8.1.7: Issues in the U.S. Education System
-
- Last updated
- Save as PDF
- Boundless
- Boundless
Unequal Access to Education
Access to education varies by geographic location, race, gender, and class.
Learning Objectives
Describe the upsides and downsides to the current educational system in the U.S.
Key Points
- In the United States, as in most countries, people with more education tend to enjoy higher economic status, power, prestige, and levels of income.
- Dropout rates are higher in certain locations and among minorities.
- In some areas, the best high schools are private high schools that may be out of reach for poorer students who cannot afford the tuition.
- U.S. public schools lag behind the schools of other developed countries in the areas of reading, math, and science.
Key Terms
- dropout rates : Dropout rates are a measurement of the proportion of students who drop out, that is, who leave a school for practical reasons, necessities, or disillusionment with the system from which the individual in question leaves.
- minority : Categories of persons who hold few or no positions of social power in a given society.
In the United States, as in most countries, people with more education tend to enjoy higher economic status, power, prestige, and levels of income. One might expect, then, that all people would try to maximize their education. After all, education is meant to be the great equalizer by which anyone can climb the rungs of the social hierarchy. However, evidence suggests that certain groups have unequal access to education.
In the United States, public schools provide free education through 12 th grade, but post-secondary college education is not free. Costs include tuition and room and board, even at public institutions. Those who are unable to afford the expense of college, therefore, have unequal access. According to a 2005 report from the OECD, the United States is tied for first place with Switzerland when it comes to annual spending per student on its public schools, with each of those two countries spending more than $11,000. However, the United States is ranked 37 th in the world in education spending as a percentage of gross domestic product. All but seven of the leading countries are in the third world, ranked high because of a low GDP. U.S. public schools lag behind the schools of other developed countries in the areas of reading, math, and science.
Even in high school, economic, family, and social demands may lead some students to drop out before finishing. Thus, sociologists have observed that dropout rates vary among different social groups. For instance, dropout rates are lowest among Asian Americans, followed closely by whites. But Hispanic, black, and Native American students drop out at rates nearly double those of Asian and white students. Overall, the dropout rate has been declining for decades, since at least the 1970s, yet it remains disproportionately high for minority students.
School funding varies by geographic location. In part, the disparities in dropout rates may be a symptom of disparities in access to high quality education. In some areas, the best high schools are private high schools that may be out of reach for poorer students who cannot afford the tuition. Even public schools may receive different rates of funding; in particular, schools in poorer areas tend to receive less funding because school funding is often tied to property taxes. Thus, students who live in poorer areas may have less access to high quality education. One of the biggest debates in funding public schools is funding by local taxes or state taxes. The federal government supplies around 8.5% of the public school system funds, according to a 2005 report by the National Center for Education Statistics. The remaining split between state and local governments averages 48.7% from states and 42.8% from local sources. However, the division varies widely. In Hawaii local funds make up 1.7%, while state sources account for nearly 90.1%.
English as a Second Language
English as a second language (ESL) refers to the use or study of English by speakers with different native languages.
Learning Objectives
Describe some of the difficulties and challenges facing ELL students in the U.S.
Key Points
- English language learners (ELL) must learn to speak and write English in addition to learning substantive content in schools.
- ELL students are often tracked with lower ability students because they have lower standardized test scores, which may inaccurately measure their academic ability.
- ELL students are more likely to drop out. In the U.S., schools may let ELL and other low-scoring students drop out in order to raise average test scores.
- ELL students may have trouble earning the English credits necessary to be accepted into college.
- On average, ELL students come from poorer families than native speakers, which presents an additional barrier to college.
- ESL programs may help ELL students form friendships and encourage social interaction, tolerance, and multicultural values.
- ESL programs may help ELL students form friendships and encourage social interaction, tolerance, and multicultural values.
Key Terms
- tolerance : The ability or practice of tolerating; an acceptance or patience with the beliefs, opinions or practices of others; a lack of bigotry.
- native speaker : A person who grew up with a particular language as their mother tongue.
- Standardized Test Scores : A standardized test is a test that is administered and scored in a consistent, or “standard”, manner.
English as a second language (ESL), English for speakers of other languages (ESOL) and English as a foreign language (EFL) all refer to the use or study of English by speakers with different native languages. Generally, English Language Learners (ELL) are refugees, immigrants, or their children. They must learn English as a Second Language (ESL) in order to function in their new host country. In the U.S. over the last twenty years, more than 70% of non-English-speaking school-age immigrants have arrived in the U.S. before they were 6 years old. At this age, they could have been taught English in school, and achieved a proficiency indistinguishable from a native speaker. In other countries, such as the Russia, France, Spain, and Germany this approach has dramatically improved reading and math test scores for linguistic minorities. Supporters of ESL programs claim they play an important role in the formation of peer networks and adjustment to school and society in their new homes. Having class among other students learning English as a second language relieves the pressure of making mistakes when speaking in class or to peers. ESL programs also allow students to meet and form friendships with other non-native speakers from different cultures, promoting racial tolerance and multiculturalism.
Potential Academic Barriers for ELL Students
Nevertheless, ELL students face predictable difficulties in learning English. Those whose native languages are drastically different from English may find it especially difficult to learn the sounds and grammar of English, while others whose native languages are more similar may have less trouble. But these students also face difficulties unrelated to learning the language itself, including the possibility of having their abilities underestimated, a higher probability of dropping out, difficulty paying for and succeeding in college, and social problems connecting with native speakers. ELL students are often tracked with lower ability students because they have lower standardized test scores, which may inaccurately measure their academic ability.
ELL students are also more likely to drop out of high school. Their higher dropout rates may be due to difficulties in keeping up in mainstream classes or to prior interruptions in their formal education. For example, some ELL students may have spent time in refugee camps where they had no opportunity to attend school. Further, some have speculated that school administrators may actually encourage ELL students to drop out because it may increase the school’s overall average test scores, which may in turn benefit the school (e.g., by ensuring continued funding).
ELL students face additional barriers to pursuing higher education. Most colleges and universities require four years of English in high school, but many will accept only one year of ESL English. ELL students who arrive in the United States relatively late may find it difficult to meet this requirement because they must spend a longer time in ESL English classes in high school, or because they might not arrive early enough to complete four years of English in high school. Consequently, some ELL students lack the required credits to apply for college.
ELL students can also face financial barriers to higher education. Those who do not place high enough on college placement exams often have to enroll in ESL courses at their universities. Often, they must pay fees for these courses in addition to tuition, and these courses may not count as credit towards graduation. These additional fees add to the financial burden faced by ELL students who often come from families of lower socioeconomic status. The latest statistics show that the median household income for school-age ELL students is $36,691 while that of non-ELL students is $60,280.
ELL students often have difficulty interacting with native speakers. ELL students may avoid interactions with native speakers because they are frustrated with or embarrassed by their English ability. Immigrant students often also lack knowledge about popular U.S. culture, which limits their conversations with native speakers to academic topics. In classroom group activities with native speakers, ELL students often do not participate, again because of embarrassment of their English, but also because of cultural differences which value silence and individual work at school over social interaction and talking in class. These interactions have been found to extend to teacher-student interactions as well. In most mainstream classrooms, teacher-led discussion is the most common form of lesson. In this setting, ELL students will fail to participate, and often have difficulty understanding teachers because they talk too fast, do not use visual aids, or use native colloquialisms. ELL students also have trouble getting involved with extracurricular activities with native speakers for similar reasons. Students fail to join extra-curricular activities because of the language barrier, cultural emphasis of academics over other activities, or failure to understand traditional pastimes in their new country.
High School Dropouts
While education can improve life chances, not everyone has equal access to education.
Learning Objectives
Recall some of the reasons why students in the U.S. may drop out of high school and the potential consequences of dropping out
Key Points
- The more education people have, the higher their income, the better their life chances, and the higher their standard of living.
- Dropout rates also vary geographically, with the lowest rates in northern states.
- The relationships students have with their peers also influence a student’s likelihood of dropping out.
Key Terms
- Academic Risk Factors : Academic risk factors refer to the performance of students in school and are highly related to school-level problems. These factors include absenteeism, grade retention, special education placement, low performance and grades, and low educational expectations.
- life chances : Life chances (Lebenschancen in German) is a political theory of the opportunities each individual has to improve his or her quality of life. The concept was introduced by German sociologist Max Weber. It is a probabilistic concept, describing how likely it is, given certain factors, that an individual’s life will turn out a certain way.
Life Chances
The more education people have, the higher their income, the better their life chances, and the higher their standard of living. In general, people with more education tend to earn higher incomes and enjoy a higher standard of living. High school dropouts are much less likely to be employed than those with high school and college degrees. Even earning a four-year degree can raise average weekly income by nearly $400.
