In opposition to the probability of subsequent amendments, it has been urged that the persons delegated to the administration of the national government will always be disinclined to yield up any portion of the authority of which they were once possessed. For my own part I acknowledge a thorough conviction that any amendments which may, upon mature consideration, be thought useful, will be applicable to the organization of the government, not to the mass of its powers; and on this account alone, I think there is no weight in the observation just stated. I also think there is little weight in it on another account. The intrinsic difficulty of governing THIRTEEN STATES at any rate, independent of calculations upon an ordinary degree of public spirit and integrity, will, in my opinion constantly impose on the national rulers the necessity of a spirit of accommodation to the reasonable expectations of their constituents. But there is yet a further consideration, which proves beyond the possibility of a doubt, that the observation is futile. It is this that the national rulers, whenever nine States concur, will have no option upon the subject. By the fifth article of the plan, the Congress will be obliged “on the application of the legislatures of two thirds of the States (which at present amount to nine), to call a convention for proposing amendments, which shall be valid, to all intents and purposes, as part of the Constitution, when ratified by the legislatures of three fourths of the States, or by conventions in three fourths thereof.” The words of this article are peremptory. The Congress “shall call a convention.” Nothing in this particular is left to the discretion of that body. And of consequence, all the declamation about the disinclination to a change vanishes in air. Nor however difficult it may be supposed to unite two thirds or three fourths of the State legislatures, in amendments which may affect local interests, can there be any room to apprehend any such difficulty in a union on points which are merely relative to the general liberty or security of the people. We may safely rely on the disposition of the State legislatures to erect barriers against the encroachments of the national authority.
If the foregoing argument is a fallacy, certain it is that I am myself deceived by it, for it is, in my conception, one of those rare instances in which a political truth can be brought to the test of a mathematical demonstration. Those who see the matter in the same light with me, however zealous they may be for amendments, must agree in the propriety of a previous adoption, as the most direct road to their own object.
The zeal for attempts to amend, prior to the establishment of the Constitution, must abate in every man who is ready to accede to the truth of the following observations of a writer equally solid and ingenious: “To balance a large state or society (says he), whether monarchical or republican, on general laws, is a work of so great difficulty, that no human genius, however comprehensive, is able, by the mere dint of reason and reflection, to effect it. The judgments of many must unite in the work; EXPERIENCE must guide their labor; TIME must bring it to perfection, and the FEELING of inconveniences must correct the mistakes which they inevitably fall into in their first trials and experiments.”(3) These judicious reflections contain a lesson of moderation to all the sincere lovers of the Union, and ought to put them upon their guard against hazarding anarchy, civil war, a perpetual alienation of the States from each other, and perhaps the military despotism of a victorious demagogue, in the pursuit of what they are not likely to obtain, but from TIME and EXPERIENCE. It may be in me a defect of political fortitude, but I acknowledge that I cannot entertain an equal tranquillity with those who affect to treat the dangers of a longer continuance in our present situation as imaginary. A NATION, without a NATIONAL GOVERNMENT, is, in my view, an awful spectacle. The establishment of a Constitution, in time of profound peace, by the voluntary consent of a whole people, is a PRODIGY, to the completion of which I look forward with trembling anxiety. I can reconcile it to no rules of prudence to let go the hold we now have, in so arduous an enterprise, upon seven out of the thirteen States, and after having passed over so considerable a part of the ground, to recommence the course. I dread the more the consequences of new attempts, because I know that POWERFUL INDIVIDUALS, in this and in other States, are enemies to a general national government in every possible shape.
Contributors and Attributions
- Authored by : Alexander Hamilton, John Jay, and James Madison. Provided by : US government . Located at : http://www.gutenberg.org/files/1404/1404-h/1404-h.htm . License : Public Domain: No Known Copyright


29.15A: Renal Disease and Failure
Renal failure uremia is a syndrome of renal failure characterized by elevated levels of urea and creatinine in the blood.
- Distinguish between acute kidney injury and chronic kidney disease
Key Points
- The type of renal failure is determined by the trend in the serum creatinine.
- In renal failure, there may be problems with increased fluid in the body (leading to swelling), increased acid levels, raised levels of potassium, decreased levels of calcium, increased levels of phosphate, and in later stages, anemia.
- The two main forms are acute kidney injury, which is often reversible with adequate treatment, and chronic kidney disease, which is often not reversible. In both cases, there is usually an underlying cause.
Key Terms
- renal calculus : A solid concretion or crystal aggregation formed in the kidneys from dietary minerals in the urine; a kidney stone.
- creatinine : A heterocyclic amine 2-amino-1-methyl-5H-imidazol-4-one formed by the metabolism of creatine.
- renal failure uremia : Uremia is a term used to loosely describe the illness accompanying kidney failure (also called renal failure), in particular the nitrogenous waste products associated with the failure of this organ.
EXAMPLES
Before dialysis or kidney transplants were widely available treatments, patients with kidney failure had progressive uremic poisoning. These days, most patients have some early symptoms of uremia as their kidney function declines, but prompt dialysis treatments or transplantation avoids most symptoms.
 The two main forms are acute kidney injury, which is often reversible with adequate treatment, and chronic kidney disease, which is often not reversible. In both cases, there is usually an underlying cause.
Diagnosis
Renal failure is mainly determined by a decrease in the glomerular filtration rate, which is the rate at which blood is filtered in the glomeruli of the kidney. This is detected by a decrease in or absence of urine production or determination of waste products (creatinine or urea ) in the blood. Depending on the cause, hematuria (blood loss in the urine) and proteinuria (protein loss in the urine) may be noted.
In renal failure, there may be problems with increased fluid in the body (leading to swelling), increased acid levels, raised levels of potassium, decreased levels of calcium, increased levels of phosphate, and in later stages, anemia. Bone health may also be affected. Long-term kidney problems are associated with an increased risk of cardiovascular disease.
Categories of Renal Failure
Renal failure can be divided into two categories: acute kidney injury or chronic kidney disease. The type of renal failure is determined by the trend in the serum creatinine. Other factors that may help differentiate acute kidney injury from chronic kidney disease include anemia and the kidney size on ultrasound. Chronic kidney disease generally leads to anemia and small kidney size.
Kidney Transplantation : Kidney transplantation requires a person to be at the end stage of renal failure.
Acute kidney injury (AKI), previously called acute renal failure (ARF), is a rapidly progressive loss of renal function, generally characterized by oliguria (decreased urine production, quantified as less than 400 mL per day in adults, less than 0.5 mL/kg/h in children or less than 1 mL/kg/h in infants); and fluid and electrolyte imbalance. AKI can result from a variety of causes, generally classified as prerenal, intrinsic, and postrenal. An underlying cause must be identified and treated to arrest the progress, and dialysis may be necessary to bridge the time gap required for treating these fundamental causes.
Chronic kidney disease (CKD) can also develop slowly and, initially, show few symptoms. CKD can be the long-term consequence of irreversible acute disease or part of a disease progression.
Acute kidney injuries can be present on top of chronic kidney disease, a condition called acute-on-chronic renal failure (AoCRF). The acute part of AoCRF may be reversible, and the goal of treatment, as with AKI, is to return the patient to baseline renal function, typically measured by serum creatinine. Like AKI, AoCRF can be difficult to distinguish from chronic kidney disease if the patient has not been monitored by a physician and no baseline (i.e., past) blood work is available for comparison.
Symptoms can vary from person to person. Someone in early stage kidney disease may not feel sick or notice symptoms as they occur. When kidneys fail to filter properly, waste accumulates in the blood and the body, a condition called azotemia. Very low levels of azotaemia may produce few, if any, symptoms. If the disease progresses, symptoms become noticeable (if the failure is of sufficient degree to cause symptoms). Renal failure accompanied by noticeable symptoms is termed uraemia.
Renal Failure Uremia
Renal failure uremia is a syndrome of renal failure that includes elevated blood urea and creatinine levels. Acute renal failure can be reversed if diagnosed early. Acute renal failure can be caused by severe hypotension or severe glomerular disease. Diagnostic tests include BUN and plasma creatinine level tests. It is considered to be chronic renal failure if the decline of renal function is to less than 25%.


1.3: Case Study
The LeBlanc Case
The Leblanc process industrial factories were very damaging to the local environment. It was an early industrial process for producing
soda ash
(sodium carbonate) that was named after its inventor. It required two stages: sodium sulfate (salt cake) produced from sodium chloride (salt, we just discussed this!) followed by reaction with coal and calcium carbonate to produce sodium carbonate. It eventually became obsolete after development of the Solvay process. The process of generating salt cake involved reacting salt with sulfuric acid which released hydrochloric acid gas, an acid that was industrially useless in the early 19th century and therefore vented into the atmosphere. Also, an insoluble, smelly solid waste (CaS,
galligu
) was produced. The inefficiency of the process was horrific! Each ton of
soda ash
, the process produced ~1.5 tons of hydrogen chloride and >1 ton of calcium sulfide, the useless waste product!
Galligu
had no economic value so it was piled in heaps and spread on fields where it weathered to release
hydrogen sulfide (what a smell!).
Leblanc soda works then became targets of lawsuits and legislation. A lawsuit from 1839 alleged that, “the gas from these manufactories is of such a deleterious nature as to blight everything within its influence and is alike baneful to health and property. The herbage of the fields in their vicinity is scorched, the gardens neither yield fruit nor vegetables; many flourishing trees have lately become rotten naked sticks. Cattle and poultry droop and pine away. It tarnishes the furniture in our houses, and when we are exposed to it, which is of frequent occurrence, we are afflicted with coughs and pains in the head ... all of which we attribute to the Alkali works.”
Therefore, in 1863, the British Parliament passed the first Alkali Act, a precursor to the first modern air pollution legislation. This Act dictated that no more than 5% of the hydrochloric acid produced by alkali plants could be vented. To comply, soda works passed it up a tower packed with charcoal where it was absorbed by water flowing in the other direction. Unfortunately, the chemical works usually dumped the resulting solution into nearby bodies of water where it promptly ended up killing fish and other aquatic life.


