Daily Archives: March 24, 2025

Bibliography: Bilingual Education (Part 1139 of 1274)

Curtin, Jolinda (1990). Family Kindergarten = Kinder para familias. The Family Kindergarten program designed and pilot tested by a bilingual kindergarten teacher at Garretson Elementary School in Corona, California, is described. Based on the premise that parents are the most important and influential educators of children, Family Kindergarten was conceived as an evening class that includes parents and children working together. It is currently offered at five elementary schools in the school district, and positive results include increased volunteerism in the schools and parents who have become advocates for school reform. The program budget is reported, along with information on suppliers, announcements, parent letters, a calendar of events, reminders, and program letterhead. Five sections, which comprise the bulk of this report, are as follows: Session I (Kindergarten Homework); Session II (Reading with Your Child); Session III (Mathematics 1); Session IV (Language Development); and Session V (Mathematics 2 and Evaluation). Each section contains…

Bermudez, Andrea B.; Rakow, Steven J. (1993). Examining Identification and Instruction Practices for Gifted and Talented Limited English Proficient Students. Underrepresentation of minority students in gifted and talented (G/T) programs is a well established fact. A study examined procedures and criteria used to identify, place, and instruct gifted and talented students with limited English proficiency (GT/LEPs) in Texas, California, Colorado, Florida, Arizona, and New York public schools, to help identify factors contributing to underrepresentation of this population in gifted and talented (GT) educational programs. GT program coordinators (n=268) in a cross-section of schools responded to a survey. Less than 20 percent had established a means for identifying GT/LEPs. Respondents identified characteristic GT student behaviors that might be masked by linguistic and cultural differences, including a variety of language, cognitive, inter-/intrapersonal, academic, and artistic skills. Almost 80 percent acknowledged the need to use different means of assessment than for mainstream students. Most used multiple sources in identifying GT/LEPs…. [PDF]

Marquez, Judith A.; Sawyer, Cheryl B. (1994). Curriculum Extension for the Gifted and Talented Student with Limited English Proficiency. This paper offers suggestions for meeting the special needs of gifted and talented (GT) students of limited English proficiency (LEP) through an extension of the differentiated curriculum. An overview of the differentiated curriculum is offered, and issues that must be addressed in meeting the needs of the GT/LEP student are discussed. Teaching strategies and methods that can be used in GT/LEP instruction, and recommended teacher characteristics, are also outlined. It is concluded that although no specific pre-packaged curriculum can be recommended to meet the needs of GT/LEP students, the criteria discussed here should be used in developing instructional strategies for this population. The curriculum, when extended using the criteria recommended here, is seen as providing the necessary foundation for both cognitive and linguistic development. (Author/MSE)… [PDF]

Duran, Richard P.; Szymanski, Margaret H. (1993). Construction of Learning and Interaction of Language Minority Children in Cooperative Learning. Report No. 45. This report analyzes the moment-by-moment construction of interaction by language minority children in a cooperative learning activity. The interaction occurred among students in a Spanish-English bilingual 3rd grade classroom as part of a cooperative learning curriculum known as Cooperative Integrated Reading and Composition (CIRC), which was especially adapted for use in bilingual classrooms by language minority students. The analysis of interaction reveals that under supportive social circumstances, children are very active in probing and questioning their own knowledge and they rely on their shared expertise to attain instructional goals and supplemental goals that are related to their own expertise and concerns. The report supports the importance of promoting learning as a constructive process wherein students actively develop new knowledge through manipulation and questioning of their existing knowledge. (Author)… [PDF]

Malave, Lilliam M. (1987). Effective Schools Research and Language Instruction Programs. This paper presents a followup of selected studies on effective schools with a population of bilingual and/or limited-English-proficient (LEP) students. Over 150 research papers on both effective schools and effective bilingual LEP instruction were reviewed. The literature was divided into three categories: (1) studies with a population including linguistically and culturally different students within a bilingual or monolingual setting; (2) evaluations about the degree of effectiveness of mostly federally-funded bilingual programs; and (3) investigations of effective bilingual instructional practices or features. It is reported that the results of a survey of 97 of the research authors demonstrate the limited extent to which the research literature recognizes LEP students in its sample populations. Implications of these findings for the planning and development of effective instructional programs for LEP students are discussed, and recommendations for future research are offered. A… [PDF]