Max Weber used the concept of “life chances” to express an individual’s access to employment opportunities and other resources. In part, life chances are determined by birth. An individual born into a wealthy family will have higher life chances than average because they will have access to greater opportunities from the moment they are born.
Education also offers a means to improve one’s life chances by improving employment opportunities and making social connections. Thus, the consequences to dropping out can be high, as they significantly decrease the opportunity to improve one’s life chances. In addition to personal costs, dropping out has social costs. Dropouts have a greater likelihood of being arrested. Ultimately, this can lower the average standard of living for society as a whole. According to estimates, the average high school dropout will cost the government over $292,000.
Academic Risk Factors
Not all students have an equal risk of dropping out. Students at risk for dropout based on academic risk factors are those who often have a history of absenteeism and grade retention, academic trouble, and more general disengagement from school life. Students may also be at risk for dropout based on social risk factors. Members of racial and ethnic minority groups drop out at higher rates than white students, as do those from low-income families, from single-parent households, and from families in which one or both parents also did not complete high school. Dropout rates also vary geographically, with the lowest rates in northern states. The highest dropout rates occur in the south and southwestern United States.
Why else might students drop out? Sociologists tend to group dropout risk factors into different categories, including academic risk factors and school-level risk factors. Academic risk factors relate to the performance of students in school. School structure, curriculum, and size may increase the exposure of students to academic risk factors. For example, students are more likely to drop out when they attend schools with less rigorous curriculum, when they attend large schools, or when they attend schools with poor student-teacher interactions.
The relationships students have with their peers also influence a student’s likelihood of dropping out. Students who build relationships with anti-social peers or who have deviant friends were more likely to drop out of school early regardless of their achievement in school. Relationships with parents can also influence a student’s decision to stay in school. The better the relationship, as demonstrated through positive interaction and parental involvement, the more likely the student will stay in school. If a student does not have a good relationship with her parents, the student is more likely to drop out even if she has good grades and good behavior.
Students who drop out of school may identify different motivations, including uninteresting classes (a lack of engagement with school life and classes), feeling unmotivated (especially by teachers who did not demand enough or were not inspirational), personal reasons (had to get a job, became a parent, had to support or care for a family member), and academic challenges (felt like they could not keep up, felt unprepared for high school, had to repeat a grade, or graduation requirements seemed out of reach).
Finally, some education researchers have noted that dropout rates may have been exacerbated by policies such as the U.S. No Child Left Behind Act that required schools to use high-stakes standardized testing as an accountability measure. These policies may have inadvertently encouraged students to drop out of high school, since teachers and administrators utilize grade retention as a strategy to improve test scores and ensure positive ratings for the school. As mentioned above, grade retention increases the likelihood that a student will drop out of school.
Violence in Schools
School violence is a serious problem in the United States, and attempts to explain it identify both individual and social risk factors.
Learning Objectives
Recall the risk factors for school violence in the U:S. and the two types of bullying
Key Points
- Individual risk factors for school violence include a tendency to externalize problems, or act out, as well as developmental delays, low IQ, and reading problems.
- Social risk factors for school violence include an unstable home environment, violent neighborhoods, and certain characteristics of a school environment.
- A neighborhood environment may contribute to school violence when a community ‘s high rates of crime or drug use spills over into the classroom.
- Bullying may be committed by one student or a group of students.
- Physical bullying is the most easily identified and includes unwanted physical contact such as pushing, kicking, and tickling. It may also include the use of weapons.
- Verbal bullying is any slanderous statements or accusations that cause the victim undue emotional distress, such as insulting someone’s appearance, laughing at someone, or directing foul language toward someone.
- Emotionally bullying is any form of bullying that damages a victim’s emotional well-being, such as spreading malicious rumors, giving someone the silent treatment, or harassment.
Key Terms
- School Violence : School violence is widely considered to have become a serious problem in recent decades in many countries, particularly violence involving weapons. This includes violence between school students as well as physical attacks by students on school staff.
- bullying : an act of physically or emotionally intimidating a weaker person to do something, especially through repeated coercion
School violence is a serious problem in the United States. This refers to violence between students as well as physical attacks by students on school staff. In 2007, a nationwide survey conducted by the Centers of Disease Control and Prevention found that, during the 30 days before they took the survey, 5.9% of students had carried a weapon to school, and 5.5% of students had skipped school because they did not feel safe. In the 12 months before they took the survey, 12.4% of students had been in a physical fight on school property at least once. Between 1996 and 2003, at least 46 individuals were killed in 27 school incidents involving the use of firearms.
While these numbers are alarming, data also shows that most crimes at school are not violent. In 2001, students between the ages of 12 and 18 were the victims of two million crimes at school, but 62% of those crimes were thefts. In part, violence receives more attention because it draws media coverage. For example, school shootings account for less than 1% of violent crimes in public schools, yet nearly every school shooting makes national headlines. Nevertheless, because school violence can have such serious consequences, educators and policymakers take the issue very seriously.
Explanations of School Violence
Attempts to explain school violence have identified several individual and social risk factors. Individual risk factors include a tendency to externalize problems, or “act out,” as well as developmental delays, low IQ, and reading problems. Social risk factors include an unstable home environment, violent neighborhoods, and certain characteristics of a school environment. A home environment may contribute to school violence if, at home, students are exposed to gun violence, parental alcoholism, domestic violence, physical abuse, sexual abuse, or harsh parental discipline. All of these may teach children that criminal and violent activities are acceptable and may increase a child’s tendency to respond to frustration with aggression. A neighborhood environment may contribute to school violence if a community has high rates of crime or drug use. A neighborhood may also expose students to deviant peers or to gangs who contribute to violence inside schools. Finally, school violence tends to be higher in certain types of schools, the characteristics of which are listed below:
- a large male population
- higher grade levels
- a history of disciplinary problems
- a high student-to-teacher ratio
- urban location
Prevention and intervention strategies may target individual students, families, the school community, or society in general. Individual-level strategies target at-risk or aggressive students and teach these students conflict resolution, problem solving, and social skills. Family-based solutions attempt to improve family relationships in order to improve students’ experiences while they are at home. School-wide strategies are designed to modify school characteristics associated with violence. Examples of this would be classroom practices that encourage student cooperation and close interaction with teachers, or the presence of police and law enforcement in schools to discourage violence. Finally, society-level prevention strategies attempt to change social and cultural conditions in order to reduce violence, regardless of where it occurs. For example, society-level strategies might try to reduce the violence portrayed in movies or music.
Bullying
In recent years, one particular type of school violence, bullying, has garnered special attention. Bullying can be committed by one student or a group of students. Typically, a group of bullies takes advantage of, or isolates, one student in particular and gains the loyalty of bystanders who, in many cases, want to avoid becoming victims themselves. Bullies typically taunt and tease their target before physically bullying their target. The targets of bullying are often students who are considered strange or different by their peers to begin with, making the situation harder for them to deal with.
Bullying is a common occurrence in most schools. According to the American Psychological Association, “approximately 40% to 80% of school-age children experience bullying at some point during their school careers. ” Bullying can be physical, verbal, and emotional. Physical bullying is the most easily identified and includes unwanted physical contact such as pushing, kicking, tickling, or the like, and may also include the use of weapons. Verbal bullying is any slanderous statements or accusations that cause the victim undue emotional distress. This can include insulting someone’s appearance, laughing at someone, or directing foul language toward someone. Emotionally bullying is any form of bullying that damages a victim’s emotional well-being, such as spreading malicious rumors, giving someone the silent treatment, or harassment. Bullying can also take place over the internet with text messaging. This “cyber-bullying” is particularly pernicious because it can be done anonymously, without detection by parents or authorities.
Homeschooling
Homeschooling is the education of children at home rather than in the setting of a school.
Learning Objectives
Sketch generally the different regulations regarding homeschooling which can be found in the United States
Key Points
- Motivations for home schooling vary, but may include dissatisfaction with the school environment, religious or moral reasons, or dissatisfaction with the quality of academic instruction provided in local schools.
- The legal status of home schooling varies by states, but in all cases, homeschooled students must meet certain requirements and are subject to certain assessments to ensure the quality of education.
- Homeschooled students have varying access to resources, including extracurricular activities.
Key Terms
- home schooling : Homeschooling or home school (also called home education or home-based learning) is the education of children at home, typically by parents but sometimes by tutors, rather than in other formal settings of public or private school.
Homeschooling is the education of children at home, typically by parents but sometimes by tutors, rather than in other formal settings of public or private school. In the United States, about 2.9% of students, or about 1.5 million children, are homeschooled. Most homeschooled children are homeschooled only, but about one in five are also enrolled in public or private schools, which they may attend for 25 hours or less each week. By enrolling part-time at a school, homeschooled students can study subjects such as foreign languages and sciences, which may be more difficult to teach at home. They may also be eligible to participate in academic and athletic extracurricular activities.
