1 Historical, Cultural and Social Contexts Students understand dance forms and styles from a diverse range of cultural environments of past and present society. They know the contributions of significant choreographers, dancers and dance organizations to dance heritage. Students analyze the philosophical beliefs, social systems and movement norms that influence the function and role of dance in the lives of people. Benchmark A: Perform and describe dances from various cultures and historical periods with emphasis on cultures addressed in social studies. 1. Identify and demonstrate the spatial formations (e.g., circle, line and couple) in dances from various cultures. 2. Perform simple movement combinations from one or more theatrical dance styles. 3. Discuss the central concepts and themes expressed in traditional, social and theatrical dances from various time periods. Benchmark B: Explain the social and historical contexts that influence the development of dance in a culture. 4. Identify cultural practices observed in selected dances. Benchmark C: Research a recognized contributor to dance (e.g., choreographer, dancer or educator) and trace the development of the individual's work to its historical and cultural influences. 5. Explore the kinds of artistic problems that dancers and choreographers solve.
2 Creative Expression and Communication Students create, interpret and perform dances to demonstrate understanding of choreographic principles, processes and structures. They understand how to use dance and movement to express ideas and to make meaning of their world. Benchmark A: Perform basic dance movements, body positions and spatial patterns from one or more dance styles or traditions. 1. Demonstrate the use of compositional structures in a dance (e.g., ABA form, chance and canon). Benchmark B: Reflect on, evaluate and refine choreographic, rehearsal and performance processes. 2. Develop and demonstrate a sense of personal discipline in rehearsal and performance processes. Benchmark C: Perform a full dance that demonstrates artistic expression and performance skill for a peer audience. 3. Demonstrate movement skill, focus and kinesthetic awareness in a dance rehearsal. 4. Create original material for a short dance study that expresses a theme or concept.
3 Analyzing and Responding Students express orally and in writing their interpretations and evaluations of dances they observe and perform. They understand and use the vocabulary of art criticism to discuss their responses to a variety of dance forms and styles. Benchmark A: Demonstrate knowledge of different approaches to art criticism when analyzing and interpreting dance performances. 1. Articulate an understanding of several ideas or images communicated by a dance performance. Benchmark B: Analyze how dance elements are used to convey concepts or themes in dance performances. 2. Use the vocabulary of art criticism to analyze how the elements of dance are organized in a performance to communicate a theme or concept. Benchmark C: Apply knowledge of dance elements, techniques, styles and choreographic forms to critique dances using defined criteria. 3. Develop criteria for evaluating dance performances and their choreographic styles.
4 Valuing the Arts/Aesthetic Reflection Students inquire about the nature and experience of dance in their lives. They reflect on the significance and value of dances they observe and perform. Students present points of view about dance and respond thoughtfully to others' points of view. Benchmark A: Articulate their viewpoints about the merits of selected dances and explain the basis for their views. 1. Explore questions about the merits of a dance work. Benchmark B: Demonstrate reasoning skills when engaging in inquiry about dance. 2. Ask clarifying questions about different reactions to the same dance and determine how varying opinions have value.
5 Connections, Relationships and Applications Students apply their knowledge of dance to the study of other arts areas and disciplines outside the arts. Students make connections between dance and healthful living. Benchmark A: Demonstrate the inter-relationship of dance content and skills to those in other academic disciplines. 1. Discuss how aspects (e.g., costumes, music, set design and text) of other art disciplines are integrated into dance performance. 2. Discuss how dance relates to and enhances the study of other content areas. Benchmark B: Identify and compare how learning strategies (e.g., collaboration, consensus building, decision making, risk taking) acquired in dance are used in dance and non-dance careers. 3. Discuss how the processes of collaboration, consensus building, decision making and risk taking are used in dance and other professions. Benchmark C: Create and demonstrate correct warm-up activities independently and in a group. 4. Discuss the benefits and importance of proper warm-up for preparation and safety in dance or exercise.
6 Historical, Cultural and Social Contexts Students understand and appreciate the historical, social, political and cultural contexts of drama/theatre in societies both past and present. Students identify significant contributions of playwrights, actors, designers, technicians, composers/lyricists, choreographers, directors, producing organizations and inventors to dramatic/theatrical heritage. Students analyze the social and political forces that have influenced and do influence the function and role of drama/theatre in the lives of people. Benchmark A: Explain the style of a dramatic/theatrical work in historical or cultural context. 1. Identify production styles. 2. Research and explain where, when and how dramatic/theatrical activities occurred in a specific time period. 3. Investigate how drama/theatre and storytelling forms past and present of various cultural groups may reflect their beliefs and traditions. Benchmark B: Compare and contrast playwrights and/or screenwriters from various time periods. 4. Discuss contributions to theatre arts of a playwright or screenwriter from a specific time period.
7 Creative Expression and Communication Students improvise, create, produce and perform dramatic/theatrical works. Students experiment with dramatic/theatrical processes, develop dramatic/theatrical skills and participate in drama/theatre. Benchmark A: Use basic acting skills (e.g., voice, posture, movement, language) to develop characterizations. 1. Create the movement and voice of a character in both comedic and dramatic situations. 2. Use sensory and memorization skills to create a character. Benchmark B: Explain the functions and interrelated nature of scenery, props, lighting, sound, costumes and makeup to create an environment appropriate for drama. 3. Analyze various design components used in a dramatic/theatrical event. Benchmark C: Explore the roles and responsibilities of various theatrical personnel. 4. Explain the roles and responsibilities of a director, stage manager and business manager. Benchmark D: Create scripted scenes based on personal experience and heritage. 5. Write a scripted scene from a prompt that provides exposition, consistent point of view, sensory details and dialogue.
8 Analyzing and Responding Standard Students respond to dramatic/theatrical texts, experiences and performances by describing the distinguishing characteristics and interpreting meaning, themes and moods. Students analyze the creative techniques used in creating and performing dramatic/theatrical works and evaluate dramatic/theatrical works using appropriate criteria. Benchmark A: Use appropriate dramatic/theatrical vocabulary, elements and principles. 1. Use appropriate dramatic/theatrical vocabulary to describe dramatic/ theatrical experiences. 2. Use script-writing techniques including stage directions. 3. Identify character types and relationships. Benchmark B: Discuss the collaborative nature of drama/theatre as a vehicle for the expression of ideas. 4. Explain how the setting of a dramatic/theatrical work affects characterization. 5. Explain the use of a production concept in a dramatic/theatrical work. 6. Differentiate among the unique characteristics of live theatre, film/video and broadcast media. Benchmark C: Articulate opinions about dramatic/theatrical work using established criteria. 7. Justify a presentation form (i.e., live theatre, film/video and broadcast media) to communicate an idea or message. 8. Critique a dramatic/theatrical performance.
9 Valuing Drama/Theatre/Aesthetic Reflection Students demonstrate an understanding of reasons why people value drama/theatre and a respect for diverse opinions regarding dramatic/theatrical preferences. Students develop personal drama/theatre philosophies and articulate the significance of drama/theatre in their lives. Benchmark A: Defend personal responses to a drama/theatre event. 1. Describe ways that drama/theatre, film/video and broadcast media express the artist's perspective and evoke a personal response. Benchmark B: Compare their personal responses to a drama/theatre event with the response of another person. 2. Identify factors that cause diverse opinions about a drama/theatre work or experience.
10 Connections, Relationships and Applications Students identify similarities and differences between drama/theatre and other art forms. Students recognize the relationship between concepts and skills learned through drama/theatre with knowledge learned in other curricular subjects, life experiences and potential careers in and outside the arts. Students recognize the benefits of lifelong learning in drama/theatre. Benchmark A: Discover the interdependence of theatre and other art forms. 1. Combine art forms to create a dramatic/theatrical experience. Benchmark B: Explain the relationship between concepts and skills used in drama/theatre with other curricular subjects. 2. Use problem-solving and cooperative skills to dramatize a story, current event or a concept from another content area. Benchmark C: Identify recurring drama/theatre ideas and concepts that occur across time periods and/or cultures. 3. Identify the cultural characteristics in selected drama/theatre performances from other countries. Benchmark D: Discuss drama/theatre skills as a foundation for lifelong learning and potential employment. 4. Work cooperatively in different roles/jobs within a dramatic/theatrical experience.
