PROGRESS IN INTERNATIONAL READING LITERACY STUDY (PIRLS)

Annotation: This article reviews the achievements of the PIRLS international assessment program.  The purpose, components of this program are mentioned.  The procedure for conducting Reading Literacy, which is considered the main focus of the International Assessment Program, is noted

Key words: education system, literacy, purpose, components, reading literacy, assessment, questionnaire

The Progress in International Reading Literacy Study (PIRLS) is a large international comparative study of the reading literacy of fourth-grade students. The study is conducted by the International Association for the Evaluation of Educational Achievement (IEA), with national sponsors in each participating education system (previously referred to as education systems). The National Center for Education Statistics (NCES), in the Institute of Education Sciences at the U.S. Department of Education, is responsible for the implementation of PIRLS in the United States. Reading literacy is one of the most important abilities that students acquire as they progress through their early school years. It is the foundation for learning across all subjects, it can be used for recreation and for personal growth, and it equips young children with the ability to participate fully in their communities and the larger society. 

Participants in PIRLS include both countries and subnational entities, both of which are referred to as education systems. PIRLS focuses on the achievement and reading experiences of children in grades equivalent to fourth grade in the United States. The study includes a written test of reading comprehension and a series of questionnaires focusing on the factors associated with the development of reading literacy. PIRLS was administered in 2001 to students in 35 education systems, in 2006 to students in 45 education systems, in 2011 to students in 53 education systems, and in 2016 to students in 61 education systems. 

Purpose PIRLS is a carefully constructed reading assessment, consisting of a test of the reading literacy of fourth-grade students and questionnaires to collect information pertaining to fourth grade students’ reading literacy evaluation. 

PIRLS has four goals: (1) develop internationally valid instruments for measuring reading literacy suitable for establishing internationally comparable literacy levels in each of the participating education systems; (2) describe on one   scale the literacy profiles of fourth-graders in school in each of the participating education systems; (3) describe the reading habits of fourth-graders in each participating education system; and (4) identify the home, school, and societal factors associated with the literacy levels and reading habits of fourth-graders in school. 

Components PIRLS assesses four broad-based comprehension processes within each of the two purposes for reading: focus on and retrieve explicitly stated information; make straightforward inferences, interpret and integrate ideas and information; and evaluate and critique content and textual elements. 

Also, PIRLS focuses on three aspects of reading literacy: purposes for reading; processes of comprehension; and student reading behaviors and attitudes. The first two aspects are measured through the PIRLS assessment component, which is administered to each participating student. The third dimension, reading behaviors and attitudes, is measured through a separate component of background questionnaires. In 2016, the PIRLS administration included the PIRLS assessment as well as ePIRLS, an assessment of online informational reading. PIRLS 2021 will present a new digital web-based delivery system called digitalPIRLS. digitalPIRLS will be offered so countries can take advantage of a full computer-based assessment. 

The digitalPIRLS assessments will include the ePIRLS assessment of online reading initiated in 2016. With digitalPIRLS, countries will experience greater operational efficiency in translation and translation verification, data entry, and scoring, without the need for printing or shipping. Digital PIRLS will be offered as a web-based system via school-based or IEA web servers, or a USB drive connected locally to a PC with the Windows Operating System. As an alternative to digitalPIRLS, countries may administer PIRLS 2021 in paper format. ePIRLS is available in 2021 only in conjunction with digitalPIRLS. For more information on digitalPIRLS, please visit the IEA website at https://www.iea.nl/. 

Source versions of all instruments (assessment booklets, the ePIRLS assessment, questionnaires, and manuals) were prepared in English and translated into the primary language or languages of instruction in each education system. In addition, it was sometimes necessary to adapt the instrument for cultural purposes, even in countries that use English as the primary language of instruction. All adaptations were reviewed and approved by the International Study Center to ensure they did not change the substance or intent of the question or answer choices. 

The first aspect of the assessment component that is targeted by PIRLS is purposes of reading. The purposes of reading component encompasses the two main reasons why young students read printed materials: for literary experience and for the acquisition and use of information. To measure the ability of students to read for literary experience, fictional texts are used; to measure students’ skills for acquiring and using information, nonfictional texts are used. In 2016, literary experience and acquiring and using information each made up 50 percent of this aspect of the PIRLS reading assessment.

The second aspect of the PIRLS assessment component is processes of comprehension, which describes how young readers interpret and make sense of text. In 2016, this aspect was composed of four categories: focusing on and retrieving explicitly stated information (20 percent), making straightforward inferences (30 percent), interpreting and integrating ideas and information (30 percent) and evaluating and critiquing content and textual elements (20 percent). 

Both PIRLS and PIRLS Literacy devote half of the assessment passages to each of the purposes for reading, while the ePIRLS online assessment focuses solely on reading to acquire and use information. The ePIRLS approach simulates websites from the Internet, through which students can navigate to accomplish school-based research projects or tasks. Because PIRLS Literacy is designed for students earlier in the process of learning to read, a larger percentage of items (50 percent of the assessment) is devoted to measuring foundational reading comprehension processes—the ability to focus on and retrieve explicitly stated information. 