Motivations for homeschooling vary, but may include dissatisfaction with the school environment, religious or moral reasons, or dissatisfaction with the quality of academic instruction provided in local schools. Surveys suggest that the most common motivations for homeschooling are concern about the school environment (e.g., safety, drugs, or negative peer pressure), a desire to provide religious or moral instruction, and dissatisfaction with academic instruction at other schools. Parents may also choose to homeschool children with special needs that the parent feels the school cannot or will not meet. Other, less common motivations include concerns about family time, finances, travel, and distance.
In the United States education is compulsory. Every state has some form of a compulsory attendance law that requires children in a certain age range to spend a specific amount of time being educated. The most common way for parents to meet these requirements is to have their children attend public school. However, parents have always had some degree of choice in where and how children are educated. Thus, the legality of homeschooling has been debated, and that debate has focused largely on whether it is legal for parents to withhold children from school and educate them in a home setting. Since the 1980s, the focus of the debate has shifted to questions about the distribution of resources and state control over homeschooling. The legality of homeschooling is generally accepted, but debate continues over whether homeschooling communities can access state school funds, facilities, and resources and whether the state can regulate areas like curricula and standardized testing.
Today, homeschooling is legal in all 50 states, although it is regulated in different ways by each state. Homeschooling laws can be divided into three categories. First, in some states, homeschooling is treated like a type of private school. In these states, homeschools are generally required to comply with the same laws that apply to other schools. Homeschools in California, Indiana, and Texas, for example, fall into this category. In other states, the requirements for homeschooling are set by the particular parameters of the compulsory attendance statute. These states’ compulsory attendance laws do not make any specific reference to “homeschooling. ” Homeschools in New Jersey, Maryland, for example, fall into this category. Third, in other states homeschool requirements are based on a statute or group of statutes that specifically applies to homeschooling. In these states, the requirements for homeschooling are set out in the relevant statutes. Often, these statutes refer to homeschooling by another name. For example, in Virginia it is “home instruction,” in South Dakota it is “alternative instruction,” and in Iowa it is “competent private instruction. ”
States also differ in the level of resources they make available to homeschooled students. A minority of states require public schools to give homeschooled students access to district resources, such as school libraries, computer labs, extracurricular activities, or even academic courses. In some communities, homeschoolers may meet with a teacher periodically for curriculum review and suggestions. Other states give districts the option of giving homeschooled students access to such resources.
Access to interscholastic athletic competition varies from state to state. Some state athletic associations ban homeschoolers from interscholastic competition, both by prohibiting homeschoolers to compete for a state federation member school as well as by prohibiting member schools to compete against independent teams made up of homeschoolers. In such states, homeschoolers may only compete amongst other homeschoolers or against schools that are not members of the state’s interscholastic athletic federation. Other states allow homeschoolers to compete for the public schools that they would otherwise attend by virtue of their residence. Still other state interscholastic athletic associations allow homeschoolers to organize teams that compete against other established schools, but do not allow homeschoolers to compete on established school teams.
Standardized Tests
A standardized test is a test that is administered and scored in a consistent manner.
Learning Objectives
Argue for or against standardized testing based on the key points attributed to proponents and critics in the text
Key Points
- Standardized tests are one common method by which schools measure students’ academic achievement, and they may also be used to measure students’ progress and teachers’ effectiveness, or in order to assess whether students are ready to progress to the next stage in their education.
- One of the main advantages of standardized testing is that the results can be empirically documented.
- Critics point out that standardized tests actually evaluate three things: what students learn in school, what they learn outside of school, and their innate intelligence.
- Critics worry that standardized tests lead teachers to “teach to the test”.
- Testing bias occurs when a test systematically favors one group over another, even though both groups may be equal on the trait the test measures.
- No Child Left Behind required that states assess educational achievement and allocate resources using standardized tests.
- Testing bias occurs when a test systematically favors one group over another, even though both groups are equal on the trait the test measures.
Key Terms
- standardized tests : A standardized test is a test that is administered and scored in a consistent, or “standard”, manner.
- No Child Left Behind : The No Child Left Behind Act of 2001 (NCLB) is a United States Act of Congress that came about as wide public concern about the state of education. NCLB is a reauthorization of the Elementary and Secondary Education Act, which included Title I, the government’s flagship aid program for disadvantaged students. NCLB supports standards-based education reform based on the premise that setting high standards and establishing measurable goals can improve individual outcomes in education.
- Testing Bias : Testing bias occurs when a test systematically favors one group over another, even though both groups are equal on the trait the test measures.
Standardized tests are one common method by which schools measures students’ academic achievement. These tests may be given periodically and repeatedly to measure students’ progress and teachers’ effectiveness, or they may be given at key points during students’ careers to assess whether they are ready to progress to the next stage in their education—often, the next grade level or college. A standardized test is a test that is administered and scored in a consistent manner. They are designed so that the questions, conditions for administering, scoring procedures, and interpretations are purportedly without bias.
Proponents of Standardized Tests
One of the main advantages of standardized testing is that the results can be empirically documented; the test scores can be shown to have a relative degree of validity and reliability, being generalizable and replicable. Standardized tests allow educators, policymakers, and admissions committees easily and fairly compare results from different students. It may be difficult to account for differences in educational culture across schools, difficulty of a given teacher’s curriculum, differences in teaching style, and techniques and biases that affect grading. This makes standardized tests useful for admissions purposes in higher education, where a school is trying to compare students from across the nation or across the world.
Opponents of Standardized Tests
Critics worry that standardized tests lead teachers to “teach to the test. ” Standardized tests can be useful tools for assessing student achievement, and they can be used to focus instruction on desired outcomes, such as reading and math skills. However, critics feel that overuse and misuse of these tests harms teaching and learning by narrowing the curriculum. While it is possible to use a standardized test without letting its contents determine curriculum and instruction, frequently what is not tested is not taught, and how the subject is tested often becomes a model for how to teach the subject.
Further, standardized tests tend to measure only one sort of knowledge, while discounting creativity and diverse modes of expression. In essence, standardized tests use a one-size-fits-all theory, which is not always an effective way to measure students’ knowledge and comprehension. Students who fail standardized tests may be diagnosed with learning disabilities or disorders instead of recognized for the skills they have, which are consequently left unchallenged and undeveloped.
Finally, critics have expressed concern that standardized tests may create testing bias. Testing bias occurs when a test systematically favors one group over another, even though both groups are equal on the trait the test measures. Critics allege that test makers and facilitators tend to represent a middle class, white background and standardized testing matches the values, habits, and language of the test makers. Students who share that background may have an advantage on standardized tests that has nothing to do with academic achievement or aptitude but is due to shared cultural background.
No Child Left Behind
In 2001, the United States passed the No Child Left Behind Act, which requires all states to test students in public schools statewide to ensure that they are achieving the desired level of minimum education. Although some states already had statewide standardized testing requirements, for many states, this act required them to create new systems. The act reinvigorated debate over the accuracy, efficacy, and justice of relying on standardized tests to measure student achievement.
However, critics charge that standardized tests have become a mandatory curriculum placed into schools without public debate and without any accountability measures of its own. Many feel this ignores basic democratic principles in that control of schools’ curricula is removed from local school boards, which are the nominal curricular authority in the U.S.
The act is especially controversial because it ties funding to standardized test schools. Under the act, students and schools must demonstrate “adequate yearly progress. ” That is, they must show some improvement every year. When a student fails to make adequate yearly progress, schools must provide tutoring or other interventions to help the student improve. When schools fail to show adequate yearly progress, they may lose funding or be taken over by the school board or state.
GED, SAT and ACT
In many places the United States, standardized tests are also used as a graduation requirement. Students must pass a standardized test in order to graduate from high school. The General Educational Development (GED) test, is often used as an alternative to a high school diploma. During high school, students may also take standardized tests as a requirement for applying to college. The most common standardized tests for applying to college are the SAT and ACT.
Gender Bias in the Classroom
Gender-based achievement gaps suggest the existence of gender bias in the classroom.
Learning Objectives
Analyze both the possible root causes of gender-based achievement gaps and its proposed solutions
Key Points
- Boys outscore girls on most high-stakes tests, including both the math and verbal sections of the SAT.
- Girls may receive negative attention bias from teachers, though much of it may be unintentional.
- Teachers may reinforce gender bias when they give more attention to boys or excuse boys’ behavior with the excuse that “boys will be boys.”
- Single-sex classrooms have been proposed as a solution to gender bias.
- Despite evidence of gender bias, girls outperform boys in reading and writing and have made steady gains in career access.