11 Historical, Cultural and Social Contexts Students demonstrate knowledge and understanding of a variety of music styles and cultures and the context of musical expression or events, both past and present. Students identify significant contributions of composers and performers to music heritage. Students analyze the historical, social and political forces that have influenced the function and role of music in the lives of people. Benchmark A: Compare and contrast styles and forms of music from various historical periods. 1. Recognize, identify and demonstrate theme and variations in the music of various cultures and/or historical periods. 2. Compare and contrast opera and American music theatre. 3. Research and identify music instruments from different historical periods and world cultures. Benchmark B: Identify composers and classify them according to chronological historical periods. 4. Identify, listen and respond to music of different composers. Benchmark C: Describe how events during various historical periods have influenced the development of music. 5. Recognize and discuss the influence of American history on the development of folk music. 6. Describe conditions under which music is created and performed in various cultures.
12 Creative Expression and Communication Students sing, play instruments, improvise, compose, read and notate music. Benchmark A: Perform a piece of music, independently or in a group, with technical accuracy and expression. 1. Sing and/or play, alone and with others, using good posture and breath control, a varied repertoire of music representing diverse genres and cultures with appropriate dynamics, expression and tempo for the work being performed. 2. Play a variety of instruments independently and with other contrasting parts. 3. Respond appropriately to the cues of a conductor. Benchmark B: Improvise or compose a short melody that includes key signature and meter signature with proper notation in treble or bass clef. 4. Create short melodies using traditional notation. 5. Improvise melodies in a call-and-response setting. 6. Read, write and perform rhythm patterns (in 2/4, 3/4 and 4/4 meter) using sixteenth through whole notes including dotted half-note and syncopated rhythms. 7. Read, write and perform diatonic melodies with fa and ti and the major scale on the treble staff in G-do using a system (e.g., solfege, numbers or letters). Benchmark C: Identify and recognize in a piece of music the following: clef, key signature, meter signature, tempo, dynamic markings and note values. 8. Identify key signatures.
13 Analyzing and Responding Students listen to a varied repertoire of music and respond by analyzing and describing music using correct terminology. Students evaluate the creating and performing of music by using appropriate criteria. Benchmark A: Describe and evaluate a piece of music using developed criteria based on elements of music and music vocabulary. 1. Identify dynamics, tempo, meter and tonality in various pieces of music aurally. 2. Identify terms related to form (e.g., DC al Fine; DC dal segno; DS al Coda; repeat signs, first and second endings). 3. Identify selected electronic and world music instruments. Benchmark B: Analyze the structure of larger music works and the sections comprised within. 4. Analyze a piece of music using music vocabulary. Benchmark C: Apply appropriate criteria to support personal preferences for music choice and evaluate the quality and effectiveness of a music performance. 5. Evaluate and describe individual and group performances. 6. Differentiate between melody and harmony.
14 Valuing Music/Aesthetic Reflection Students demonstrate an understanding of reasons why people value music and a respect for diverse opinions regarding music preferences. Students articulate the significance of music in their lives. Benchmark A: Reflect on and describe how music performance and settings affect audience response. 1. Describe audience etiquette associated with various music performances and settings. Benchmark B: Reflect on why others may have different music preferences. 2. Identify and discuss aesthetic qualities in their performances and in the performances of others. 3. Demonstrate how music communicates meaning through text, feelings, moods or images. 4. Identify elements of music that contribute to aesthetic qualities in a specific music work. Benchmark C: Justify one's personal preference of music choice using music vocabulary. 5. Explain how expressive music elements determine the quality of a composition. 6. Develop and apply criteria to support personal preferences for specific music works.
15 Connections, Relationships and Applications Students identify similarities and differences between music and other arts disciplines. Students recognize the relationship between concepts and skills learned through music with knowledge learned in other curricular subjects, life experiences and potential careers in and outside the arts. Students develop a desire for lifelong learning in music. Benchmark A: Compare and contrast common terms used in and for the interpretation of music and other arts disciplines. 1. Interpret music through dance, drama and visual art. 2. Identify the use of similar elements in music and other art forms and compare how ideas and emotions are expressed in each art form using the same elements. 3. Define basic arts terms (e.g., texture, color, form, movement) associated with various art forms and use them to describe music events. Benchmark B: Demonstrate ways that subject matter of other disciplines is interrelated with that of music. 4. Describe how knowledge of music connects to learning in other subject areas. Benchmark C: Identify various ways music affects their lives. 5. Discuss how culture influences music. Benchmark D: Identify various careers in music. 6. Identify the specific skills needed to be a musician.
16 Historical, Cultural and Social Contexts Students understand the impact of visual art on the history, culture and society from which it emanates. They understand the cultural, social and political forces that, in turn, shape visual art communication and expression. Students identify the significant contributions of visual artists to cultural heritage. They analyze the historical, cultural, social and political contexts that influence the function and role of visual art in the lives of people. Benchmark A: Compare and contrast the distinctive characteristics of art forms from various cultural, historical and social contexts. 1. Identify visual forms of expression found in different cultures. 2. Compare and contrast art forms from various regions and cultural traditions of North America. Benchmark B: Create a work of art which incorporates the style or characteristics of artwork from a culture other than their own. 3. Compare and contrast the artistic styles observed in artwork from various cultures. 4. Demonstrate the way art materials are used by artists to create different styles (e.g., paint applied spontaneously in expressionism and more carefully in minimalism). Benchmark C: Demonstrate knowledge of historical influences on contemporary works of art and make predictions about influences on the future of visual art. 5. Examine how social, environmental or political issues affect design choices (e.g., architecture, public art and fashion). Benchmark D: Research culturally or historically significant works of art and discuss their roles in society, history, culture or politics.
17 6. Explain how art galleries, museums and public art contribute to the documentation and preservation of art history. 7. Describe the lives, works and impact of key visual artists in a selected period of United States History.
18 Creative Expression and Communication Students create artworks that demonstrate understanding of materials, processes, tools, media, techniques and available technology. They understand how to use art elements, principles and images to communicate their ideas in a variety of visual forms. Benchmark A: Apply knowledge of materials, tools, media, techniques and processes to communicate subject matter, themes or ideas in a variety of visual forms. 1. Use observational and technical skills to achieve the illusion of depth in two-dimensional space (e.g., value, perspective and placement of objects). 2. Explore different approaches to creating art (e.g., by artist, style or historical period). Benchmark B: Create two- and three-dimensional original artwork that demonstrates personal visual expression and communication. 3. Identify and communicate sources of ideas (e.g., personal experience, interests, nature or common objects) for their artworks. Benchmark C: Achieve artistic purpose and communicate intent by selection and use of appropriate media. 4. Apply problem-solving strategies to improve the creation of artwork. Benchmark D: Use current, available technology to refine an idea and create an original, imaginative work of art. 5. Use current, available technology to explore imagery and create visual effects. Benchmark E: Identify and explain reasons to support artistic decisions in the creation of art work. 6. Identify reasons for personal, artistic decisions.
19 Analyzing and Responding Students identify and discriminate themes, media, subject matter and formal technical and expressive aspects in works of art. They understand and use the vocabulary of art criticism to describe visual features, analyze relationships and interpret meanings in works of art. Students make judgments about the quality of works of art using the appropriate criteria. Benchmark A: Apply the strategies of art criticism to describe, analyze and interpret selected works of art. 1. Compare and analyze how art elements and principles are used for expressive purposes (e.g., strong mood, explosive shapes and rhythmic patterns). 2. Compare the works of different artists on the basis of purpose and style (e.g., functional/nonfunctional and representational/abstract). 3. Explain and discuss multiple meanings in selected artworks. Benchmark B: Present and support an individual interpretation of a work of art. 4. Apply observation and analysis skills to derive meaning in a selected artwork and explain their thought processes. Benchmark C: Establish and use criteria for making judgments about works of art. 5. Use specific criteria individually and in groups to assess works of art.
