6.3.9: Management Skills Application Exercises
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1. You might find it interesting to look at your own bases of power in an organization you have worked with. To do this, simply think of your present or past job, and complete this self-assessment. When you have finished, refer to Appendix B for scoring procedures.
What Are Your Bases of Power?
Instructions: Using a current or former job, answer each of the following items by circling the response that most suits your answer.
2. It might be interesting for you to evaluate your own level of political behavior. To do this, complete this self-assessment. When you have finished, score your questionnaire according to the procedure outlined in Appendix B .
How Political Are You?
Instructions: To determine your political appreciation and tendencies, please answer the following questions. Select the answer that better represents your behavior or belief, even if that particular behavior or belief is not present all the time.


22.14B: Gastric Phase
- Outline the gastric phase of digestion
The gastric phase is a period in which swallowed food and semi-digested protein ( peptides and amino acids ) activate gastric activity. About two-thirds of gastric secretion occurs during this phase. Ingested food stimulates gastric activity in two ways: by stretching the stomach and by raising the pH of its contents. Stretching activates two reflexes: a short reflex is mediated through the myenteric nerve plexus; and a long reflex is mediated through the vagus nerves and brainstem.
Gastric Secretion
Gastric secretion is stimulated chiefly by three chemicals:
- Acetylcholine (ACh). This is secreted by the parasympathetic nerve fibers of both the short and long reflex pathways.
- Histamine. This is a paracrine secretion from the enteroendocrine cells in the gastric glands.
- Gastrin. This is a hormone produced by enteroendocrine G cells in the pyloric glands.
All three of these stimulate parietal cells to secrete hydrochloric acid and intrinsic factor. The chief cells secrete pepsinogen in response to gastrin and especially ACh, and ACh also stimulates mucus secretion.
As dietary protein is digested, it breaks down into smaller peptides and amino acids that directly stimulate the G cells to secrete even more gastrin: this is a positive feedback loop that accelerates protein digestion.
Small peptides also buffer the stomach acid so the pH does not fall excessively low. As digestion continues and these peptides empty from the stomach, the pH drops lower and lower. Below pH of 2, stomach acid inhibits the parietal cells and G cells: this is a negative feedback loop that winds down the gastric phase as the need for pepsin and HCl declines.
The gastric phase of digestion : During the gastric phase, gastrin is secreted. The stomach stretches and churns while enzymes break down proteins.
Key Points
- The gastric phase accounts for about two-thirds of gastric secretions.
- Ingested food stimulates gastric activity by stretching the stomach and raising the pH of its contents; this causes a cascade of events that leads to the release of hydrochloric acid by the parietal cells that lower the pH and break apart the food.
- Gastric secretion is stimulated chiefly by three chemicals: acetylcholine (ACh), histamine, and gastrin.
- Below pH of 2, stomach acid inhibits the parietal cells and G cells; this is a negative feedback loop that winds down the gastric phase as the need for pepsin and HCl declines.
Key Terms
- gastric phase : The second phase of digestion that follows mastication (chewing) and takes place in the stomach.


5.1: Electrical systems
An electrical system has two main conditions: it is closed or it is open. Closed means the circuit is complete and conducting. Open means the circuit is incomplete and no current flows.
There are different electrical systems, identified by voltage. The term low voltage is relative and its definition varies by context. The Canadian Electrical Code defines low voltage as from 31 V to 750 V and systems operating at 30 volts or less.
Automotive systems normally use direct current and are rated up to 24 volts. Residential alternating current voltage may be 120 or 240 volts. Lighting and small appliances normally use 120 volts. Clothes dryers, stoves, and ovens use 240 volts. Shop equipment also uses either 120 or 240 volts. Most hand-held electric tools and many shop tools use 120 volts or battery power. Some equipment, such as electric welders, use 240 volts.


1.3.6: The Global Positioning System (GPS)
The Global Positioning System consists of three parts:
- Earth orbiting satellites,
- control and monitoring stations across the Earth, and
- GPS receivers owned by individuals.
A set of 24 satellites orbiting the Earth every 12 hours broadcasting their position and time. A ground-based receiver listens to the signals from four or more satellites, comparing the time transmissions of each with its own clock. Given that signal travels at a known rate of speed, the receiver can calculate the distance between the satellite and receiver. Combining the position of the satellite at the time of transmission with the distance, the receiver is able to determine its location.
Differential GPS uses a base station of an exact known location and a mobile unit to determine position. GPS determines location by computing the difference between the time that a signal is sent by a satellite and the time it is received by a GPS receiver. The base station calculates its position from satellite signals and compares this location to the known location. The base station broadcasts the range errors they're seeing from GPS satellites to the remote receiver. The mobile receiver uses these correction messages, correlated with the satellite signals its receiving, to determine position.
GPS is being employed in a variety of ways. GPS is widely used for ground, air, and sea navigation. It is used to produce highly accurate maps and record land deformation caused by earthquakes and volcanic eruptions. GPS is showing up in a number of commercial products available to the public from standalone units to automobiles, cell phones, and digital cameras interfaces. A popular use of gps units is geocaching, a high-tech "treasure" hunting game.
Assess your basic understanding of the preceding material by "Looking Back: Tools of the Geographer" or continue reading.


Exercise \(\PageIndex{1}\)
A study was conducted of Long Beach School District schools regarding how many require school uniforms. In 2006, of the 296 schools questioned, 184 said they required school uniforms. (Gentile & Imberman, 2009) Find the proportion of schools that require a school uniform.
-
A Center for Disease Control (CDC) study conducted in 2008, found that out of 32,601 children in Arizona, 507 had autism. (CDC, 2012) Find the proportion of children in Arizona who had autism in 2008.
