bluuebunny/crossref_metadata_2025 huggingface dataset:
The Assessment of Alexithymia Across Positive and Negative Emotions: The Psychometric Properties of the Iranian Version of the Perth Alexithymia Questionnaire
Authors: Mousavi Asl Esmaeil , Mahaki Behzad , Khanjani Sajad , Mohammadian Youkhabeh
Published: October 2020

Background: Construct of Alexithymia is important for understanding psychopathology that its assessment is of high interest as persons with difficulty in processing their emotions (either positive and negative) are more vulnerable to psychopathology problems. Objectives: The current study aimed to determine the psychometric properties of the Perth Alexithymia questionnaire (PAQ), and to describe appropriate measures for the field of clinical psychology and psychiatry. Methods: The Persian version of the PAQ was produced through forward translation, reconciliation, and back translation. The study population was all staff (soldiers) of the army force in Tehran, Iran, in 2018 - 2019. Two hundred and fifty four soldiers were selected by convenience sampling method. The following questionnaires were used to collect data: the PAQ, The Deliberate Self-Harm inventory (DSHI), Borderline Personality scale (STB), Cognitive Flexibility inventory (CFI), and Self-Compassion scale (SCS) short-form. The construct validity of the PAQ was evaluated using confirmatory factor analysis, divergent, and convergent validity. Internal Consistency and test-retest reliability (2 weeks’ interval) were applied to evaluate reliability. Data were analyzed using LISREL (version 8.8) and SSPS (version 22). Results: PAQ and its subscales were found as valid and reliable measures, with good internal consistency and good test-retest reliability. The PAQ showed good internal consistency (Cronbach’s α = 0.91). Concerning the convergent validity, PAQ and its subscales showed a significant positive correlation with self-report measures of DSHI and STB (P < 0.05). However, they were negatively correlated with Self-Compassion scale (SCS) short-form and CFI (P < 0.05), which demonstrated a good divergent validity. Moreover, while the results of this study support the five-factor models of the PAQ (RMSEA = 0.08, NFI = 0.94, CFI= 0.95), the two-factor model does not fit the data. Conclusions: The PAQ showed good validity and reliability and can be useful for evaluating Alexithymia in the army force samples. The PAQ can be considered promising as a measure in Alexithymia-related research and clinical settings.
Measuring the effects of Bitcoin forks on selected cryptocurrencies using event study methodology
Authors: Tomić Nenad
Published: October 2020

The objective of the study is to determine whether the Bitcoin forks have produced significant effects on the cryptocurrency market. The event study methodology is used in this paper in order to determine the statistical significance of the abnormal return of leading cryptocurrencies after three Bitcoin forks. The forks were viewed as three isolated events, with the estimations windows and the event windows constructed separately for each of them. There were statistically significant negative effects related to the creation of Bitcoin Gold and Bitcoin SV. Contrary to expectations, there was no statistically important effect throught out the most famous Bitcoin forking and emergence of Bitcoin Cash. Although cryptocurrencies are a current topic, the literature lacks quantitative research dealing with price changes. Without quantitative analysis, it is difficult to conclude whether the return change is a consequence of a statistically significant event The analysis would therefore provide the tool to determine the statistical significance of their impact on the market. A small number of observed cryptocurrencies is the main limitation of this research. Future researches could cover a wider scope of the market and include other famous cases of forking, for example, the Ethereum forks.
The relationship between banks' credit activity and economic growth: An empirical research for the Republic of Serbia
Authors: Grbić Milka , Luković Stevan
Published: October 2020

The subject matter of the research study conducted in this paper is the interactive relationship between banks' credit activity and economic growth. In connection with that, the paper is aimed at examining the existence and direction of the cause and effect relationship between the credit activity of the banking sector and the overall economic activity in the Republic of Serbia. The quarterly data related to the period from 2003 to 2019 were collected for the purposes of the research. The share of the loans granted to enterprises in the GDP and the share of the loans granted to households in the GDP are used as the indicators of the credit activity in the study, whereas the real GDP growth rate is determined as the indicator of economic growth. Given the fact that the observed time series are of the different order of integration, the analysis is conducted within the VAR model by applying the Toda-Yamamoto procedure of the Granger causality test. The results of the research show a significant unidirectional causal relationship according to Granger, which starts from the direction of banks' credit activity towards economic growth. The results of the conducted research study can be useful to the makers of the economic policy and the creators of a strategy for the development of the national economy.
The influence of sociodemographic factors on the development of anxiety during the COVID-19 pandemic
Authors: Jandrić-Kočić Marijana , Knežević Snežana
Published: October 2020