20 Valuing the Arts/Aesthetic Reflection Students understand why people value visual art. They present their beliefs about the nature and significance of selected artworks and the reasons for holding these beliefs. Students reflect on and respect diverse points of view about artworks and artifacts. Benchmark A: Demonstrate aesthetic inquiry and reflection skills when participating in discussions about the nature and value of art. 1. Pose questions that can be answered by an aesthetic study of artworks. 2. Recognize that different assumptions and theories of art lead to different interpretations of artworks. Benchmark B: Analyze diverse points of view about artworks and explain the factors that shape various perspectives. 3. Explain how personal experience can influence choosing one artwork over another.
21 Connections, Relationships and Applications Students connect and apply their learning of visual art to the study of other arts areas and disciplines outside the arts. They understand relationships between and among concepts and ideas that are common across subjects in the curriculum. Students recognize the importance of lifelong learning and experience in visual art. Benchmark A: Demonstrate the role of visual art in solving an interdisciplinary problem. 1. Compare and contrast how visual art is used in musical, theatrical or dance productions and provide examples. Benchmark B: Apply and combine visual art, research and technology skills to communicate ideas in visual form. 2. Use technology to conduct information searches, research topics and explore connections to visual art. Benchmark C: Use key concepts, issues and themes to connect visual art to various content areas. 3. Use artwork to communicate and enhance understanding of concepts in other subject areas (e.g., science, English language arts, mathematics and social studies). Benchmark D: Use words and images to explain the role of visual art in community and cultural traditions and events. 4. Investigate the types of cultural objects artists create and their role in everyday environment.


Islam in the Classroom: What the Textbooks Tell Us
Part Two of Five
/authors/id./author_detail.aspGilbert T. Sewall
May 13, 2008
ISLAM'S FOUNDATIONS AND PAST
Seventh-grade world history textbooks introduce Islam's origins, creeds, and core beliefs as a blend of history and scripture, weaving together revelation, legend, and fact. "Muslims believe that God had spoken to Muhammad through the angel," says the Holt book before going on to explain that "Muhammad reported new revelations about rules for Muslim government, society, and worship. God told Muhammad that Muslims should face Mecca when they pray." Teachers' Curriculum Institute's History Alive! features a passage set off in large print and italics, a Muslim prayer from the Qur'an:
Recite - in the name of thy Lord!
Who created man from blood coagulated.
Recite! Thy Lord is wondrous kind,
Who by the pen has taught mankind things they knew not.
In its narration of Islam's foundation story, the Prentice Hall volume concludes with a variant translation of the same extract, this time set off in heavy boldface type:
Seeking peace of mind, Muhammad retreated to a cave to think and reflect. One night in 610, according to Islamic beliefs, Muhammad had a vision and began to receive revelations. The angel Gabriel appeared before him and told him to spread God's word:
Proclaim in the name of your Lord who created!
Created man from a clot of blood.
Proclaim: Your Lord is the Most Generous,
Who teaches by the pen;
Teaches man what he knew not. (Qur'an 96:1-3)
To set the scene of the origins of Islam and the teachings of Muhammad, the McDougal Littell volume features a lavishly illustrated page. Its central organizing motif is an inspirational but fictionalized tale about a seventh-century Muslim family traveling on the first hajj (pilgrimage) to Mecca and the religious experience of two seventh-century children, Ayesha and Yazid. It states, "Nearly 100,000 have gathered for the journey." The very size of the pilgrimage is a gross exaggeration. "Ayesha and Yazid stand with their parents for hours, praying in the blistering sun. But that memory soon fades when the sister and brother learn that they will spend the evening camping under the stars." Ayesha and Yazid camping under the stars, under the watchful eye of the Prophet. The children later "agree with their parents that being near Muhammad was especially meaningful." The enthusiasm of this invented story contrasts with standard textbook diction, which rarely expresses much emotion.
TCI's lessons on Islam's foundations are more wordy, detailed, and complex, containing stilted language that seem scripted or borrowed from devotional, not historical, material. The chapter entitled "The Prophet Muhammad" begins with the story of Abraham and Hagar in the desert:
Makkah (Mecca) was an ancient place of worship. According to Arab and Muslim tradition, many centuries before Muhammad was born, it was here that God tested the faith of the prophet Abraham by commanding that he leave his wife Hagar and baby Ishmael in a desolate valley. As Abraham's wife desperately searched for water, a miracle happened. A spring bubbled up at her son's feet. The spring became known as Zamzam. Over time, people settled near it, and Abraham built a house of worship called the Ka'ba.
Such detail runs through entire chapters of History Alive! Seventeen pages after this passage, the book reminds students of this foundation story in an extensive section on the Five Pillars. It continues its storytelling in ornate, enthusiastic language:
The Fifth Pillar of Faith is hajj, the pilgrimage to the holy city of Makkah. . . . Upon arrival, Muslims announce their presence with these words: "Here I am, O God, at thy command!" They go to the great Mosque, which houses the Ka'ba. . . . Muslims believe that Abraham built the Ka'ba as a shrine to honor God. The pilgrims circle the Ka'ba seven times, which is a ritual mentioned in the Qur'an. Next, they run along a passage between two small hills, as did Hagar, Abraham's wife, when she searched for water for her baby Ishmael. As you may remember, Muslims believe that a spring called Zamzam miraculously appeared at Hagar's feet. The pilgrims drink from the Zamzam well.
In the Holt seventh-grade volume two pages highlight a long prayer from the Qur'an to Allah "the Merciful." The format is identical to that used on pages in the Holt sixth-grade volume that cover the Bible. This device typifies the ruling editorial principle of cultural equivalency: equal time for equal faiths, two pages each, using the same layout. One aspect of the scriptural quotations is strikingly different. The biblical passages are ethical teachings canonical in the Western tradition. The Qur'anic passage is poetic and devotional, more like the Lord's Prayer or Apostles Creed. It begins:
In the Name of Allah, the Compassionate, the Merciful
It is the Merciful who has taught the Qur'an.
He created man and taught him articulate speech.
The sun and the moon pursue their ordered course. The plants and
the trees bow down in adoration.
In Islam this prayer serves a purpose different from ethical teaching - veneration and adoration of the Prophet -a difference that textbooks leave unexamined and unstated.
Among the textbooks examined, the editorial caution that marks coverage of Christian and Jewish beliefs vanishes in presenting Islam's foundations. With material laden with angels, revelations, miracles, prayers, and sacred exclamations; the story of the Zamzam well; and the titles "Messenger of God" and "Prophet of Islam," the seventh-grade textbooks cross the line into something other than history, that is, scripture or myth.
Lavish textbook praise of Islam continues after the presentation of these foundation stories. Some textbooks provide glowing declarations of Muslim social conscience. The Holt volume, trying to summarize Islam's organizing principle, says: "People should help the poor." It adds: "Helping and caring for others is important in Islam." Muhammad "taught equality," says Teachers' Curriculum Institute's History Alive! "He told followers to share their wealth and to care for the less fortunate in society." The Holt seventh-grade volume says, "Fasting also reminds Muslims of people in the world who struggle to get enough food." TCI says, "Muhammad told his followers to make sure their guests never left a table hungry." The textbook continues, noting that Muhammad learned "about Arab traditions, such as being kind to strangers and helping orphans, widows, and other needy members of society." These effusive formulations stop just short of invention and raise questions about the sources of information.
The textbooks feature manifold contributions of Islam to the arts and science, expanding coverage to a degree that seems out of proportion to the relative slimness of the material that the same volumes dedicate to European achievements. TCI devotes thirteen text-heavy pages to textiles, calligraphy, design, books, city building, architecture, mathematics, medicine, polo, and chess, some of it spun like cotton candy:
Singing was an essential part of Muslim Spain's musical culture. Musicians and poets worked together to create songs about love, nature, and the glory of the empire. Vocalists performed the songs accompanied by such instruments as drums, flutes, and lutes. Although this music is lost today, it undoubtedly influenced later musical forms in Europe and North Africa.
Undoubtedly, the TCI volume declares. Yet the book acknowledges that the music is lost and the claims are speculative. Empty text dilates Islamic achievements.