-
The temperatures (in degrees Fahrenheit) for the first 10 days of July 2013 in Phoenix, AZ are given in the table below ("Weather underground," 2013).
|
112
|
108
|
111
|
108
|
106
|
|
111
|
112
|
113
|
107
|
104
|
-
Find the mean, median, and mode for the data set.
-
Find the range, variance, and standard deviation for the data set.
-
Find the five-number summary and the interquartile range (IQR) for the data set.
-
Draw a box-and-whiskers plot for the data set.
-
The number of traffic fatalities involving a driver with a blood alcohol content of 0.1 or more is given in the table for the southern states in 2013 ("Traffic fatalities by," 2013).
|
260
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904
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394
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366
|
177
|
194
|
|
264
|
430
|
423
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345
|
278
|
134
|
-
Find the mean, median, and mode for the data set.
-
Find the range, variance, and standard deviation for the data set.
-
Find the five-number summary and the interquartile range (IQR) for the data set.
-
Draw a box-and-whiskers plot for the data set.
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A new sedan car in 2013 or 2014, which has a gas mileage in the city of 40 to 50 mpg, had the following prices ("Motor trend," 2013).
|
$38,700
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$26,200
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$39,780
|
$27,200
|
$38,700
|
|
$24,360
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$39,250
|
$35,925
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$35,555
|
$26,140
|
|
$24,995
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$28,775
|
$24,200
|
$34,755
|
$25,990
|
-
Find the mean, median, and mode for the data set.
-
Find the range, variance, and standard deviation for the data set.
-
Find the five-number summary and the interquartile range (IQR) for the data set.
-
Draw a box-and-whiskers plot for the data set.
-
The prices of an airline flight from New York City to Los Angeles on September 7, 2013 around 8 am, and returning September 14, 2013 are given in the table below ("Expedia," 2013).
|
$317
|
$351
|
$378
|
|
$397
|
$327
|
$334
|
|
$337
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$383
|
$327
|
-
Find the mean, median, and mode for the data set.
-
Find the range, variance, and standard deviation for the data set.
-
Find the five-number summary and the interquartile range (IQR) for the data set.
-
Draw a box-and-whiskers plot for the data set.
-
The gas prices (in $/gallon) at all gasoline stations in Flagstaff, AZ, on July 16, 2013 are given in the table below ("Arizona gas prices," 2013).
|
3.45
|
3.47
|
3.48
|
3.48
|
3.48
|
3.49
|
|
3.51
|
3.51
|
3.51
|
3.55
|
3.55
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3.56
|
|
3.59
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3.59
|
3.59
|
3.59
|
3.65
|
3.65
|
|
3.65
|
3.65
|
3.66
|
3.67
|
3.69
|
3.69
|
|
3.69
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3.69
|
3.69
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3.69
|
3.69
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3.69
|
|
3.69
|
|
|
|
|
|
Using a calculator, find the mean, median, standard deviation, and five-number summary.
-
The city gas mileage (in mpg) of 2011 small pick-up trucks that are four-wheel drive are given in the table below ("Fuel efficiency guide," 2011).
|
17
|
18
|
17
|
14
|
16
|
16
|
|
14
|
14
|
15
|
17
|
18
|
17
|
|
14
|
16
|
16
|
14
|
14
|
15
|
|
14
|
18
|
18
|
16
|
14
|
|
Using a calculator, find the mean, median, standard deviation, and five-number summary.
-
Sustainability Victoria, in Australia, surveys all Victorian local communities on waste and recycling services every year. A random sample of 10 local communities reported the number of households served in that community in 2008 and the data is given in the table below ("2001-02 to 2007-08," 2009).
|
7,551
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4,907
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45,439
|
46,000
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46,000
|
|
49,732
|
38,264
|
39,195
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40,374
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40,500
|
-
Find the mean and median of the data set.
-
Find the mean and the median of the data set with the two lowest data values (7,551 and 4,907) removed.
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Discuss what happened to the mean and the median when the two lowest data values (7,551 and 4,907) are removed.
-
Natural gas consumptions (in billions of cubic feet) for selected countries in South America are listed in the following table ("International energy statistics," 2013).
|
1629
|
87
|
885
|
199
|
|
312
|
8
|
202
|
961
|
-
Find the mean and median of the data set.
-
Find the mean and median with the highest data value of 1629 removed.
-
Discuss what happened to the mean and median when the highest data value (1629) is removed.
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Suppose your child takes a test to evaluate whether or not your child is at risk for Attention Deficit Hyperactivity Disorder (ADHD). One assessment for ADHD is the Behavior Assessment System for Children, Second Edition (BASC-2) survey. After taking this survey a child is rated on several different qualities. One of the qualities is aggression, where a high score represents a tendency towards being aggressive.
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What does this percentile mean?
-
What does this percentile mean about your child and this quality of ADHD?
 Your score on the mathematics section of the general GRE puts you in the 90th percentile.
-
What does this percentile mean?
-
Did you pass (score of 70% or better) the mathematics section of the general GRE?
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The IQ of a person follows a normal distribution and has a mean of 100 and a standard deviation of 15. Using this information, find the following:
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What percentage of the people have IQ scores between 85 and 115?
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What percentage of the people have IQ scores between 70 and 100?
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What percentage of the people have IQ scores between 130 and 145?
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What percentage of the people have IQ scores above 145?
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The mean systolic blood pressure of people in the U.S. is 124 with a standard deviation of 16. Assume that systolic blood pressure follows a normal distribution.
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What percentage of the people in the U.S. have systolic blood pressure between 108 and 124?
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What percentage of the people in the U.S. have systolic blood pressure between 92 and 156?
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What percentage of the people in the U.S. have systolic blood pressure between 76 and 108?
-
What percentage of the people in the U.S. have systolic blood pressure above 156?
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The mean diastolic blood pressure of people in the U.S. is 77 with a standard deviation of 11. Assume that diastolic blood pressure follows a normal distribution.