Introduction/Aim: The COVID-19 pandemic poses a serious threat to global mental health. Fear of death, social distancing, economic problems, changes in the education system, and cessation of normal daily functioning induce psychiatric disorders, primarily anxiety. The research aimed to determine the influence of sociodemographic factors on the development of anxiety during the COVID-19 pandemic. Methods: The cross-sectional study, over two months, included 200 persons without symptoms of COVID-19, 60.0% of women and 40.0% of men, with an average age of 51.0 ± 9.2 years. One hundred people reported to the family medicine clinic of the Health Care Center Krupa on the River Una for examinations or administrative reasons, and another hundred were accompanied by them. In addition to the general questionnaire, the Generalized Anxiety Disorder-7 (GAD-7) Self-Assessment Symptom Intensity Questionnaire was used. The ch2 - test and Fisher's test were used for the statistical analysis. Discussion: 105 (52.5%) participants included in the study had symptoms of anxiety (35.0% mild symptoms of anxiety, 15.5% moderate symptoms of anxiety, 2.0% severe symptoms of anxiety). Anxiety was slightly more common in men (56.2%) than in women (50.0%), as well as in the oldest (60-79 years) (92.6%) than in younger participants (12.5% for age 20-39 and 44.7% for ages 40-59). The frequency of anxiety was lower in persons with higher (33.3%) than lower education (44.5% of participants with primary and 46.6% of participants with high school). A slightly higher frequency of anxiety was among the employed (69.5%) than among the unemployed (43.0%), as well as among persons living in urban (80.8%) in comparison to those living in rural (42.6%) areas. Anxiety problems were experienced by 51.3% of participants living in marriage or extramarital union and 56.8% of participants who were not married or in an extramarital union. People with anxiety were significantly more likely to be aged 60-79 than people without anxiety. There were no significant differences between these groups in terms of gender, level of education, employment, place of residence and marital status of the participants. Conclusion: Every other person in this study had some form of anxiety. Further research in this area and proposing adequate prevention programs are needed.
Message from the Editorial Panel
Authors: Horak Virginia
Published: October 2020

The past nine years. since the publication of the first NCTM Standards, have been exciting ones that ushered 1n a national focus on teachmg and learning mathematics We all have been compelled to examine what we teach. how we teach, and l1ow we assess our students' learning. But now is not the time to say, “We have made it: we have done that.” Mathematics education is not only alive and well in 1998. but 1t remams dynamic and evolvmg. The mathematics education community and NCTM, in particular.
A Geometric Puzzle That Leads to Fibonacci Sequences
Authors: Ruff Benjamin
Published: October 2020

Mathematics teachers are constantly challenged to find problems that bring to their students the intellectual pleasure of searching, discovering, generalizing, and finding new and unexpected relationships. An elementary geometric puzzle, familiar to many high school students and teachers, offers a means to roam into several seemingly unrelated areas. The following investigation suggests a way to do some mathematical research while maintaining a playful and informal approach.
Media Clips
Authors: Wood Dorothy
Published: October 2020

We welcome and encourage submissions to this department, which will comprise resources that teachers can use immediately or file away for future use. The assignments generated by these entries may range from starters for an entire class to ful lblown projects for optional individual pursuit. Each lesson, though, should help convince our students that mathematics is useful, current, and newsworthy. Please send submissions to Media Clips, Mathematics Teacher, 1906 Association Drive, Reston, VA 22091-1593.
Reader Reflections
Authors: Manes Michelle
Published: October 2020

A variable expression that uses x and y can be visualized by drawing a lattice that evaluates the expression for lattice points in a coordinate plane. Lattice points are points having integral coordinates.
Fractal Cards: A Space for Exploration in Geometry and Discrete Mathematics
Authors: Simmt Elaine , Davis Brent
Published: October 2020

Fractal geometry has become a topic of widespread interest in recent years as evidenced by brisk sales of books tracing the emergence of the field and the ever-increasing popularity of computer-generated images. As reflected in earlier issues of the Mathematics Teacher, the topic is also well represented in discussions among mathematics educators.
Keep Counting Those Boxes-There's More
Authors: Grassl Richard M. , Mingus Tabitha T. Y.
Published: October 2020

Afamous, well-traveled, and relatively easy counting problem is that of determining the number of squares of aU sizes on a checkerboard. In this article, we pose and solve several related extensions involving enumerating squares and rectangles. Preservice and in-service secondary teachers participating in a problem-solving course at the University of Northern Colorado produced most of the investigations and conclusions illustrated here. In addition, a recent statewide mathematics contest, attended by about a thousand students in grades 7–12, included versions of the explorations. We were pleased that a significant number of students successfully rose to the challenge. Given appropriate guidance, these problems can be a source for wonderful classroom explorations and discovery for both the student and teacher.
Solutions to Calendar
Authors: McLoughlin John Grant
Published: October 2020