Bamford, Kathryn W.; Mizokawa, Donald T. (1991). Cognitive and Language Development in an Additive-Bilingual Program: Report after Four Observations. The fourth phase of a longitudinal study focusing on the cognitive and language development of children in a primary-grade Spanish immersion program (SIP) is reported. Subjects were the remaining 13 members of an SIP cohort beginning in 1987, 15 members of a standard program comparison classroom, 18 members of another class in the 1987 SIP cohort, 37 members of a second SIP cohort, and 17 members of a same-grade standard-program comparison group. Classroom observations were made in fall 1987 (first SIP cohort only) and in the spring of 1988, 1989, and 1990. The children were tested individually on three measures, including: a test of nonverbal problem-solving ability, an English vocabulary measure, and a Spanish vocabulary test. Results indicate that while the SIP children demonstrated significant gains in nonverbal problem-solving over comparison classrooms between the first and second observations in grade 2 and maintained their gains at grade 3, the difference had attenuated by…

Garcia, Eugene E.; Kagan, Sharon L. (1991). Educating Culturally and Linguistically Diverse Preschoolers: Moving the Agenda. Despite growing interest in children's policy and in research regarding childhood bilingualism and language acquisition, the early care and education of linguistically and culturally diverse preschoolers remains a matter of much concern. Relative inattention at the level of policy to the needs and interests of such children is due to several causes, including widely and tenaciously held personal beliefs, political ideologies, misperceptions regarding the lack of a demographic imperative, and disciplinary fragmentation among academics. Four fundamental isssues must be addressed if policy and practice in this domain are to improve. The issues are: (1) socialization, resocialization, and the family/child relationship; (2) modalities of instruction; (3) contextually discontinuous strategies; and (4) sub-system creation versus system reform. Each issue is discussed. Action principles and leadership strategies are presented in hopes of moving an action agenda to ensure that linguistically… [PDF]

Gunderson, Lee; Murphy, Sandra (1981). Developmental Characteristic of the Writing of Urban Students at Grades 2, 5, 8, and 11. A study examined (1) developmental differences in the writing of urban students, (2) the syntactic complexity associated with differing modes of written discourse, and (3) the relationship among grade level, mode of discourse, and writing quality. Subjects were approximately 1,200 second, fifth, eighth, and eleventh grade students from large metropolitan schools that had mean scores in total reading below the fiftieth percentile on the Comprehensive Test of Basic Skills and were receiving Elementary and Secondary Education Act funding. The subjects each completed descriptive, argumentative, and narrative writing tasks. Writing samples of 20 randomly chosen subjects at each grade level were selected for analysis. Of these students, approximately 17% were Spanish surnamed, 24% Black, 12% Filipino, 20% Asian, 18% White, and 9% other. The writing samples were scored for total number of words, number of t-units, and quality, holistically determined. Results showed that over the four…

Hirsch, Linda (1989). Are Principles of Writing across the Curriculum Applicable to ESL Students in Content Courses? Research Findings. Two research studies conducted at the bilingual Hostos Community College of the City University of New York suggest that the classroom performance of adult, advanced, and post English-as-a-Second-Language (ESL) students benefits from the students' participation in tutor-led groups that focus on a particular course's content and employ talk and writing as learning aids. The first study of 60 students found significant differences between the mean grades of students participating in the tutor-led groups and the mean grades of a control set of students. In the second, corroborative study of 164 students, the tutored students received higher average grades and were less likely to fail or drop out of a class. The results of these studies demonstrate the importance of writing and talk in the learning process, and, based on qualitative evaluation of the data, it appears that expressive talk is an equal if not greater contributor to the learning process than is writing. The results also… [PDF]

McLaughlin, Barry (1985). Second-Language Learning in Early Childhood: Some Thoughts for Practitioners. There is much that can be done in early childhood education programs to foster second language learning in young children. The research literature on early childhood bilingualism clearly indicates that children can learn two languages simultaneously without apparent effort, without cognitive strain or interference in learning either language adequately. Young children will learn languages best in an environment where the languages are clearly separated by persons. Caregivers can facilitate language learning by talking in an appropriate way to young language learners, as they do intuitively and spontaneously when communicating with a child, and by providing a stimulating and diverse linguistic environment with meaningful social interactions, including those with native-speaking peers. There is considerable evidence from ethnographic research that children from minority cultures learn better when classroom interactional patterns match patterns they are accustomed to, and teachers need…