2.18: Safety Needs
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Once a person's physiological needs are relatively satisfied, his/her safety needs take precedence and dominate behavior. In the absence of physical safety – due to war, natural disaster, family violence, childhood abuse, etc. – people may (re-)experience post-traumatic stress disorder or transgenerational trauma. In the absence of economic safety – due to economic crisis and lack of work opportunities – these safety needs manifest themselves in ways such as a preference for job security, grievance procedures for protecting the individual from unilateral authority, savings accounts, insurance policies, disability accommodations, etc. This level is more likely to be found in children as they generally have a greater need to feel safe.
Safety and Security needs include:


14.3: The Soil
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- Tom Buckley
- University of California, Davis
Skills to Develop
- Describe how soils are formed
- Explain soil composition
- Describe a soil profile
Plants obtain inorganic elements from the soil, which serves as a natural medium for land plants. Soil is the outer loose layer that covers the surface of Earth. Soil quality is a major determinant, along with climate, of plant distribution and growth. Soil quality depends not only on the chemical composition of the soil, but also the topography (regional surface features) and the presence of living organisms. In agriculture, the history of the soil, such as the cultivating practices and previous crops, modify the characteristics and fertility of that soil.
Soil develops very slowly over long periods of time, and its formation results from natural and environmental forces acting on mineral, rock, and organic compounds. Soils can be divided into two groups: organic soils are those that are formed from sedimentation and primarily composed of organic matter, while those that are formed from the weathering of rocks and are primarily composed of inorganic material are called mineral soils . Mineral soils are predominant in terrestrial ecosystems, where soils may be covered by water for part of the year or exposed to the atmosphere.
Soil Composition
Soil consists of these major components (Figure \(\PageIndex{1}\)):
- inorganic mineral matter, about 40 to 45 percent of the soil volume
- organic matter, about 5 percent of the soil volume
- water and air, about 50 percent of the soil volume
The amount of each of the four major components of soil depends on the amount of vegetation, soil compaction, and water present in the soil. A good healthy soil has sufficient air, water, minerals, and organic material to promote and sustain plant life.
Exercise \(\PageIndex{1}\)
Soil compaction can result when soil is compressed by heavy machinery or even foot traffic. How might this compaction change the soil composition?
- Answer
-
The air content of the soil decreases.
The organic material of soil, called humus , is made up of microorganisms (dead and alive), and dead animals and plants in varying stages of decay. Humus improves soil structure and provides plants with water and minerals. The inorganic material of soil consists of rock, slowly broken down into smaller particles that vary in size. Soil particles that are 0.1 to 2 mm in diameter are sand . Soil particles between 0.002 and 0.1 mm are called silt , and even smaller particles, less than 0.002 mm in diameter, are called clay . Some soils have no dominant particle size and contain a mixture of sand, silt, and humus; these soils are called loams .
Soil Formation
Soil formation is the consequence of a combination of biological, physical, and chemical processes. Soil should ideally contain 50 percent solid material and 50 percent pore space. About one-half of the pore space should contain water, and the other half should contain air. The organic component of soil serves as a cementing agent, returns nutrients to the plant, allows soil to store moisture, makes soil tillable for farming, and provides energy for soil microorganisms. Most soil microorganisms—bacteria, algae, or fungi—are dormant in dry soil, but become active once moisture is available.
Soil distribution is not homogenous because its formation results in the production of layers; together, the vertical section of a soil is called the soil profile . Within the soil profile, soil scientists define zones called horizons. A horizon is a soil layer with distinct physical and chemical properties that differ from those of other layers. Five factors account for soil formation: parent material, climate, topography, biological factors, and time.
Parent Material
The organic and inorganic material in which soils form is the parent material . Mineral soils form directly from the weathering of bedrock , the solid rock that lies beneath the soil, and therefore, they have a similar composition to the original rock. Other soils form in materials that came from elsewhere, such as sand and glacial drift. Materials located in the depth of the soil are relatively unchanged compared with the deposited material. Sediments in rivers may have different characteristics, depending on whether the stream moves quickly or slowly. A fast-moving river could have sediments of rocks and sand, whereas a slow-moving river could have fine-textured material, such as clay.
Climate
Temperature, moisture, and wind cause different patterns of weathering and therefore affect soil characteristics. The presence of moisture and nutrients from weathering will also promote biological activity: a key component of a quality soil.
Topography
Regional surface features (familiarly called “the lay of the land”) can have a major influence on the characteristics and fertility of a soil. Topography affects water runoff, which strips away parent material and affects plant growth. Steeps soils are more prone to erosion and may be thinner than soils that are relatively flat or level.
Biological factors
The presence of living organisms greatly affects soil formation and structure. Animals and microorganisms can produce pores and crevices, and plant roots can penetrate into crevices to produce more fragmentation. Plant secretions promote the development of microorganisms around the root, in an area known as the rhizosphere . Additionally, leaves and other material that fall from plants decompose and contribute to soil composition.
Time
Time is an important factor in soil formation because soils develop over long periods. Soil formation is a dynamic process. Materials are deposited over time, decompose, and transform into other materials that can be used by living organisms or deposited onto the surface of the soil.
Physical Properties of the Soil
Soils are named and classified based on their horizons. The soil profile has four distinct layers: 1) O horizon; 2) A horizon; 3) B horizon, or subsoil; and 4) C horizon, or soil base (Figure \(\PageIndex{2}\)). The O horizon has freshly decomposing organic matter—humus—at its surface, with decomposed vegetation at its base. Humus enriches the soil with nutrients and enhances soil moisture retention. Topsoil—the top layer of soil—is usually two to three inches deep, but this depth can vary considerably. For instance, river deltas like the Mississippi River delta have deep layers of topsoil. Topsoil is rich in organic material; microbial processes occur there, and it is the “workhorse” of plant production. The A horizon consists of a mixture of organic material with inorganic products of weathering, and it is therefore the beginning of true mineral soil. This horizon is typically darkly colored because of the presence of organic matter. In this area, rainwater percolates through the soil and carries materials from the surface. The B horizon is an accumulation of mostly fine material that has moved downward, resulting in a dense layer in the soil. In some soils, the B horizon contains nodules or a layer of calcium carbonate. The C horizon , or soil base, includes the parent material, plus the organic and inorganic material that is broken down to form soil. The parent material may be either created in its natural place, or transported from elsewhere to its present location. Beneath the C horizon lies bedrock.
Exercise \(\PageIndex{2}\)
Which horizon is considered the topsoil, and which is considered the subsoil?
- Answer
-
The A horizon is the topsoil, and the B horizon is subsoil.
Some soils may have additional layers, or lack one of these layers. The thickness of the layers is also variable, and depends on the factors that influence soil formation. In general, immature soils may have O, A, and C horizons, whereas mature soils may display all of these, plus additional layers (Figure \(\PageIndex{3}\)).
Career Connections: Soil Scientist
A soil scientist studies the biological components, physical and chemical properties, distribution, formation, and morphology of soils. Soil scientists need to have a strong background in physical and life sciences, plus a foundation in mathematics. They may work for federal or state agencies, academia, or the private sector. Their work may involve collecting data, carrying out research, interpreting results, inspecting soils, conducting soil surveys, and recommending soil management programs.
Many soil scientists work both in an office and in the field. According to the United States Department of Agriculture (USDA): “a soil scientist needs good observation skills to analyze and determine the characteristics of different types of soils. Soil types are complex and the geographical areas a soil scientist may survey are varied. Aerial photos or various satellite images are often used to research the areas. Computer skills and geographic information systems (GIS) help the scientist to analyze the multiple facets of geomorphology, topography, vegetation, and climate to discover the patterns left on the landscape.” 1 Soil scientists play a key role in understanding the soil’s past, analyzing present conditions, and making recommendations for future soil-related practices.
Summary
Plants obtain mineral nutrients from the soil. Soil is the outer loose layer that covers the surface of Earth. Soil quality depends on the chemical composition of the soil, the topography, the presence of living organisms, the climate, and time. Agricultural practice and history may also modify the characteristics and fertility of soil. Soil consists of four major components: 1) inorganic mineral matter, 2) organic matter, 3) water and air, and 4) living matter. The organic material of soil is made of humus, which improves soil structure and provides water and minerals. Soil inorganic material consists of rock slowly broken down into smaller particles that vary in size, such as sand, silt, and loam.
Soil formation results from a combination of biological, physical, and chemical processes. Soil is not homogenous because its formation results in the production of layers called a soil profile. Factors that affect soil formation include: parent material, climate, topography, biological factors, and time. Soils are classified based on their horizons, soil particle size, and proportions. Most soils have four distinct horizons: O, A, B, and C.
Footnotes
- 1 National Resources Conservation Service / United States Department of Agriculture. “Careers in Soil Science.” soils.usda.gov/education/facts/careers.html
Glossary
- A horizon
- consists of a mixture of organic material with inorganic products of weathering
- B horizon
- soil layer that is an accumulation of mostly fine material that has moved downward
- bedrock
- solid rock that lies beneath the soil
- C horizon
- layer of soil that contains the parent material, and the organic and inorganic material that is broken down to form soil; also known as the soil base
- clay
- soil particles that are less than 0.002 mm in diameter
- horizon
- soil layer with distinct physical and chemical properties, which differs from other layers depending on how and when it was formed
- humus
- organic material of soil; made up of microorganisms, dead animals and plants in varying stages of decay
- loam
- soil that has no dominant particle size
- mineral soil
- type of soil that is formed from the weathering of rocks and inorganic material; composed primarily of sand, silt, and clay
- O horizon
- layer of soil with humus at the surface and decomposed vegetation at the base
- organic soil
- type of soil that is formed from sedimentation; composed primarily of organic material
- parent material
- organic and inorganic material in which soils form
- rhizosphere
- area of soil affected by root secretions and microorganisms
- sand
- soil particles between 0.1–2 mm in diameter
- silt
- soil particles between 0.002 and 0.1 mm in diameter
- soil profile
- vertical section of a soil
- soil
- outer loose layer that covers the surface of Earth


3.0: Introduction
Swimming pools have long been a popular means of recreation, exercise, and physical therapy. Since it is impractical to refill large pools with fresh water on a frequent basis, pool water is regularly treated with chemicals to prevent the growth of harmful bacteria and algae. Proper pool maintenance requires regular additions of various chemical compounds in carefully measured amounts. For example, the relative amount of calcium ion, Ca 2 + , in the water should be maintained within certain limits to prevent eye irritation and avoid damage to the pool bed and plumbing. To maintain proper calcium levels, calcium cations are added to the water in the form of an ionic compound that also contains anions; thus, it is necessary to know both the relative amount of Ca 2 + in the compound and the volume of water in the pool in order to achieve the proper calcium level. Quantitative aspects of the composition of substances (such as the calcium-containing compound) and mixtures (such as the pool water) are the subject of this chapter.