The seventh-grade world history textbooks reviewed avoid all conflict and bloodshed in describing Islam's push out of Arabia and rapid conquest of most of the Mediterranean world. They fail to explain how Islam spread in the seventh and eighth centuries. Islam appears out of nowhere, spreads smoothly and by implication without conflict. Once it was common to state that Islam was spread by the sword. Now, textbooks imply, it moves peacefully with traders. Islam is "brought" to apparently willing populations. People adopt it freely. TCI says, "An Arab man named Muhammad introduced Islam to the people of the Arabian peninsula." The book continues, "Although the first Muslims lived in Arabia, Islam spread through the Middle East." But non-Arabs did not passively "become" Muslim. They were conquered. Islam did not just spread. The Arab-Islamic conquest ended many centuries of Greek culture and Christian worship in the eastern Mediterranean. Sudden Muslim control of Syria, Egypt, and Persia was followed by the Muslim conquest of western Africa, Spain, and the Indus Valley.
Textbooks are trying, perhaps, to correct a misconception. Historically, as a conqueror, Islam was no crueler than its many adversaries. The notion that Mohammedanism was a "religion of the sword" forced upon the masses by bloodthirsty fanatics is based on a false reading of history that was discredited fifty years ago and is a view rejected by contemporary specialists. Michel Gurfinkiel of the Jean-Jacques Rousseau Institute notes that the Islamic empire that swept beyond Arabia and quickly overran the mightiest powers of the day, Byzantium (Greece) and Persia, did so through alliances with religious rebels and internal political factions that did not share the beliefs of the regime. In Islam's history the slaughter of conquered infidels was discouraged. Sometimes the fate of the conquered was slavery. Sometimes it was limited tolerance by the Islamic regime. In Islam's early conquests Christians, Jews, and Zoroastrians were to be the tax base of the state. One reason that conquered non-Arabic people became Muslims was to avoid being taken as slaves or to have preferential rights under Muslim law. Conversion gradually became a problem for the state as its tax base declined. Yet the idea of Islamic belligerence has lingering currency, not without reason. Efraim Karsh of King's College London documents the long history of warring inclination and territorial ambition that makes Islam unique among the world's major faiths, and the Economist magazine wonders, "Why is Islam involved in quite so many modern wars of religion?"
Students receive a different message from textbooks, one that points in another direction. As in the McDougal Littell volume, they read, "There was much blending of cultures under Muslim rule. Over time, many peoples in Muslim-ruled territories converted to Islam. They were attracted by Islam's message of equality and hope for salvation." McDougal Littell's Teacher's Annotated Edition reiterates this theme, telling instructors to stress that "many conquered people became Muslims [because] they found Islam's message of equality and hope attractive." What, exactly, was this "message of equality" and hope that teachers are told to stress?
In explaining jihad, several textbooks make an effort to cleanse it of belligerence. Defining jihad is admittedly difficult, as definitions in circulation vary radically. The common assertion now is that translating jihad as "holy war" is entirely wrong and that old translations are incorrect. But in fact, authorities and scholarship of varying perspectives conceive jihad to be a sacred obligation to extend Islam's power - religious and territorial - by persuasion or force.
Jihad is "sacred" or "holy" struggle. Jihad is also a "just struggle" against the disbeliever. It is a religious struggle. A religion professor and college textbook author, Jamal J. Elias, says, "The concept of jihad covers all activities that either defend Islam or else further its cause." Jihad is constructed as a "holy war" in much Muslim scripture. Historically, jihad involves efforts to subjugate or convert, impose sharia, and take political and military control over non-Muslim territory. Today, in government circles, in the foreign policy establishment, in the international community, among newswriters and editorialists and academics, that is how the word jihad is used. It is how Middle Eastern terrorists and Al Qaeda use the term. When Saddam Hussein was executed in 2006, his final words were: "I am a militant and I have no fear for myself. I have spent my life in jihad and fighting aggression."
Islamic scripture is inconsistent toward infidels, but a harsh, punitive, and aggressive voice, not a charitable or kindly one, prevails. Sam Harris, author of The End of Faith, observes that punishment and humiliation are leitmotifs in Qur'anic scripture. Given radical Islam's mind-set, and observing the contemporary clash of the Sunni and Shia sects, Harris wonders why U.S. religious moderates and cultural leaders refuse to look critically at the element of violence inherent in the Islamic project. The idea that Islam is a peaceful religion merely hijacked by a few extremists, Harris and others warn, is a dangerous fantasy. "Fighting is prescribed for you" (2:216) and "Slay the infidel wherever you find them" (4:89) are only two of many suras that suggest a degree of intolerance and aggression. Yet the Islamic organizations that act as academic reviewers for textbook publishers assure editors that jihad is something entirely different. It is a struggle against evil impulses, they say, misunderstood by the rest of us and in no way bellicose. To characterize jihad as holy war, they insist, would be a grave textbook error, yet a 2007 Pentagon-based study shows almost conclusively that Islamic law sanctions violence and that the Islamist threat to world security has a doctrinal basis.
New definitions of jihad started to circulate in U.S. history textbooks and classrooms in the 1990s. The engine was a 1994 Council on Islamic Education "guide" for publishers that maintained jihad meant "‘to exert oneself' or ‘to strive.' Other meanings include ‘endeavor, strain, effort, diligence, struggle. . . .' It should not be understood to mean ‘holy war,' a common misrepresentation." Soon, jihad underwent a definitional overhaul. In this amazing cultural reorchestration, the pioneer was a Houghton Mifflin world history textbook, Across the Centuries, still firmly established in junior high schools. Across the Centuries said jihad is a struggle "to do one's best to resist temptation and overcome evil." Jihad was reimagined as an "inner struggle" and element of Muslim self-improvement. These changes reflected the intersection of multiculturalism, suddenly a trendy social studies construct, and Houghton Mifflin's commercial ambitions in social studies. Then and later, appearing from nowhere, the California-based Council on Islamic Education would become a fixture on the textbook scene.
Change was soon evident as well among high school textbooks. From 2001 on, Connections to Today, Prentice Hall's market-dominant high school world history then and now, and several spin-off versions customized for California and other states, listed Shabbir Mansuri and Susan Douglass of the Council on Islamic Education as academic reviewers. The textbook says: "Some Muslims look on jihad, or effort in God's service, as another duty. Jihad has often been mistakenly translated simply as ‘holy war.' In fact, it may include acts of charity or an inner struggle to achieve spiritual peace, as well as any battle in defense of Islam." As early as 2002 another high-profile textbook, Patterns of Interaction, a high school world history textbook published by Houghton Mifflin under the McDougal Littell imprint, did not mention jihad. Houghton Mifflin's multigrade series then dropped jihad from textbooks; by 2005 Houghton Mifflin had apparently removed jihad from its entire series of social studies textbooks. The advisory role of the Council on Islamic Education in making these editorial decisions remains unclear.
But this was only the beginning. Among the history textbooks adopted by California in 2005, some definitions of jihad are more extreme and less valid. History Alive, the TCI textbook that Lodi and Scottsdale parents so objected to, provides the most detailed - and misleading - definition of jihad among seventh-grade textbooks reviewed:
The word jihad means "to strive." Jihad represents the human struggle to overcome difficulties and do things that are pleasing to God. Muslims strive to respond positively to personal difficulties as well as worldly challenges. For instance, they might work to become better people, reform society, or correct injustice.
Then, in the next paragraph, which differentiates the "lesser" and "greater" jihad, the textbook tangles the subject and also seems slightly deceptive:
Jihad has always been an important Islamic concept. One hadith, or account of Muhammad, tells about the prophet's return from a battle. He declared that he and his men had carried out the "lesser jihad," the external struggle against oppression. The "greater jihad," he said, was the fight against evil within oneself. Examples of the greater jihad include working hard for a goal, giving up a bad habit, getting an education, or obeying your parents when you may not want to.
Continuing the definition, TCI lapses into florid prose that invites questions about textual sources and scripting:
Another hadith says that Muslims should fulfill jihad with the heart, tongue, and hand. Muslims use the heart in their struggle to resist evil. The tongue may convince others to take up worthy causes, such as funding medical research. Hands may perform good works and correct wrongs.
Then it continues:
Sometimes, however, jihad becomes a physical struggle. The Qur'an tells Muslims to fight to protect themselves from those who would do them harm or to right a terrible wrong.