(1986). Samuel Gompers High School Bilingual Mini-School 1984-1985. OEA Evaluation Report. In 1984-85, the Bilingual Mini-School was in its second year of a 3-year funding cycle at Samuel Gompers High School (Bronx, New York). The program provided instruction in English as a second language (ESL) and native language arts, in addition to bilingual instruction in mathematics, science, and social studies, to 84 Spanish-speaking students of limited English proficiency (LEP). In addition, program students were enrolled in several specialized vocational courses in the mainstream. The program proposed to meet students' academic and vocational/technical needs by minimizing the linguistic barriers that prevented them from participating in a mainstream instructional setting. The program also aimed at helping students meet the academic requirements for a high school diploma. Title VII funds supported all program staff positions. Development activities for staff included monthly meetings, attendance at workshops, and university courses. Efforts to involve parents of participating…

(1986). Evander Childs High School Cooperative Work-Study Program for Bilingual Students 1983-1984. OEA Evaluation Report. In its final year of a 2-year funding cycle, the Cooperative Work-Study Program for Bilingual Students offered bilingual instruction, career exploration programs, and supportive services to approximately 220 students in grades 9 through 12 at a high school in Bronx, New York. Almost all students were Hispanic and most were non-native born and of limited English proficiency. The program goal was to develop students' proficiency in English and to increase their career awareness, while preserving students' native language and culture. In English language development, students surpassed the proposed objectives. Posttest means in reading and writing were significantly greater than the pretest means; in mathematics, posttest scores were significantly greater than pretest scores. When compared with mainstream students, program students had a significantly higher pass rate in English courses, in global history, and in spring semester mathematics courses. A higher proportion of program…

Morrison, F.; Wightman, M. (1983). Performance of Grade 10 Core French Students. Results of Testing the Listening, Reading, Writing and Speaking Skills of Students in the Schools of the Ottawa and Carleton Boards of Education. Part II. Tenth Annual Report, December 1983. Grade 10 core French students in the Ottawa and Carleton schools were tested for French language skills to assess the skill level acquired by students at this stage of the French second language program and to investigate the suitability of existing tests. The study involves students at three levels: in general, advanced, and enriched courses, in the 11th year of a program beginning in kindergarten and providing the maximum French language exposure specified in Ontario guidelines. Four language skills (listening, speaking, reading, and writing) were tested at each course level, and information about student French language background was also collected. Results showed a distinct difference in the performance levels of students at the three course levels, with higher scores often related to longer program participation. Very few sex differences were found except in enriched courses, where a disproportionately small number of boys achieved higher mean scores on some measures. Results…

Terdy, Dennis (1984). \So What Do You Do in There Anyway?\. There is a widespread lack of understanding of what bilingual and English-as-a-second-language (ESL) instruction consist of, and the day-to-day classroom operations are not easy to explain. Both bilingual and ESL instruction have seen rapid expansion in recent years, and the instructional and curricular approaches have been refined. It has been found that rather than emphasizing only discrete language skills, ESL teachers need to provide learning strategies that will apply to the acquisition of language skills beyond the specialized bilingual or ESL program. Sources are suggested for learning strategies in oral language, reading, and writing, as well as for articulation of the specialized program with mainstream instruction. Bilingual and ESL instructors have three basic responsibilities at all levels, to: (1) know fully the methodologies and curricula of the respective fields; (2) know and teach strategies in the essential skill areas of listening, speaking, reading, and writing;…

Abbott, Muriel M. (1985). Theoretical Considerations in the Measurement of the English-Language Proficiency of Limited-English-Proficient Students. Limited-English-proficient (LEP) students who are not sufficiently proficient in English to participate effectively in an English-speaking instructional environment must be identified for placement in an appropriate educational program. Their progress through an instructional program that is designed to improve their acquisition of English language skills must also be measured both for purposes of exiting from the program and for program evaluation. Both placement and evaluation require a measure that assesses different levels of English-language proficiency. Attention is directed to the concept of language proficiency, how best to measure it with relevance to curriculum, appropriate levels of difficulty, and a meaningful frame of reference for the interpretation of scores for different populations. Attention is also directed to issues concerned with constructing an instrument that can serve both placement and evaluation purposes; that is, an instrument that can differentiate…