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What percentage of the people in the U.S. have diastolic blood pressure between 77 and 88?
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What percentage of the people in the U.S. have diastolic blood pressure between 66 and 88?
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What percentage of the people in the U.S. have diastolic blood pressure between 55 and 99?
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What percentage of the people in the U.S. have diastolic blood pressure below 55
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The mean height of men in the U.S. is 69.1 inches with a standard deviation of 2.9 inches. Assume that height follows a normal distribution.
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What percentage of the males in the U.S. have height between 74.9 and 77.8 inches?
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What percentage of the males in the U.S. have height between 60.4 and 77.8 inches?
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What percentage of the males in the U.S. have height between 63.3 and 72 inches?
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What percentage of the males in the U.S. have heights below 63.3 inches?
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The IQ of a person follows a normal distribution and has a mean of 100 and a standard deviation of 15. Find the z-score for an IQ score of 134. Is this value unusual? Why or why not?
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The mean systolic blood pressure of people in the U.S. is 124 with a standard deviation of 16. Assume that systolic blood pressure follows a normal distribution. Find the z-score for a systolic blood pressure of 135. Is this value unusual? Why or why not?
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The mean diastolic blood pressure of people in the U.S. is 77 with a standard deviation of 11. Assume that diastolic blood pressure follows a normal distribution. Find the z-score for a diastolic blood pressure of 54. Is this value unusual? Why or why not?
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The mean height of mean in the U.S. is 69.1 inches with a standard deviation of 2.9 inches. Assume that height follows a normal distribution. Find the z-score for a man who is 64 inches tall. Is this value unusual? Why or why not?
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The IQ of a person follows a normal distribution and has a mean of 100 and a standard deviation of 15. Find the five-number summary.
-
The mean systolic blood pressure of people in the U.S. is 124 with a standard deviation of 16. Assume that systolic blood pressure follows a normal distribution. Find the five-number summary.
-
The mean diastolic blood pressure of people in the U.S. is 77 with a standard deviation of 11. Assume that diastolic blood pressure follows a normal distribution. Find the five-number summary.
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The mean height of mean in the U.S. is 69.1 inches with a standard deviation of 2.9 inches. Assume that height follows a normal distribution. Find the five-number summary.
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It can be shown that a man’s height and a man’s weight have a positive correlation. Does this mean that a man’s height causes him to be a certain weight? Explain.
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Engine size and city gas mileage have a negative correlation. Does this mean that the engine size causes the gas mileage of a car? Explain.
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Suppose 10 men had their height and weight measured. The data is below. Draw a scatter plot of the data. Describe what relationship you can see from the graph.
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Height (inches)
|
67
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72
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74
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65
|
70
|
72
|
74
|
69
|
68
|
70
|
|
Weight (pounds)
|
185
|
202
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226
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165
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221
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217
|
218
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189
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201
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185
|
-
Nine midsize 2011 hybrid cars’ city gas mileage and engine size are recorded below ("Fuel efficiency guide," 2011). Draw a scatter plot of the data. Describe what relationship you can see from the graph.
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Engine Size
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4.4
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2.5
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2.4
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5.0
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2.5
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2.5
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2.5
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2.4
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1.8
|
|
City MPG
|
17
|
41
|
25
|
19
|
41
|
41
|
33
|
31
|
51
|


9.5: Discrimination in the Workforce
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Sexual Harassment
Sexual harassment is a serious problem disproportionately affecting women in the workplace. It is defined by the federal Equal Opportunity Commission guidelines as:
It is unlawful to harass a person (an applicant or employee) because of that person’s sex.
 For example, it is illegal to harass a woman by making offensive comments about women in general. 288
However, sexual harassment varies widely, and there are often misconceptions of what actually does constitute as being harassment. In 1986 the first case concerning sexual harassment reached the Supreme Court with Meritor Savings Bank v. Vinson . The Court established that sexual harassment incudes the creation of an abusive or hostile work environment and the victim identifying the harassments as “unwelcome advances.”
People of all sexes and genders can (and do) experience sexual harassment in the workplace. However, women outnumber men in these experiences; many working women will experience sexual harassment at some point in their careers. While some report this harassment, some leave their jobs to escape the harassing environment, which can have lasting effects on career attainment and create financial stress. 289
LGBTQ+ Employees, Workplace Discrimination and Harassment
8.1 million LGBTQ+ workers (16 and over) live in the U.S. 290 In recent years, there have been increased efforts for the advancement of LGBTQ+ rights at work in the United States. For example, 2020 saw a landmark Supreme Court ruling that protected LGBTQ+ people from workplace discrimination stating 1964 Civil Rights Act protects gay, lesbian, and transgender employees from discrimination based on sex. However, there has also been some pushback. For example, some states have filed lawsuits seeking to overturn directives allowing transgender workers and students to use bathrooms that correspond with their gender identity.
According to a report from UCLA School of Law’s Williams Institute, almost 30% LGBTQ+ employees reported experiencing at least one form of employment discrimination (being fired or not hired) because of their sexual orientation or gender identity at some point in their lives. And LGBTQ+ employees of color report this form of discrimination at a slightly higher rate than White LGBTQ+ employees. 291 The study states:
Transgender employees were also significantly more likely to experience discrimination based on their LGBT status than cisgender LGB employees: Nearly half (48.8%) of transgender employees reported experiencing discrimination (being fired or not hired) based on their LGBT status compared to 27.8% of cisgender LGB employees. More specifically, over twice as many transgender employees reported not being hired (43.9%) because of their LGBT status compared to LGB employees (21.5%). 292
In addition, LGBTQ+ employees reported having experienced harassment at a higher rate than non-LBGTQ+ employees with almost 38% reporting they had experiences either physical, verbal, or sexual harassment in the workplace.