Problems 1 7 and 25, 26, and 28 are adapted from Recreational Math Problems for High School Students Book I and Book II (revised 1984). The problems were used in Wellington County (Ontario) mathematics contests and prepared for the Grand Valley Mathematics Association under the guidance of Gary Flewelling. Problems 8 13 are adapted from Puzzles for Pleasure by Barry R. Clarke (Cambridge: Cambridge University Press, 1994). Problem 14 was contributed by Agnes Tuska and Larry Cusick, both of California State University-Fresno, 5245 North Backer Ave., Fresno, CA 93740. Problems 15 24 were submitted by Elias Jonas, Truman Middle College, 1145 West Wilson, Chicago, IL 60640. Problem 27 is taken from 101 Puzzle Problems by Nathaniel B. Bates and Sanderson M. Smith (Concord, Mass.: Bates Publishing Co., 1980).
Technology Tips: Using Spreadsheets to Analyze the Historical Perspectives of Apportionment
Authors: Iovinelli Robert
Published: October 2020

One topic that I cover in my evening class for liberal arts students is the mathematics of apportionment. Even when done with a calculator, the investigations with this problem setting are often tedious, and the students quickly become bored with what appeared to be mundane arithmetic calculations. In an attempt to quell this counterproductive attitude, I turned to the computer lab, where students can use a spreadsheet to do the calculations. This decision proved to be extremely productive, as the students' attitudes became positive and the quality of work showed a level of excellence associated with highly motivated students. When I introduced this technique of using a spreadsheet and computer into my secondary-level classroom, the results were equally gratifying.
Students Generating Test Items: A Teaching and Assessment Strategy
Authors: Odafe Victor U.
Published: October 2020

The more students invest in their own learning process, the more they will learn. This widely documented view is supported by publications from the mathematics-reform community. For example, the National Research Council's (NRC) Moving beyond Myths (1991) and Everybody Counts (1989) and NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) have called for changes in the teaching and learning of mathematics.
Tacoma Shuffle
Authors: Holden Lyman S. , Holden Loyce K.
Published: October 2020

The key concepts discussed in this article include problem-solving activities, mathematical induction, proof by induction, and use of the phrase “without loss of generality.” Several problem-solving tools are illustrated, such as trial and error, working backward, and seeing patterns. The computer application illustrates recursive and iterative functions using C language.
Solutions to Calendar
Authors: McLoughlin John Grant
Published: October 2020

Problems 1-8, 10, 11, and 13-17 were prepared by HarrisS. Shultz, California State University, Fullerton, P. O. Box 6850, Fullerton, CA 92834-6850. Problems 18-29 and problem 31 were submitted by Marian Small, Faculty of Education, University of New Brunswick, Fredericton, NB E3B 6E3. Problems 9 and 12 were contnbuted by M1chael A. Stueben, 4651 Brentleigh Court, Annandale, VA 22003. Problem 30 was taken from 101 Puzzle Problems by Nathaniel B. Bates and Sanderson M. Smith (Concord, Mass.: Bates Publishing Co., 1980).
Technology Tips: Exploring Hill Ciphers with Graphing Calculators
Authors: St. John Dennis
Published: October 2020

Throughout history, coded messages have been used for various reasons. Today's students are fascinated by the secretive nature of these codes, and this fascination can lead them to explore the mathematics of cryptography. The simplest codes are called substitution ciphers. In these codes, each letter is replaced by another number or letter in the alphabet. These codes are easy to crack, or decode, because of the relative frequency of letters in messages. For example, e is the most often used letter in the English language; therefore, the substituted value for e is relatively easy to determine. One way to make substitution codes more difficult to crack is to group letters and then encode the groups of letters. A particular application of this strategy, one that combines matrix multiplication and modular arithmetic, is known as the Hill cipher (Anton and Rorres 1987). This article explains coding and decoding messages using Hill ciphers. These ciphers are an interesting example of an application of matrices called for in NCTM's Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) for grades 9-12. A graphing calculator will facilitate the matrix and modular arithmetic used in the coding and decoding procedures.
Maclaurin's Theorem for High School Calculus Students
Authors: Bruyn Ysbrand de
Published: October 2020

As an extra enrichment topic in the high school calculus course that I teach, I have occasionally dealt with Maclaurin's theorem. Although Maclaurin's series may be an unusual topic in a high school calculus course, the approximation of such functions as the sine, cosine, and exponential by polynomials is significant and interesting enough for students to learn about and is therefore worthwhile as an extra topic.
Products
Authors: Oehm Gerald L.
Published: October 2020

Prices on software, books, and materials are subject to change. Consult the suppliers for the current prices. The comments reflect the reviewer's opinions and do not imply endorsement by the National Council of Teachers of Mathematics.
Projects: Building a Professional Network: Mathematics Teachers as Learners and Researchers
Authors: Tinto Patricia P. , Shelly Barbara A. , Zarach Nancy J.
Published: October 2020