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Bibliography: Multicultural Education (Part 1176 of 1259)

(1992). The Boston Globe's Top 25 Books in Multicultural Reading for Youngsters. Young Reader, spec iss Aut. This issue of a newsletter about children and reading briefly describes 25 of the best choices in multicultural children's literature. The list includes picture books and novels for young readers. Each book review provides author, illustrator, and publisher names; the title; the age for which the book is appropriate; and a description of the plot and illustrations. The list includes books in the following cultures: (1) Eskimo; (2) Caribbean; (3) African American; (4) Hispanic American; (5) Ukrainian; (6) Chinese; (7) Middle Eastern; (8) Jewish; (9) Native American; (10) Korean; (11) Cambodian; and (12) Turkish. (JB)…

Mahiri, Jabari (1998). Shooting for Excellence: African American and Youth Culture in New Century Schools. Two African American teachers teach English in the same inner-city high school. One teacher is successful–her students read, interact, and strive for success. The other teacher's students are frequently disruptive or are asleep. This book probes deep into the causes of classroom success and failure, as well as other issues that affect American schools today, and demonstrates how two connected cultures–of African Americans and of youth–cannot be ignored if change is to be effected in education. Through a series of ethnographic studies, the dynamics of effective learning, in which the concept of teacher as coach takes on new meaning, is revealed. The book's scope encompasses computer technology, multiculturalism, tracking, race relations, the canon, and specific aspects of African American culture, such as signifying and receiver-centered discourse. The book's closing chapter projects a vision of an American high school 10 years from now. (NKA)… [PDF]

Klein, Margaret E. (1998). A Comparison of Multicultural Characters in the Annotations of Two Recommended High School Reading Lists Published Thirty-One Years Apart. This content analysis sought to examine the annotations in two editions of "Books for You" (a recommended reading list for high school students) published thirty-one years apart (1964 and 1995) to determine if the roles, settings, and importance of multicultural characters has changed in any way. The percentage of annotations was compared to United States Census population, including the following ethnic groups: African American, Native American, Asian/Pacific Islanders, Hispanic Americans, and those of mixed race. The results of the study show that the percentage of multicultural literature on this recommended reading list increased from 1964 to 1995 for all but Asian/Pacific Islanders. There was a dramatic increase in the number of books with settings in the United States. With the exception of Asian/Pacific Islanders, multicultural characters increased in importance. In general, the roles these characters occupied became somewhat less stereotypical, but not necessarily… [PDF]

Abrahamson, Brant; Smith, Fred (1997). Thinking about Religion from a Global Perspective. The Student Text begins with a comparison of Eastern and Western World Religions. The three interrelated Abrahamic faiths are compared with Hindu-Buddhist traditions. Subsequent chapter titles are: \New Religions,\\Religion and Morality,\\Religion and Science,\\Religion and Human Life,\\A Historical Perspective\ and \Getting Together.\ An \Annotated Bibliography\ follows the easily-read chapters. Analysis Materials is a booklet with a wide variety of items, and instructors can select those best suited for students given the time available. There are case studies, multiple single-page readings (with questions for discussion) as well as illustrations designed to trigger thought and motivate student-produced artwork. The three case studies are \Beginning and Change in Religion,\\New Age Religion\ and \Religion and Exercising Influence.\ The last helps students spot abusive or deceptive procedures wherever they are found. Selections not duplicated for students make excellent teacher…

Risinger, C. Frederick (1992). Trends in K-12 Social Studies. ERIC Digest. Drawing on contemporary research literature, recently developed curriculum guides, and blue-ribbon reports, this digest reviews 10 contemporary trends in K-12 social studies in the United States. Trends are as follows: (1) History, history, and more history; (2) More geography, too; (3) Using literature to teach social studies; (4) Focus on the multicultural nature of American society; (5) Renewed attention to western civilization; (6) Renewed attention to ethics and values; (7) Increased attention to the role of religion; (8) Attention to contemporary and controversial issues; (9) Covering issues in depth; and (10) Writing, writing, and more writing. (DB)… [PDF]