There have been some efforts to dismantle systemic barriers to employment, work performance, and career progression for trans* employees. In Being Transgender at Work the authors suggest employers and businesses offer LGBTQ+ affirming benefits, craft inclusive policies or programs (i.e.: HR reviewing policies and removing gender-specific language from things like dress codes), foster inclusive environments through normalizing the use of pronouns (i.e.: in emails or zoom screens), and providing gender neutral bathrooms. 293
Age Discrimination
61% of U.S. workers at or over the age of 45 reported witnessing or experiencing ageism in the workplace. 294 72% of women say they have experienced age discrimination in the workplace, compared to 57% of men. 295 Ageism is prejudice or discrimination on the grounds of a person's age, and it can occur in subtle ways like being removed from projects, replaced by younger coworkers, or not offered professional development opportunities. The impact of age discrimination (like other forms) can have harsh effects in a person's career. Gendered ageism refers to differences in ageism faced by women and men. 296
From 1990 to 2017, there was a 15% increase in the number of Age Discrimination in Employment Act charges by women at or over the age of 40, and charges by men within the same age bracket decreased by 18%. 297 Older women face marginalization based on gendered youthful (and literally impossible for any aging person to maintain) beauty ideals in addition to the unfounded societal biases that older employees are less innovative, dedicated, capable, adaptive, or generally less qualified. Here, the intersectional marginalizing factors of age and gender merge.
When searching for employment, older women experience more employment rejections than older men. 298 A study found that younger women (under age 45) are more likely to be called back for another interview (almost double the rate for older women). 299
The wage gap between men and women actually increases with age. One effect of corporate downsizing is the increased number of older, more experienced workers being laid off. Often times, this group is seen as too young to retire but too old or too experienced (expensive) to hire. For women over 40, age can complicate securing a job. Women over 40 typically earn even less than the average of the wage disparity between men and women, and if they are returning to the workforce after an absence, they often return to lower paying or part-time jobs.
Gendered Discrimination against People with (Dis)abilities
Women with disabilities are often labeled as being too dependent, passive, incapable, or incompetent. Work disabilities are more common among older women than young women. At the same time, many women who are unable to participate in the workforce continue to do their own cooking, cleaning, and home maintenance (“unproductive work”). Women with disabilities, in general, have lower educational attainment than do women who do not report having disabilities, which often times can exclude them from applying for higher paying jobs. There is a lengthy list of reasons why women with disabilities have lower educational attainment: being too ill to complete school, missing a lot of school, not having fair access to adequate educational programs, etc.
Added to these challenges is discrimination from the prejudices of employers. Women with disabilities often have to make special (and costly) arrangements to be able to participate in the workforce, having sometimes to arrange transportation, or extra support in the home or with childcare.
288
United States Equal Employment Opportunity Commission.
https://www.eeoc.gov/sexual-harassment
289
McLaughlin, H., Uggen, C., & Blackstone, A. (2017). The Economic and Career Effects of Sexual Harassment on Working Women.
Gender & Society
, 31(3), 333–358.
290
Kerith J. Conron & Shoshana K. Goldberg, Williams Inst. (2020). LGBT People in the US Not Protected by State Non-Discrimination Statutes.
291
Sears, B., Mallory, C., Flores, A. R, & Conron, K. J. (2021). LGBT People’s Experiences of Workplace Discrimination and Harassment.
UCLA: The Williams Institute
.
292
Ibid
293
Baboolall, D., Sarah Greenberg, Maurice Obeid, and Jill Zucker. (2021). Being Transgender at Work. McKinsey Quarterly, McKinsey & Company.
294
Rebecca Perron, The Value of Experience: Age Discrimination Against Older Workers Persist (AARP, 2018).
295
(2017). 10 Things You Should Know About Age Discrimination.
AARP
.
https://www.aarp.org/work/age-
discrimination/facts-in-the-workplace/
296
Sophie Beaton, Gendered Ageism in the Canadian Workforce (Samuel Center for Social Connectedness, 2019).
297
U.S. Equal Employment Opportunity Commission, “Chart Data for the State of Age Discrimination and Older Workers in the U.S. 50 Years After the Age Discrimination in Employment Act (ADEA);” U.S. Equal Employment Opportunity Commission, “Age Discrimination.”
298
Noah Higgins-Dunn, “Older Workers Are America’s Fastest-growing Labor Pool—And the Least Protected from Workplace Discrimination,”
CNBC
, April 13, 2019
299
David Neumark, Ian Burn, and Patrick Button, “Age Discrimination and Hiring of Older Workers,”
Federal Reserve Bank of San Francisco
, February 27, 2017.


15.8A: Overview of the Thyroid Gland
The thyroid gland, in the anterior neck, controls body metabolism, protein synthesis, and a body’s responsiveness to other hormones.
- Summarize the anatomy and purpose of the thyroid gland
Key Points
- The thyroid gland controls how quickly the body uses energy, makes proteins, and controls how sensitive the body is to other hormones. It participates in these processes by producing thyroid hormones, the principal ones being triiodothyronine (T3) and thyroxine (T4).
- Hormones released from the thyroid regulate the rate of metabolism and affect the growth and rate of function of many other systems in the body.
- The thyroid also produces calcitonin, which plays a role in calcium homeostasis.
- Hormonal output from the thyroid is regulated by thyroid-stimulating hormone (TSH) produced by the anterior pituitary, which itself is regulated by thyrotropin-releasing hormone (TRH) produced by the hypothalamus.
- The thyroid gland (the thyroid in vertebrate anatomy ) is one of the largest endocrine glands.
Key Terms
- thyroid-stimulating hormone : Also known as TSH or thyrotropin, this is a hormone that stimulates the thyroid gland to produce thyroxine (T4), and then triiodothyronine (T3), which stimulates the metabolism of almost every tissue in the body. It is a glycoprotein hormone, synthesized and secreted by thyrotrope cells in the anterior pituitary gland, that regulates the endocrine function of the thyroid gland.