TCI leaves "those who would do them harm" and "right a terrible wrong" to the reader's imagination. The textbook's chapter summary reads: "Muslims also have the duty of jihad, or striving to overcome challenges as they strive to please God." Since TCI describes jihad as being "the struggle against oppression," students who hear of repeated Islamic calls to jihad against Christians and Jews that include the destruction of the United States and Israel must wonder who and what is at fault.
Other seventh-grade textbook definitions of jihad are ambivalent. The Holt volume defines jihad most accurately among the textbooks reviewed as "to make an effort, or to struggle. Jihad refers to the inner struggle people go through in their effort to obey God and behave according to Islamic ways. Jihad can also mean the struggle to defend the Muslim community, or, historically, to convert people to Islam. The word has also been translated as holy war." The Prentice Hall volume offers a more acceptable and informative passage despite the unadorned declaration of Islamic tolerance:
The successful spread of Islam and Muslim rule was based on several factors. One was the decline of the Byzantine and Persian empires. Years of warfare had left these empires weak and vulnerable.
A second factor in the Muslims' success was the skill of Arab armies. They were expert in the use of soldiers on horseback. They struck quickly and with deadly force in harsh desert environments.
A third factor was the energy and religious zeal of Arab warriors. They fought under the banner of jihad or "holy struggle." In Arabic, jihad refers to striving hard in God's cause. Sometimes it means a person's internal struggle to live by Muslim principles. But it can also mean waging war to spread the Islamic faith.
Another factor helping the Arabs was their tolerance for other religions.
A final factor in the Muslim's success was the rapid appeal of Islam itself. Islam offered followers a direct path to God and salvation.
The Holt and Prentice Hall definitions of jihad may be imperfect, yet they provide essential definitions that the Glencoe and McDougal Littell seventh-grade volumes do not. These two latter volumes fail to acknowledge jihad. The material has simply been deleted. This deliberate omission required editorial self-censorship at McGraw-Hill, and at Houghton Mifflin, where editors had previously whitewashed the definition of jihad in Across the Centuries.
Part Three will continue the focus on Islam's Foundations and Past.
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The constructivist teaching experiment is used in formulating explanations of children’s mathematical behavior. Essentially,
a teaching experiment consists of a series of teaching episodes and individual interviews that covers an extended period of
time—anywhere from 6 weeks to 2 years. The explanations we formulate consist of models—constellations of theoretical constructs—that
represent our understanding of children’s mathematical realities. However, the models must be distinguished from what might
go on in children’s heads. They are formulated in the context of intensive interactions with children. Our emphasis on the
researcher as teacher stems from our view that children’s construction of mathematical knowledge is greatly influenced by
the experience they gain through interaction with their teacher. Although some of the researchers might not teach, all must
act as model builders to ensure that the models reflect the teacher’s understanding of the children.
KeywordsConstructivist teaching experiment-Model building-Clinical interview-Teaching episode-Counting scheme-Teacher as researcher
A total of 602 students (59.5% female) from academically selected schools in Germany were tested at three time points--end of Grade 7, end of Grade 10, and middle of Grade 12--in order to investigate the relationships between academic interest and achievement in mathematics. In addition, sex differences in achievement, interest, and course selection were analyzed. At the end of Grade 10, students opted for either a basic or an advanced mathematics course. Data analyses revealed sex differences in favor of boys in mathematics achievement, interest, and opting for an advanced mathematics course. Further analyses by means of structural equation modeling show that interest had no significant effect on learning from Grade 7 to Grade 10, but did affect course selection--that is, highly interested students were more likely to choose an advanced course. Furthermore, interest at the end of Grade 10 had a direct and an indirect effect (via course selection) on achievement in upper secondary school. In addition, results suggest that, at least from Grade 7 to Grade 10, achievement affected interest--that is, high achievers expressed more interest than low achievers. Findings underline the importance of interest for academic choices and for self-regulated learning. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
A yearlong experimental study showed positive effects of a professional development project that involved 19 urban elementary schools, 180 teachers, and 3735 students from one of the lowest performing school districts in California. Algebraic reasoning as generalized arithmetic and the study of relations was used as the centerpiece for work with teachers in Grades 1-5. Participating teachers generated a wider variety of student strategies, including more strategies that reflected the use of relational thinking, than did nonparticipating teachers. Students in participating classes showed significantly better understanding of the equal sign and used significantly more strategies reflecting relational thinking during interviews than did students in classes of nonparticipating teachers. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to examine teachers' perceptions and children's application of the model method. The subjects were 14 primary teachers from 4 schools and 151 Primary 5 children. The model method affords higher ability children without access to letter-symbolic algebra a means to represent and solve algebraic word problems. Partly correct solutions suggest that representation is not an all-or-nothing process in which model drawing is either completely correct or completely incorrect. Instead, an incorrect solution could be the consequence of misrepresentation of a single piece of information. Our findings offer avenues of support in word problem solving to children of average ability. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
The purpose of this article is to sketch a hypothetical descriptive framework of statistical knowledge for teaching. Because statistics is a discipline in its own right rather than a branch of mathematics, the knowledge needed to teach statistics is likely to differ from the knowledge needed to teach mathematics. Doing statistics involves many primarily nonmathematical activities, such as building meaning for data by examining the context and choosing appropriate study designs to answer questions of interest. Although there are differences between mathematics and statistics, the two disciplines do share common ground in that statistics utilizes mathematics. This connection suggests that existing research on mathematical knowledge for teaching can help inform research on statistical knowledge for teaching. I propose the use of research from the Learning Mathematics for Teaching (LMT) project to help shape the discussion. I conclude by identifying areas of needed research and suggesting directions for teacher education efforts in statistics. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
In this rejoinder to Baroody and colleagues (2007) (see record
2007-03311-003), I point out that there are several areas of agreement between my position and that of Baroody et al.--most notably that both procedural knowledge and conceptual knowledge are of critical importance in students' learning of mathematics. However, there are issues on which Baroody et al. and I do not agree. In particular, I elaborate on the idea that procedures can be known deeply, flexibly, and with critical judgment--positive learning outcomes that are exclusively about students' knowledge of procedures and not necessarily a result of connections to conceptual knowledge. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
This editorial written by Steve Williams is about research articles in the JRME. The author comments that as difficult as it can be (and usually is), he nevertheless feels strongly that there is great value in shortening, tightening, and focusing a research report before submitting it. It benefits editors, reviewers, readers, and authors, and results in more timely and interesting publications. Moreover, the author wants to assure readers that he feels your pain. He is currently in the process of reducing an accepted manuscript by 1,000 words of his choice, at the suggestion of a kind editor who he realizes (despite his occasional grumbling) has the best interests of him, the manuscript, and its readers at heart. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
There has been increased engagement in studying discourse in the field of mathematics education. But what exactly is a discourse, and how do researchers go about analyzing discourses? This study examines 108 articles from 6 international journals in mathematics education by asking questions such as these: In which traditions and in relation to which kinds of epistemological assumptions are the articles situated? How is the concept of discourse used and defined? How are mathematical aspects of the discourse accentuated? The results of this study show that a variety of conceptualizations are used for analyzing discourses but also that many articles would benefit from strengthening those conceptualizations by explicitly defining the concept of discourse, situating the article in relation to epistemological assumptions, and relating the work to other discourse studies in mathematics education. (Contains 14 footnotes and 7 tables.)
Overall scale scores from the National Assessment of Educational Progress (NAEP) indicate that there was only minimal improvement in the mathematics performance of high school students between 1978 and 2004. Using recently released data from the Long-Term Trend (LTT) NAEP, this study describes the content covered on the LTT NAEP and the performance of 17-year-old students on that content. In addition, it demonstrates that although overall gains in performance were small, there were areas within mathematics in which performance improved substantially and others in which students in 2004 did not do as well as their counterparts of the 1970s and 1980s. Specifically, performance on 3 items involving multiplication of whole numbers by fractions deteriorated but performance improved on most tasks involving percents and geometry. Performance was stable on most items assessing algebraic reasoning and logical reasoning and was stable or improved modestly on items assessing estimation, interpretation of tables and graphs, and understanding of integers. (Contains 3 figures, 8 tables, and 9 footnotes.)