Key Terms
- The SAT : SAT Reasoning Test (formerly Scholastic Aptitude Test and Scholastic Assessment Test): a national exam taken annually by high school juniors and seniors.
- achievement gap : The observed and persistent disparity between the performance of groups of students defined by gender, race/ethnicity and socioeconomic status, based on a number of educational measures.
- gender bias : A prejudicial stance towards males or females
Gender-based achievement gaps (especially in math and science ) suggest the existence of gender bias in the classroom.
Although most people would like to believe gender bias in the classroom is no longer a problem, evidence points to a persistent achievement gap between boys and girls. Although girls tend to stay in school longer, have better attendance records, and earn better report card grades, boys outscore girls on most high-stakes tests, including both the math and verbal sections of the SAT. Men also outscore women on standardized tests for graduate school, law school, and medical school.
Dissecting Classroom Gender Bias
If test score gaps are evidence of gender bias, where does that gender bias come from? Numerous explanations have been proposed:
- Women and girls may choose to take fewer advanced math or science courses, or they may be discouraged from doing so.
- Cultural norms could influence girls to prepare for their expected role of keeping a home and nurturing children, though such norms are less stringently enforced than in the past.
- Teachers may interact with boys and girls in ways that reinforce gender roles and gender inequality.
Of course, few teachers would admit to bringing gender bias into the classroom, and much of their influence may be unintentional. Nevertheless, teachers may reinforce gender bias when they give more attention to boys or excuse boys’ behavior with the excuse that “boys will be boys. ” Teachers may also reinforce gender bias simply by drawing distinctions between boys and girls. For example, lining up students or seating them by gender affirms the idea that boys and girls should be treated differently. Teachers may also influence students by the way they give praise, encourage a student to correct or expand an answer, criticize, or accept without evaluating a response. Research suggests teachers are more likely to respond to boys with praise or encouragement, whereas they are more likely to respond to girls by simply accepting or acknowledging a response without evaluating it. Because girls are typically socialized to be quiet and passive, teachers may need to actively encourage their participation in class in order to avoid boy-dominated discussion, or a situation in which boys receive more feedback from and interaction with teachers because they more actively participate in class.
One proposed solution to gender bias in the classroom is to separate boys and girls in single-sex classrooms. Theoretically, single-sex classrooms would help students focus without distracting interactions with children of the opposite gender. They could also decrease pressure on girls who feel nervous participating in boy-dominated class discussion. However, empirical studies give mixed evidence as to the efficacy of single-sex schooling, and critics worry that it constitutes a separate-but-equal form of discrimination.
Career Access
Despite evidence of gender bias, female career access has made steady gains in recent years, due largely to the women’s rights movement. More women are now able to work outside the home; although some may be driven to work not as an expression of liberty or equality, but out of economic necessity. Still, women earn only about 75 cents for every dollar earned by men, and many work in low status, sex-stereotyped occupations. In part, that may be due to the college majors women choose. But why, one might ask, would women be more likely to choose college majors that will not benefit them in careers? Sociologists would point to social influences and cultural expectations.
The “Boy Code”
Further, though most research and debate about gender bias in the classroom focuses on bias against girls, recent evidence suggests that boys may be falling behind girls, especially in literacy. In fact, the latest national test scores, collected by the National Assessment of Educational Progress, show that girls have met or exceeded the reading performance of boys at all age levels; by fourth grade, boys have fallen two years behind girls in their reading and writing skills. The male literacy gap has been attributed to sex-based differences in brain function as well as to social factors like the expectations set by an unwritten “boy code” to discourages boys from expressing emotions. This boy code may make male students less likely to share opinions about literature or express frustrations or difficulties to teachers. Thus, just as social pressures may convince some girls they cannot excel at science or math, social pressures may convince some boys they cannot succeed in reading and writing.
The gendering of school subjects may, in itself, lead to gender bias in the classroom, and, further down the line, gender inequality in the workforce.
The Gifted
There is no standard definition of “gifted,” nor a standard way of implementing gifted education.
Learning Objectives
List the various forms of education for the gifted and the controversies around gifted education
Key Points
- Common forms of education for the gifted have included acceleration, pull-out, cluster grouping and summer enrichment.
- According to the 1972 Marland Report, gifted youth are more likely than average to experience academic failure and develop social and emotional problems.
- Gifted education received federal support during the Cold War, but that support has recently been eroded.
- Controversies exist over the appropriateness of different forms of gifted education and their emotional effects on students.
Key Terms
- cluster grouping : Cluster grouping is the gathering of four to six gifted and talented or high achieving students in a single classroom for the entire school day.
- gifted : Endowed with special, in particular intellectual, abilities.
- pull-out : Gifted students are pulled out of a heterogeneous classroom to spend a portion of their time in a gifted class.
Though gifted education programs are widespread, there is no standard definition of “gifted,” nor a standard way of implementing gifted education. Gifted education programs are justified by a two-pronged argument: First, gifted and talented youth are not adequately challenged by the standard curriculum and therefore require accelerated curricula or enrichment activities to reach their full potential. Second, gifted and talented youth are inherently at-risk.
This second argument may seem counter-intuitive, but it has gained general credibility. This argument was formally articulated by the 1972 Marland Report by then U.S. Commissioner of Education S. P. Marland. According to the report, gifted youth are more likely than average to experience academic failure and to develop social and emotional problems. Gifted students may experience social rejection and difficulty making friends, as well as grapple with fear of failure and perfectionism. They may intentionally play down their abilities in order to make friends. They are also more prone to depression, anxiety and disengagement, as well as to behavior problems and drug and alcohol abuse. This may be in part due to a need for stimulation beyond what they receive in a typical classroom.
Since the early 20 th century, definitions of “gifted” have been based on IQ, or intelligence quotient. Different schools may set different cut-offs for defining giftedness, but a common standard is the top 2% of students with an IQ score of about 140 or above. More general definitions of giftedness may also evaluate students’ capability in areas like intellectual, creative, artistic, or leadership capacity, or in specific academic fields. Evaluations may be based on portfolios of student work, classroom observations, and achievement measures.
The 2002 No Child Left Behind law shifted attention away from gifted students. The law aims to bring proficiency of all students to grade level, but critics note it does not address the needs of gifted students who perform above grade level. The act imposes punishments on schools, administrators and teachers when students do not achieve to the plan’s designs, but does not address any achievement standards for high functioning students. This forces schools and teachers to spend their time with low achieving students. As a result of this law, many fear, gifted services have been eroding
Forms of Gifted Education
Gifted education programs take many forms, including a combination of acceleration, pull-out or cluster grouping, and enrichment activities. Acceleration programs may compact curriculum or allow students to self-pace. In compacting, students are pre-tested to determine which skills or content they have already mastered, thus allowing students to skip repetitive practice. This reduces boredom and frees time to work on more challenging material. In self-pacing, students advance at their own speeds. In general, acceleration programs advance students to higher-level material suited to their abilities and preparedness – students may skip grades, skip ahead in particular subjects, or enroll at local community colleges.
An alternative to acceleration is pull-out or cluster grouping, in which gifted students are removed from regular classrooms. In pull-out programs, gifted students spend most of the school day with a regular classroom of mixed abilities, but may be pulled out for an hour or part of a day to practice critical thinking drills, creative exercises, or subjects not introduced in standard curriculums. Pull-out programs are generally ineffective at promoting academic achievement since they do not align with the regular curriculum.
Finally, summer enrichment presents gifted students with extra material above and beyond the standard curriculum. Students spend school days with a regular classroom, but also complete enrichment activities given as a modified assignment by the regular classroom teacher. These could include formal programs like Odyssey of the Mind or academic competitions like National History Day. Summer enrichment programs typically operate like summer camps, as students pay a fee to attend and may enroll in programs that typically focus on one subject. In any case, enrichment work is done in addition to regular school work.
Controversy
Controversies concerning gifted education are varied and often highly politicized. They are as basic as agreeing upon the appropriateness of the term “gifted” or the definition of “giftedness. ” For example, does “giftedness” refer to performance or potential? Many students do not exhibit both at the same time. Measures of general intelligence also remain controversial. Early IQ tests were notorious for producing higher IQ scores for privileged races and classes and lower scores for disadvantaged subgroups. Although IQ tests have changed substantially over the past half century, and many objections to the early tests have been addressed by “culture neutral,” IQ testing remains controversial.
Educational Reform in the U.S.
Education reforms aim at redressing some societal ills, such as gender-, and class-based inequities, or instructional ineffectiveness.
Learning Objectives
Outline the main motivations for educational reform and the timeline of its various manifestations
Key Points
- Educational reform has been closely tied to efforts to promote democracy.
- Another motivation for reform is the desire to address socioeconomic problems, such as health, wealth and well being, which many people see as having roots in unequal access to education.