12.1: How can we create equity in the classroom?
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by: Anthony D. Richardson
INTRODUCTION
There are many avenues we can take toward equity in the school. We will discuss Culture, School Size, Gender, Learning, and Funding. Five important topics needed for equity in the classroom. Before you can fair assessment of anything a person faces, they must try to understand the what, when, why and how. Equity is what every Teacher, Principal, School Super Attendant, and Parent should strive for.
CULTURE
Year 2004 represented the 50th anniversary of Brown v. Board of Education of Topeka, Kansas (1954), the Supreme Court decision outlawing racial segregation in schools. Brown v. Board has been called the defining legal decision of the 20th century, framing as it did the United States’ struggle with issues of race and racial equality. In that decision, the justices clearly state that they were striking down segregation in public schools both to increase educational equity and to eliminate the racial stigma associated with segregation.
Despite a wide range of efforts over the past 50 years, issues of racial and ethnic stigma and its relationship to identity and motivation remain central issues for those interested in creating racially equitable educational settings today. I argue that efforts to improve educational equity can only advance when a corresponding effort is made to reduce racial and ethnic stigma.
In the 50 years since the first Brown decision, we have learned a great deal about both the value of diverse learning environments for student development and how to create effective diverse learning environments. Nevertheless, as we come to understand that the racial and ethnic stigma discussed in Brown continues to play a central role in modern educational outcomes and inequities, we can direct our reform efforts in productive ways.
- First, teachers much acknowledge how deficit-based notions of diverse students continue to permeate traditional school thinking, practices, and placement, and critique their own thoughts and practices to ensure they do not reinforce prejudiced behavior.
- Second, culturally relevant pedagogy recognizes the explicit connection between culture and learning, and sees students’ cultural capital as an asset and not a detriment to their school success.
- Third, culturally relevant teaching is mindful of how traditional teaching practices reflect middle-class; European-American cultural values, and thus seeks to incorporate a wider range of dynamic and fluid teaching practices outcomes through the amelioration of stigma
Note
Culture ... impacts our lives by determining what is important and what is not,what makes sense and what does not. The culture then makes these constructions available to the young and to new initiates for appropriation and use in transforming their participation in that culture. Learning, then, becomes a matter of changes in one's relation to the culture(s) to which one is connected.
SCHOOL SIZE
A large-scale quantitative study using nationally representative and longitudinal data attempted to identify the ideal size of a high school, based on student learning. The study explored these issues for about 10,000 students in 800 public and private schools in the United States. Although most research on this topic has been framed within a "bigger versus smaller" mode, the objective here was to estimate an appropriate balance point between student learning and school size. Achievement gains in mathematics and reading over the course of high school were found to be largest in middle-sized high schools (600-900 students). Schools of this size were also favored in terms of social equity, in that they had weaker relationships between student socioeconomic status (SES) and achievement. Lee and Smith also found that even though the same "ideal size" was consistent across schools identified by their average SES and minority concentrations, school size was a more important factor in determining learning in schools enrolling more disadvantaged students.
Investigating the effects of school size in Chicago's (K-8) elementary schools, another study also found favorable effects for smaller schools in terms of student learning and teachers' willingness to take responsibility for their students' learning. Although without exception, teachers and students reported that social relations were more personal in the smaller high schools; this was not always seen as a benefit. A few students in the smaller high schools reported that they were unable to "live down" the negative reputations of their older siblings or even parents. Some teachers in such schools had to work hard to keep a modicum of privacy.
Sociological theory suggests that human interactions and ties become more formal as organizations grow. Organizational growth generates new bureaucratic structures, as connections between individuals become less personal. These structures can inhibit communal organization. This general theory has been confirmed in research identifying the organizational characteristics of effective schools. In school climate studies, for example, size operates as an ecological feature of the social structure, part of the physical environment that influences the nature of social interactions. In general, the sociological evidence about high schools suggests that social relations are generally more positive in smaller schools.
GENDER
As young people move into adolescence, they begin to explore gender roles. Finding their way through this potential minefield is complicated and challenging for middle school students. The process of determining the variations in masculinity and femininity is largely a social function, not a biological one. What it means to be a man, and what it means to be a woman, is communicated to children by all the adults in a child's life, including teachers.
Boys and girls create very distinct cultures; when they are in same-gender groups they act and play very differently. Girls are talkative and cooperative, boys are competitive and physical. Teachers need to understand these differences and be purposeful in the treatment of each so as to send the healthiest messages to adolescents.
In 1992 the American Association of University Women (AALUW) published a groundbreaking study about how schools were not meeting the needs of young girls. Their schools shortchanged girls in many ways: when questioned in class, girls were less likely to receive a prompt to clarify thinking if they answered incorrectly; boys were more regularly called on, and if not, they were just as likely to shout out an answer, leaving girls to sit quietly; and girls were not encouraged to take advanced math and science classes (AAUW 1992). Perhaps not surprisingly, then, in their middle school years, girls stopped being successful in math and science.
So what do we do? The first thing is to become aware of the differences between genders. Once these differences are explained and accepted, educators must be proactive in the way boys and girls are treated in schools. Indeed, there are distinct advantages to educating boys and girls together appropriately, for in doing so, each gender will begin to see how the other thinks, feels, responds, and reacts. Such understanding is in itself a major goal for gender-friendly classrooms.
We should also consider the nature of the differences between boys and girls. Creating a gender-friendly classroom does not mean that you create gender-specific activities, divide your classroom, or even insist on single-sex classes. Students should at some times have an opportunity to work in a gender-matched activity, while at other times they should learn to function in a more typical gender-mismatched one. This allows students to experience instructional times that are more comfortable for students when the activities are matched to their nature. But they also learn to function outside that comfort area when they are in a mismatched situation, and thus strengthen weaker areas.
For teachers the imperative is to learn about the differences in gender. Teachers need to accept that learning occurs differently for each gender, and to measure out activities and experiences that favor one some of the time, and the other some of the time.   When boys see girls appropriately modeling relationship behaviors, the boys learn how to be more sensitive and open. Likewise, when girls see the appropriate use of assertiveness that boys learn early, the girls see that this can be used to their advantage as well.
LEARNING
Human beings, in our conscious hours at least, are always learning. We cannot do otherwise; learning is an involuntary human activity. What varies among us is what we learn, how our learning is put to use and reinforced, and what learning is valued by a particular group of people at a particular time—our education. The result is that, while everyone learns, some learn to survive and some learn to thrive.
Unfortunately, access to the learning experiences that help people to thrive, though these depend on context, are not equally or equitably available to everyone. And although there may be value in all types of learning experiences, a deep understanding in the field of education of the range of learning experiences available to people who thrive is the first step toward ensuring adequate access to these experiences for all.
Schools, then, are only one of society's educative institutions. Although schools may be the most widely recognized of such institutions, a theory of education must encompass not just a theory of schooling but also a theory of the relation of various educative interactions and institutions with one another and to the members of the society at large. And a vision of educational equity must become a vision of providing access not just to schooling but also to these other resources.
Holistic approach to learning
- High quality early childhood education programs
- Rigorous and challenging curricula for all students
- High quality teaching
- Effective, sustained educational leadership
- Appropriate class sizes
- Mental and physical health care services
- Appropriate academic support for English language learners
- Appropriate academic support for special education students
- Appropriate academic support for children in areas of highly concentrated poverty
- Effective after-school, community, and summer programs
- Effective parental involvement and family support
-
Policies that foster racially and economically diverse schools
FUNDING
Throughout the United States, wide performance gaps exist between poor and minority students and their peers in other groups. The inequities that result in those performance gaps carry enormous costs, not only for the children and families involved, but for the nation as a whole. The annual price tag of inadequately educating our young people is staggering, in the realm of $250 billion per year in health and welfare costs, criminal justice expenses, and lost tax revenues. The heavy toll on the social and civic fabric of the nation is an additional, inestimable price that we all pay every year.
If we are to meet the global economic challenges of an increasingly "flat world," if we are to prepare our students to be capable civic participants in our democratic society, and if we are to fulfill the moral imperative of ensuring that a child's racial/ethnic, socioeconomic, or family background no longer predicts that child's educational attainment or level of achievement, we need a comprehensive approach to educational equity that attends to the full array of factors that affect educational opportunity.
Since late in the 20th century, there has been a burgeoning of initiatives, programs, projects, and activities that fall under the umbrella of what we are calling "comprehensive educational equity" by seeking to integrate education and supports and services in other areas that enhance students' abilities to succeed.
A wide range of institutions, from federal and state governments to national and local foundations, to individual schools, carries out some type of "comprehensive educational equity" effort. The delivery models employed include community, full-service, and extended schools; comprehensive early childhood programs; school-linked services projects; school-community partnerships; private interagency commissions; family support and education programs; integrated-services initiatives; comprehensive community initiatives; and state programs and broad national legislation.
Within these models, individual efforts have varying goals, rationales, methodologies, scopes, participants, scales, and time frames. The proliferation of these efforts provides a rich and complex field of study for potential models, best practices, and policy direction on which to build. Their many variations point to challenges for study, evaluation, and replication.
CONCLUSION
Equity in the class room is not an easy task, but a necessity. As we continue to create equity in our classrooms were contributing and enhancing peoples lives. We are better equipping students, parents, communities, America, and the World. We must recognize what is going on with our students by communicating with them in order to make the right assessment. We as educators must think outside the box. Times are changing so the way we educate must change as well.
Exercise \(\PageIndex{1}\)
1. What does not create effective diverse learning environments?
A. Teachers much acknowledge how deficit-based notions of diverse students continue to permeate traditional school thinking, practices, and placement, and critique their own thoughts and practices to ensure they do not reinforce prejudiced behavior.
B. Culturally relevant pedagogy recognizes the explicit connection between culture and learning, and sees students’ cultural capital as an asset and not a detriment to their school success.
C. Culturally relevant teaching is mindful of how traditional teaching practices reflect middle-class; European-American cultural values, and thus seeks to incorporate a wider range of dynamic and fluid teaching practices outcomes through the amelioration of stigma.
D. Disregard cultural differences and teach a rigid and structured class that focuses on passing the SOL's.
2. How does school size does effect the a classroom?
A. Estimates an appropriate balance point between student learning and school size.
B. Study found favorable effects for larger schools in terms of student learning and teachers' willingness to take responsibility for their students' learning.
C. Study found similar effects for larger schools in terms of student learning and teachers' willingness to take responsibility for their students' learning environment.
D. It does not effect the classroom and learning environment at all.
3. What is the differences between genders?
A. Girls are competitive and boys are talkative and cooperate.
B. Boys and girls create very distinct cultures; when they are in same-gender groups they act and play very differently.
C. Girls are talkative and cooperative, boys are competitive and physical.
D. The only difference is how they are raised in the home.
4. Why is learning not equal from school to school?
A. Access to the learning experiences that help people to thrive, though these depend on context, are not equally or equitably available to everyone becuause?
B. Everyone does not have the same access.
C. All the responsibility is on the schools.
D. Every can go to the public library.
5. What is the annual price tag of inadequately educating our young people?
A. Inestimable price that we all pay every year.
B. Whatever the amount of money we get from the lottery.
C. The annual price tag of inadequately educating our young people is staggering, in the realm of $250 billion per year in health and welfare costs, criminal justice expenses, and lost tax revenues.
D. The annual price tag of inadequately educating our young people is only $500 million per year.
- Answer
-
1. ( D)
2. (B)
3. (C)
4. (A)
5. (C)
References
Edmund, W., Gordon, M., Rebeell A. (2007) Toward a Comprehensive System of Education for All Children. Teachers College Record , 109 no.7, 1836–43
Lee, V., Ready, D., Welner, K. (2004) Education Equity and School Structure: School Size, Overcrowding, and School-Within-School. Teachers College Record , 106 no.10, 1989-2014
David, K. (2006) Boys and Girls Together: A Case for Creating Gender-Friendly Middle School Classrooms. The Clearing House , 79 no.6, 247-51
Hertzog, N. (2005) Equity and Access: Creating General Education Classrooms Responsive to Potential Giftedness. Journal for the Education of the Gifted , 29 no.2 213-57
Shutkin, D. (2004) Thinking of the Other: Constructivist Discourse and Cultural Difference in the Field of Educational Technology. Journal of Educational Thought , 38 no.1 67-93
Zirkel, S. (2005) Ongoing Issues of Racial and Ethnic Stigma in Education 50 Years after Brown v. Board. The Urban Review , 37 no.2 107-26