Also, PIRLS Literacy has shorter reading passages with easier vocabulary and syntax. The second component, background questionnaires, collects information on reading behaviors and attitudes (the third aspect of reading literacy targeted by PIRLS), and helps to provide a context for the performance scores. These questionnaires focus on such topics as students’ attitudes and beliefs about learning, their habits and homework, and their lives both in and outside of school; teachers’ attitudes and beliefs about teaching and learning, teaching assignments, class size and organization, instructional practices, and participation in professional development activities; and principals’ viewpoints on policy and budget responsibilities, curriculum and instruction issues, and student behavior, as well as descriptions of the organization of schools and courses. 

Assessment. In the main PIRLS assessment, each student completes a reading comprehension assessment booklet, which contains two blocks of passages that form the foundation of the PIRLS reading literacy test. Half of the assessment blocks contain passages of literary text which include realistic stories and traditional tales, and half contain passages of informational texts including chronological and non-chronological articles, a biographical article, and an informational leaflet. The passages of text are followed by questions about the text, which the student answers using constructed-response and multiple-choice response options.

REFERENCES:
1. Kennedy, A.M., Mullis, I.V.S., Martin, M.O., and Trong, K.L. (2007). PIRLS 2006 Encyclopedia: A Guide to Reading Education in the Forty PIRLS 2006 Countries. Boston College, International Study Center. Chestnut Hill, MA. https://timssandpirls.bc.edu/pirls2006/encyclopedia.ht ml. 

2.Mullis, I.V.S., Martin, M.O., Kennedy, A.M., and Flaherty, C.L. (2002). PIRLS 2001 Encyclopedia: A Reference Guide to Reading Education in the Countries Participating in IEA’s Progress in International Reading Literacy Study (PIRLS). Boston College, International Study Center. Chestnut Hill, MA. 
https://timss.bc.edu/pirls2001i/PIRLS2001_Pubs_ER. html. 

3.Mullis, I.V.S., Martin, M.O., Kennedy, A.M., and Foy, P. (2007). PIRLS 2006 International Report: IEA’sProgress in International Reading Literacy Study in Primary Schools in 40 Countries. Boston College, International Study Center. Chestnut Hill, MA. https://timssandpirls.bc.edu/pirls2006/intl_rpt.html. 

4.Mullis, I.V.S., Martin, M.O., Minnich, C.A., Drucker, K.T., & Ragan, M.A. (Eds.). (2012). PIRLS 2011 
Encyclopedia: Education Policy and Curriculum in Reading, Volumes 1 and 2. Boston College, International Study Center. Chestnut Hill, MA. https://timssandpirls.bc.edu/pirls2011/encyclopedia-pirls.html. 
5.Uses of Data Green, P.J., Herget, D., and Rosen, J. (2009). User’s Guidefor the Progress in International Reading Literacy Study (PIRLS): 2006 Data Files, and Database with United States Specific Variables (NCES 2009-050).

Aziza Amonova is a 3rd grade student of the Faculty of Primary Education of Jizzakh State Pedagogical University. Currently, she has about 40 scientific articles and two methodological manuals.  In addition, she participated in about 25 different forums and conferences.

“Stepmother” by Ahmed Lutfi Kazanchi

The work “Stepmother” is about the kindness and love of a believer and caressing the heads of orphans, showing them mercy and kindness.

The ideas of the work are manifested in the image of Fatima, a Muslim woman. At a time when people are not able to give good education to their children, they are not able to say sweet things, Fatima’s love for Khayria’s two sisters, pampering her with sweet words, what does she do to her child the fear of hurting an orphan’s soul will shake the heart of any person. The main ideas of the work are about humanity, how to treat orphans.

He can be an example to people who do not know how to treat their children well, who are not afraid to hurt the heart of an orphan.
Our mothers and sisters should read this work to know God, to understand oneself, to understand what a Muslim should be, what actions are obligatory in Islam. Our fathers and brothers should study in order to learn to fear someone’s rights, humanity, and refrain from
sinful things. In my opinion, this work is not suitable only for young people. The work is intended for everyone to read.

“Since handing over the righteous one to an orphan, after every prayer, hoping for the grace of God, who is able to do everything, “Oh, Lord, grant Samiham to a pure orphan, grant my daughter a happy and prosperous marriage, just as you have answered my prayers with justice until today, grant me this marriage. He did not forget to pray to Habibi Akram, the Sultan of orphans, strangers, and orphans. She wants to go out and live on her own, not to live alone, but to show love to people who grew up with a broken heart and hard to love, together with her righteous daughters, and wants to reduce those defects even a little. because he asks Allah Almighty for this in every prayer.

It is true that this work tells about the fate of orphans whose mothers died for certain reasons and were left in the hands of their stepmothers. But unfortunately, today there are people who give their loved ones to orphanages and sell their children for money. Looking at them, the characters in this work seem to us to be a little bit good. That is why I think that it is necessary to increase the publication of this work, and to strengthen the promotion of reading the work.

As soon as I started reading the work, my heart cried without it. After reading the book, I decided to change. I have no doubt that I will leave this world unscathed if my life is like that of Fatima.