Mathematics Teacher/Researchers Collaborating for Collaboration in the Classroom (MTRC3) is a unique staff-development program that has created a local network of teachers committed to rethinking their classroom practice. The project, which was funded by the National Science Foundation, supports teachers in their efforts to build collaborative-learning communities and to carry out teacher-directed classroom-based research.
The Case for Chaos
Authors: Bedford Crayton W.
Published: October 2020

Chaos theory and fractal geometry have begun to appear as separate units in the mathematics curriculum of many high schools. Many more, however, have found these units appealing but impossible to squeeze into an already packed program. Yet a number of students at these same schools complete a precalculus sequence before the end of their senior year and find themselves, for one reason or another, not ready to go right on to the calculus. Typically, schools offer such students semester courses in probability, statistics, discrete mathematics or computer programming. In this article, I make a case for expanding this offering to include a semester of chaos theory that pulls together all those appealing units that may be scattered through the curriculum. After a brief overview of chaos theory and fractal geometry, I outline eight units that could constitute such a course and include a list of useful resources. For a number of years, I have taught a course based on this outline to precalculus students whose enthusiastic response is the motivation for this article.
Algebra for All: To Encourage “Algebra for All,” Start an Algebra Network
Authors: Davis Suzanne , Thompson Denisse R.
Published: October 2020

In 1994, the National Council of Teachers of Mathematics issued a position statement titled “Algebra for Everyone … More Than a Change in Enrollment Patterns” (NCTM 1994). Success in addressing this call will involve changes on many fronts. Although curriculum changes will be an essential ingredient, teachers at all levels will need to assume responsibility for fostering algebraic thinking. This article describes the efforts in one large county in the Southeast to provide professional development and encourage dialogue among elementary, middle, and high school teachers about issues related to algebraic thinking. This dialogue is essential in helping teachers appreciate their role in the development of algebra as a K–12 concept. By constantly weaving algebraic ideas into the curriculum at all levels, the district's teachers hope to give students the necessary background to pursue successfully the formal study of algebra.
Geoboard Quadrilaterals
Authors: Kennedy Joe , McDowell Eric
Published: October 2020

Recognizing geometric shapes and noting their special properties are important steps in learning geometry. Much of what you want students to learn about squares, rectangles, and trapezoids can be accomplished with geoboard figures. Some of what is lost in generality is gained in accuracy of construction, whether with pegs and rubber bands or with pencil and dot paper. If segments should be parallel, perpendicular, equal—or whatever—they look that way on geoboards.
Activities: The Conic Sections in Taxicab Geometry: Some Investigations for High School Students
Authors: Prevost Fernand J.
Published: October 2020

The urban world in which many of us live does not lend itself to the metric of Euclidean geometry. Assuming that the avenues are perpendicular to the streets in a city, the distance from “fifth and fifty-first” to “seventh and thirty-fourth” is not the familiar Euclidean distance found by applying the Pythagorean theorem. The distance must instead be measured in blocks from fifth to seventh avenues and then from fifty-first to thirty-fourth streets. This taxicab metric, one of several me tries used in mathematics (Eisenberg and Khabbaz 1992), is practical for many applications and helps students pursue interesting investigations while deepening their understanding of familiar topics.
Performing Operations with Matrices on Spreadsheets
Authors: Pagon Dusan
Published: October 2020

Although created mainly for other purposes, spreadsheets appear to be useful in mathematics education. For instance, Russell (1992) writes about spreadsheet activities in middle school mathematics in his book with the same title. In a Mathematics Teacher article, Hunt (1995) describes how he uses spreadsheets to teach students synthetic substitution, synthetic division, and Newton's method. Our experience shows that the same tool can be useful for performing matru operations and, further on, for introducing students to basic concepts of linear algebra. The interested reader can find additional examples of using spreadsheets in high school mathematics in Sjostrand's (1994) book, which deals with Excel spreadsheets.
The Divisibility of xn − yn by x − y: A Constructive Example
Authors: French Francis G.
Published: October 2020

The divisibility of xa − yn by x − y, where n is a positive integer and x # y, offers a rare opportunity to investigate and construct an inductive proof. I have used the following example to help my students better understand the nature of inductive reasoning and inductive proofs, since the expression can be investigated, hypothesized, tesLed, and modeled both physically and pictorially, at least to three dimensions. My students consisted of middle school and high school teachers in an in-service setting. Most were unfamHiar with the use of physical models and manipulatives, the applications of which were the purpose of the in-service sessions. In the application that follows, they were asked to humor their teacher and pretend that they were high school students. They good-naturedly agreed.
Technology Reviews
Authors: Burke William
Published: October 2020