- thyroxine : A hormone (an iodine derivative of tyrosine), produced by the thyroid gland, that regulates cell metabolism and growth.
In vertebrates, the thyroid gland is one of the largest endocrine glands. It is found in the neck, below the thyroid cartilage that forms the laryngeal prominence, or Adam’s apple. The isthmus (the bridge between the two lobes of the thyroid) is located inferior to the cricoid cartilage.
The thyroid gland controls how quickly the body uses energy, makes proteins, and controls how sensitive the body is to other hormones. It participates in these processes by producing thyroid hormones, the principal ones being triiodothyronine (T3) and thyroxine (sometimes referred to as tetraiodothyronine (T4)).
These hormones regulate the rate of metabolism and affect the growth and rate of function of many other systems in the body. T3 and T4 are synthesized from both iodine and tyrosine.
The thyroid also produces calcitonin, which plays a role in calcium homeostasis. The hormonal output from the thyroid is regulated by thyroid-stimulating hormone (TSH) produced by the anterior pituitary, which itself is regulated by thyrotropin-releasing hormone (TRH) produced by the hypothalamus.
Thyroid system : Thyroid function is regulated by the actions of the hypothalamus and pituitary gland.
Anatomy of the Thyroid Gland
The thyroid gland is a butterfly-shaped organ and is composed of two cone-like lobes or wings, lobus dexter (right lobe) and lobus sinister (left lobe), connected via the isthmus. The organ is situated on the anterior side of the neck, lying against and around the larynx and trachea, reaching posteriorly the oesophagus and carotid sheath.
It starts cranially at the oblique line on the thyroid cartilage (just below the laryngeal prominence, or Adam’s Apple), and extends inferiorly to approximately the fifth or sixth tracheal ring. It is difficult to demarcate the gland’s upper and lower border with vertebral levels because it moves in position in relation to these structures during swallowing.


5.6: Environmental Design
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Rich learning environments with a variety of activities enhance young children’s learning and development. In an environment in which children have the opportunity to make observations, ask questions, plan investigations, gather and interpret information, and communicate findings and ideas (CDE 2012b, 53), they explore concepts in domains such as science, math, and history–social science. Dance, music, and drama not only introduce children to the arts and allow them to explore creative processes, they also provide opportunities for children to learn to regulate their behavior and take the perspective of another person. [1]
[1] California Preschool Program Guidelines by the California Department of Education is used with permission (pg 2)


9.5: Application to Real Polynomials
If \(p\) is a polynomial in \(\mathbb{R}[x]\) , it follows from the Fundamental Theorem of Algebra that it does have roots, but they may be complex. If it has complex roots, they must occur in complex conjugate pairs.
THEOREM 9.46. Let \(p \in \mathbb{R}[x]\) . Let \(\alpha\) be a root of \(p\) . Then so is \(\bar{\alpha}\) .
PROOF. Let \(p(x)=\sum_{k=0}^{N} a_{k} x^{k}\) . Then \[p(\alpha)=\sum_{k=0}^{N} a_{k} \alpha^{k}=0,\] SO \[p(\bar{\alpha})=\sum_{k=0}^{N} a_{k} \bar{\alpha}^{k}=\overline{p(\alpha)}=0 .\] Let \(\alpha=a+i b\) . Then \[\begin{aligned} (x-\alpha)(x-\bar{\alpha}) &=(x-(a+i b))(x-(a-i b)) \\ &=x^{2}-2 a x+a^{2}+b^{2} \\ &=(x-a)^{2}+b^{2} . \end{aligned}\] So applying the Fundamental Theorem of Algebra to the real polynomial \(p\) , we first factor out the real roots, and for each pair of complex conjugate roots we get a factor as in (9.47). Thus we get:
THEOREM 9.48. Let \(p \in \mathbb{R}[x]\) be a polynomial of degree \(N\) . Then \(p\) can be factored into a product of linear factors \(\left(x-c_{k}\right)\) and quadratic factors \(\left(\left(x-a_{k}\right)^{2}+b_{k}^{2}\right)\) : \[p(x)=c\left(\prod_{k=1}^{N_{1}}\left(x-c_{k}\right)\right)\left(\prod_{j=1}^{N_{2}}\left(\left(x-a_{j}\right)^{2}+b_{j}^{2}\right)\right)\] for some (not necessarily distinct) real numbers \(c, c_{j}, a_{j}, b_{j}\) . We have \(N_{1}+2 N_{2}=N\) , and the factoring is unique, up to ordering and replacing any \(b_{j} b y-b_{j}\) .


6.4: Identity during the American Revolution
The American Revolution in effect created multiple civil wars. Many of the resentments and antagonisms that fed these conflicts predated the Revolution, and the outbreak of war acted as the catalyst they needed to burst forth. In particular, the middle colonies of New York, New Jersey, and Pennsylvania had deeply divided populations. Loyalty to Great Britain came in many forms, from wealthy elites who enjoyed the prewar status quo to runaway slaves who desired the freedom that the British offered.
LOYALISTS
Historians disagree on what percentage of colonists were Loyalists; estimates range from 20 percent to over 30 percent. In general, however, of British America’s population of 2.5 million, roughly one-third remained loyal to Great Britain, while another third committed themselves to the cause of independence. The remaining third remained apathetic, content to continue with their daily lives as best they could and preferring not to engage in the struggle.
Many Loyalists were royal officials and merchants with extensive business ties to Great Britain, who viewed themselves as the rightful and just defenders of the British constitution. Others simply resented local business and political rivals who supported the Revolution, viewing the rebels as hypocrites and schemers who selfishly used the break with the Empire to increase their fortunes. In New York’s Hudson Valley, animosity among the tenants of estates owned by Revolutionary leaders turned them to the cause of King and Empire.