4.2: Cartesian Coordinates
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The Cartesian coordinate system is introduced in Section 4.1. Concepts described in that section – i.e., the dot product and cross product – are described in terms of the Cartesian system. In this section, we identify some additional features of this system that are useful in subsequent work and also set the stage for alternative systems; namely the cylindrical and spherical coordinate systems.
Integration Over Length
Consider a vector field \({\bf A}=\hat{\bf x}A({\bf r})\), where \({\bf r}\) is a position vector. What is the integral of \({\bf A}\) over some curve \(\mathcal{C}\) through space? To answer this question, we first identify a differential-length segment of the curve. Note that this segment of the curve can be described as
\[d{\bf l} = \hat{\bf x}dx + \hat{\bf y}dy + \hat{\bf z}dz \nonumber \]
The contribution to the integral for that segment of the curve is simply \({\bf A}\cdot d{\bf l}\). We integrate to obtain the result; i.e.,
\[\int_{\mathcal C}{ {\bf A}\cdot d{\bf l} } \nonumber \]
For example, if \({\bf A}=\hat{\bf x}A_0\) (i.e., \(A({\bf r})\) is a constant) and if \(\mathcal{C}\) is a straight line from \(x=x_1\) and \(x=x_2\) along some constant \(y\) and \(z\), then \(d{\bf l} = \hat{\bf x}dx\), \({\bf A}\cdot d{\bf l}=A_0 dx\), and subsequently the above integral is
\[\int_{x_1}^{x_2}{ A_0 dx } = A_0\left(x_2-x_1\right) \nonumber \]
In particular, notice that if \(A_0=1\), then this integral gives the length of \({\mathcal C}\). Although the formalism seems unnecessary in this simple example, it becomes very useful when integrating over paths that vary in more than one direction and with more complicated integrands.
Note that the Cartesian system was an appropriate choice for preceding example because this allowed two of the three basis directions (i.e., \(y\) and \(z\)) to be immediately eliminated from the calculation. Said differently, the preceding example is expressed with the minimum number of varying coordinates in the Cartesian system. Here’s a counter-example. If \({\mathcal C}\) had been a circle in the \(z=0\) plane, then the problem would have required two basis directions to be considered – namely, both \(x\) and \(y\). In this case, another system – namely, cylindrical coordinates (Section 4.3) – minimizes the number of varying coordinates (to just one, which is \(\phi\)).
Integration Over Area
Now we ask the question, what is the integral of some vector field \({\bf A}\) over some surface \({\mathcal S}\)? The answer is
\[\int_{\mathcal S}{\mathbf{A} \cdot d\mathbf{s}} \label{m0004_eFlux} \]
We refer to \(d\bf s\) as the differential surface element, which is a vector having magnitude equal to the differential area \(ds\), and is normal (perpendicular) to each point on the surface. There are actually two such directions. We’ll return to clear up the ambiguity in a moment. Now, as an example, if \(\bf A=\hat{\bf z}\) and \(\mathcal{S}\) is the surface bounded by \(x_1\le x \le x_2\), \(y_1\le y \le y_2\), then
\[d{\bf s} = \hat{\bf z}~dx~dy \nonumber \]
since \(dx\,dy\) is differential surface area in the \(z=0\) plane and \(\hat{\bf z}\) is normal to the \(z=0\) plane. So \(\mathbf {A} \cdot d\mathbf {s}=dx dy\), and subsequently the integral in Equation \ref{m0004_eFlux} becomes
\[\int_{x_1}^{x_2}\int_{y_1}^{y_2}{dx~dy} = \left(x_2-x_1\right)\left(y_2-y_1\right) \nonumber \]
Note that this has turned out to be a calculation of area.
Once again, we see the Cartesian system was an appropriate choice for this example because this choice minimizes the number of varying coordinates; in the above example, the surface of integration is described by a constant value of \(z\) with variable values of \(x\) and \(y\). If the surface had instead been a cylinder or a sphere, not only would all three basis directions be variable, but also the surface normal would be variable, making the problem dramatically more complicated.
Now let’s return to the issue of the direction of \(d{\bf s}\). We chose \(+\hat{\bf z}\), but why not choose \(-\hat{\bf z}\) – also a normal to the surface – as this direction? To answer simply, the resulting area would be negative. “Negative area” is the expected (“positive”) area, except with respect to the opposite-facing normal vector. In the present problem, the sign of the area is not important, but in some problems this sign becomes important. One example of a class of problems for which the sign of area is important is when the quantity of interest is a flux . If \({\bf A}\) were a flux density, then the integration over area that we just performed indicates the magnitude and direction of flux, and so the direction chosen for \(d{\bf s}\) defines the direction of positive flux. Section 2.4 describes the electric field in terms of a flux (i.e., as electric flux density \({\bf D}\)), in which case positive flux flows away from a positively-charged source.
Integration Over Volume
Another common task in vector analysis is integration of some quantity over a volume. Since the procedure is the same for scalar or vector quantities, we shall consider integration of a scalar quantity \(A(\bf r)\) for simplicity. First, we note that the contribution from a differential volume element
\[dv = dx~dy~dz \nonumber \]
is \(A(\mathbf{r})~dv\), so the integral over the volume \(\mathcal V\) is
\[\int_{\mathcal V} A(\mathbf{r})~dv \nonumber \]
For example, if \(A(\mathbf{r})=1\) and \(\mathcal{V}\) is a cube bounded by \(x_1\le x \le x_2\), \(y_1\le y \le y_2\), and \(z_1\le z \le z_2\), then the above integral becomes
\[\int_{x_1}^{x_2}\int_{y_1}^{y_2}\int_{z_1}^{z_2}{dx~dy~dz} = \left(x_2-x_1\right)\left(y_2-y_1\right)\left(z_2-z_1\right) \nonumber \]
i.e., this is a calculation of volume.
The Cartesian system was an appropriate choice for this example because \({\mathcal V}\) is a cube, which is easy to describe in Cartesian coordinates and relatively difficult to describe in any other coordinate system.