Prices on software, books, and materials are subject to change. Consult the suppliers for the current prices. The comments reflect the reviewer's opinions and do not imply endorsement by the National Council of Teachers of Mathematics.
Soundoff!: What I Wish I Had Known about Mathematics When I Started Teaching: Suggestions for Teacher-Preparation Programs
Authors: Cuoco Al
Published: October 2020

The views expressed in “Soundoff!” reflect the views of the author and not necessarily those of the Editorial Panel of the Mathematics Teacher or the National Council of Teachers of Mathematics. Readers are encouraged to respond to this editorial by sending doublespaced letters to the Mathematics Teacher for possible publication in “Reader Reflections.” Editorials from readers are welcomed.
Algebra for all: An EXCELlent Bridge to Algebra
Authors: Friedlander Alex
Published: October 2020

A possible quick answer to “Why use spreadsheets?” is “Because they are there.” This reply is not as superficial or teasing as it may seem. The wide use of spreadsheets, such as Excel, in many fields has made them common, relatively inexpensive, powerful, and user-friendly tools that have become almost as popular as word processors.
The Cevian Problem
Authors: DeTemple Duane W. , Fitting Marjorie Ann
Published: October 2020

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) challenges the teacher to shift away from memorization and set procedures. Instead, teachers should emphasize developing flexible strategies of problem solving, finding multiple representations, and making connections to other areas of mathematics and to the real world. The cevian problem presented here illustrates how to implement this shift of emphasis.
Connecting Research to Teaching: Teaching the Language of Mathematics
Authors: Krussel Libby , Dunham Penelope H.
Published: October 2020

The belief that mathematics is a language is not new. One often hears this sentiment in conversations among mathematicians, and many students resonate to the idea of mathematics as a “foreign” language. A consensus on this issue does not exist in the mathematics community, however. Hersh (1997) asserts that mathematics is just a jargon, a semi-dialect—he calls it “math lingo.” He points out that if mathematics is a language, then people must be able to make such statements as “I am cold" in that language. Magnus (1997) also disputes the claim that mathematics is a language, preferring to describe it as making use of a special language and having some functions of a language but not being a language in its own right. Bullock (1994, 736) disagrees, claiming that indeed mathematics is a language.
Up the Creek with a Paddle
Authors: Haug Mikel
Published: October 2020

Do I have to know how to do any math for geography?” Although Luke was hoping to find a niche where he needed as little mathematics as possible, his question brought to mind all the practical mathematics that I had used in college geography projects. I was motivated to develop an extended hands-on project for my eighth-grade mathematics classes in which they were to determine the probability that a local creek would flood. This project can be easily adapted to almost any secondary-level mathematics class.
Dice and Disease in the Classroom
Authors: Stor Marilyn , Briggs William L.
Published: October 2020

Students are aware that germs spread disease. They also know, at least on an intellectual level, that they can avoid catching some diseases by avoiding risky encounters with infected individuals. The definition of risky encounter varies with the illness. For example, such illnesses as the common cold may be spread by an activity as common as shaking hands, whereas AIDS is frequently spread by sexual contact. Cures do not yet exist for either of these illnesses. The goal of this activity is to model the exponential growth of the common cold, AIDS, or any other communicable disease. The activity underscores the effect that a friend's— or partner's—previous behavior may have on a current relationship and on society at large. As a part of this activity, students develop a sequence of mathematical models that accurately describes the classroom activity.
Discuss with your colleagues: Quotations for Every Mathematics Class
Authors: Fleron Julian F.
Published: October 2020

For the past several years, I have started each of my classes with a “quotation of the day," which I write on the side chalkboard. This practice has successfully engaged students.
Sharing Teaching Ideas: Geometric Constructions: Visualizing and Understanding Geometry
Authors: Sanders Cathleen V.
Published: October 2020

Geometric constructions can enrich students’ visualization and comprehension of geometry, lay a foundation for analysis and deductive proof, provide opportunities for teachers to address multiple intelligences, and allow students to apply their creativity to mathematics.
Standards 2000: Refining Our Efforts
Authors: Lappan Glenda
Published: October 2020

Since its inception in 1920, the National Council of Teachers of Mathematics (NCTM) has assumed the responsibility of providing broad national leadership in mathematics education. To establish a focus for discussion on improving the mathematics education of every student in states and provinces across North America, NCTM published three Standards documents from 1989 through 1995, addressing curriculum, teaching, and assessment. The Standards present a focus and vision—not a single path or algorithm—for building excellent mathematics programs.
Connecting Research to Teaching: Geometry Classroom Pictures: What's Developing?
Authors: Wohlhuter Kay A. , Dunham Penelope H.
Published: October 2020

