •
2012 •
STAGING KNOWLEDGE AND EXPERIENCE: HOW TO TAKE ADVANTAGE OF REPRESENTATIONAL TECHNOLOGIES IN EDUCATION AND TRAINING?
Paired Graphics: An Exploratory Study of Graphicacy2012 •
Standarts and Monitoring in Education, № 2
Informative Value Estimation of the Basic Statements of the School Math Course (RUS)2019 •
Journal of Computer Assisted Learning
Characteristics of multimedia textbooks that affect post-test scores2003 •
Trames. Journal of the Humanities and Social Sciences
THE RELATIONSHIP OF TEXT FEATURES TO THE LEVEL OF INTEREST IN SCIENCE TEXTS2010 •
Computers & Education
What is important in electronic textbooks for students of different achievement levels?2008 •
Review of International Geographical Education Online
Comparative Analysis of the Quality of Visuals in Geography Textbooks for ISCED 1 and ISCED 2 Levels of Education2007 •
CERME 6–WORKING GROUP 15
What works in the classroom-project on the history of mathematics and the collaborative teaching practice2009 •
Journal of Quantitative Linguistics
A Reading Comprehension Formula of Reader and Text Characteristics1999 •
ICERI2018 Conference, Seville, Spain, 2018
THE INFORMATION-CYBERNETIC APPROACH TO THE PROBLEM OF THE TRAINING PROCESS CONTROL: THE IMITATING MODELING RESULTS2018 •
International Journal of Research - GRANTHAALAYAH
Content Analysis of Diagrammatic Representations in Upper Primary Science Textbooks2017 •
Textbook Quality A Guide to Textbook Standards
Textbook Quality - A Guide to Textbook Standards2013 •
2010 •
Journal of International Cooperation in Education
Current Trends in History and Social Studies Textbook Research2012 •
2000 •
State-of-the-Art and Future Perspectives. Proceedings of the 1st International Baltic Symposium on Science and Technology Education (BalticSTE2015)
STATE-OF-THE-ART AND FUTURE PERSPECTIVESGIREP-EPEC & PHEC 2009
Using math in physics: Warrants and epistemological frames2009 •
GIREP-EPEC & PHEC 2009
Mathematization in Physics Lessons: Problems and PerspectivesThe American Statistician
Six online statistics courses: Examination and review2005 •