Ahmed Lufti Kazanchi’s Stepmother is available here.

Hamrokulova Zilola Sherali’s daughter was born on June 26, 2006 in the village of Kyzilcha, Nurota District, Navoi Region of the Republic of Usbekistan.Nowadays,she is studying “Foreign Languages” at the academic lyceum of the Navoi State University of Mining and Technology. In her spare time, she writes poems. She has published her creative works in world-famous magazines of several foreign countries.

WORD COMPOSITION COMPARISON IN UZBEK, RUSSIAN AND KARAKALPAK LANGUAGES

Nukus State Pedagogical Institute 

named after Ajiniyaz

First level student of  Uzbek language 

foreign language groups 

Faculty of  Turkish Languages

USANOVA QADEMAY MURATBAY QIZI 

Phone: +99891 305 69 79

Email: qademayusanova@gmail.com

The nature of word forms in Uzbek, Russian and Karakalpak languages is determined primarily by the fact that the Russian language is a flective language, the Uzbek and Karakalpak language is an agglutinative language.

Words in Uzbek, Russian and Karakalpak languages are separated into grammatical sections based on certain character traits. Word categories are initially classified into independent words, auxiliary words, modal words, exclamations, and imitation words. From these, the feature of shapeshifting is characteristic only of independent words. Change of form is referred to as speciation in relation to nouns, as tussification in relation to verbs. 

Russian words are divided into two parts as head shapes: base and completion. The place of completion in Russian words is extremely large, since the completion indicates which category of the word is and expresses the mutual grammatical relationship of the words. In general, in the Russian language, the endings come to denote rod, number, agreement, tense, person and other grammatical meanings. The completion, separated from the base of the word, does not represent a specific grammatical meaning in itself. The concrete grammatical meaning and function of the completion is determined in the sentence, context.  Completion in Russian is an integral part of the word. The word cannot be fully formed without completion. 

In Uzbek, the initial form of words does not have the same completion as in Russian. For this reason, the initial form is synonymous with the base of the word. Affixes that add to the base of the word and express grammatical meaning will not be as colorful in Uzbek as in Russian from form and meaning jiht. For example: uyda, qishloqda, maktabda, soat beshda, mart oyida – at home, in the village, at school, at Five O’clock, like in March.

In Russian, the completion will consist of only one morpheme and can simultaneously represent several grammatical meanings. For example: the –a completion of the книга word in the книга сестры compound indicates the jensky rod, the unit, the head agreement, the –ы completion of the сестры word indicates the jensky Rod, The Unit, The Crow agreement. 

When dividing a word in Karakalpak into a base and a suffix, their base can be used as a singular word at all times . For example: ten’iz, ten’izge, ten’i zden – to the sea, to the sea, like from the sea. 

The made word will consist of a STEM as well as a word-making morpheme. In Uzbek, Russian, and Karakalpak languages, word-making morphemes are also quite different from each other depending on their place in the word. 

In Uzbek, the yasama word composition is mostly in the form of” base+word-making affix”. For example: like ish-chi, bog‘-bon, bog‘-dor-Chi-lik. The pre-base consonant of word-making morphemes is not unique to Uzbek, nor to Turkic languages in general. Only a few prefixes are found, such as be -, ba -, no -, ser – borrowed from Tajik. It is with morphemes that an adjective is made. For example: begʻam, badavlat, sermahsul, noma’lum – impeccable, wealthy, prolific, like the unknown. 

Russian word-making Affixes are associated with the basis, and the basis cannot be used separately without them. For example: the base -ня in the words принять, занять, отнять – accept, borrow, take away cannot be a single word in itself. In Russian, word-making affixes can be used both before the base and after the base, and between the base. 1. Prefixes are used before the base: пере-вод, со-автор, у-ход – translation, co-author, care.  2. Suffixes are added after the base: like зл-ость, тка-ч, учи-тель – anger, weaver, teacher. 3. Among the compound bases, the interfixes –o -,- e -,- i – are used that attach them: рыболов, водопровод, пешеход – angler, water pipe, pedestrian.

Affixes that make a word in Karakalpak are easily distinguished from the base. Without the base word-word-making affixes, yak can also be used as a word: like aqil-li, aqil-siz, aqil-lasiw – smart, foolish, consult. In Karakalpak, word-making Affixes are added only after the base: a’dep-li-lik, taza-la, ten-im, kesh-ki – decency, cleansing, unum, evening. Karakalpak lacks interfixes and prefixes. Sometimes the biy -, na- morphemes entered from the Persian language are added in front of some base, serving to give them only the meaning of indivisibility: biymezgil, nama’lim, biyjuwap – not in time, unknown, unanswered. 

In Uzbek, when different morphemes are added to the base of a word and a new word is made, the base usually does not change. For example: friend-friends, work-worker, month-like monthly. When verbs are toned or a new word is made, the phenomenon of falling, alternating vowel sounds occurs in Uzbek: ong-angla, yosh-yasha, son – sana – to understand, live, date. 