During the war, all the states passed confiscation acts, which gave the new revolutionary governments in the former colonies the right to seize Loyalist land and property. To ferret out Loyalists, revolutionary governments also passed laws requiring the male population to take oaths of allegiance to the new states. Those who refused lost their property and were often imprisoned or made to work for the new local revolutionary order.
William Franklin, Benjamin Franklin’s only surviving son, remained loyal to Crown and Empire and served as royal governor of New Jersey, a post he secured with his father’s help. During the war, revolutionaries imprisoned William in Connecticut; however, he remained steadfast in his allegiance to Great Britain and moved to England after the Revolution. He and his father never reconciled.
As many as nineteen thousand colonists served the British in the effort to put down the rebellion, and after the Revolution, as many as 100,000 colonists left, moving to England or north to Canada rather than staying in the new United States (Figure 6.4.1). Eight thousand whites and five thousand free blacks went to Britain. Over thirty thousand went to Canada, transforming that nation from predominately French to predominantly British. Another sizable group of Loyalists went to the British West Indies, taking their slaves with them.
Hannah Ingraham was eleven years old in 1783, when her Loyalist family removed from New York to Ste. Anne’s Point in the colony of Nova Scotia.
[Father] said we were to go to Nova Scotia, that a ship was ready to take us there, so we made all haste to get ready. . . . Then on Tuesday, suddenly the house was surrounded by rebels and father was taken prisoner and carried away. . . . When morning came, they said he was free to go.
We had five wagon loads carried down the Hudson in a sloop and then we went on board the transport that was to bring us to Saint John. I was just eleven years old when we left our farm to come here. It was the last transport of the season and had on board all those who could not come sooner. The first transports had come in May so the people had all the summer before them to get settled. . . .
We lived in a tent at St. Anne’s until father got a house ready. . . . There was no floor laid, no windows, no chimney, no door, but we had a roof at least.  We toasted the bread and all sat around the bowl and ate our breakfast that morning and mother said: “Thank God we are no longer in dread of having shots fired through our house. This is the sweetest meal I ever tasted for many a day.”
What do these excerpts tell you about life as a Loyalist in New York or as a transplant to Canada?
SLAVES AND INDIANS
While some slaves who fought for the Patriot cause received their freedom, revolutionary leaders—unlike the British—did not grant such slaves their freedom as a matter of course. Washington, the owner of more than two hundred slaves during the Revolution, refused to let slaves serve in the army, although he did allow free blacks. (In his will, Washington did free his slaves.) In the new United States, the Revolution largely reinforced a racial identity based on skin color. Whiteness, now a national identity, denoted freedom and stood as the key to power. Blackness, more than ever before, denoted servile status. Indeed, despite their class and ethnic differences, white revolutionaries stood mostly united in their hostility to both blacks and Indians.
In the Revolutionary War, some blacks, both free and enslaved, chose to fight for the Americans (Figure 6.4.2). Others chose to fight for the British, who offered them freedom for joining their cause. Read the excerpts below for the perspective of a black veteran from each side of the conflict.
Boyrereau Brinch was captured in Africa at age sixteen and brought to America as a slave. He joined the Patriot forces and was honorably discharged and emancipated after the war. He told his story to Benjamin Prentiss, who published it as The Blind African Slave in 1810.
Finally, I was in the battles at Cambridge, White Plains, Monmouth, Princeton, Newark, Frog’s Point, Horseneck where I had a ball pass through my knapsack. All which battels [sic] the reader can obtain a more perfect account of in history, than I can give. At last we returned to West Point and were discharged [1783], as the war was over. Thus was I, a slave for five years fighting for liberty. After we were disbanded, I returned to my old master at Woodbury [Connecticut], with whom I lived one year, my services in the American war, having emancipated me from further slavery, and from being bartered or sold. . . . Here I enjoyed the pleasures of a freeman; my food was sweet, my labor pleasure: and one bright gleam of life seemed to shine upon me.
Boston King was a Charleston-born slave who escaped his master and joined the Loyalists. He made his way to Nova Scotia and later Sierra Leone, where he published his memoirs in 1792. The excerpt below describes his experience in New York after the war.
When I arrived at New-York, my friends rejoiced to see me once more restored to liberty, and joined me in praising the Lord for his mercy and goodness. . . . [In 1783] the horrors and devastation of war happily terminated, and peace was restored between America and Great Britain, which diffused universal joy among all parties, except us, who had escaped from slavery and taken refuge in the English army; for a report prevailed at New-York, that all the slaves, in number 2000, were to be delivered up to their masters, altho’ some of them had been three or four years among the English. This dreadful rumour filled us all with inexpressible anguish and terror, especially when we saw our old masters coming from Virginia, North-Carolina, and other parts, and seizing upon their slaves in the streets of New-York, or even dragging them out of their beds. Many of the slaves had very cruel masters, so that the thoughts of returning home with them embittered life to us. For some days we lost our appetite for food, and sleep departed from our eyes. The English had compassion upon us in the day of distress, and issued out a Proclamation, importing, That all slaves should be free, who had taken refuge in the British lines, and claimed the sanction and privileges of the Proclamations respecting the security and protection of Negroes. In consequence of this, each of us received a certificate from the commanding officer at New-York, which dispelled all our fears, and filled us with joy and gratitude.
What do these two narratives have in common, and how are they different? How do the two men describe freedom?