This bibliography provides information and brief annotations for 148 papers reporting research into the effectiveness of self-paced instruction in mathematics. The citations are organized into three major categories: research summaries (8 papers), studies comparing the effectiveness of self-paced programs with that of more traditional programs (101 papers), and studies designed to analyze or evaluate specific components of self-paced programs (39 papers). The papers annotated deal with mathematics instruction at all levels from the primary grades through college, and with a variety of cognitive and affective criteria for judging the effectiveness of instruction. Each annotation notes the grade levels at which the study was performed and summarizes the major findings. (SD)
This listing of research related to mathematics education provides brief annotations for articles and dissertations (K-12) published in 1975. Studies on college-level and other post-secondary school levels are also listed, but without annotations. (SD)
This is the seventh annual listing of research on mathematics education published in JRME . The research for K–12 is organized alphabetically by author(s) within three categories—research summaries, journal-published reports, and dissertation abstracts. The subset of Piagetian-oriented research is listed separately in each of the latter two divisions. The K–12 listing is followed by references to articles and dissertations at the college and other postsecondary levels. All entries are annotated this year.
An annual annotated listing of research on mathematics education is presented. The research is organized alphabetically by author(s) within three categories (research summaries, journal-published reports, and dissertation abstracts). Grade and age levels are indicated for each reference. An index of general topics is appended to help readers locate studies of particular interest. Included in the listing are studies in which mathematics education was not the sole or primary focus of the research. While most of these peripheral studies are not annotated, those studies specific to mathematics are annotated, and most annotations indicate one principal finding of the study. (MK)
This is the 12th annual listing of research on mathematics education. The research noted is alphabetically organized by author(s) within the following three categories: (1) research summaries; (2) journal-published reports; and (3) dissertation abstracts. Grade or age level is indicated for each reference. Included in the listing are studies in which mathematics education was not the sole or primary focus of research. While most of these peripheral studies are not annotated, those specific to mathematics are. Most annotations indicate one principle finding of the study. A list of the journals searched is provided, and the number of references from each cited journal is noted. An index of general topics is appended to help readers locate studies of particular interest. (MP)
This is the 13th annual listing of research on mathematics education. Annotated references are organized alphabetically by author within three categories: (1) research summaries; (2) journal-published reports; and (3) dissertation abstracts. An index is also provided to help locate references to designated mathematical topics. Topic areas include: achievement; algebra; arithmetic operations; attitudes/anxiety; calculators and computers; cognitive style; diagnosis and remediation; ethnic and social variables; geometry and measurement; learning; learning disabilities; mathematics materials; number and numeration; organizing for instruction; problem-solving; sequencing; sex differences; and test analysis. Accompanying the author's name in this index is a grade-level designation. In addition, each annotation listed in the three major categories also includes a grade-level (or age-level) designation. Annotations generally indicate one principal finding of a study, although most have additional findings. Therefore, the original report should be checked for other results as well as for limitations affecting the validity of the findings. Several studies in which mathematics education was not the primary focus are also included. Such studies are usually not annotated. (JN)
Lists references of 16 research summaries, 152 articles, and 220 dissertations alphabetically by author within each category. Provides the grade or age level for each reference. A brief abstract is presented for most of the references. Journals searched and author index by content are included. (YP)
Debates about the future of school mathematics in the United States often center on whether standards-based instruction is improving or undermining students' achievement. Critical for making progress in these debates is information about the actual nature of classroom practice in U.S. classrooms. This article focuses on one key element of classroom practice--teaching--and presents the results of two studies of randomly selected, nationally representative U.S. eighth-grade mathematics lessons that were videotaped as part of the TIMSS 1995 and 1999 Video Studies. (Contains 4 figures, 6 tables and 11 footnotes.)
California is one of 4 states that have accelerated addition and subtraction basic-facts memorization. This article reports on teacher practices, first-grade achievement of the standard, and a broader conception of basic-facts competence. Even among students from the highest performing schools, fewer than 11% made progress toward the memorization standard equivalent to their progress through the school year. Several negative correlations between instructional strategies and student retrieval suggest that teachers may benefit from professional development targeted at basic-facts teaching and learning. Textbook reliance was negatively correlated with basic-facts retrieval, suggesting that educators and policymakers may want to reexamine assumptions about the efficacy of traditional first-grade textbooks. This study's findings may prove useful to teachers, professional development trainers, and textbook publishers as they consider ways to improve basic-facts learning among early elementary children. (Contains 5 figures, 11 tables and 12 footnotes.)
This article is about 8 African American middle school boys who have experienced success in mathematics. Working within a phenomenological methodological framework, the researcher investigated the limitations these students encounter and the compensating factors they experience. Critical race theory was the theoretical framework for this study; counter-storytelling was utilized to capture the boys' experiences, which is in stark contrast to the dominant literature concerning African American males and mathematics. Five themes emerged from the data: (a) early educational experiences, (b) recognition of abilities and how it was achieved, (c) support systems, (d) positive mathematical and academic identity, and (e) alternative identities.
Each of 20 high school algebra teachers taught a lesson on direct variation to one first-year algebra class. The students (N=455) had not previously been taught this topic in class. Before the lessons were taught, each teacher was given a list of lesson objectives. Immediately after each lesson, a posttest that focused on the lesson objectives was administered. The teachers were not shown the posttest before they taught their lessons. Correlations were found between the mean posttest scores for the classes and several variables pertaining to teacher discourse.
A substantial amount of research in mathematics education seeks to document disparities in achievement between middle-class White students and students who are Black, Latina/Latino, First Nations, English language learners, or working class. I outline the dangers in maintaining an achievement-gap focus. These dangers include offering little more than a static picture of inequities, supporting deficit thinking and negative narratives about students of color and working-class students, perpetuating the myth that the problem (and therefore solution) is a technical one, and promoting a narrow definition of learning and equity. (Contains 1 footnote.)
Using data from the Longitudinal Study of American Youth (LSAY), we examined the extent to which students' mathematics coursework regulates (influences) the rate of growth in mathematics achievement during middle and high school. Graphical analysis showed that students who started middle school with higher achievement took individual mathematics courses earlier than those with lower achievement. Immediate improvement in mathematics achievement was observed right after taking particular mathematics courses (regular mathematics, prealgebra, algebra I, trigonometry, and calculus). Statistical analysis showed that all mathematics courses added significantly to growth in mathematics achievement, although this added growth varied significantly across students. Regular mathematics courses demonstrated the least regulating power, whereas advanced mathematics courses (trigonometry, precalculus, and calculus) demonstrated the greatest regulating power. Regular mathematics, prealgebra, algebra I, geometry, and trigonometry were important to growth in mathematics achievement even after adjusting for more advanced courses taken later in the sequence of students' mathematics coursework. (Contains 4 tables, 8 figures, and 7 footnotes.)
Materials were written for an entire year's course in geometry in which transformations were used to develop the concepts of congruence, similarity, and symmetry, as well as being a vehicle for proof. This paper presents a study involving 413 students using these materials and 483 control students, comparing performance on standard geometry content and attitudes. Preliminary studies were done on perceptual, arithmetic, and algebraic skills. Student comprehension of transformation-related concepts, the problem of implementation, and attitudes of teachers were informally studied. While the data indicated that the experimental Ss could learn the material, few differences were detected with the measures employed--a significant difference ($p) in favor of the C group was found on the posttest of standard geometry content. Pre- (September) and posttest (June) student attitude data indicated a change in mean score, less positive, for both E and C groups ($p for the C group). Attitude differences between E and C were not significant. Informal feedback from a teacher questionnaire indicated a favorable reaction to the experimental materials.
In this article we describe gender gaps in mathematics achievement and attitude as measured by the U.S. National Assessment of Educational Progress (NAEP) from 1990 to 2003. Analyzing relationships among achievement and mathematical content, student proficiency and percentile levels, race, and socioeconomic status (SES), we found that gender gaps favoring males (1) were generally small but had not diminished across reporting years, (2) were largest in the areas of measurement, number and operations (in Grades 8 and 12) and geometry (in Grade 12), (3) tended to be concentrated at the upper end of the score distributions, and (4) were most consistent for White, high-SES students and non-existent for Black students. In addition, we found that female students' attitudes and self-concepts related to mathematics continued to be more negative than those of male students. (Contains 6 footnotes, 3 figures, and 4 tables.)