2.23: Complex Numbers
Evaluating the Square Root of a Negative Number
Whenever we have a situation where we have a square root of a negative number we say there is no real number that equals that square root. For example, to simplify \(\sqrt{-1}\), we are looking for a real number \(x\) so that \(x^{2}=-1\). Since all real numbers squared are positive numbers, there is no real number that equals \(–1\) when squared.
Mathematicians have often expanded their numbers systems as needed. They added \(0\) to the counting numbers to get the whole numbers. When they needed negative balances, they added negative numbers to get the integers. When they needed the idea of parts of a whole they added fractions and got the rational numbers. Adding the irrational numbers allowed numbers like \(\sqrt{5}\). All of these together gave us the real numbers and so far in your study of mathematics, that has been sufficient.
But now we will expand the real numbers to include the square roots of negative numbers. We start by defining the imaginary unit \(i\) as the number whose square is \(–1\).
The imaginary unit \(i\) is the number whose square is \(-1\).
\(i^{2}=-1 \text { or } i=\sqrt{-1}\)
We will use the imaginary unit to simplify the square roots of negative numbers.
If \(b\) is a positive real number, then
\(\sqrt{-b}=\sqrt{b} i\)
We will use this definition in the next example. Be careful that it is clear that the \(i\) is not under the radical. Sometimes you will see this written as \(\sqrt{-b}=i \sqrt{b}\) to emphasize the \(i\) is not under the radical. But the \(\sqrt{-b}=\sqrt{b} i\) is considered standard form.
Write each expression in terms of \(i\) and simplify is possible:
- \(\sqrt{-25}\)
- \(\sqrt{-7}\)
- \(\sqrt{-12}\)
Solution :
a.
\(\sqrt{-25}\)
Use the definition of the square root of negative numbers.
\(\sqrt{25} i\)
Simplify.
\(5i\)
b.
\(\sqrt{-7}\)
Use the definition of the square root of negative numbers.
\(\sqrt{7} i\)
Simplify.
Be careful that it is clear that \(i\) is not under the radical sign.
c.
\(\sqrt{-12}\)
Use the definition of the square root of negative numbers.
\(\sqrt{12} i\)
Simplify \(\sqrt{12}\).
\(2 \sqrt{3} i\)
Write each expression in terms of \(i\) and simplify if possible:
- \(\sqrt{-81}\)
- \(\sqrt{-5}\)
- \(\sqrt{-18}\)
- Answer
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- \(9i\)
- \(\sqrt{5} i\)
- \(3 \sqrt{2} i\)
Now that we are familiar with the imaginary number \(i\), we can expand the real numbers to include imaginary numbers. The complex number system includes the real numbers and the imaginary numbers. A complex number is of the form \(a+bi\), where \(a, b\) are real numbers. We call \(a\) the real part and \(b\) the imaginary part.
A complex number is of the form \(a+bi\), where \(a\) and \(b\) are real numbers.
A complex number is in standard form when written as \(a+bi\), where \(a\) and \(b\) are real numbers.
If \(b=0\), then \(a+bi\) becomes \(a+0⋅i=a\), and is a real number.
If \(b≠0\), then \(a+bi\) is an imaginary number.
If \(a=0\), then \(a+bi\) becomes \(0+bi=bi\), and is called a pure imaginary number.
We summarize this here.
| \(a+bi\) | ||
| \(b=0\) |
\(a+0 \cdot i\) \(a\) |
Real number |
| \(b\neq 0\) | \(a+bi\) | Imaginary number |
| \(a=0\)R |
\(0+bi\) \(bi\) |
Pure imaginary numbe4 |
The standard form of a complex number is \(a+bi\), so this explains why the preferred form is \(\sqrt{-b}=\sqrt{b} i\) when \(b>0\).
The diagram helps us visualize the complex number system. It is made up of both the real numbers and the imaginary numbers.
Adding and Subtracting Complex Numbers
We are now ready to perform the operations of addition, subtraction, multiplication and division on the complex numbers—just as we did with the real numbers.
Adding and subtracting complex numbers is much like adding or subtracting like terms. We add or subtract the real parts and then add or subtract the imaginary parts. Our final result should be in standard form.
Add: \(\sqrt{-12}+\sqrt{-27}\)
Solution :
\(\sqrt{-12}+\sqrt{-27}\)
Use the definition of the square root of negative numbers.
\(\sqrt{12} i+\sqrt{27} i\)
Simplify the square roots.
\(2 \sqrt{3} i+3 \sqrt{3} i\)
Add.
\(5 \sqrt{3} i\)
Add: \(\sqrt{-8}+\sqrt{-32}\)
- Answer
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\(6 \sqrt{2} i\)
Remember to add both the real parts and the imaginary parts in this next example.
Simplify:
- \((4-3 i)+(5+6 i)\)
- \((2-5 i)-(5-2 i)\)
Solution :
a.
\((4-3 i)+(5+6 i)\)
Use the Associative Property to put the real parts and the imaginary parts together.
\((4+5)+(-3 i+6 i)\)
Simplify.
\(9+3i\)
b.
\((2-5 i)-(5-2 i)\)
Distribute.
\(2-5 i-5+2 i\)
Use the Associative Property to put the real parts and the imaginary parts together.
\(2-5-5 i+2 i\)
Simplify.
\(-3-3 i\)
Simplify:
- \((2+7 i)+(4-2 i)\)
- \((8-4 i)-(2-i)\)
- Answer
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- \(6+5i\)
- \(6-3i\)
Multiplying Complex Numbers
Multiplying complex numbers is also much like multiplying expressions with coefficients and variables. There is only one special case we need to consider. We will look at that after we practice in the next two examples.
Multiply: \(2 i(7-5 i)\)
Solution :
\(2 i(7-5 i)\)
Distribute.
\(14 i-10 i^{2}\)
Simplify \(i^{2}\).
\(14 i-10(-1)\)
Multiply.
\(14 i+10\)
Write in standard form.
\(10+14i\)
Multiply: \(-3 i(2+4 i)\).
- Answer
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\(12+6i\)
In the next example, we multiply the binomials using the Distributive Property or FOIL .
Multiply: \((3+2 i)(4-3 i)\)
Solution :
\((3+2 i)(4-3 i)\)
Use FOIL.
\(12-9 i+8 i-6 i^{2}\)
Simplify \(i^{2}\) and combine like terms.
\(12-i-6(-1)\)
Multiply.
\(12-i+6\)
Combine the real parts.
\(18-i\)
Multiple: \((5-3 i)(-1-2 i)\)
- Answer
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\(-11-7i\)
In the next example, we could use FOIL or the Product of Binomial Squares Pattern .
Multiply: \((3+2 i)^{2}\)
Solution :
| Use the Product of Binomial Squares Pattern, \((a+b)^{2}=a^{2}+2 a b+b^{2}\). | |
| Simplify. | |
| Simplify \(i^{2}\). | |
| Simplify. |
Multiply: \((-2-5 i)^{2}\)
- Answer
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\(-21-20 i\)
Since the square root of a negative number is not a real number, we cannot use the Product Property for Radicals. In order to multiply square roots of negative numbers we should first write them as complex numbers, using \(\sqrt{-b}=\sqrt{b}i\).This is one place students tend to make errors, so be careful when you see multiplying with a negative square root.
Multiply: \(\sqrt{-36} \cdot \sqrt{-4}\)
Solution :
To multiply square roots of negative numbers, we must first write them as complex numbers.
\(\sqrt{-36} \cdot \sqrt{-4}\)
Write as complex numbers using \(\sqrt{-b}=\sqrt{b}i\).
\(\sqrt{36} i \cdot \sqrt{4} i\)
Simplify.
\(6 i \cdot 2 i\)
Multiply.
\(12i^{2}\)
Simplify \(i^{2}\) and multiply.
\(-12\)
Multiply: \(\sqrt{-49} \cdot \sqrt{-4}\)
- Answer
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\(-14\)
In the next example, each binomial has a square root of a negative number. Before multiplying, each square root of a negative number must be written as a complex number.
Multiply: \((3-\sqrt{-12})(5+\sqrt{-27})\)
Solution :
To multiply square roots of negative numbers, we must first write them as complex numbers.
\((3-\sqrt{-12})(5+\sqrt{-27})\)
Write as complex numbers using \(\sqrt{-b}=\sqrt{b}i\).
\((3-2 \sqrt{3} i)(5+3 \sqrt{3} i)\)
Use FOIL.
\(15+9 \sqrt{3} i-10 \sqrt{3} i-6 \cdot 3 i^{2}\)
Combine like terms and simplify \(i^{2}\).
\(15-\sqrt{3} i-6 \cdot(-3)\)
Multiply and combine like terms.
\(33-\sqrt{3} i\)
Multiply: \((-2+\sqrt{-8})(3-\sqrt{-18})\)
- Answer
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\(6+12 \sqrt{2} i\)
We first looked at conjugate pairs when we studied polynomials. We said that a pair of binomials that each have the same first term and the same last term, but one is a sum and one is a difference is called a conjugate pair and is of the form \((a−b),(a+b)\).
A complex conjugate pair is very similar. For a complex number of the form \(a+bi\), its conjugate is \(a−bi\). Notice they have the same first term and the same last term, but one is a sum and one is a difference.
A complex conjugate pair is of the form \(a+bi,a-bi\).
We will multiply a complex conjugate pair in the next example.
Multiply: \((3-2 i)(3+2 i)\)
Solution :
\((3-2 i)(3+2 i)\)
Use FOIL
\(9+6 i-6 i-4 i^{2}\)
Combine like terms and simplify \(i^{2}\).
\(9-4(-1)\)
Multiply and combine like terms.
\(13\)
Multiply: \((-2+5 i) \cdot(-2-5 i)\)
- Answer
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\(29\)
From our study of polynomials, we know the product of conjugates is always of the form \((a-b)(a+b)=a^{2}-b^{2}\).The result is called a difference of squares . We can multiply a complex conjugate pair using this pattern.
The last example we used FOIL. Now we will use the Product of Conjugates Pattern .
Notice this is the same result we found in Example 8.8.9.
When we multiply complex conjugates, the product of the last terms will always have an \(i^{2}\) which simplifies to \(−1\).
\(\begin{array}{c}{(a-b i)(a+b i)} \\ {a^{2}-(b i)^{2}} \\ {a^{2}-b^{2} i^{2}} \\ {a^{2}-b^{2}(-1)} \\ {a^{2}+b^{2}}\end{array}\)
This leads us to the Product of Complex Conjugates Pattern: \((a-b i)(a+b i)=a^{2}+b^{2}\)
If \(a\) and \(b\) are real numbers, then
\((a-b i)(a+b i)=a^{2}+b^{2}\)
Multiply: \((8-2 i)(8+2 i)\)
Solution :
| Use the Product of Complex Conjugates Pattern, \((a-b i)(a+b i)=a^{2}+b^{2}\). | |
| Simplify the squares. | |
| Add. |
Multiply: \((-5+4 i)(-5-4 i)\)
- Answer
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\(41\)
Dividing Complex Numbers
Dividing complex numbers is much like rationalizing a denominator. We want our result to be in standard form with no imaginary numbers in the denominator.
Divide: \(\frac{4+3 i}{3-4 i}\)
Solution :
| Step 1 : Write both the numerator and denominator in standard form. | They are both in standard form. | \(\frac{4+3 i}{3-4 i}\) |
| Step 2 : Multiply the numerator and denominator by the complex conjugate of the denominator. | The complex conjugate of \(3-4i\) is \(3+4i\). | \(\frac{(4+3 i)\color{red}{(3+4 i)}}{(3-4 i)\color{red}{(3+4 i)}}\) |
| Step 3 : Simplify and write the result in standard form. |
Use the pattern \((a-b i)(a+b i)=a^{2}+b^{2}\) in the denominator. Combine like terms. Simplify. Write the result in standard form. |
\(\begin{array}{c}{\frac{12+16 i+9 i+12 i^{2}}{9+16}} \\ {\frac{12+25 i-12}{25}} \\ {\frac{25 i}{25}} \\ {i}\end{array}\) |
Divide: \(\frac{2+5 i}{5-2 i}\)
- Answer
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\(i\)
We summarize the steps here.
How to Divide Complex Numbers
- Write both the numerator and denominator in standard form.
- Multiply both the numerator and denominator by the complex conjugate of the denominator.
- Simplify and write the result in standard form.
Divide, writing the answers in standard form: \(\frac{-3}{5+2 i}\)
Solution :
\(\frac{-3}{5+2 i}\)
Multiply the numerator and denominator by the complex conjugate of the denominator.
\(\frac{-3(5-2 i)}{(5+2 i)(5-2 i)}\)
Multiply in the numerator and use the Product of Complex Conjugates Pattern in the denominator.
\(\frac{-15+6 i}{5^{2}+2^{2}}\)
Simplify.
\(\frac{-15+6 i}{29}\)
Write in standard form.
\(-\frac{15}{29}+\frac{6}{29} i\)
Divide, writing the answer in standard form: \(\frac{4}{1-4 i}\)
- Answer
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\(\frac{4}{17}+\frac{16}{17} i\)
Be careful as you find the conjugate of the denominator.
Divide: \(\frac{5+3 i}{4 i}\)
Solution :
\(\frac{5+3 i}{4 i}\)
Write the denominator in standard form.
\(\frac{5+3 i}{0+4 i}\)
Multiply the numerator and denominator by the complex conjugate of the denominator.
\(\frac{(5+3 i)(0-4 i)}{(0+4 i)(0-4 i)}\)
Simplify.
\(\frac{(5+3 i)(-4 i)}{(4 i)(-4 i)}\)
Multiply.
\(\frac{-20 i-12 i^{2}}{-16 i^{2}}\).
Simplify the \(i^{2}\).
\(\frac{-20 i+12}{16}\)
Rewrite in standard form.
\(\frac{12}{16}-\frac{20}{16} i\)
Simplify the fractions.
\(\frac{3}{4}-\frac{5}{4} i\)
Divide: \(\frac{3+3 i}{2 i}\)
- Answer
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\(\frac{3}{2}-\frac{3}{2} i\)
Simplifying Powers of \(i\)
The powers of \(i\) make an interesting pattern that will help us simplify higher powers of \(i\). Let’s evaluate the powers of \(i\) to see the pattern.
\(\begin{array}{ccc}{i^{1}} \qquad& {i^{2}} & {i^{3}} \qquad& {i^{4}} \\ {i} \qquad& {-1} \qquad& {i^{2}\cdot i} \qquad& {i^{2}\cdot i^{2}}\\ {}\qquad& {}\qquad& {-1\cdot i}\qquad& {(-1)(-1)}\\ {}\qquad&{}\qquad&{-i}&{1}\end{array}\)
\(\begin{array}{cccc}{i^{5}} \qquad& {i^{6}} \qquad& {i^{7}} \qquad& {i^{8}} \\ {i^{4} \cdot i} \qquad& {i^{4} \cdot i^{2}} \qquad& {i^{4} \cdot i^{3}} \qquad& {i^{4} \cdot i^{4}} \\ {1 \cdot i} \qquad& {1 \cdot i^{2}} \qquad& {1 \cdot i^{3}} \qquad& {1 \cdot 1} \\ {i} \qquad& {i^{2}} & {i^{3}} \qquad& {1} \\ {}&\qquad&{-1} & {-i}\end{array}\)
We summarize this now.
\(\begin{array}{ll}{i^{1}=i} \qquad& {i^{5}=i} \\ {i^{2}=-1} \qquad& {i^{6}=-1} \\ {i^{3}=-i} \qquad& {i^{7}=-i} \\ {i^{4}=1} \qquad& {i^{8}=1}\end{array}\)
If we continued, the pattern would keep repeating in blocks of four. We can use this pattern to help us simplify powers of \(i\). Since \(i^{4}=1\), we rewrite each power, \(i^{n}\), as a product using \(i^{4}\) to a power and another power of \(i\).
We rewrite it in the form \(i^{n}=\left(i^{4}\right)^{q} \cdot i^{r}\), where the exponent, \(q\), is the quotient of \(n\) divided by \(4\) and the exponent, \(r\), is the remainder from this division. For example, to simplify \(i^{57}\), we divide \(57\) by \(4\) and we get \(14\) with a remainder of \(1\). In other words, \(57=4⋅14+1\). So we write \(i^{57}=\left(1^{4}\right)^{14} \cdot i^{1}\) and then simplify from there.
Simplify: \(i^{86}\)
Solution :
\(i^{86}\)
Divide \(86\) by \(4\) and rewrite \(i^{86}\) in the \(i^{n}=\left(i^{4}\right)^{q} \cdot i^{r}\) form.
\(\left(1^{4}\right)^{21} \cdot i^{2}\)
Simplify.
\((1)^{21} \cdot(-1)\)
Simplify.
\(-1\)
Simplify: \(i^{75}\)
- Answer
-
\(-1\)