- In the 1980s, conservative reformers tried to limit federal involvement in education, and E.D. Hirsch argued education must teach cultural literacy.
- In the 1990s and 2000s, reformers pushed for outcomes-based education with an emphasis on assessment.
- Teachers’ unions are considered by many to be the major barrier to continued reform.
- Persistent issues in educational reform include school funding, school choice, and alternatives to public education.
- Teachers’ unions are considered by many to be the major barrier to continued reform.
Key Terms
- school choice : School choice is a term used to describe a wide array of programs aimed at giving families the opportunity to choose the school their children will attend.
- cultural literacy : Knowledge of and ability to discuss the history of and major concepts underlying a culture, particularly one’s own and those of one’s peers.
- outcomes-based education : Outcome-based education (OBE) is a student-centered learning philosophy that focuses on empirically measuring student performance, which are called outcomes. OBE contrasts with traditional education, which primarily focuses on the resources that are available to the student, which are called inputs.
Education reform has been pursued for a variety of specific reasons, but, generally, most reforms aim at redressing some societal ills, such as poverty-, gender-, or class-based inequities, or perceived ineffectiveness.
The idea that all children should be provided with a high level of education is a relatively recent idea, and has arisen largely in the context of Western democracy in the twentieth century. In fact, educational reform has been closely tied to efforts to promote democracy. Many students of democracy desire to improve education in order to improve the quality of governance in democratic societies. The necessity of good public education follows logically if one believes that the quality of democratic governance depends on the ability of citizens to make informed, intelligent choices, and education can improve these abilities. In the United States, for example, democratic education was promoted by Thomas Jefferson, who advocated ambitious reforms for public schooling in Virginia.
Another motivation for reform is the desire to address socioeconomic problems, which many people see as having roots in unequal access to education. Starting in the twentieth century, people have attempted to argue that small improvements in education can have large returns in such areas as health, wealth and well being. For example, in developing countries, increases in women’s literacy rates were correlated with increases in women’s health, and increasing primary education was correlated with increasing farming efficiencies and income. Even in developed countries, an individual’s level of education may predict the type of career and level of income that person can expect to achieve.
Other education reforms have been motivated by attempts to improve the effectiveness of instruction. Many modern reforms have attempted to move away from a model of education in which a teacher lectures and delivers facts to a passive student audience. For example, M. Montessori argued that education must take into account the individual needs of each child. John Dewey suggested that effective education poses problems and puzzles that motivate children to learn.
Over the years, education reform has focused on different goals. From the 1950s to the 1970s, many of the proposed and implemented reforms in U.S. education stemmed from the Civil Rights Movement and related trends; examples include ending racial segregation and busing for the purpose of desegregation, affirmative action, and banning of school prayer. In general, these reforms gave more students from more diverse backgrounds access to education.
In the 1980s, the momentum of education reform moved from the left to the right. For example, E.D. Hirsch put forth an influential attack on progressive education. He argued that progressive education failed to teach “cultural literacy,” the facts, phrases, and texts that Hirsch asserted every American had once known and were still essential for decoding basic texts and maintaining communication. Hirsch’s ideas remain significant through the 1990s and into the twenty-first century and are incorporated into classroom practice through textbooks and curricula published under his own imprint.
In the 1990s, most states and districts adopted Outcome-Based Education (OBE) in some form or another. Under OBE, a state would create a committee to adopt standards and choose a quantitative instrument (often, a standardized test) to assess whether the students knew the required content or could perform the required tasks. During this period, the U.S. Congress also set the standards-based National Education Goals (Goals 2000). Many of these goals were based on the principles of outcomes-based education, and not all of the goals were attained by the year 2000 as was intended. The standards-based reform movement culminated in the No Child Left Behind Act of 2001. In general, OBE reforms attempt to increase accountability in education. Rather than reforming the educational process, they focus on the effects that process achieves by measuring outcomes (e.g., student achievement).
A central issue for educational reform advocates today is school choice. Debates over school choice focus on advocates’ claim that school choice can promote excellence in education through competition. A highly competitive “market” for schools would eliminate the need to otherwise enforce accountability from the top down. According to advocates, schools would naturally regulate themselves and attempt to raise standards in order to attract students. Most proposals for school choice call for vouchers. Public education vouchers would permit guardians to select and pay any school, public or private, with public funds currently allocated to local public schools. In theory, children’s guardians will naturally shop for the best schools, much as is already done at the college level.
Many attribute the purportedly slow pace of reform in the United States to the strength of teachers’ unions. In some school districts, labor agreements with teachers’ unions may restrict the ability of school systems to implement merit pay and other reforms. In general, union contracts are more restrictive in districts with high concentrations of poor and minority students.
Contributors and Attributions
CC licensed content, Specific attribution


5.13: Conclusion
During the early 1900s, the world was subjected to depressions, wars, and revolutions, killing millions of people and bringing poverty and oppression to much of the world. Art movements during this period reflected the chaotic world around them and the revolt of artists against the standards and norms of the past. The artists experimented with materials, forms, images, colors, and whatever was available to bring the new and innovative ideas of art to the world. Throughout history, the female form was painted or sculpted as a popular format. In the early 1900s, the radical, new styles of multiple movements portrayed the female in various methods, from bold, brash use of color to exaggerated features, geometric shapes, and minimalistic objects. The sights and scenes of the vast continent of North America created a broad set of images for artists. Science, technology, mechanization, and industry were common themes to depict the workers' isolation, poverty, working conditions, or plight.


13.4: Mechanisms of Evolution
By the end of this section, you will be able to do the following:
- Describe the four basic causes of evolution: natural selection, mutation, genetic drift, and gene flow
- Explain how each evolutionary force can influence the allele frequencies of a population
The Hardy-Weinberg equilibrium principle says that allele frequencies in a population will remain constant in the absence of the four factors that could change them. Those factors are natural selection, mutation, genetic drift, and migration (gene flow). In fact, we know they are probably always affecting populations.
Natural Selection
Natural selection has already been discussed. Alleles are expressed in a phenotype. Depending on the environmental conditions, the phenotype confers an advantage or disadvantage to the individual with the phenotype relative to the other phenotypes in the population. If it is an advantage, then that individual will likely have more offspring than individuals with the other phenotypes, and this will mean that the allele behind the phenotype will have greater representation in the next generation. If conditions remain the same, those offspring, which are carrying the same allele, will also benefit. Over time, the allele will increase in frequency in the population.
Mutation
Mutation is a source of new alleles in a population. Mutation is a change in the DNA sequence of the gene. A mutation can change one allele into another, but the net effect is a change in frequency. The change in frequency resulting from mutation is small, so its effect on evolution is small unless it interacts with one of the other factors, such as selection. A mutation may produce an allele that is selected against, selected for, or selectively neutral. Harmful mutations are removed from the population by selection and will generally only be found in very low frequencies equal to the mutation rate. Beneficial mutations will spread through the population through selection, although that initial spread is slow. Whether or not a mutation is beneficial or harmful is determined by whether it helps an organism survive to sexual maturity and reproduce. It should be noted that mutation is the ultimate source of genetic variation in all populations—new alleles, and, therefore, new genetic variations arise through mutation.
Genetic Drift
Another way a population’s allele frequencies can change is genetic drift (Figure \(\PageIndex{1}\)), which is simply the effect of chance. Genetic drift is most important in small populations. Drift would be completely absent in a population with infinite individuals, but, of course, no population is this large. Genetic drift occurs because the alleles in an offspring generation are a random sample of the alleles in the parent generation. Alleles may or may not make it into the next generation due to chance events including mortality of an individual, events affecting finding a mate, and even the events affecting which gametes end up in fertilizations. If one individual in a population of ten individuals happens to die before it leaves any offspring to the next generation, all of its genes—a tenth of the population’s gene pool—will be suddenly lost. In a population of 100, that 1 individual represents only 1 percent of the overall gene pool; therefore, it has much less impact on the population’s genetic structure and is unlikely to remove all copies of even a relatively rare allele.
Imagine a population of ten individuals, half with allele A and half with allele a (the individuals are haploid). In a stable population, the next generation will also have ten individuals. Choose that generation randomly by flipping a coin ten times and let heads be A and tails be a . It is unlikely that the next generation will have exactly half of each allele. There might be six of one and four of the other, or some different set of frequencies. Thus, the allele frequencies have changed and evolution has occurred. A coin will no longer work to choose the next generation (because the odds are no longer one half for each allele). The frequency in each generation will drift up and down on what is known as a random walk until at one point either all A or all a are chosen and that allele is fixed from that point on. This could take a very long time for a large population. This simplification is not very biological, but it can be shown that real populations behave this way. The effect of drift on frequencies is greater the smaller a population is. Its effect is also greater on an allele with a frequency far from one half. Drift will influence every allele, even those that are being naturally selected.