Adler, Sol, Ed.; King, Deborah A., Ed. (1994). Oral Communication Problems in Children and Adolescents. Second Edition. This book provides an overview of communication disorders and their causes and provides suggestions for strategies to be used by the classroom teacher in collaboration with the speech-language pathologist and audiologist to enhance communication skills development. Chapters have the following titles and authors: \Articulation Disorders\ (Rhonda S. Work); \Language Deficiencies\ (Asa J. Brown); \Language Differences\ (Nicholas G. Bountress); \The Multicultural Student in the Classroom\ (Steven J. Cloud); \Stuttering: A Disorder of Fluency\ (Pearl A. Gordon); \Voice Disorders\ (Mary H. Pannbacker and Grace F. Middleton); \Hearing Impairment\ (Allan O. Diefendorf and others); and \Educational Considerations for Students with Hearing Impairment\ (Ralph G. Leverett and others). (Each paper contains references.) (JDD)…

Clouse, R. Wilburn; Hughes, Judy A. (1994). Issues Affecting the Professoriate in the 1990s. This review of the literature examines five issues affecting college faculties in the 1990s and identifies various views on these issues while providing a general overview. A section on multiculturalism identifies it as one of the leading issues facing faculty. This section looks at views on the challenges of racial diversity; racial tension; and increased diversity by gender, cultural background, and disability. A section on organizational factors looks at administrative changes affecting faculty many of which are linked to fiscal considerations. This section covers views on the fiscal crisis, faculty attrition and status, merit pay, and the information explosion. A section on mission raises some broad issues about the mission of U.S. higher education and treats theoretical versus practical applications and university-industry alliances. A section on professional factors addresses approaches to faculty evaluation, staff development, and scholarly communication. The final section… [PDF]

Savage, John F. (1994). Teaching Reading Using Literature. Written for teachers who are moving toward a greater use of literature for reading and writing instruction, this book discusses planning and implementing a reading and writing program for pupils that uses literature as a major component in teaching children how to read. Chapters in the book contain boxed sections with practical suggestions for applying theory to practice, along with special sections that offer "food for thought" and resources such as book lists. Suggestions for in-class and field-based assignments follow each chapter. Chapters in the book are: (1) Literature and Literacy in the Elementary Classroom; (2) The World of Children's Literature; (3) Organizing and Managing a Literature-Based Program; (4) Early Literacy; (5) Word Study: Vocabulary and Learning to Read; (6) Reading Comprehension: Understanding Narrative Text; (7) Literacy across the Curriculum: Comprehending Expository Text; (8) The Role of the Library in a Literature-Based Program; (9) Sharing…

Bruno, Paula (1993). The Wisdom Is Now (Project WIN) Final Evaluation Report, 1992-93. OREA Report. The Wisdom Is Now (Project WIN) was designed to increase student English proficiency, native language proficiency, and academic achievement, increase parent involvement, and encourage staff development at the High School for the Humanities and the School of Fashion industries in New York City. It served a total of 349 students of limited English proficiency (LEP), their parents, and their teachers. Students received instruction in English as a Second Language (ESL), native language arts (NLA), and the content area subjects of mathematics, science, and social studies. Teachers of the participating students had the opportunity to attend monthly staff development meetings and receive tuition reimbursement for relevant college courses. The project sponsored a variety of parental involvement activities, including workshops and counseling services. Project WIN met its specific objectives for increasing students' familiarity with American culture and citizenship, cultural pride, attitude… [PDF]

Rohrlich, Beulah F. (1993). Expecting the Worst (or the Best!). What Exchange Programs Should Know about Student Expectations. Occasional Papers in Intercultural Learning, Number 16. Approximately 500 undergraduate students, representing colleges and universities across the United States, who were about to embark on a semester-long credit-bearing sojourn sponsored by Syracuse University (New York) to one of four locations (London, Strasbourg, Madrid, and Florence) were surveyed about their aspirations and attitudes regarding language, food and health, and adjustment/homesickness. Findings indicated: only three percent of respondents stated that learning the host language was the prime reason for studying abroad; just half of the respondents had a positive attitude toward language acquisition; 59 percent had positive expectations about the host country's food, while 27 percent had negative attitudes; 64 percent had positive expectations concerning matters of health; 80 percent felt positively about adjusting to a new lifestyle and a different academic setting; and homesickness was not expected to be a serious concern. Findings prompted a revision of a 1989 chart… [PDF]