In the NCTM's curriculum standards, teachers find a clear vision of mathematics classrooms as rich environments where students can explore, conjecture, reason logically, and connect mathematics with the real world. The Standards’ vision assumes that teachers will use strategies that promote students’ active participation in the learning process. For geometry, especially, those strategies should include activities that foster the interplay of deductive and inductive reasoning (NCTM 1989).
Implementing the Professional Standards for Teaching Mathematics: Thinking Deeply about Knowing Mathematics
Authors: Masingila Joanna O.
Published: October 2020

Most prospective secondary mathematics teachers know quite a bit of mathematics, and they know that they know quite a bit of mathematics. However, they may not be aware that some of their mathematical knowledge is not conceptually deep, connected, or broad.
Message From the Editorial Panel: Welcome to Our Focus Issue on the Concept of Proof
Authors: Dodge Wally , Horak Virginia , Masunaga David
Published: October 2020

The concept of proof is one concerning which the pupil should have a growing and increasing understanding. It is a concept which not only pervades his work in mathematics but is also involved in all situations where conclusions are to be reached and decisions to be made. Mathematics has a unique contribution to make in the development of this concept, and up to the present time teachers of mathematics have, in general, assumed this contribution can best be made in the tenth year through the study of demonstrative geometry. The practice resulting from this assumption has tended to isolate the concept of proof, whereas this concept may well serve to unify the mathematical experiences of the pupil.
Types of Students’ Justifications
Authors: Sowder Larry , Harel Guershon
Published: October 2020

"I just know it.” “Ms. Flores told us last year." "You can see it from the drawing.” "I did some examples. ” "Our group found a pattern.” “I think I have a proof”
Sharing Ideas about Teaching Proving
Authors: Reid David A.
Published: October 2020

At first glance a mathematics class in the People's Republic of China seems far removed from teaching modeled on the NCTM's Standards and other reform documents. Lessons are tightly controlled by the teacher, rapid recall and quick thinking are highly valued, and students rarely work together.
Characterizing Students’ Understandings of Mathematical Proof
Authors: Knuth Eric J. , Elliott Rebekah L.
Published: October 2020

For many secondary-level mathematics teachers and students, the notion of mathematical proof often conjures up images of mathematical rigor in the form of two-column proofs. Yet in recent years, many mathematics educators have been reexamining the nature of mathematical proof in the secondary curriculum.
Implementing the Assessment Standards for School Mathematics
Authors: Thompson Denisse R. , Senk Sharon L.
Published: October 2020

Recommendations in the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and in the Assessment Standards for School Mathematics (NCTM 1995) encourage teachers to incorporate into their curriculum and assessment practices more tasks that require students to construct their own responses, as opposed to primarily using tasks for which a response is provided, such as true-orfalse or multiple-choice tasks. Constructed responses enable students to demonstrate their depth of understanding of mathematics and give teachers greater insight into their students' knowledge of concepts. But when students are required to write about mathematics or explain their solution strategies, teachers want to know how to score such responses. Teachers have therefore become more interested in issues related to rubrics. A rubric is a set of guidelines for evaluating students' responses to one or more tasks. A general rubric is a broad outline that indicates vatious levels of performance and the factors that teachers should consider when specifying performance levels; a task-specific rubric interprets the general rubric for a specific task and specifies the particular mathematical aspects of the task that determine each level of performance (NCTM 1995; California Mathematics Council 1993).
Distribution of the Banned Lithuanian Press in Čekiškė Region
Authors: Stepukonienė Inga
Published: October 2020

Although in the second half of the nineteenth century a multicultural environment prevailed in the town of Čekiškė, the banned Lithuanian press was actively distributed there. The Lithuanians living in the nearby villages bought forbidden Lithuanian publications, which were distributed by book smugglers. Initially, Lithuanian prayer books and ABC primers were distributed in town markets, and later the first Lithuanian newspapers, Aušra and Varpas, other publications, and literature. Local residents were actively engaged in it. In addition, some quite active people would sell small religious paraphernalia near churches. The book smugglers from Čekiškė and its environs brought the Lithuanian press mainly from Prussia, where they often travelled together with the book smugglers of Ariogala and Vilkija regions. Press distributors maintained close contact with the priests of their town and of the said regions. Having graduated from the seminaries of Seinai or Kaunas, the priests who worked in Čekiškė and Ariogala became not only zealous supporters of the banned Lithuanian press, but also its distributors. Many of them suffered repression and were constantly transferred from one parish to another. Ieva Ivanauskienė and Mykolas Račkus, who distributed the banned Lithuanian press until the lift of its ban and even later, were the most zealous book smugglers of Čekiškė. People of great courage and ingenuity and capable of acting even in the most difficult circumstances, they bravely joined the book smugglers of this region. Povilas Višinskis, a publicist, writer, and cultural figure, who lived in the vicinity of Čekiškė for some time, devoted considerable efforts to creating and publishing Lithuanian publications. Thus, the people of Čekiškė region helped to bring about an important event – the lifting of the ban on the Lithuanian press – on 7 May 1904.
Historical Articles in the Lithuanian Periodical Press, 1904–1918: A Quantitative Approach
Authors: Krutulys Titas
Published: October 2020