In Russian, however, the phenomenon of sound exchange occurs at the base of a word with the addition of a word-making or word-changing morpheme to the composition of the word. For example: 

1. Consonant sounds alternate: ходить – хожу, ухо – уши, друг – друзья – дружеский, писать – пишу – walking – walking, ear – ears, friend – friends – friendly, writing – writing.  

2. Vowel sounds alternate when verbs are stressed or a new word is made: говорить – разговаривать рыть – рой, пыть – пей – talk – talk dig – swarm, pyt – drink. 

3. In some cases, with a change in completion, a new sound appears in the core: любить – люблю – любишь, терпить – терплю – терпишь – . 

4. When The Shape of some words is changed, the vowel sounds in the base fall: сон – сна, уголок – уголки, день – дни – sleep – sleep, corner – corners, day – days. 

In Karakalpak, the base morpheme is considered to be the main lexical meaning of the word. For example: ko‘riw, ko‘rgish, ko‘rgizbe, ko‘rsetpe. In Karakalpak, the basis is always singular and has a lexical meaning. Therefore, it is not difficult to divide the word into a base and a suffix. For example: in the words basshi, basliq, basqariw, basla, the bas word can be used as a basis, singly. 

In Karakalpak, the basis does not change when word-making or word-changing morphemes are added to the composition of the word. Only in some cases, that is, when a morpheme is added, the end of which begins with vowel sounds, such as p, k, q, they alternate to b, g, g‘ sounds. For example: aq-agʻim, aq-agʻariw, toʻk – toʻgin, kitap-kitabiy – white-flow, white-flow, spill-spill, book-reader. 

It is also worth mentioning that each language relies on the statutes defined in the word composition of the morpheme. In Russian words, first, the pristavka (if there is one), the base, followed by the suffix and the suffix:  без – пол – ез – ный – useless. In Uzbek, however, the base is initially followed by the word-making affix, the word-changing affix: like the oʻqi-tuv-chi-lik – teaching. In Karakalpak, however, a word is made by first adding a base, followed by a word-making affix, followed by a form-making affix: kitap-sha-larinʻizdi – your books . This in turn can cause some difficulties in the comparative study of Uzbek and Russian, Russian and Karakalpak languages. 

REFERENCES:

1. Azizov O va boshqalar O‘zbek va rus tillarining qiyosiy grammatikasi Toshkent.1965.

2. Azizov O. Safaev A. Jamolxonov. O‘zbek va rus tillarining qiyosiy grammatikasi. Toshkent.1986.

3. Bekbergenov A. Rus haʻm qaraqalpaq tillerininʻ salıstırmalı grammatikası. Noʻkis. 1995.

Usmanova Kademay was born on October 9, 2003 in Nukus, Republic of Karakalpakstan. She successfully graduated from school No. 15 in Nukus. He participated in various events and Science Olympiads at the school and took the corresponding places. He can speak Uzbek, Russian, Karakalpak, Kazakh and Turkish fluently.

She is currently a 1st Stage Student of the Nukus State Pedagogical Institute named after Ajiniyaz.

She also has a place in the international arena! In particular, he is a member of India’s All India Council for technical skill development, Argentina’s Juntos Por Letras, Egypt’s creation forum for Culture, Arts and peace, and India’s Iqra Foundation. Her scientific work has been published in Europe, USA, Belgium, India, Russia, Turkey, Italy, Poland, Germany, Belarus, the Netherlands, the United Kingdom. 

ECOLOGICAL PROBLEMS OF THE PRESENT TIME AND SOLUTIONS ABOUT THEM

Currently, as a result of human activity, drastic changes have occurred in the biosphere, and many environmental problems are arising as a result of these changes. Due to growth, science and technology development and increasing human needs, environmental problems have intensified.

We divide environmental problems into the following groups

1. Global (universal)

2. Regional (regional)

3. Local (local)

1. Global (universal) ecological problems can be defined as problems caused by natural and natural anthropogenic and purely anthropogenic effects observed around the world.

Let’s get acquainted with such problems

-island problem

– greenhouse effect

– fresh water problem

-problem of tropical and subtropical forests

-problem of tropical and subtropical forests

-ozone problem

– the problem of the decrease in the number of flora and fauna – the increase of carbon dioxide in the air

– excessive release of waste gases into the air

– world ocean pollution

– disappearance of fertile soil layer

– desertification

– increase of household waste – atmospheric pollution

– pollution of the lithosphere

– pollution of the hydrosphere – salinity

– the failure of pastures

THE ISLAND PROBLEM. The Aral Sea was considered one of the largest seas until recently. It was important for fishing, hunting, transportation and recreation. The development of irrigated agriculture in Amudarya and the flow of water from the Syrdarya has decreased dramatically. As a result, the Aral Sea has become an unusable area due to its high salinity level. The dried bottom area is 4.2 million hectares and has become a source of dust and salt distribution to the surrounding areas.

The amount of salt in the water is up to 112 g. Currently, the sea level is dropping by 80-110 cm. The region of the Aral Sea has become a large dust area. The problem of the island has a serious impact on the health of the people living in the area

In the last 10 years, the death rate has doubled. The amount of salts in the urine of 90% of children has increased. Anemia has occurred in 80% of women. From this area, 80 to 100 tons of dust rises into the atmosphere every year and reaches the Pamir, Tianshan, Greenland, and even the Arctic glaciers.