For slaves willing to run away and join the British, the American Revolution offered a unique occasion to escape bondage. Of the half a million slaves in the American colonies during the Revolution, twenty thousand joined the British cause. At Yorktown, for instance, thousands of black troops fought with Lord Cornwallis. Slaves belonging to George Washington, Thomas Jefferson, Patrick Henry, and other revolutionaries seized the opportunity for freedom and fled to the British side. Between ten and twenty thousand slaves gained their freedom because of the Revolution; arguably, the Revolution created the largest slave uprising and the greatest emancipation until the Civil War. After the Revolution, some of these African Loyalists emigrated to Sierra Leone on the west coast of Africa. Others removed to Canada and England. It is also true that people of color made heroic contributions to the cause of American independence. However, while the British offered slaves freedom, most American revolutionaries clung to notions of black inferiority.
Powerful Indian peoples who had allied themselves with the British, including the Mohawk and the Creek, also remained loyal to the Empire. A Mohawk named Joseph Brant, whose given name was Thayendanegea (Figure 6.4.3), rose to prominence while fighting for the British during the Revolution. He joined forces with Colonel Barry St. Leger during the 1777 campaign, which ended with the surrender of General Burgoyne at Saratoga. After the war, Brant moved to the Six Nations reserve in Canada. From his home on the shores of Lake Ontario, he remained active in efforts to restrict white encroachment onto Indian lands. After their defeat, the British did not keep promises they’d made to help their Indian allies keep their territory; in fact, the Treaty of Paris granted the United States huge amounts of supposedly British-owned regions that were actually Indian lands.
PATRIOTS
The American revolutionaries (also called Patriots or Whigs) came from many different backgrounds and included merchants, shoemakers, farmers, and sailors. What is extraordinary is the way in which the struggle for independence brought a vast cross-section of society together, animated by a common cause.
During the war, the revolutionaries faced great difficulties, including massive supply problems; clothing, ammunition, tents, and equipment were all hard to come by. After an initial burst of enthusiasm in 1775 and 1776, the shortage of supplies became acute in 1777 through 1779, as Washington’s difficult winter at Valley Forge demonstrates.
Funding the war effort also proved very difficult. Whereas the British could pay in gold and silver, the American forces relied on paper money, backed by loans obtained in Europe. This first American money was called Continental currency; unfortunately, it quickly fell in value. “Not worth a Continental” soon became a shorthand term for something of no value. The new revolutionary government printed a great amount of this paper money, resulting in runaway inflation. By 1781, inflation was such that 146 Continental dollars were worth only one dollar in gold. The problem grew worse as each former colony, now a revolutionary state, printed its own currency.
WOMEN
In colonial America, women shouldered enormous domestic and child-rearing responsibilities. The war for independence only increased their workload and, in some ways, solidified their roles. Rebel leaders required women to produce articles for war—everything from clothing to foodstuffs—while also keeping their homesteads going. This was not an easy task when their husbands and sons were away fighting. Women were also expected to provide food and lodging for armies and to nurse wounded soldiers.
The Revolution opened some new doors for women, however, as they took on public roles usually reserved for men. The Daughters of Liberty, an informal organization formed in the mid-1760s to oppose British revenue-raising measures, worked tirelessly to support the war effort. Esther DeBerdt Reed of Philadelphia, wife of Governor Joseph Reed, formed the Ladies Association of Philadelphia and led a fundraising drive to provide sorely needed supplies to the Continental Army. In “The Sentiments of an American Woman” (1780), she wrote to other women, “The time is arrived to display the same sentiments which animated us at the beginning of the Revolution, when we renounced the use of teas, however agreeable to our taste, rather than receive them from our persecutors; when we made it appear to them that we placed former necessaries in the rank of superfluities, when our liberty was interested; when our republican and laborious hands spun the flax, prepared the linen intended for the use of our soldiers; when exiles and fugitives we supported with courage all the evils which are the concomitants of war.” Reed and other elite women in Philadelphia raised almost $300,000 in Continental money for the war.
Read the entire text of Esther Reed’s “The Sentiments of an American Woman” on a page hosted by the University of Michigan-Dearborn.
Women who did not share Reed’s elite status nevertheless played key economic roles by producing homespun cloth and food. During shortages, some women formed mobs and wrested supplies from those who hoarded them. Crowds of women beset merchants and demanded fair prices for goods; if a merchant refused, a riot would ensue. Still other women accompanied the army as “camp followers,” serving as cooks, washerwomen, and nurses. A few also took part in combat and proved their equality with men through violence against the hated British.
Section Summary
The American Revolution divided the colonists as much as it united them, with Loyalists (or Tories) joining the British forces against the Patriots (or revolutionaries). Both sides included a broad cross-section of the population. However, Great Britain was able to convince many slaves to join its forces by promising them freedom, something the southern revolutionaries would not agree to do. The war provided new opportunities, as well as new challenges, for slaves, free blacks, women, and Indians. After the war, many Loyalists fled the American colonies, heading across the Atlantic to England, north to Canada, or south to the West Indies.
Review Questions
Which of the following statements best represents the division between Patriots and Loyalists?
Most American colonists were Patriots, with only a few traditionalists remaining loyal to the King and Empire.
Most American colonists were Loyalists, with only a few firebrand revolutionaries leading the charge for independence.
American colonists were divided among those who wanted independence, those who wanted to remain part of the British Empire, and those who were neutral.
The vast majority of American colonists were neutral and didn’t take a side between Loyalists and Patriots.
C
Which of the following is not one of the tasks women performed during the Revolution?
holding government offices
maintaining their homesteads
feeding, quartering, and nursing soldiers
raising funds for the war effort
A
Critical Thinking Questions
How did the colonists manage to triumph in their battle for independence despite Great Britain’s military might? If any of these factors had been different, how might it have affected the outcome of the war?
How did the condition of certain groups, such as women, blacks, and Indians, reveal a contradiction in the Declaration of Independence?
What was the effect and importance of Great Britain’s promise of freedom to slaves who joined the British side?
How did the Revolutionary War provide both new opportunities and new challenges for slaves and free blacks in America?