7.3: Contemporary Structures
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2. What contemporary organizational structures are companies using?
Although traditional forms of departmentalization still represent how many companies organize their work, newer, more flexible organizational structures are in use at many firms. Let’s look at matrix and committee structures and how those two types of organizations are helping companies better leverage the diverse skills of their employees.
Matrix Structure
The matrix structure (also called the project management approach) is sometimes used in conjunction with the traditional line-and-staff structure in an organization. Essentially, this structure combines two different forms of departmentalization, functional and product, that have complementary strengths and weaknesses. The matrix structure brings together people from different functional areas of the organization (such as manufacturing, finance, and marketing) to work on a special project. Each employee has two direct supervisors: the line manager from her or his specific functional area and the project manager. Exhibit 7.7 shows a matrix organization with four special project groups (A, B, C, D), each with its own project manager. Because of the dual chain of command, the matrix structure presents some unique challenges for both managers and subordinates.
Exhibit 7.7 Matrix Organization (Attribution: Copyright Rice University, OpenStax, under CC BY 4.0 license.)
Advantages of the matrix structure include:
- Teamwork. By pooling the skills and abilities of various specialists, the company can increase creativity and innovation and tackle more complex tasks.
- Efficient use of resources. Project managers use only the specialized staff they need to get the job done, instead of building large groups of underused personnel.
- Flexibility. The project structure is flexible and can adapt quickly to changes in the environment; the group can be disbanded quickly when it is no longer needed.
- Ability to balance conflicting objectives. The customer wants a quality product and predictable costs. The organization wants high profits and the development of technical capability for the future. These competing goals serve as a focal point for directing activities and overcoming conflict. The marketing representative can represent the customer, the finance representative can advocate high profits, and the engineers can push for technical capabilities.
- Higher performance. Employees working on special project teams may experience increased feelings of ownership, commitment, and motivation.
- Opportunities for personal and professional development. The project structure gives individuals the opportunity to develop and strengthen technical and interpersonal skills.
Disadvantages of the matrix structure include:
- Power struggles. Functional and product managers may have different goals and management styles.
- Confusion among team members. Reporting relationships and job responsibilities may be unclear.
- Lack of cohesiveness. Team members from different functional areas may have difficulty communicating effectively and working together as a team.
Although project-based matrix organizations can improve a company’s flexibility and teamwork, some companies are trying to unravel complex matrix structures that create limited accountability and complicate day-to-day operations. Some CEOs and other top managers suggest that matrix structures make it easier to blame others when things don’t go as planned. 7
Committee Structure
In committee structure , authority and responsibility are held by a group rather than an individual. Committees are typically part of a larger line-and-staff organization. Often the committee’s role is only advisory, but in some situations the committee has the power to make and implement decisions. Committees can make the coordination of tasks in the organization much easier. For example, Novartis, the huge Swiss pharmaceutical company, has a committee structure, which reports to its board of directors. The company’s executive committee is responsible for overseeing the business operations of group companies within the global organization and consists of the CEO, CFO, head of HR, general counsel, president of operations, head of biomedical research, global head of drug development, CEOs of the pharmaceutical and oncology units, and CEOs of Sandoz and Alcon, other Novartiscompanies. Members of the executive committee are selected by the company’s board of directors. 8
Committees bring diverse viewpoints to a problem and expand the range of possible solutions, but there are some drawbacks. Committees can be slow to reach a decision and are sometimes dominated by a single individual. It is also more difficult to hold any one individual accountable for a decision made by a group. Committee meetings can sometimes go on for long periods of time with seemingly little being accomplished.
CONCEPT CHECK
- Why does the matrix structure have a dual chain of command?
- How does a matrix structure increase power struggles or reduce accountability?
- What are advantages of a committee structure? Disadvantages?