During the last 4 years, 1.5 million hectares of the dry part of the seabed has been turned into forest and shrubland. The addition of another 700,000 hectares shows the magnitude of the work being carried out in our country. In 2017, the United Nations established a multilateral partnership trust fund for human security. provides practical assistance to the population of the State Program for the Development of Aral Sea Regions in 2017-2021, with the relevant decisions of the Cabinet of Ministers on the creation of a “Green Belt” in the Aral Sea and Aral Sea Regions, neighboring Khorezm, Bukhara, and Navoi regions works are being carried out. The presidential decision to approve the concept of development of the forest system in our Republic until 2030 proves that these goals are strategic.

2. Regional (regional) problems are problems specific to certain regions caused by industrial sectors, enterprises and improper irrigation of land.

We will get acquainted with such problems – industrial waste of natural waters – problems in the agro-industrial complex.

Today, we are making progress in all fields in our country.

This achievement leads to the aggravation of the environmental situation along with the introduction of new technologies in industrial production. In recent years, along with the growth of industrial sectors, environmental pollution is also increasing. Due to the activities of industrial sectors, harmful dust and gaseous compounds are released into the environment in large quantities, and it is allowed to have a direct negative impact on the environment.

3. Local (native) environmental problems are problems specific to certain regions, even if they arise as a result of harmful emissions from all sectors of the national economy, industry and transport. The gases released from them damage the atmosphere and have a negative effect on human health. 70%-80% of air pollution comes from motor vehicles.

Garbage. The epidemiological and hygienic importance of keeping cities and villages clean is very great. The cleanliness and beauty of residential areas, the flow of water from irrigation canals, the presence of trees and green areas help prevent infectious diseases. leads to accumulation. In order to keep people’s residences clean, it is necessary to dispose of garbage in the garbage chute on time. Garbage and garbage not only cause various infectious and worm diseases, but also cause indigestion and nausea in people. Taking into account the sanitary and epidemiological danger of garbage when loading them into garbage trucks.

When unloading, the participation of people should be reduced as much as possible. According to a special schedule, garbage trucks take away the collected garbage. Liquid waste is removed using sewage pipes. Thus, the issue of waste is one of the important problems in ecology, and if it is collected and processed or sorted according to hygienic requirements, it has gained great importance for the environment and human health.

CONCLUSION Humanity takes all the things necessary for living and living from mother nature. Over the years, as a result of the increase in human needs, nature has been ruthlessly used, neglecting its precious benefits, using animals, plants and all natural resources as much as it wants (inappropriately) for its own selfish purposes.

We are in the vortex of huge environmental problems due to the great changes in the biosphere. In order to avoid the above problems and to improve the ecology, we must form an ecological culture in the population, form a deeper and more comprehensive understanding of caring for the environment and preserving it. teaching and, if necessary, learning is important.

AUTHOR : Sardor Yaxshilikov

https://www.facebook.com/profile.php?id=100089598570169&mibextid=ZbWKwL

ON THE CONCEPT OF INTEGRAL, HISTORY OF ORIGIN AND SOME COUNTER-EXAMPLES

Abstract. In the article is given information about the integral concept and the history of its origin. In addition to the Riemann integral, which is covered in the school program, a number of other integrals (Riemann-Stiltes, Daniell, Alfred Haar, Henstock-Kurzweil, Ito and Stratonovich, Chokvet) are described. The difference between integrals is explained with the help of specific examples. The concept of definite integral and its use in practical problems were explained in detail, counter-examples of some theorems were presented. 

Keywords: infinitesimal, area, volume of a solid, integral, indefinite integral, surface, surface integral, sign of indefinite integral, counter derivative.

INTRODUCTION

 In mathematics, the integral defines the values of functions that describe displacement, area, volume, and other concepts resulting from the integration of infinitesimals. The process of finding integrals is called integration. Along with differentiation, integration is one of the basic, important concepts of mathematics and serves as a tool for solving problems involving the area of an arbitrary shape, the length of a curve, and the volume of a solid in mathematics and physics. 

RESEARCH MATERIALS AND METHODOLOGY

Integrals can be further generalized depending on the type of function, as well as the field in which the integration is performed. For example, a line integral for a function of two or more variables is defined and the interval of integration is replaced by the formula representation of the curve connecting the two endpoints of the interval. In surface integrals, the curve is calculated by replacing a part of the surface in three-dimensional space. The first documented technique capable of calculating integrals is the exhaustion method of the ancient Greek astronomer Eudoxus (ca. 370 BC), who is known to have tried to find areas and volumes by dividing them into infinitely many divisions. This method was further studied and developed by Archimedes in the 3rd century BC. It was used to calculate the area of a circle, the surface and volume of a sphere, the area of an ellipse, the area of the lower part of a parabola, and the volume of a segment. That is, it is not wrong to say that the revolution of integrals occurred during this period.