Coelho, Elizabeth (1994). Learning Together in the Multicultural Classroom. Pippin Teacher's Library. Intended for teachers who work with culturally mixed student populations in Canada, this book is about methods of classroom and curriculum organization that promote effective cognitive and affective development in a linguistically and racially diverse setting. The book focuses on developing practical approaches to and techniques for small group work that can be implemented in the classroom. Pointing out that schools will now need to educate students to perform in a technological, information-oriented workplace, the book argues that traditional pedagogy no longer functions in such an environment and that teaching methods that democratize the classroom are in order. The book describes how several strands of learning (cooperative learning, classroom "talk" as a tool for learning, and–for nonnative speakers–interaction in the target language in a non-threatening forum) can be integrated into and implemented in the classroom. Although the activities described in the book are…

Grider, Clint (1994). Implementation of a Multicultural Curriculum: A Case Study. This paper presents a case study of the issues facing a hypothetical university that is attempting to devise and implement a multicultural core curriculum. It focuses on the actions of the chair of the Academic Affairs Council of the university, who must work with the Council and the Faculty Senate to develop the core curriculum. After allowing faculty representatives from a number of minority groups to have input on the curriculum change, the Council voted to add two new categories of courses to the core curriculum to meet the multicultural requirement. To the chairman's surprise, the faculty senate approves the measure by only a narrow margin after heated debate. A groundswell of protest to the move arises from many students, faculty, parents, and alumni of the conservative institution. The president of the university then threatens to veto the curriculum change, an unprecedented move. After presenting the case, the paper analyzes the chairman's leadership skills, criticizing his… [PDF]

Hamilton, Robert E., Ed. (1992). Lesson Plans on African History and Geography: A Teaching Resource. This document presents lesson plans for instruction concerning the history and geography of the continent of Africa. Topics include: (1) "The Challenge of Teaching African History and Culture" (Robert Hamilton); (2) "A Physical Overview of Africa" (Robert Hamilton and Kim Lilly); (3) "A Cultural Overview of Africa" (Robert Hamilton and Kim Lilly); (4) "Early Christianity in Egypt and Ethiopia" (Dona J. Stewart); (5) "Islam" (Dona J. Stewart and Robert Hamilton); (6) "The Saharan Caravan Trade" (George Burson); (7) "African Diaspora" (Walter F. Urbanek); (8) "Zimbabwe" (Sylvia C. Udall); (9) "African Runaway Slave Communities: Palmares and Florida" (Linda B. Mager); (10) "Christianity in Africa: 1500 to the Present" (Robert Hamilton); and (11) "Modern Africa" (George Burson). The document also includes a list of maps, a foreword and preface, acknowledgements, and a discussion… [PDF]

Skelton, Sarah C. (1991). Our Shrinking World: The Need for Cultural Awareness. This paper discusses the characteristics of middle school students and teachers, and provides suggestions for the development of cultural awareness at the middle school level. Between the ages of 10 and 14 years, adolescents experience rapid physical growth, changes in social relationships and in emotions, and changes in intellectual development from concrete to abstract operations. Middle school educators must keep these changes in mind if they are to provide a high quality educational environment. Cultural awareness education programs should increase students' knowledge of cultures and minority groups, and minimize students' prejudice toward others who are different. A cultural awareness program should include: (1) an interdisciplinary approach; (2) interesting curricular materials; (3) development of skills in analysis and critical thinking; and (4) materials and activities which are authentic and multidimensional, and involve cognitive and affective skills. A reference list of…

(1984). Multicultural Mathematics Posters and Activities. A set of 18 posters, each 28 cm x 43 cm and printed on parchmentlike paper, and an activity book for teachers in middle and secondary schools make up this publication. The posters illustrate the ideas that mathematics spans centuries and cultures, and is both useful and enjoyable. The activity book emphasizes problem solving, with a focus on interdisciplinary applications of mathematics, and is designed to encourage minority students to pursue mathematics beyond the minimum requirements for graduation. The activities are referenced to the posters, and concern the following topics: the calculator's ancestors, magic squares, ancient systems of numeration, geometry with meaning, traditional round houses, tangrams, Oware, once upon a time, arabic geometrical pattern and design, Mayan numerals, Pa-Kua, Tower of Brahma, strategy games and puzzles, Japanese optical and geometric art, Egyptian rope stretchers, Shongo networks, Pascal's triangle, and Golden Ratio. (MNS)…

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