28: Invertebrates
Invertebrate animals are those without a cranium and defined vertebral column or spine. In addition to lacking a spine, most invertebrates also lack an endoskeleton. A large number of invertebrates are aquatic animals, and scientific research suggests that many of the world’s species are aquatic invertebrates that have not yet been documented.
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- 28.0: Prelude to Invertebrates
- A brief look at any magazine pertaining to our natural world, such as National Geographic, would show a rich variety of vertebrates, especially mammals and birds. To most people, these are the animals that attract our attention. Concentrating on vertebrates, however, gives us a rather biased and limited view of biodiversity, because it ignores nearly 97 percent of the animal kingdom, namely the invertebrates.
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- 28.1: Phylum Porifera
- The simplest of all the invertebrates are the Parazoans, which include only the phylum Porifera: the sponges. Parazoans (“beside animals”) do not display tissue-level organization, although they do have specialized cells that perform specific functions. Sponge larvae are able to swim; however, adults are non-motile and spend their life attached to a substratum.
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- 28.2: Phylum Cnidaria
- Phylum Cnidaria includes animals that show radial or biradial symmetry and are diploblastic, that is, they develop from two embryonic layers. Nearly all (about 99 percent) cnidarians are marine species. Cnidarians contain specialized cells known as cnidocytes (“stinging cells”) containing organelles called nematocysts (stingers). These cells are present around the mouth and tentacles, and serve to immobilize prey with toxins contained within the cells.
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- 28.3: Superphylum Lophotrochozoa
- Animals belonging to superphylum Lophotrochozoa are protostomes, in which the blastopore, or the point of involution of the ectoderm or outer germ layer, becomes the mouth opening to the alimentary canal. This is called protostomy or “first mouth.” In protostomy, solid groups of cells split from the endoderm or inner germ layer to form a central mesodermal layer of cells. This layer multiplies into a band and then splits internally to form the coelom.
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- 28.4: Superphylum Ecdysozoa
- The superphylum Ecdysozoa contains an incredibly large number of species. This is because it contains two of the most diverse animal groups: phylum Nematoda (the roundworms) and Phylum Arthropoda (the arthropods). The most prominant distinguising feature of Ecdysozoans is their tough external covering called the cuticle. The cuticle provides a tough, but flexible exoskeleton tht protects these animals from water loss, predators and other aspects of the external environment.
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- 28.5: Superphylum Deuterostomia
- The phyla Echinodermata and Chordata (the phylum in which humans are placed) both belong to the superphylum Deuterostomia. Recall that protostome and deuterostomes differ in certain aspects of their embryonic development, and they are named based on which opening of the digestive cavity develops first. The word deuterostome comes from the Greek word meaning “mouth second,” indicating that the anus is the first to develop.
Thumbnail: Drosophila melanogaster. (CC BY-SA 2.5; André Karwath aka Aka via Wikimedia Commons ).


10.10.2: Dementia and Alzheimer’s Disease
Dementia is a rather broad category of any type of cognitive decline with age that begins to affect a person’s memory, their capacity to function in daily life, and eventually their ability to take care of themselves (CDC, 2024a). Probably the most significant and familiar type of dementia is Alzheimer’s disease, which is characterized by troubles with memory, language, and thinking. It is thought to be caused by the buildup and changes of specific proteins in the brain, which cause damage to neurons. This damage results in chronic inflammation and potentially even shrinkage of brain tissue. Alzheimer’s disease is progressive and eventually deadly, killing more people than breast cancer and prostate cancer combined (Alzheimer’s Association, 2024b).
It is estimated that almost 7 million Americans currently live with Alzheimer’s disease, and by 2050 that number could be as high as 13 million (Alzheimer’s Association, 2024b). Age is the most common risk factor: it affects approximately 10.9% of people over the age of 65, and 33.4% of those over 85. Specific genes have been identified in the process of developing Alzheimer’s disease - one of them being the APOE-e4 gene that helps create a protein for transporting cholesterol in the blood. Protective factors include maintaining cardiovascular health with nutrition and exercise, as well as fostering social connections and intellectual stimulation. Education may also be protective by helping develop a “cognitive reserve” in mid-life, thus delaying symptoms, or it may also be associated with other healthy behaviors (such as not smoking and exercise) or a corelary with socioeconomic status and other social determinants of health (Alzheimer’s Association, 2024a). Physical activity and exercise in a variety of forms has been shown to have a very powerful protective effect on the brain. It can both prevent and delay symptoms of Alzheimer’s or dementia of any type (Foreman, 2020).


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Chapter 25: The Urinary System
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25.1: Introduction
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The urinary system has roles you may be well aware of: cleansing the blood and ridding the body of wastes probably come to mind. However, there are additional, equally important functions played by the system.
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25.2: Physical Characteristics of Urine
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Characteristics of the urine change, depending on influences such as water intake, exercise, environmental temperature, nutrient intake, and other factors (Table 25.1.1). Some of the characteristics such as color and odor are rough descriptors of your state of hydration. For example, if you exercise or work outside, and sweat a great deal, your urine will turn darker and produce a slight odor, even if you drink plenty of water. Athletes are often advised to consume water until urine is cleear.
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25.3: Gross Anatomy of Urine Transport
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Rather than start with urine formation, this section will start with urine excretion. Urine is a fluid of variable composition that requires specialized structures to remove it from the body safely and efficiently. Blood is filtered, and the filtrate is transformed into urine at a relatively constant rate throughout the day. This processed liquid is stored until a convenient time for excretion.
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25.4: Gross Anatomy of the Kidney
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25.5: Microscopic Anatomy of the Kidney
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The renal structures that conduct the essential work of the kidney cannot be seen by the naked eye. Only a light or electron microscope can reveal these structures. Even then, serial sections and computer reconstruction are necessary to give us a comprehensive view of the functional anatomy of the nephron and its associated blood vessels.
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25.6: Physiology of Urine Formation
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Having reviewed the anatomy and microanatomy of the urinary system, now is the time to focus on the physiology. You will discover that different parts of the nephron utilize specific processes to produce urine: filtration, reabsorption, and secretion. You will learn how each of these processes works and where they occur along the nephron and collecting ducts. The physiologic goal is to modify the composition of the plasma and, in doing so, produce the waste product urine.
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25.7: Tubular Reabsorption
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With up to 180 liters per day passing through the nephrons of the kidney, it is quite obvious that most of that fluid and its contents must be reabsorbed. That recovery occurs in the PCT, loop of Henle, DCT, and the collecting ducts ). Various portions of the nephron differ in their capacity to reabsorb water and specific solutes.
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25.8: Regulation of Renal Blood Flow
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It is vital that the flow of blood through the kidney be at a suitable rate to allow for filtration. This rate determines how much solute is retained or discarded, how much water is retained or discarded, and ultimately, the osmolarity of blood and the blood pressure of the body.
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25.9: Endocrine Regulation of Kidney Function
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Several hormones have specific, important roles in regulating kidney function. They act to stimulate or inhibit blood flow. Some of these are endocrine, acting from a distance, whereas others are paracrine, acting locally.
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25.10: Regulation of Fluid Volume and Composition
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The major hormones influencing total body water are ADH, aldosterone, and ANH. Circumstances that lead to fluid depletion in the body include blood loss and dehydration. Homeostasis requires that volume and osmolarity be preserved. Blood volume is important in maintaining sufficient blood pressure, and there are nonrenal mechanisms involved in its preservation, including vasoconstriction, which can act within seconds of a drop in pressure.
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25.11: The Urinary System and Homeostasis
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All systems of the body are interrelated. A change in one system may affect all other systems in the body, with mild to devastating effects. A failure of urinary continence can be embarrassing and inconvenient, but is not life threatening. The loss of other urinary functions may prove fatal.