In addition, a similar method was developed in China in the 3rd century AD by Liu Hui, who used it to find the area of a circle. This method was later used in the 5th century by Chinese father and son mathematicians Zu Chongji and Zu Geng to find the volume of a sphere. And in the Middle East, Hasan Ibn al-Haytham, a man known in Latin countries as Alhazen (ca. 965 – 1040 AD), developed the formula for the sum of four powers. He used these results to calculate (create) what is now called the integral of a function, in which he was able to calculate the volume of a paraboloid using integral squares and sum-of-fours formulas. The next important advances in integral calculus did not appear until the 17th century.

At this time, Cavalieri’s work “By the method of indivisibles” and several works of Fermat began to form the basis of modern calculus. The next steps were taken at the beginning of the 17th century by Barrow and Torricelli, who put forward the first ideas about the connection between the operations of integration and differentiation. Barrow gives the first proof of the fundamental theorem of integral calculus. Wallis generalizes Cavalieri’s method to compute integrals of 𝑥 to general powers, including negative powers and fractional powers. The greatest success in the calculus of integrals occurred in the 17th century when Leibniz and Newton independently discovered the fundamental theorem of the integral calculus. They show the connection between integration and differentiation. This relation, together with the relative ease of differentiation, could also be used to calculate integrals. In particular, the fundamental theorem of calculus allows solving a much wider class of problems. Equally important was the comprehensive mathematical system developed by Leibniz and Newton. It allowed precise analysis of functions within continuous fields. This method eventually became the basis of modern calculus, and these calculations were taken directly from Leibniz’s writings.

Although Newton and Leibniz provided a systematic approach to the operation of integration, their work lacked a certain degree of rigor, and some mathematicians of their time considered these calculations to be non-general. A more robust result could be achieved by developing computational limits. The operation of integration was first officially recognized by Riemann in the creation of strict laws using definite limits. Although all finite piecewise continuous functions are Riemann integrable on a finite interval, later more general functions where Riemann’s definition does not apply were considered, especially in the concepts of Fourier analysis, and Lebesgue developed another gauge-based definition of the integral.

DESIRE

Brave steps bold
When you see it in the search 
A useful person
Words are true.

Reporter, TV journalist
There are many names, the goal is the same 
It burns for people to see
Working together solidarity 

I felt an intention in my heart
My desires are increasing day by day
What profession to choose now 
It's hard not to go to the fireplace

WHAT IF STUDENTS ARE AT DIFFERENT LEVELS IN THE CLASSROOM? 

                                   3rd year  student of English philology 

              faculty,  Karshi  State University

                    SHOSURA KHUSENOVA TOSHTEMIR QIZI

                                                                                                         

 ABSTRACT                      

This article discusses the problem of pupils having varying levels and some useful approaches to use in the classroom. Differentiated, according to the author, is a strategy that “tailors instruction to meet the individual needs, strengths, and interests of all learners.” The article also offers numerous methods for putting diversified education into practice, including flexible grouping, giving students a choice, and using materials effectively.

 Keywords:

Mixed-level students, formative assessment, multi-sensory instruction, peer-tutoring,   set different academic expectations, ESL multilevel activities.

INTRODUCTION

Before you’ve even had a chance to finish passing the worksheet around to the entire class, you  have  a   student, let’s call him Billy, who has finished it. Another student, Lily, is seated in the back and has no idea how to approach the situation at all.  Not the best scenario, would you say? Unfortunately, it does occasionally occur, and it can worry TEFL instructors of all experience levels. What do you do then?  Do you move on and leave poor old student Lily to keep their fingers crossed and hope for the best, or do you leave student Billy to sit there and fidget while the rest of the class catches up? Neither seems seem good, don’t they?

Despite being in the same class, students may not all be at the same academic level. This is evident in all classes, but it can be particularly obvious in a class intended to teach a language to non-native speakers. It is the responsibility of the teacher to recognize these variations in students’ skill levels and adjust their lesson plans accordingly. Like any other teacher, all of the above-mentioned situations happened to me in my classroom when I started my teaching career.

WHAT HAPPENED IN THIS CASE?

Students in the class were at various levels, and a number of issues occurred that affected both my performance as a teacher as well as the students’ performances.

1. Boredom: When the topic seemed too simple for advanced students, they felt bored and disengaged.

2. Frustration and low self-esteem: Struggling students could not keep up with the class’s pace because they did  not comprehend  the topic, they  grew frustrated and disappointed. While advanced students became overconfident and underestimated the difficulty of upcoming obstacles, struggling students had low self-esteem and believed they were not smart enough.

3. Burnout and stress: I also suffered from having to accommodate students with varying levels of ability in the same lesson. I always had to try to make sure everyone in a heterogeneous classroom was being challenged and learning the material.

WHAT APPROACHES TAKEN?

 Regardless of the students’ individual ability levels, I searched for numerous techniques to create a challenging and supportive learning atmosphere where all students would be encouraged to realize their maximum potential. When trying to solve the issues, I started with diagnostic testing. The exam comprised questions that gauged whether or not students would possess the expected abilities required to grasp the new ideas in the course. Test results identified students’ particular needs and gaps in their knowledge, enabling me to classify them based on their developmental stage. I made a chart with the student’s name, grade, and any special requirements. To simply erase as fresh information was needed to track the pupils’ development, I used a pencil. After starting the class off with a warm-up exercise for the entire group, I moved on to a pairwork activity (cross-ability) and a small-group activity (like-ability), assisted students by moving from group to group, and finished with an activity or game for the entire class.