ART CONNECTION
Do you think genetic drift would happen more quickly on an island or on the mainland?
Genetic drift can also be magnified by natural or human-caused events, such as a disaster that randomly kills a large portion of the population, which is known as the bottleneck effectthat results in a large portion of the genome suddenly being wiped out (Figure \(\PageIndex{2}\)). In one fell swoop, the genetic structure of the survivors becomes the genetic structure of the entire population, which may be very different from the pre-disaster population. The disaster must be one that kills for reasons unrelated to the organism’s traits, such as a hurricane or lava flow. A mass killing caused by unusually cold temperatures at night, is likely to affect individuals differently depending on the alleles they possess that confer cold hardiness.
Another scenario in which populations might experience a strong influence of genetic drift is if some portion of the population leaves to start a new population in a new location, or if a population gets divided by a physical barrier of some kind. In this situation, those individuals are unlikely to be representative of the entire population which results in the founder effect. The founder effect occurs when the genetic structure matches that of the new population’s founding fathers and mothers. The founder effect is believed to have been a key factor in the genetic history of the Afrikaner population of Dutch settlers in South Africa, as evidenced by mutations that are common in Afrikaners but rare in most other populations. This is likely due to a higher-than-normal proportion of the founding colonists, which were a small sample of the original population, carried these mutations. As a result, the population expresses unusually high incidences of Huntington’s disease (HD) and Fanconi anemia (FA), a genetic disorder known to cause bone marrow and congenital abnormalities, and even cancer. 1
CONCEPT IN ACTION
Visit the University of Arizona Biology Project (new window) to learn more about genetic drift and to run simulations of allele changes caused by drift.
Gene Flow
Another important evolutionary force is gene flow, or the flow of alleles in and out of a population resulting from the migration of individuals or gametes (Figure \(\PageIndex{3}\)). While some populations are fairly stable, others experience more flux. Many plants, for example, send their seeds far and wide, by wind or in the guts of animals; these seeds may introduce alleles common in the source population to a new population in which they are rare.
Art Connections
Figure \(\PageIndex{1}\): Do you think genetic drift would happen more quickly on an island or on the mainland?
- Answer
-
Genetic drift is likely to occur more rapidly on an island, where smaller populations are expected to occur.
Footnotes
- 1 A. J. Tipping et al., “Molecular and Genealogical Evidence for a Founder Effect in Fanconi Anemia Families of the Afrikaner Population of South Africa,” PNAS 98, no. 10 (2001): 5734-5739, doi: 10.1073/pnas.091402398.
Contributors and Attributions
Remixed and/or curated from the following works:
- Fowler, S., Roush, R., & Wise, J. (2013). 11.2 Mechanisms of Evolution . In Concepts of Biology . OpenStax (CC BY 4.0; Access for free at https://openstax.org/books/concepts-biology/pages/1-introduction ).


9: Family Spending and Budgeting
Assisting a patient and their family to effectively manage their money may be an important task for a Home Health Aide/Personal Care Aide. It is also important for the HHA/PCA who assists patients with shopping to be sure to effectively utilize a patient’s money by observing cost-saving techniques. This module focuses on how to assist a patient and their family with managing their money. We will discuss how to record expenditures and how to shop effectively in order to reduce costs for the family. Home Health Aides/Personal Care Aides should remember to always follow the Care Plan to decide whether or not they should provide assistance with money management and shopping and they should keep accurate records when they do so.


11.9: Oxidation of Alkenes - Cleavage to Carbonyl Compounds
-
- Last updated
- Save as PDF
Objective
After completing this section, you should be able to
- write an equation to describe the cleavage of an alkene by ozone, followed by reduction of the ozonide so formed with either sodium borohydride or zinc and acetic acid.
- predict the products formed from the ozonolysis-reduction of a given alkene.
- write an equation to describe the cleavage of an alkene by potassium permanganate.
- predict the products from the oxidative cleavage of a given alkene by potassium permanganate.
- use the results of ozonolysis-reduction, or cleavage with permanganate, to deduce the structure of an unknown alkene.
- identify the reagents that should be used in the oxidative cleavage of an alkene to obtain a given product or products.
- write the equation for the cleavage of a 1,2-diol by periodic acid, and draw the structure of the probable intermediate.
- predict the product or products that will be formed from the treatment of a given 1,2-diol with periodic acid.
- use the results of hydroxylation/1,2-diol cleavage to deduce the structure of an unknown alkene.
Key Terms
Make certain that you can define, and use in context, the key terms below.
- molozonide
- ozonide
- ozonolysis
Study Notes
Ozonolysis , or ozonolysis-reduction, refers to the treatment of an alkene with ozone followed by a suitable reducing agent to break down complex double-bond-containing compounds into smaller, more easily identified products. From the identity of the products formed, it may be possible to deduce the structure of the original double-bond-containing substance. Ozonolysis will feature prominently in many of the road-map problems that you will encounter in this course.
A molozonide is an unstable, cyclic intermediate that is initially formed when an alkene reacts with ozone.
Alkenes can also be cleaved by other oxidizing agents such as potassium permanganate. However, KMnO 4 will carry the oxidation further than ozonolysis, so products can be slightly different. Note within the summary of the following reactions that ozonolysis produces aldehydes and ketones, while KMnO 4 can oxidize all the way to to carbon dioxide and carboxylic acid.
Diol cleavage is another example of a redox reaction; periodic acid, HIO 4 , is reduced to iodic acid, HIO 3 .
Ozonolysis is a method of oxidatively cleaving alkenes or alkynes using ozone (\(O_3\)), a reactive allotrope of oxygen. The process allows for carbon-carbon double or triple bonds to be replaced by double bonds with oxygen. This reaction is often used to identify the structure of unknown alkenes. by breaking them down into smaller, more easily identifiable pieces. Ozonolysis also occurs naturally and would break down repeated units used in rubber and other polymers. On an industrial scale, azelaic acid and pelargonic acids are produced from ozonolysis.
The gaseous ozone is first passed through the desired alkene solution in either methanol or dichloromethane. The first intermediate product is an ozonide molecule which is then further reduced to carbonyl products. This results in the breaking of the Carbon-Carbon double bond and is replaced by a Carbon-Oxygen double bond instead.
Reaction Mechanism
Step 1:
The first step in the mechanism of ozonolysis is the initial electrophilic addition of ozone to the Carbon-Carbon double bond, which then form the molozonide intermediate. Due to the unstable molozonide molecule, it continues further with the reaction and breaks apart to form a carbonyl and a carbonyl oxide molecule.
Step 2:
The carbonyl and the carbonyl oxide rearranges itself and reforms to create the stable ozonide intermediate. Since some ozonides are explosive, it is immediately reacted with a reductive workup to then convert the ozonide molecule into the desired carbonyl products. A typical reductive workup is zinc metal in acetic acid. A variety of carbonyl products could result depending on the starting alkene. For example, a tetrasubstituted alkene would yield two ketone products, while a trisubstituted alkene would yield one ketone product and one aldehyde product.
While there are other options for oxidative cleavage of the double bond, this is the most commonly used reaction.
Exercise \(\PageIndex{1}\)
- Answer
-
Exercise \(\PageIndex{2}\)
Draw the structure of the product or products obtained in each of the following reactions:
- Answer
-
Exercise \(\PageIndex{3}\)
Exercises 1( a ) and 1( b ), above, indicate that it is not possible to distinguish between cis and trans isomers of alkenes using oxidative cleavage.
- Answer
-
Both isomers give the same product or products.
References
- Vollhardt, K., Schore, N. Organic Chemistry: Structure and Function. 5th ed. New York, NY: W. H. Freeman and Company, 2007.
- Shore, N. Study Guide and Solutions Manual for Organic Chemistry. 5th ed. New York, NY: W.H. Freeman and Company, 2007.


4.13: The Yuan Dynasty
The last major dynasty prior to China’s early modern period is the Yuan [you-an] Dynasty . Like earlier neighbors lying to the north of the Song, the Yuan was also a northern conquest dynasty. The key players here were steppe nomads living on the grasslands of Mongolia, known as Mongols, and their leader Genghis Khan. The story of their rise and how they created the largest territorial empire in the history of the world properly belongs to Chapter Eleven, which covers Central Asia, so we here only provide a brief introduction. The most important point to bear in mind is that the Mongols conquered many countries, including China, and incorporated them into a large Eurasian empire.