1.7: Many-Electron Atoms
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Learning Objectives
- To write the electron configuration of any element and relate its electron configuration to its position in the periodic table.
The quantum mechanical model allowed us to determine the energies of the hydrogen atomic orbitals; now we would like to extend this to describe the electronic structure of every element in the Periodic Table. The process of describing each atom’s electronic structure consists, essentially, of beginning with hydrogen and adding one proton and one electron at a time to create the next heavier element in the table; however, interactions between electrons make this process a bit more complicated than it sounds. All stable nuclei other than hydrogen also contain one or more neutrons. Because neutrons have no electrical charge, however, they can be ignored in the following discussion. Before demonstrating how to do this, however, we must introduce the concept of electron spin and the Pauli principle.
Orbitals and their Energies
Unlike in hydrogen-like atoms with only one electron, in multielectron atoms the values of quantum numbers n and l determine the energies of an orbital. The energies of the different orbitals for a typical multielectron atom are shown in Figure \(\PageIndex{1}\). Within a given principal shell of a multielectron atom, the orbital energies increase with increasing l . An ns orbital always lies below the corresponding np orbital, which in turn lies below the nd orbital.
These energy differences are caused by the effects of shielding and penetration , the extent to which a given orbital lies inside other filled orbitals. For example, an electron in the 2 s orbital penetrates inside a filled 1 s orbital more than an electron in a 2 p orbital does. Since electrons, all being negatively charged, repel each other, an electron closer to the nucleus partially shields an electron farther from the nucleus from the attractive effect of the positively charged nucleus. Hence in an atom with a filled 1 s orbital, the effective nuclear charge ( Z eff ) experienced by a 2 s electron is greater than the Z eff experienced by a 2 p electron. Consequently, the 2 s electron is more tightly bound to the nucleus and has a lower energy, consistent with the order of energies shown in Figure \(\PageIndex{1}\).
Due to electron shielding, \(Z_{eff}\) increases more rapidly going across a row of the periodic table than going down a column.
Notice in Figure \(\PageIndex{1}\) that the difference in energies between subshells can be so large that the energies of orbitals from different principal shells can become approximately equal. For example, the energy of the 3 d orbitals in most atoms is actually between the energies of the 4 s and the 4 p orbitals.
Electron Spin: The Fourth Quantum Number
When scientists analyzed the emission and absorption spectra of the elements more closely, they saw that for elements having more than one electron, nearly all the lines in the spectra were actually pairs of very closely spaced lines. Because each line represents an energy level available to electrons in the atom, there are twice as many energy levels available as would be predicted solely based on the quantum numbers \(n\), \(l\), and \(m_l\). Scientists also discovered that applying a magnetic field caused the lines in the pairs to split farther apart. In 1925, two graduate students in physics in the Netherlands, George Uhlenbeck (1900–1988) and Samuel Goudsmit (1902–1978), proposed that the splittings were caused by an electron spinning about its axis, much as Earth spins about its axis. When an electrically charged object spins, it produces a magnetic moment parallel to the axis of rotation, making it behave like a magnet. Although the electron cannot be viewed solely as a particle, spinning or otherwise, it is indisputable that it does have a magnetic moment. This magnetic moment is called electron spin .
In an external magnetic field, the electron has two possible orientations (Figure Figure \(\PageIndex{2}\)). These are described by a fourth quantum number ( m s ), which for any electron can have only two possible values, designated +½ (up) and −½ (down) to indicate that the two orientations are opposites; the subscript s is for spin. An electron behaves like a magnet that has one of two possible orientations, aligned either with the magnetic field or against it.
The Pauli Exclusion Principle
The implications of electron spin for chemistry were recognized almost immediately by an Austrian physicist, Wolfgang Pauli (1900–1958; Nobel Prize in Physics, 1945), who determined that each orbital can contain no more than two electrons. He developed the Pauli exclusion principle: No two electrons in an atom can have the same values of all four quantum numbers (n, l, m l , m s ).
By giving the values of n , l , and m l , we also specify a particular orbital (e.g., 1 s with n = 1, l = 0, m l = 0). Because m s has only two possible values (+½ or −½), two electrons, and only two electrons , can occupy any given orbital, one with spin up and one with spin down. With this information, we can proceed to construct the entire periodic table, which was originally based on the physical and chemical properties of the known elements.
Example \(\PageIndex{1}\)
List all the allowed combinations of the four quantum numbers ( n , l , m l , m s ) for electrons in a 2 p orbital and predict the maximum number of electrons the 2 p subshell can accommodate.
Given: orbital
Asked for: allowed quantum numbers and maximum number of electrons in orbital
Strategy:
- List the quantum numbers ( n , l , m l ) that correspond to an n = 2 p orbital. List all allowed combinations of ( n , l , m l ).
- Build on these combinations to list all the allowed combinations of ( n , l , m l , m s ).
- Add together the number of combinations to predict the maximum number of electrons the 2 p subshell can accommodate.
 There are only three possible combinations of ( n , l , m l ): (2, 1, 1), (2, 1, 0), and (2, 1, −1).
B Because m s is independent of the other quantum numbers and can have values of only +½ and −½, there are six possible combinations of ( n , l , m l , m s ): (2, 1, 1, +½), (2, 1, 1, −½), (2, 1, 0, +½), (2, 1, 0, −½), (2, 1, −1, +½), and (2, 1, −1, −½).
C Hence the 2 p subshell, which consists of three 2 p orbitals (2 p x , 2 p y , and 2 p z ), can contain a total of six electrons, two in each orbital.
Exercise \(\PageIndex{1}\)
List all the allowed combinations of the four quantum numbers ( n , l , m l , m s ) for a 6 s orbital, and predict the total number of electrons it can contain.
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(6, 0, 0, +½), (6, 0, 0, −½); two electrons
Magnetic Quantum Number (ml) & Spin Quantum Number (ms): Magnetic Quantum Number (ml) & Spin Quantum Number (ms), YouTube(opens in new window) [youtu.be] (opens in new window)
Summary
The arrangement of atoms in the periodic table arises from the lowest energy arrangement of electrons in the valence shell. In addition to the three quantum numbers ( n , l , m l ) dictated by quantum mechanics, a fourth quantum number is required to explain certain properties of atoms. This is the electron spin quantum number ( m s ), which can have values of +½ or −½ for any electron, corresponding to the two possible orientations of an electron in a magnetic field. The concept of electron spin has important consequences for chemistry because the Pauli exclusion principle implies that no orbital can contain more than two electrons (with opposite spin).


8.9: Assignment- Developing and Delivering Business Presentations
Your task is to revisit the presentation you created for Module 7: Public Speaking and submit a revised final version.
In this version of your presentation you will incorporate the feedback from your peer group and you will use the voice over feature in PowerPoint to narrate your revised presentation.
Along with the narrated slides, you will submit a short essay (minimum 300 words) to document and reflect on any revisions you made based on the peer feedback you received. Please discuss what and why you changed or added anything, and how these changed made the presentation stronger.
Your PowerPoint presentation should have a minimum of 4 slides: a title page, content slides, and conclusion. Each slide you include in the presentation must be narrated using the voice over function. Email a final copy of your presentation and your revision essay to your instructor.
Assignment Resources
Grading Rubric
| Criteria | Not Evident | Developing | Exemplary | Points |
|---|---|---|---|---|
| Submit your revised slide deck |
0 pts
No slide deck submitted |
5 pts
Slide deck has not been revised to reflect peer review |
10 pts
Slide deck has been revised to reflect peer review |
10 pts |
| Provided voice over functionality for each slide |
0 pts
No response to peers |
5
pts
Voice over only appears on some slides |
10 pts
Voice over is on all slides |
10 pts |
| Speak with appropriate volume, speed, and clarity |
0 pts
No presentation completed |
5 pts
Presentation cannot be heard, is too fast or too slow, or cannot be understood |
10 pts
Presentation is spoken at an adequate volume, speed, and clarity |
10 pts |
| Present your slides effectively |
0 pts
No presentation completed |
5 pts
Presentation is disjointed, unprofessional, or too reliant on slide deck text |
10 pts
Presentation is professional and feels cohesive |
10 pts |
| Submit reflection essay on slide deck revisions |
0 pts
No essay submitted |
5
pts
Essay is not at least 300 words long |
10 pts
Essay is at least 300 words long, and discusses the improvements made to the slide deck |
10 pts |
| Total: | 50 pts |
Contributors and Attributions
- Assignment: Developing and Delivering Business Presentations. Provided by : Lumen Learning. License : CC BY: Attribution
- How to create voice-over narration for your PowerPoint Presentation. Authored by : Dawn Dubriel. Provided by : YouTube. Located at : https://www.youtube.com/watch?v=3uk4CU7uobM . License : Public Domain: No Known Copyright


4: Early American Sociology Last updated Save as PDF Page ID 88314 Allison Hurst Oregon State University 4.1: Biography of Early American Sociologists 4.2: Comparison of Spencer and Ward by Barnes (1919) 4.3: Thorstein Veblen, on Labor(1898) 4.4: Charlotte Perkins Gilman, Women and Economics (1898) 4.5: Du Bois on The Study of Social Problems (1898) 4.6: Jane Addams, “Trade Unions and Public Duty” (1899) 4.7: Edward A. Ross on Social Control (1900) 4.8: Charles A. Ellwood on Revolution (1905) 4.9: Charles Horton Cooley, “Social Consciousness” (1907) 4.10: Lester Ward, “Social Classes” (1908) 4.11: Franklin H. Giddings on Theory and Public Policy (1911) 4.12: Small on the Sociological Point of View (1920) Thumbnail: W. E. B. Du Bois, with beard and mustache, around 50 years old. (Public Domain; Cornelius Marion Battey via Wikipedia )


5.12: Comma Overuse
- Recognize the standard uses of commas
A sure way to irritate educated readers of your work is to give them an overabundance of commas. It is easy but dangerous to take the attitude that Sally once did in a Peanuts comic strip, asking Charlie Brown to correct her essay by showing her “where to sprinkle in the little curvy marks.”
Perhaps the best way to troubleshoot your particular comma problems, especially if they are serious, is to identify and understand the patterns of your errors. We tend to make the same mistakes over and over again; in fact, many writers develop the unfortunate habit of automatically putting commas into slots such as these:
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between the subject and verb of a sentence
- Example: My mother, is a wonderful cook.
- Example: The judge, jury, and audience, were all surprised by this admission.
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in between compound subjects or compound verbs
- Example: My brother, and my sister both hate broccoli with a passion.
- Example: Jesse tripped, and fell into a rosebush.
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before any preposition
- Example: I signaled quietly to Harriet that she had spinach, in her teeth.
- Example: All Juan wanted to do was to have some time outside walking, through the forest.
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before or after any conjunction
- Example: I challenged Mr. Burton to an arm-wrestling match and, he beat me twice.
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Example:
Joey tossed the ball, and watched his dog run after it.
- Remember that you DO need a comma before a conjunction that is separating two independent clauses.
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before a list
- Example: My favorite things to eat for breakfast are, bacon, eggs, and cereal.
All of these are places where commas should not go, even if they sound correct in your head or if it’s a place you might pause while speaking aloud. Fixing these comma mistakes will require you to be very intentional about how you write, and to analyze your sentences and figure out what parts of speech fall where in your sentence. It may be time-consuming, but it will get easier as you get more comfortable with it.
Just as it is common for someone to have to look up the same tricky word dozens of times before committing its proper spelling to memory, you may need to reference comma rules multiple times before they feel natural to use. As you improve your comma usage, you will learn to recognize and re-evaluate your sentence patterns, and the rewards are numerous. There is no foolproof or easy way to understand all standard uses of commas, but a great place to start is reminding yourself of the comma’s basic function as a separator and justifying the separation of elements. In the end, you simply must make a habit of reading, writing, and revising with comma correctness in mind.
Complete the practice exercises in the interactive below to ensure you know when to use, and when not to use, a comma.
https://lumenlearning.h5p.com/content/1290907159447907288/embed
Contributors and Attributions
- Revision and Adaptation.. Provided by : Lumen Learning. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
- Style For Students Online.. Authored by : Joe Schall. Provided by : The Pennsylvania State University. Located at : https://www.e-education.psu.edu/styleforstudents/ . Project : Penn State's College of Earth and Mineral Sciences' OER Initiative. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
- Commas Interactive. Provided by : Excelsior College OWL. Located at : https://owl.excelsior.edu/writing-refresher/grammar-refresher/comma-refresher/ . License : CC BY: Attribution
- Image of Charlie Brown. Authored by : oficialjuanbarros. Provided by : Pixabay. Located at : pixabay.com/photos/snowman-charlie-brown-happy-toy-2603789/. License : Other . License Terms : pixabay.com/service/terms/#license