Formative assessment: Throughout the learning process, students were continuously evaluated to help them understand their strengths and flaws. Formative assessment data was used to modify lessons and offer specialized support to all students.

Selecting materials: Because there were a lot of students with comparable English proficiency levels, finding a core textbook for the class became helpful. The same textbook series needed to be used on more than one level. The use of a theme-based strategy was the best decision. One excellent strategy to keep the classroom environment feeling like a class in a multilevel setting is to keep all of your kids working on activities and lessons that are centered on the same theme. Thus, I used this strategy. It did not only make the pupils feel that they were all a part of the same group, but it also saved my time and helped me feel more organized. The theme was then used as the basis for further activities like games and debates. 

Doing different tasks with the same material/technology and setting different expectations according to their abilities: 

Where teachers use the same material with the whole class, differentiation can still take   place. We can encourage students to do different tasks depending on their abilities. For instance, a reading text may contain sets of questions at three distinct levels. The better pupils will accomplish the first two sets easily, but they will have to put in a lot of effort on the third, the teacher instructs the class. The least capable kids might not make it past the first set. In a language learning activity, the teacher can request basic repetition from certain pupils while requesting more complicated statements from others. When asking students for answers or opinions, the teacher can make it clear that some students will only need to say one word, while others will be expected to provide longer, more in-depth responses. She can make sure that students are given roles or responsibilities that are appropriate for their level in role-plays and other speaking or group exercises. This technique was also one that I enjoyed most using because it helped to create a friendly atmosphere and meet every student’s academic needs. As a result, boredom among advanced students and low self-esteem among struggling students started to lessen.

Multi-sensory instruction: This method involves teaching English language skills utilizing all five senses (sight, sound, touch, and taste) and creating multiple ways to learn and understand the same concept, taking into account different learning styles, abilities, and interests. To engage students with different learning styles, teachers might use a variety of teaching materials such visual aids, audio recordings, and hands-on exercises. According to this, the lessons were held using different teaching styles integratedly. For example, when teaching topic vocabularies about transport, sheets with pictures and their translations were distributed at first. This was important to differentiate the spelling and pronunciation by seeing them on paper and pronouncing them. Listening tasks, word puzzles, and making up sentences were the next stages of the teaching process of new words. At the end of the lesson, the results were as expected.

Peer tutoring: In this approach, students of various skill levels are paired up so they can benefit from one another’s knowledge. For instance, in a writing class, an advanced student might be partnered with a struggling student so that the advanced student can mentor and help the struggling student. Remind students that teaching is the best way to learn, and encourage them to volunteer as peer tutors. Think about getting a volunteer. The students were so eager to teach each other because, in my opinion, working in groups, teamwork, and other activities were the reasons for having strong relationships in the classroom like a family.

Personalized Learning Plans: Students can go at their own speed and receive focused training in areas where they require more assistance or challenge by having individual learning plans made for them based on their  strengths  and  limitations. In their workbooks, there were main tasks and optional tasks, and students were given tasks based on their abilities. Fast learners did optional tasks besides the main ones while their partners were accomplishing the main, compulsory task of the book.

Play games: Games are a great way to involve all levels of English learners. Even a game geared towards beginners can give advanced students a chance to practice speaking and listening. Plus, all students are more likely to learn when they’re having fun!

Pick teams: Choose teams strategically, make sure that no team contains only advanced students and no team contains primarily beginning students. The teams will be diverse, which will make everyone feel included and challenged. By choosing team captains and allowing them to alternately choose teammates, you might also allow students to choose their teams. Because advanced students are likely to be chosen first and then beginners, the teams will likely contain a mix of students from each level. 

Active participation: Due to the active participation required, games aid in learning. Even better, give the victors a prize like an extra credit point. Everyone will be compelled to join since this will promote competition. The participation is what helps English language learners at all levels. In order to give pupils practice speaking, choose a game that involves speaking, such as “I Spy” if you are teaching colors. Choose games that can be played in pairs or small groups, like “Twenty Questions,” to increase participation because every student will have a chance to participate.

Having fun:  Even if the game isn’t the most difficult for your advanced pupils, your students will still have fun and practice their English if you pick one they like. A strong learning incentive is enjoyment! Your kids will be more motivated to practice their English if they have the opportunity to engage in something silly or competitive. This repetition will help learners at all levels feel more at ease with unfamiliar terminology and grammatical structures. As a matter of fact, the majority of the teaching process consisted of playing games. Games not only helped learn the language in an easy manner, but they also gave a chance to put the knowledge obtained into practice. 

The following activities were the most used ones to teach in a balanced way.