This retrospective study examined the impact of prior mathematics achievement on the relationship between high school mathematics curricula and student postsecondary mathematics performance. The sample (N = 4,144 from 266 high schools) was partitioned into 3 strata by ACT mathematics scores. Students completing 3 or more years of a commercially developed curriculum, the University of Chicago School Mathematics Project curriculum, or National Science Foundation-funded curriculum comprised the sample. Of interest were comparisons of the difficulty level and grade in their initial and subsequent college mathematics courses, and the number of mathematics courses completed over 8 semesters of college work. In general, high school curriculum was not differentially related to the pattern of mathematics grades that students earned over time or to the difficulty levels of the students' mathematics course-taking patterns. There also was no relationship between high school curricula and the number of college mathematics courses completed. (Contains 9 tables and 1 footnote.)
The article discusses the ways that less successful mathematics students used graphing software with capabilities similar to a basic graphing calculator to solve algebra problems in context. The study is based on interviewing students who learned algebra for 3 years in an environment where software tools were always present. We found differences between the work of these less successful students and the traditional problem-solving patterns of less successful students. These less successful students used the graphing software to obtain a broader view, to confirm conjectures, and to complete difficult operations. However, they delayed using symbolic formalism, and most of their solution attempts focused on numeric and graphic representations. Their process of reaching a solution was found to be relatively long, and the graphing software tool was often not used at all because it did not support symbolic formulation and manipulations. (Contains 12 figures and 1 table.)
Currently, there are more theories of learning in use in mathematics education research than ever before (Lerman & Tsatsaroni, 2004). Although this is a positive sign for the field, it also has brought with it a set of challenges. In this article, I identify some of these challenges and consider how mathematics education researchers might think about, and work with, the multiple theories available. I present alternatives to views of the competition or supersession of theories and indicate the kinds of discussions that will support effective theory use in mathematics education research. I describe the potential for mathematics education researchers to make informed, justified choices of a theory or theories to address particular research agendas. (Contains 10 footnotes.)
Although students of all levels of education face serious difficulties with proof, there is limited research knowledge about how instruction can help students overcome these difficulties. In this article, we discuss the theoretical foundation and implementation of an instructional sequence that aimed to help students begin to realize the limitations of empirical arguments as methods for validating mathematical generalizations and see an intellectual need to learn about secure methods for validation (i.e., proofs). The development of the instructional sequence was part of a 4-year design experiment that we conducted in an undergraduate mathematics course, prerequisite for admission to an elementary (Grades K-6) teaching certification program. We focus on the implementation of the instructional sequence in the last of 5 research cycles of our design experiment to exemplify our theoretical framework (in which cognitive conflict played a major role) and to discuss the promise of the sequence to support the intended learning goals. (Contains 5 tables, 4 figures, and 15 footnotes.)
In this article, we use data from a large-scale Brazilian national assessment to discuss the relation between reform teaching and equity in mathematics education. We study the dimensionality of teaching style to better qualify what reform teaching means. We then use hierarchical linear models to explore whether reform teaching is associated with student achievement in mathematics and with student socioeconomic status (SES). Our results indicate that reform and traditional teaching are not opposite sides of a one-dimensional axis. They also emphasize both that reform teaching is related to higher school average achievement in mathematics and that the dissemination of reform teaching contributes to minimize the achievement gap between students who attend schools with low average SES and students who attend schools with high average SES. However, our results also show that reform is associated with an increase in within-school inequality in the social distribution of achievement.
This article reports on an investigation of how teachers of geometry perceived an episode of instruction presented to them as a case of engaging students in proving. Confirming what was hypothesized, participants found it remarkable that a teacher would allow a student to make an assumption while proving. But they perceived this episode in various ways, casting the episode as one of as many as 10 different stories. Those different castings of the episode make use of intellectual resources for professional practice that practitioners could use to negotiate the norms of a situation in which they had made a tactical but problematic move. This collection of stories attests to the effectiveness of the technique used for eliciting the rationality of mathematics teaching: By confronting practitioners with episodes of teaching in which some norms have been breached, one can learn about the rationality underlying the norms of customary teaching. ["Seeing a Colleague Encourage a Student to Make an Assumption while Proving: What Teachers Put in Play when Casting an Episode of Instruction" was written with Gloriana Gonzalez.] (Contains 14 footnotes and 3 figures.)
The Mathematics Attitude Inventory, designed to measure the attitudes toward mathematics of secondary students, and its accompanying user's manual, are described. The six scales measure perception of mathematics teachers, value of mathematics, self-concept in mathematics, and anxiety toward, enjoyment of, and motivation in mathematics. (MK)
Response to an earlier article in JRME in which the authors propose a constructivist alternative to the representational view of mind. Argues that the original article misinterprets the postepistemological perspective, confuses ontological and epistemological issues, and mistakes the pragmatic force of the constructivist argument. (45 references) (Author/MKR)
In this experimental study, prospective elementary school teachers enrolled in a mathematics course were randomly assigned to (a) concurrently learn about children's mathematical thinking by watching children on video or working directly with children, (b) concurrently visit elementary school classrooms of conveniently located or specially selected teachers, or (c) a control group. Those who studied children's mathematical thinking while learning mathematics developed more sophisticated beliefs about mathematics, teaching, and learning and improved their mathematical content knowledge more than those who did not. (Contains 5 figures, 6 footnotes and 6 tables. Appended are: IMAP's Seven Beliefs Assessed; and Odds Ratios.)
Remarks adapted from the Presidential Address at the 74th Annual Meeting of the National Council of Teachers of Mathematics in April 1996 charge educators with believing that every student can learn mathematics, every teacher must have adequate support and professional development opportunities, and every parent must have a vested interest in achieving higher standards for mathematics education. (AIM)
Eight sixth-grade students received individualized instruction on the addition and subtraction of fractions in a one-to-one setting for 6 weeks. Instruction was specifically designed to build upon the student's prior knowledge of fractions. It was determined that all students possessed a rich store of prior knowledge about parts of wholes in real world situations based upon whole numbers. Students related fraction symbols and procedures to prior knowledge in ways that were meaningful to them; however, there was a danger of this prior knowledge interfering when it reflected algorithmic procedures rather than fraction ideas in real world situations. (Author/PK)
This article examines a calculus graphing schema and the triad stages of schema development from Action-Process-Object-Schema (APOS) theory. Previously, the authors studied the underlying structures necessary for students to process concepts and enrich their knowledge, thus demonstrating various levels of understanding via the calculus graphing schema. This investigation built on this previous work by focusing on the thematization of the schema with the intent to expose those possible structures acquired at the most sophisticated stages of schema development. Results of the analyses showed that these successful calculus students, who appeared to be operating at varying stages of development of their calculus graphing schemata, illustrated the complexity involved in achieving thematization of the schema, thus demonstrating that thematization was possible.
This article discusses the challenge of improving the interrelationships between research and practice in mathematics education, and it outlines actions being taking to respond to that challenge. The need for improvement is bidirectional. The practice of classroom mathematics teaching needs to be better informed by an understanding of the implications of existing bodies of research, and researchers need to learn more from the insights and knowledge of practitioners. Building on its series of initiatives designed to use research to guide mathematics teaching and learning, NCTM has made a new commitment to a flexible, nimble, and sustainable initiative that will strengthen the bidirectional link between research and practice. This initiative includes the development of Research Analyses, Briefs, and Clips (ABCs), research syntheses designed through collaboration of teacher leaders and researchers to inform instructional leaders and policymakers about research perspectives on critical issues of practice. (Contains 1 figure and 8 footnotes.)