The paper is focused on historical articles in the periodical press of 1904 to 1918 from a quantitative point of view. This period was significant because the year 1904 marks the beginning of the legitimate Lithuanian periodical press and also the period of Lithuanian political diversification, while 1918 starts the period of the Republic of Lithuania. History was an important part of the Lithuanian national movement and it helped to create the Lithuanian identity. On the other hand, the historical significance of historical articles in the Lithuanian periodical press is usually overrated or unclear. This study shows that during this period, historical articles make up only about 1.8 per cent of the whole list of topics of articles. Meanwhile, such themes as politics, economics, religion, and literature were much more popular. However, it also shows clear progress of Lithuanian historical articles from only 27 articles in 1904 to 358 articles in 1918. This progress was uneven and we can distinguish four quantitative upswings: in 1905, 1910, 1914, and 1918. Analysis of the most common topics in Lithuanian historical articles showed that the history of the Lithuanian countryside was the most popular. Thus, the history of places close to most of the Lithuanians living in the countryside was more common than the history of the Lithuanian cities. The most popular periods of Lithuanian history was the period from the thirteenth to the fifteenth centuries and the history of the nineteenth century. Among historical events, the most popular were the Battle of Žalgiris, the abolition of serfdom in 1861, and lifting the ban on the Lithuanian press in 1904. Foreign history was also quite popular in Lithuanian periodicals. The article also deals with the relation of different Lithuanian political ideologies to historical articles. While two right-wing political groups, Lithuanian nationalists and Lithuanian Christian Democrats, wrote widely on historical topics and especially liked the period of the thirteenth to the fifteenth centuries and the nineteenth century in Lithuanian history, the Lithuanian left-wing or centre-left political parties, Lithuanian Social Democrats and Lithuanian Democrats, wrote about the past and overall history of Lithuania much less: they were mostly interested in the history of the nineteenth century and in foreign history.
Processes of Cultural Memory in Contemporary Lithuanian Culture
Authors: Mykolaitytė Aurelija
Published: October 2020

The article explains what cultural memory is and what processes of cultural memory are most noticeable in today’s Lithuanian culture. The works by Aleida Assmann and Jan Assmann, which continue research on memory started by Maurice Halbwachs and Pierre Nore and supplement them with new insights into the contemporary global world of today, were chosen for the theoretical basis. The concept of cultural memory, which is defined as texts, images, and rituals, is particularly important. This theoretical basis underlies the study of works by Lithuanian authors. It has been noticed that modern Lithuanian culture is moving from local to global memory, contemporary artists aim at creating for an international audience, and new ways of expression are being sought. On the other hand, frequent succumbing to the commercialisation of art is observed. Thus, culture is at its turning point and is shifting from one cultural environment to another. While confusion is particularly evident in the creation of political memory, cultural memory is much more open to today’s challenges. It is in a living relationship with its history that still raises questions about the Holocaust, resistance, and exile, and this relationship maintains its significance.
The development of active thinking in the process of teaching language disciplines
Authors: Suvorova Nadezhda Nikolaevna , Novikova Tat'yana  Arkad'evna
Published: October 2020

The subject of this research is the formation of skills of the architecture of speech that corresponds to the norms of the Russian literary language among students majoring nonlinguistic specialties. The object of this research is the process of teaching language subjects using the “crib notes” method. The goal consist in testing the effectiveness of such teaching method. Methodological substantiation of the methods of pedagogical research consists in the activity, personal and systemic approaches. Methods of pedagogical research contain empirical (study and generalization of pedagogical experience, analysis of students’ performance, observation, conversation), data processing methods (mathematical, statistical). A pedagogical experiment was conducted as method of studying the pedagogical process in the modified and accurately considered conditions. The described in the article “crib notes” method applicable to studying language disciplines not only structures the knowledge, but also helps the students to memorize easily reproduce the learnt material, develops creative abilities of future engineers, even in the area of cognition and development of literary and formalized speech architecting skills. The scientific novelty consists in combination of language material and the competences of future engineers to present information in the form of diagrams, tables, and systems. This allows employing this method in studying not only the selected language topics, but entire disciplines as well.
Gender aspects of manifestation of teaching styles on the background of digitalization of education
Authors: Nikulova Galina Anatol'evna , Bobrova Lyubov' Nikolaevna
Published: October 2020