ESL MULTILEVEL ACTIVITIES

ESL Multilevel Activity 1 – Buddy Reading

This exercise is open to classes of any size. For instance, pupils pair up for buddy reading. In this mixed-ability activity, one student reads while their “buddy” corrects the reader’s pronunciation. With adults, it is frequently simple because it is akin to studying with others outside of class. Do demonstrate this for the group first, though. It is advantageous for all sides when higher-level students keep an eye on lower-level students. Interesting though it may seem, having lower-level students observe higher-level students frequently aids the latter in being aware of the mistakes they do.

ESL  Multilevel  Activity 2 – Peer Editing

Similar to this, peer editing enables students to assess each other’s work and provide feedback that is appropriate for their skill levels. Independently, students can write rough drafts. More complicated and lengthy writings can be written by advanced ESL students than by their peers. The final step before drafting the final draft is peer editing. Along with grammar and punctuation, students can talk about the text’s content. Of course, playing games is the ultimate multilayer ESL activity. The beauty of games is that, despite students having widely varying English proficiency levels, they are typically excellent at fostering meaningful connection between them. So that all pupils may take part in the games together, teach the required grammatical rules and new vocabularies beforehand.

ESL Multilevel Activity 3– How it’s Made

“How it is made” requires directions on assembling something.

Instructions on how to assemble something are needed for the activity How It’s Made. Making peanut butter sandwiches or other straightforward meals is enjoyable, despite the fact that it involves some preparation. Every student must select where they fit in after discussing their task with the other students that have the same stage in the process. Use this technique with Lego, puzzles, or blocks. Give the more knowledgeable students longer instructions or more complicated processes. Putting the wheels on the Lego car is an easy task for beginners. The model’s instructions can be made slightly larger by photocopying them. Then, divide them up and assign one or two paragraphs to each student. To ensure sufficient instruction, it’s ideal to have one model for every three or four students. For maximum participation and speaking practice, it is recommended to have one model for every three or four pupils.

How It is Made Variant

If you do not have any instructions on hand, another strategy is to explain that no pupil may move a piece without first speaking. A pupil MUST speak in English if they wish to pick up some material to see if it fits the model. For example, using a crossword with some red flowers: Advanced pupils describe their actions in real time, saying things like, “I’m just going to test if this small red piece fits on here… it looks like that it  might be a part of a flower. Oh no, that’s wrong. Instead of saying, “I think this is a flower,” or “It fits/it does not fit,” a lower level student would say, “I think this is.” Students may also repeat any line; it is not necessary for it to be associated in any way with the model’s or puzzle’s theme. So a beginner student could say, “I like pears.” They are now qualified to attempt a component on the puzzle or model thanks to their input. Working in multiple groups, they can compete against one another to determine who finishes first.

ESL  Multilevel  Activity 4 – Jigsaw Reading

 Jigsaw reading takes little time to set up. Choose a reading text to start with, then use activities to introduce the vocabulary and grammar. Next, divide the text into sections, giving more difficult passages to advanced students and shorter, easier passages to lower-level students. The article or tale is then read silently by each student. After reading, students can either write or present an oral summary of the article or story. As an alternative, students might recreate the article in the proper order and compare it to the original text together. Give each student three or four images that are similar but not identical and instruct them to work in pairs. So, for instance, put four images of cars that are similar on the board or table. One student responds to the questions posed by the other pupils while holding a duplicate image of one of the cars. These pupils use questions to whittle down their options and identify the corresponding image. Because asking questions is harder than answering them, the more advanced students should do so.

RESULT: At the end of the term, a huge difference was witnessed. Precisely, a strong relationship between students, a strong desire to help each other and study together, improvement in slow learners’ language capability, and consolidated knowledge because of games and practices are just a few examples of the approach taken.

CONCLUSION

However, multi-level-class problems have advantages. Yes, advantages!

Everyone’s social abilities, but notably those of high achievers, are enhanced in heterogeneous teams. High achievers by definition have no issues with academic material. Their need for improvement in interpersonal connections is frequently greater. High achievers gain coaching, encouragement, praise, tutoring, and patient waiting skills in mixed teams. Our high achievers develop their leadership abilities by putting them to use in their teams.

In short, multi-level classes are not easy to teach, but are certainly an excellent opportunity to develop one’s teaching skills. This is a vast topic. 

Enjoy your vocations !

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1.  https://www.teflcourse.net/blog/5-strategies-of-teaching-mixed-ability-classroom-ittt-tefl-blog/

2.   https://www.fluentu.com/blog/educator-english/different-levels-of-esl-students/

3.  https://www.kaganonline.com/free_articles/dr_spencer_kagan/396/10-Reasons-to-Use-Heterogeneous-Teams

4.  https://www.richmondshare.com.br/multi-level-classrooms-a-challenge-worth-facing/

5.  https://www.i-to-i.com/tefl-blog/tefl-classroom-and-expert-advice/how-to-teach-mixed-ability-classes/

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7.https://larryferlazzo.edublogs.org/2011/09/05/the-best-resources-on-teaching-multilevel-eslefl-classes/

8. Jeremy Harmer, How to teach English new edition

9. https://www.fluentu.com/blog/educator-english/different-levels-of-esl-students/

10. Teaching English to Multi-Level Classes | Teaching Tips | English Club

https://www.englishclub.com/teaching-tips/teaching-multi-level-classes.php