The recent releases of two major international comparative studies that addressed mathematics--the Trends in International Mathematics and Science Study 2003 (TIMSS 2003) and the Program for International Student Assessment 2003 (PISA 2003)--provide opportunities and challenges for mathematics education researchers interested in using the findings, instruments, and conceptual and theoretical perspectives of these studies as catalysts for secondary analysis and additional research. In particular, a number of important questions in mathematics education in the United States can be pursued, using various resources from these studies as a base, by mathematics education researchers and mathematicians collaborating with statisticians and assessment experts. We highlight some of the main findings of TIMSS 2003 and PISA 2003, and suggest how some of the instruments that were used in these studies, as well as the conceptual frameworks and priorities that guided them, might be beneficial in pursuing pressing questions in such areas as the role of curriculum in mathematics performance, the ways in which social contextual variables interact with mathematics learning, and the challenges in measuring the ability to use mathematics in real-world situations.
Presents remarks from the Presidential Address at the 75th Annual Meeting of the National Council of Teachers of Mathematics held in Minneapolis in April, 1997. Two major challenges addressed were the need to change classroom practice and the need to rethink the definition of "basic". (AIM)
This case-study research investigated changing teacher roles associated with two teachers' use of innovative mathematics materials at Grade 6. Using daily participant observation and regular interviews with the teachers and the project staff member responsible for providing in-school support, a picture emerged of changing teacher roles and of those factors influencing the process of change. One teacher demonstrated little change in either espoused beliefs or observed practice over the course of the study. The second teacher demonstrated increasing comfort with posing nonroutine problems to students and allowing them to struggle together toward a solution, without suggesting procedures by which the problems could be solved. He also increasingly provided structured opportunities for students' reflection on activities and learning. Major influences on this teacher's professional growth appeared to be the provision of the innovative materials and the daily opportunity to reflect on classroom events in conversations and interviews with the researcher.
The major objective of this study was to investigate differential performances among 5-year-old children when using transitivity of matching relations. Instruments were constructed to measure the subjects' (1) knowledge of matching relations, (2) ability to conserve the relations, and (3) proficiency in making inferences using the transitive property of the relations. Three specially designed tests, administered individually to 21 boys and 21 girls, assessed knowledge of relational terminology, level of conservation and performance on manipulative tasks (matching, comparing, judging quantitative relations among objects). A surprising result of this investigation was that subjects in the high category of conservation did not perform significantly better on transitivity than subjects in the low category of conservation for each relation. In general, differential performance on transitivity between equivalence and order relational groups occurred only within the high conservation level. An extensive comparison is made between present results and Smedslund's (1963a) data for conservation and transitivity of discontinuous quantity. (WY)
Twelve middle school students working in pairs used a computer microworld to explore an introductory curriculum in transformation geometry. The microworld linked a symbolic representation (a set of simple Logo commands) with a visual display that showed the effects of each transformation. Worksheets were designed with the objective of encouraging the students to find and express mathematical patterns in the domain. The students were successful in constructing an accurate working understanding of the transformations. There was a tendency for symbolic overgeneralization in some activities, but the students were able to use visual feedback from the microworld and discussions with their partners to correct their own errors.
The study investigated the strategies that 7- to 12-year-old children spontaneously apply to the solution of novel combinatorial problems. The children were individually administered a set of six problems involving the dressing of toy bears in all possible combinations of tops and pants (twodimensional) or tops, pants, and tennis rackets (three-dimensional). Two sets of solution procedures were identified, each comprising a series of five increasingly complex strategies ranging from trial-and-error approaches to sophisticated odometer procedures. Results suggested that experience with the two-dimensional problems enabled children to adopt and subsequently transform their efficient 2-D odometer strategy (where one item is held
constant) into the most sophisticated 3-D odometer strategy, which involved working simultaneously with two constant items. The study highlights the importance of discrete mathematics as a source of problem-solving activities in which children are motivated to create, modify, and extend their own theories.
In this study, a researcher-teacher examined seventh-graders' experiences with a problem-centered curriculum and pedagogy. Analyses of interviews, surveys, teaching journal entries, and audio recordings focused on differences between lower- and higher-socioeconomic status (SES) students' reactions to learning mathematics through problem solving. While higher-SES students displayed confidence and solved problems with an eye toward the intended mathematical ideas, the lower-SES students preferred more external direction and sometimes approached problems in a way that allowed them to miss their intended mathematical point. The lower-SES students more often became "stuck" in the open and contextualized nature of the problems. An examination of sociological literature revealed ways in which these patterns in the data could be related to more than individual differences in temperament or achievement between the children. This study suggests that class cultural differences could relate to students' approaches to learning mathematics through solving open, contextualized problems. This paper discusses equity-related challenges to be faced as well as interventions that could be helpful in our attempts to center mathematics instruction around problem solving. Contains 32 references. (Author)
The purpose of this study was to compare the classroom processes of girls and boys who differed in confidence in their ability to learn mathematics. The students were observed daily during their seventh-grade mathematics classes for 3 to 4 weeks. All 93 students observed (i.e., the target students) scored at or above the mean on a standardized test of mathematics achievement. Trained observers recorded characteristics of each verbal interaction between a target student and the teacher and the amount of time each target student spent on task in mathematics. Boys were involved in more public interactions with their teacher than girls were. High- and low-confidence students differed very little in their interactions with the teacher. Differences between boys and girls in their interactions with the teacher varied from classroom to classroom.
This article reports on models of teaching that developed as outgrowths of a study of middle-grades mathematics classes. Grounded theory methodology and sociolinguistic tools were used to move from classroom observations and interviews to line-by-line coding of classroom discourse, to mapping the flow of talk and verbal assessment moves, to a multilevel analysis of the relationships of forms of talk and verbal assessment, and, ultimately, to models of teaching that promote discourse on a continuum from univocal (conveying meaning) to dialogic (constructing meaning through dialogue). Three specific cases are highlighted that represent deductive (associated with univocal), inductive (associated with dialogic), and mixed (a hybrid of deductive and inductive) models of teaching. Teaching practices associated with each model are illustrated and discussed.
Examines the changes that have been evolving in teaching and learning practices in mathematics classrooms by reflecting on issues in the past and present. Discusses what should be done in order to prepare students for the future. Contains 16 references. (ASK)
This article considers the question of what specific actions a teacher might take to create a culture of inquiry in a secondary school mathematics classroom. Sociocultural theories of learning provide the framework for examining teaching and learning practices in a single classroom over a two-year period. The notion of the zone of proximal development (ZPD) is invoked as a fundamental framework for explaining learning as increasing participation in a community of practice characterized by mathematical inquiry. The analysis draws on classroom observation and interviews with students and the teacher to show how the teacher established norms and practices that emphasized mathematical sense-making and justification of ideas and arguments and to illustrate the learning practices that students developed in response to these expectations.
Mathematics teachers' selection and implementation of instructional tasks were analyzed before, during, and after their participation in a professional development initiative that focused on selecting and enacting cognitively challenging mathematical tasks. Data collected from 18 secondary mathematics teacher participants included tasks and student work from teachers' classrooms, lesson observations, and interviews. Ten secondary mathematics teachers who did not participate in the professional development initiative served as the contrast group and participated in 1 lesson observation each. Analysis of the data indicated that, following their participation in the professional development initiative, project teachers more frequently selected high-level tasks as the main instructional tasks in their classrooms and had improved the maintenance of high-level cognitive demands. Significant differences existed between project teachers and the contrast group in task selection and implementation. These differences were not influenced by the use of Standards-based or conventional curricula in project teachers' classrooms. (Contains 1 footnote, 8 tables, and 3 figures.)
This study investigated introductory calculus students' spontaneous reasoning about limit concepts guided by an interactionist theory of metaphorical reasoning developed by Max Black. In this perspective, strong metaphors are ontologically creative by virtue of their emphasis (commitment by the producer) and resonance (support for high degrees of elaborative implication). Analysis of 120 students' written and verbal descriptions of their thinking about challenging limit concepts resulted in the characterization of 5 clusters of strong metaphors. These clusters were based on the objects, relationships, and logic related to intuitions about (a) a collapse in dimension, (b) approximation and error analyses, (c) proximity in a space of point-locations, (d) a small physical scale beyond which nothing exists, and (e) the treatment of infinity as a number. Students' reasoning with these metaphors had significant implications for the images they formed and the claims and justifications they provided about multiple limit concepts. (Contains 4 tables and 1 figure.)