The object of this research is the process of transformation of individual characteristics and preferences of the participants of educational process in the conditions of Informatization of education. The subject of this research is the gender-stylistic peculiarities of students and pedagogues in the context of digitalization. Analysis is conducted on the gender aspects of educational process and gender differentiation trends. Special attention is given to the role of information technologies in achieving gender equality and importance of considering students’ stylistic orientation. The goal of this work is to determine the presence of gender differences and stylistic preferences of educational process participants within the framework of its Informatization and digitalization for development of ways of for considering individual preferences in organization and formation of learning environment. The stylistic profile of respondents was defined in accordance with the model of D. Kolb based on methodology of P. Honey and A. Mumford, adapted by the authors of the article. It included the questions specifying the stylistic orientation of students and pedagogues towards IT sphere. For quantitative assessment of manifestation of teaching styles was applied the method of semantic differential, which allows expressing the degree of agreement/disagreement with the proposed statement. The obtained data give a perspective on the peculiarities of formedness of stylistic preferences in acquisition of knowledge among the pedagogues and students on a gender basis. The more distinct gender differences in the teaching styles are revealed among the pedagogues, and their leveling is noticed among young generation. The dominant teaching styles for the majority of respondents became the ones of theoretical orientation (thinking and theoretical), which can be attributed to the impact of being engaged in IT sphere. The acquired results underline the need to draw attention to the absence of organic development of teaching styles of the students and allow determining further vectors of research – a comparative analysis of stylistic orientation of the participants of educational process based on age indicators. 
Theoretical foundations of actors training in Chinese theatrical schools
Authors: Yu Yadong
Published: October 2020

This article is dedicated to the work with students in Russian and Chinese theatrical schools, which is structured on the elements of acting techniques determined by the “Stanislavsky system” as the leading theoretical foundation in the training of novice actors. It is noted the assisting methods in the process of actors training is the methods and approaches towards drama training applied by Vsevolod Meyerhold and Nikolai Demidov. Leaning on the national and foreign experiments, the professors are guided by personal long-term artistic experience and theory of acting art, trying to make this course on the basis of substantial scientific theory and practice. The author claims that actors training in China leans on the Meyerhold system, with focus on development of self-control, control over body, voice and emotions, orientation towards manipulation of the character, coupled with random body movements as the basis. Professional acting technique training in Chinese theatrical schools is founded on the basic knowledge of professional skills for improving the laws of physical body movement, emotional control, cognition and interpretation of the character.
On the quality indicators of automated control systems software
Authors: Tikhanychev Oleg Vasilyevich
Published: October 2020

The subject of the research is the process of developing automated control systems software. The object of the research is the quality control system of this process. The regulatory documents establish a list of the main characteristics of program quality assessment, which, as practice has shown, does not fully meet its purpose, providing not quality control, but verification of the compliance of programs with the customer's requirements formulated in the terms of reference. One of the reasons for this lies in the impossibility of evaluating exclusively quantitative indicators of the quality of systems, including both technical means and a person. An attempt to use world practice, for example, relatively successful quality models from the ISO / IEC 25000: 2014 standards have not yet been implemented: the model itself is allowed to be used by regulatory documents (GOST R ISO / IEC 25010-2015), but the quality indicators described in it are not accepted. Private improvements to existing methods do not solve the problem systematically. The article uses general scientific methods of analysis and synthesis. Based on the analysis of existing approaches to assessing the quality of software development, proposals for improving this process are synthesized.The article formulates a scientific and practical problem and offers one of the approaches to its solution, based on the refinement of existing methods for assessing quality based on the model described in GOST R ISO / IEC 25010, taking into account the real needs of users, interpreted through reducing the likelihood of errors of the first and second kind arising from the use of software. The solution of the formulated problem will provide a general increase in the efficiency of automated control through the use of quantitative and qualitative assessments of the software being developed.
Investigation of random access computer networks operating in a diffusion environment with an increasing number of subscriber stations
Authors: Vavilov Viacheslav
Published: October 2020

Improving the performance of various types of communication networks in the modern world remains an urgent task, in connection with which research is underway to create hardware that expands the throughput of physical channels, new network protocols are being developed and existing network protocols are being modified, mathematical and computer modeling of data transmission mechanisms in communication networks is being carried out. The speed and reliability of data transmission over networks also depends on a number of factors, the nature of the influence of which is random. The combination of such factors is called a random environment. If the change in the states of the medium is continuous, then we speak of a diffusion medium. The object of the research is communication networks controlled by multiple access protocols and functioning in a random (diffusion) environment. The research tool for multiple access networks is the mathematical apparatus of the theory of finite-difference and differential equations, the theory of random processes and the theory of queuing. The proposed mathematical model of communication networks in a diffusion environment is investigated by an asymptotic method. The scientific novelty of the work lies in the fact that for the first time a mathematical model of a multiple access network operating in a diffusion environment was proposed and an asymptotic study was carried out. The asymptotic average of the normalized number of claims in the orbit (the source of repeated calls) and the deviation from this average are found, and the probability density of the values of the process of changing the number of claims in the orbit is obtained.