In the twelfth century CE, the Mongols were one of many tribes of nomadic pastoralists living on the steppes of Central Asia. Although these tribes were made up of peoples of differing ethnicity, they held in common a way of life. Since the steppe was unsuited to farming, they relied principally on their herds, but also on what they could obtain by trading with neighboring sedentary peoples. The nomads lived in temporary campsites, periodically breaking down their yurts and relocating as the seasons required. Since the tribes often fought with each other or turned to raiding, nomads were also excellent at mounted warfare. Their chieftain leaders–referred to as khans–were usually selected based on skill in battle and charisma.
Undoubtedly, the most famous khan in Central Asian history is Genghis Khan. In the late twelfth century, he accrued an army of loyal followers and began to subdue tribes across the Mongolian steppe. In 1206 CE, at a gathering of tribal leaders, he was proclaimed Universal Khan of a tribal confederation. Using a powerful military with a tight command structure, Genghis proceeded to unleash a wave of campaigning in northern China and Central Asia, thereby adding much territory to a growing Mongol Empire (see Map \(\PageIndex{1}\)). After he died in 1227 CE, this empire was divided into four khanates, each of which went to one of his four sons as their territorial inheritance.
Tolui, Genghis Khan’s youngest son, was granted the Mongol homeland as well as subjugated territory in northern China held by the Jin Dynasty. But this rugged warrior died in 1232 at the young age of forty, so the task of managing Chinese territory fell to Tolui’s capable wife Sorghagtani Beki and her second son, Kublai Khan (1215 – 1294 CE). Unlike his predecessors, who largely treated Chinese as chattel and ruthlessly exploited their towns and villages, Kublai saw the advantages of taking a more enlightened approach. With the advice of Chinese advisors, he adopted Chinese-style methods for governing China. In fact, after Kublai was elected as the fifth Universal Khan in 1260, he chose to move his capital from Mongolia to Beijing, making it the center of his khanate. He then took on the trappings of a Chinese-style sovereign and, in 1273, declared the founding of the Great Yuan Dynasty. Accordingly, he asserted that the Mandate of Heaven had been transferred to him from the Song Dynasty.
Kublai then engaged in a decade of conquest that concluded with the fall of the Song. This victory over the Song Dynasty, China required careful preparation. The Song was located in the southern two-thirds of China, where the terrain was matted with lakes, rivers, and canals. The Mongols had little experience with naval warfare, so they turned to Chinese advisors to build a navy. Mongol cavalry boarded the ships and floated down rivers leading to the Song capital, laying siege to cities along the way. When they reached it in 1276, Kublai’s generals took the capital without bloodshed. The regent to the young Song emperor worked out conditions for surrender to them. Hence, the Mongol Yuan Dynasty had won control over China. After Kublai died, nine of his descendants ruled as emperors until the dynasty fell to native rebellions in 1368.
Historians differently assess the impact of Mongol Yuan rule on China. Earlier generations of historians judged that violent Mongol conquests devastated the land and led to a population drop. The Mongol style of rule was despotic. Rather than sustain the openness of Chinese society and use the merit-based examination system to bring talent into their government, Mongol rulers placed Chinese in rigid occupational categories and suspended the exams. Many capable men simply avoided official service and turned to other professions.
Recent studies, however, offer a more positive assessment. Because Yuan rulers followed the counsel of Confucian advisors and adopted traditional Chinese methods for governing, for most Chinese life went on as before. Early on, much attention was also paid to the farming population. To promote agriculture, Yuan rulers provided relief measures and promoted the formation of rural cooperatives. Also, Mongols highly valued crafts and implemented policies that greatly benefited artisans and promoted their work. Hence, arts such as textiles and ceramics flourished (see Figure \(\PageIndex{1}\)). Finally, the assessment of Yuan rule in China should be linked to a broader assessment of the impact of Mongol rule on world history (see Chapter Eleven). While duly acknowledging the devastation caused by Mongol conquests, historians also find much merit in Mongol patronage of arts and support for constructions projects and advancements in the areas of medicine and astronomy. Most importantly, the massive Eurasian empire they forged initiated a new era of trade and contacts between Europe and China, as well as the regions lying between.


14.7: Fluid Dynamics
- Describe the characteristics of flow
- Calculate flow rate
- Describe the relationship between flow rate and velocity
- Explain the consequences of the equation of continuity to the conservation of mass
The first part of this chapter dealt with fluid statics, the study of fluids at rest. The rest of this chapter deals with fluid dynamics, the study of fluids in motion. Even the most basic forms of fluid motion can be quite complex. For this reason, we limit our investigation to ideal fluids in many of the examples. An ideal fluid is a fluid with negligible viscosity . Viscosity is a measure of the internal friction in a fluid; we examine it in more detail in Viscosity and Turbulence . In a few examples, we examine an incompressible fluid—one for which an extremely large force is required to change the volume—since the density in an incompressible fluid is constant throughout.
Characteristics of Flow
Velocity vectors are often used to illustrate fluid motion in applications like meteorology. For example, wind—the fluid motion of air in the atmosphere—can be represented by vectors indicating the speed and direction of the wind at any given point on a map. Figure \(\PageIndex{1}\) shows velocity vectors describing the winds during Hurricane Arthur in 2014.
Another method for representing fluid motion is a streamline . A streamline represents the path of a small volume of fluid as it flows. The velocity is always tangential to the streamline. The diagrams in Figure \(\PageIndex{2}\) use streamlines to illustrate two examples of fluids moving through a pipe. The first fluid exhibits a laminar flow (sometimes described as a steady flow), represented by smooth, parallel streamlines. Note that in the example shown in part (a), the velocity of the fluid is greatest in the center and decreases near the walls of the pipe due to the viscosity of the fluid and friction between the pipe walls and the fluid. This is a special case of laminar flow, where the friction between the pipe and the fluid is high, known as no slip boundary conditions. The second diagram represents turbulent flow , in which streamlines are irregular and change over time. In turbulent flow, the paths of the fluid flow are irregular as different parts of the fluid mix together or form small circular regions that resemble whirlpools. This can occur when the speed of the fluid reaches a certain critical speed.
Flow Rate and its Relation to Velocity
The volume of fluid passing by a given location through an area during a period of time is called flow rate \(Q\), or more precisely, volume flow rate. In symbols, this is written as
\[Q = \frac{dV}{dt} \label{14.13}\]
where \(V\) is the volume and \(t\) is the elapsed time. In Figure \(\PageIndex{3}\), the volume of the cylinder is \(Ax\), so the flow rate is
\[Q = \frac{dV}{dt} = \frac{d}{dt} (Ax) = A \frac{dx}{dt} = Av \ldotp\]
The SI unit for flow rate is m 3 /s, but several other units for \(Q\) are in common use, such as liters per minute (L/min). Note that a liter (L) is 1/1000 of a cubic meter or 1000 cubic centimeters (10 −3 m 3 or 10 3 cm 3 ).
Flow rate and velocity are related, but quite different, physical quantities. To make the distinction clear, consider the flow rate of a river. The greater the velocity of the water, the greater the flow rate of the river. But flow rate also depends on the size and shape of the river. A rapid mountain stream carries far less water than the Amazon River in Brazil, for example. Figure \(\PageIndex{3}\) illustrates the volume flow rate. The volume flow rate is \(Q = \frac{dV}{dt} = Av\), where A is the cross-sectional area of the pipe and v is the magnitude of the velocity.
The precise relationship between flow rate \(Q\) and average speed \(v\) is
\[Q = Av,\]
where \(A\) is the cross-sectional area and \(v\) is the average speed. The relationship tells us that flow rate is directly proportional to both the average speed of the fluid and the cross-sectional area of a river, pipe, or other conduit. The larger the conduit, the greater its cross-sectional area. Figure \(\PageIndex{3}\) illustrates how this relationship is obtained. The shaded cylinder has a volume \(V = Ad\), which flows past the point \(P\) in a time \(t\). Dividing both sides of this relationship by \(t\) gives
\[\frac{V}{t} = \frac{Ad}{t} \ldotp \label{eq14.14A} \]
We note that \(Q = \frac{V}{t}\) and the average speed is \(v = \frac{d}{t}\). Thus Equation \ref{eq14.14A} becomes
\[Q = Av.\]
Figure \(\PageIndex{4}\) shows an incompressible fluid flowing along a pipe of decreasing radius. Because the fluid is incompressible, the same amount of fluid must flow past any point in the tube in a given time to ensure continuity of flow. The flow is continuous because they are no sources or sinks that add or remove mass, so the mass flowing into the pipe must be equal the mass flowing out of the pipe. In this case, because the cross-sectional area of the pipe decreases, the velocity must necessarily increase. This logic can be extended to say that the flow rate must be the same at all points along the pipe. In particular, for arbitrary points 1 and 2,
\[\begin{split} Q_{1} & = Q_{2}, \\ A_{1} v_{1} & = A_{2} v_{2} \ldotp \end{split} \label{14.14}\]
This is called the equation of continuity and is valid for any incompressible fluid (with constant density). The consequences of the equation of continuity can be observed when water flows from a hose into a narrow spray nozzle: It emerges with a large speed—that is the purpose of the nozzle. Conversely, when a river empties into one end of a reservoir, the water slows considerably, perhaps picking up speed again when it leaves the other end of the reservoir. In other words, speed increases when cross-sectional area decreases, and speed decreases when cross-sectional area increases.
Since liquids are essentially incompressible, the equation of continuity is valid for all liquids. However, gases are compressible, so the equation must be applied with caution to gases if they are subjected to compression or expansion.
A nozzle with a diameter of 0.500 cm is attached to a garden hose with a radius of 0.900 cm. The flow rate through hose and nozzle is 0.500 L/s. Calculate the speed of the water:
- in the hose and
- in the nozzle.
Strategy
We can use the relationship between flow rate and speed to find both speeds. We use the subscript 1 for the hose and 2 for the nozzle.
Solution
- We solve the flow rate equation for speed and use \(\pi r_{1}^{2}\) for the cross-sectional area of the hose, obtaining $$v = \frac{Q}{A} = \frac{Q}{\pi r_{1}^{2}} \ldotp$$ Substituting values and using appropriate unit conversions yields $$v = \frac{(0.500\; L/s)(10^{-3}\; m^{3}/L)}{(3.14)(9.00 \times 10^{-3}\; m)^{2}} = 1.96\; m/s \ldotp$$
- We could repeat this calculation to find the speed in the nozzle v 2 , but we use the equation of continuity to give a somewhat different insight. The equation states $$A_{1} v_{1} = A_{2} v_{2} \ldotp$$Solving for v 2 and substituting \(\pi r^{2}\) for the cross-sectional area yields $$v_{2} = \frac{A_{1}}{A_{2}} v_{1} = \frac{\pi r_{1}^{2}}{\pi r_{2}^{2}} v_{1} = \frac{r_{1}^{2}}{r_{2}^{2}} v_{1} \ldotp$$ Substituting known values, $$v_{2} = \frac{(0.900\; cm)^{2}}{(0.250\; cm)^{2}} (1.96\; m/s) = 25.5\; m/s \ldotp$$
Significance
A speed of 1.96 m/s is about right for water emerging from a hose with no nozzle. The nozzle produces a considerably faster stream merely by constricting the flow to a narrower tube.
The solution to the last part of the example shows that speed is inversely proportional to the square of the radius of the tube, making for large effects when radius varies. We can blow out a candle at quite a distance, for example, by pursing our lips, whereas blowing on a candle with our mouth wide open is quite ineffective.
Mass Conservation
The rate of flow of a fluid can also be described by the mass flow rate or mass rate of flow. This is the rate at which a mass of the fluid moves past a point. Refer once again to Figure \(\PageIndex{3}\), but this time consider the mass in the shaded volume. The mass can be determined from the density and the volume:
\[m = \rho V = \rho Ax \ldotp\]
The mass flow rate is then
\[\frac{dm}{dt} = \frac{d}{dt} (\rho Ax) = \rho A \frac{dx}{dt} = \rho Av,\]
where \(\rho\) is the density, A is the cross-sectional area, and v is the magnitude of the velocity. The mass flow rate is an important quantity in fluid dynamics and can be used to solve many problems. Consider Figure \(\PageIndex{5}\). The pipe in the figure starts at the inlet with a cross sectional area of A 1 and constricts to an outlet with a smaller cross sectional area of A 2 . The mass of fluid entering the pipe has to be equal to the mass of fluid leaving the pipe. For this reason the velocity at the outlet (v 2 ) is greater than the velocity of the inlet (v 1 ). Using the fact that the mass of fluid entering the pipe must be equal to the mass of fluid exiting the pipe, we can find a relationship between the velocity and the cross-sectional area by taking the rate of change of the mass in and the mass out:
\[\begin{split} \left(\dfrac{dm}{dt}\right)_{1} & = \left(\dfrac{dm}{dt}\right)_{2} \\ \rho_{1} A_{1} v_{1} & = \rho_{2} A_{2} v_{2} \ldotp \end{split} \label{14.15}\]
Equation \ref{14.15} is also known as the continuity equation in general form. If the density of the fluid remains constant through the constriction—that is, the fluid is incompressible—then the density cancels from the continuity equation,
\[A_{1} v_{1} = A_{2} v_{2} \ldotp\]
The equation reduces to show that the volume flow rate into the pipe equals the volume flow rate out of the pipe.


4.2: Möbius Geometry
We spent a fair amount of time studying Möbius transformations in Chapter 3, and this will pay dividends now.
Möbius Geometry is the geometry \((\mathbb{C}^+,{\cal M}),\) where \(\cal M\) denotes the group of all Möbius transformations.
Without actually stating it, we essentially proved that \(\cal{M}\) is a group of transformations. Namely, we proved that the inverse of a Möbius transformation is again a Möbius transformation, and that the composition of two Möbius transformations is a Möbius transformation. We remark that the identity map on \(\mathbb{C}^+\text{,}\) \(T(z) = z\text{,}\) is a Möbius transformation (of the form \(T(z) = \dfrac{(az+b)}{(cz+d)}\text{,}\) where \(a = d = 1,\) and \(b = c = 0)\text{,}\) so \(\cal M\) is a group.
Below we recast the key results from Chapter 3 in geometric terms:
- Any two clines are congruent in Möbius Geometry (Theorem \(3.4.10\)).
- The set of all clines is a minimally invariant set of Möbius Geometry (Theorems \(3.4.5\) and Theorem \(3.4.10\)).
- The cross ratio is an invariant of Möbius Geometry (Theorem \(3.4.8\)).
- Angle measure is an invariant of Möbius Geometry (Theorem \(3.4.5\)).
While we're at it, let's restate three other facts about Möbius transformations:
- Any transformation in \(\cal{M}\) is uniquely determined by the image of three points.
- If \(T\) in \(\cal{M}\) is not the identity map, then \(T\) fixes exactly \(1\) or \(2\) points.
- Möbius transformations preserve symmetry points.
What else? Euclidean distance is not an invariant function of Möbius Geometry. To see this, one need look no further than the map \(T(z) = \dfrac{1}{z}\text{.}\) If \(p = 2\) and \(q = 3\) (two points on the real axis) then \(d(p,q)=|p - q| = 1\text{.}\) However, their image points \(T(p) = \dfrac{1}{2}\) and \(T(q) = \dfrac{1}{3}\) have a Euclidean distance between them of \(\dfrac{1}{6}\). So our old-fashioned notion of distance goes out the window in Möbius geometry.
We emphasize that angles are preserved in Möbius geometry, which is a good thing. Why is this a good thing? Remember that in the distant past, humanity set out looking for a geometry in which Euclid's first 4 postulates hold true, but the 5 th one fails. The 4 th postulate states that all right angles equal one another. This means that if Ralph is holding a right angle over in the corner, and Randy is holding one down the block somewhere, we ought to be able to transform one onto the other and see that the angles are the same. Transformations do not change angles.
Rather than pursue the very general Möbius geometry, we take the preceeding facts and apply them straight away to two of its special “subgeometries,” hyperbolic geometry and elliptic geometry.
Exercises
Which figures in Figure \(4.2.1\) are congruent in \((\mathbb{C}^+,\cal{M})\text{.}\)
- Answer
-
\(A \cong F\text{;}\) \(B \cong G\text{;}\) \(C \cong E\text{.}\)
Describe a minimally invariant set in \((\mathbb{C}^+,\cal{M})\) containing the “triangle” comprised of the three vertices \(0\), \(1\), and \(i\) and the three Euclidean line segments connecting them. Be as specific as possible about the members of this set.
Suppose \(p\) and \(q\) are distinct, finite points in \(\mathbb{C}^+\text{.}\) Let \(G\) consist of all elliptic Möbius transformations that fix \(p\) and \(q\text{.}\) We consider the geometry \((\mathbb{C}^+,G)\text{.}\)
- Show that \(G\) is a group of transformations.
- Determine a minimally invariant set in \((\mathbb{C}^+,G)\) that contains the Euclidean line through \(p\) and \(q\text{.}\)
- Determine a minimally invariant set in \((\mathbb{C}^+,G)\) that contains the perpendicular bisector of segment \(pq\text{.}\)
- For any point \(z \neq p, q\) in \(\mathbb{C}^+\text{,}\) characterize all points in \(\mathbb{C}^+\) congruent to \(z\text{.}\)
- Is \((\mathbb{C}^+,G)\) homogeneous?
Repeat the previous exercise for the set \(G\) consisting of all hyperbolic Möbius transformations that fix \(p\) and \(q\text{.}\)