Describe the ideology of republicanism. As a political philosophy, how did republicanism compare to the system that prevailed in Great Britain?
Describe the backgrounds and philosophies of Patriots and Loyalists. Why did colonists with such diverse individual interests unite in support of their respective causes? What might different groups of Patriots and Loyalists, depending upon their circumstances, have hoped to achieve by winning the war?
Glossary
- confiscation acts
- state-wide acts that made it legal for state governments to seize Loyalists’ property
- Continental currency
- the paper currency that the Continental government printed to fund the Revolution


1.5: Exploring Cognition
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What do we think?
Cognitive theories focus on how our mental processes or cognitions change over time. We will examine the ideas of two cognitive theorists: Jean Piaget and Lev Vygotsky.
Piaget: Changes in thought with maturation
Jean Piaget (1896-1980) is one of the most influential cognitive theorists in development inspired to explore children’s ability to think and reason by watching his own children’s development. He was one of the first to recognize and map out the ways in which children’s intelligence differs from that of adults. He became interested in this area when he was asked to test the IQ of children and began to notice that there was a pattern in their wrong answers! He believed that children’s intellectual skills change over time that that maturation rather than training brings about that change. Children of differing ages interpret the world differently.
Jean Piaget.
Making sense of the world
Piaget believed that we are continuously trying to maintain cognitive equilibrium or a balance or cohesiveness in what we see and what we know. Children have much more of a challenge in maintaining this balance because they are constantly being confronted with new situations, new words, new objects, etc. When faced with something new, a child may either fit it into an existing framework ( schema ) and match it with something known ( assimilation ) such as calling all animals with four legs “doggies” because he or she knows the word doggie, or expand the framework of knowledge to accommodate the new situation ( accommodation ) by learning a new word to more accurately name the animal. This is the underlying dynamic in our own cognition. Even as adults we continue to try and “make sense” of new situations by determining whether they fit into our old way of thinking or whether we need to modify our thoughts.
Stages of Cognitive Development
Piaget outlined four major stages of cognitive development. Let me briefly mention them here. We will discuss them in detail throughout the course.For about the first two years of life, the child experiences the world primarily through their senses and motor skills. Piaget referred to this type of intelligence as sensorimotor intelligence. During the preschool years, the child begins to master the use of symbols or words and is able to think of the world symbolically but not yet logically. This stage is the preoperational stage of development. The concrete operational stage in middle childhood is marked by an ability to use logic in understanding the physical world. In the final stage, the formal operational stage the adolescent learns to think abstractly and to use logic in both concrete and abstract ways.
Criticisms of Piaget’s Theory
Piaget has been criticized for overemphasizing the role that physical maturation plays in cognitive development and in underestimating the role that culture and interaction (or experience) plays in cognitive development. Looking across cultures reveals considerable variation in what children are able to do at various ages. Piaget may have underestimated what children are capable of given the right circumstances.
Vygotsky: Changes in thought with guidance
Lev Vygotsky (1896-1934) was a Russian psychologist who wrote in the early 1900s but whose work was discovered in the United States in the 1960s but became more widely known in the 1980s. Vygotsky differed with Piaget in that he believed that a person not only has a set of abilities, but also a set of potential abilities that can be realized if given the proper guidance from others. His sociocultural theory emphasizes the importance of culture and interaction in the development of cognitive abilities. He believed that through guided participation known as scaffolding, with a teacher or capable peer, a child can learn cognitive skills within a certain range known as the zone of proximal development.  Maybe it was brushing their teeth or preparing food. Chances are you spoke to them and described what you were doing while you demonstrated the skill and let them work along with you all through the process. You gave them assistance when they seemed to need it, but once they knew what to do-you stood back and let them go. This is scaffolding and can be seen demonstrated throughout the world. This approach to teaching has also been adopted by educators. Rather than assessing students on what they are doing, they should be understood in terms of what they are capable of doing with the proper guidance. You can see how Vygotsky would be very popular with modern day educators. We will discuss Vygotsky in greater depth in upcoming lessons.
Putting it all together: Ecological Systems Model
Urie Brofenbrenner (1917-2005) provides a model of human development that addresses its many influences. Brofenbrenner recognized that human interaction is influenced by larger social forces and that an understanding of those forces is essential for understanding an individual. The individual is impacted by microsystems such as parents or siblings; those who have direct, significant contact with the person. The input of those is modified by the cognitive and biological state of the individual as well. And these influence the person’s actions which in turn influence systems operating on him or her. The mesosystem includes larger organizational structures such as school, the family, or religion. These institutions impact the microsystems just described. For example, the religious teachings and traditions may guide the child’s family’s actions or create a climate that makes the family feel stigmatized and this indirectly impacts the child’s view of self and others. The philosophy of the school system, daily routine, assessment methods, and other characteristics can affect the child’s self-image, growth, sense of accomplishment, and schedule thereby impacting the child, physically, cognitively, and emotionally. These mesosystems both influence and are influenced by the larger contexts of community referred to as the exosystem. A community’s values, history, and economy can impact the organizational structures it houses. And the community is influenced by macrosystems which are cultural elements such as global economic conditions, war, technological trends, values, philosophies, and a society’s responses to the global community. In sum, a child’s experiences are shaped by larger forces such as the family, schools, and religion, and culture. All of this occurs in an historical context or chronosystem. Bronfenbrenner’s model helps us combine each of the other theories described above and gives us a perspective that brings it all together.


25.4: Creating an Atmosphere of Trust and Mutual Respect
By the end of this section, you should be able to:
- Describe factors that lead to mistrust of the U.S. health care system.
- Identify strategies to promote trust in the U.S. health care system.
- Establish goals that encourage cultural responsiveness and humility.
- Engage in regular self-reflection to actively challenge and unlearn biases.
The level of trust that different groups have in the health care system differs. Factors that can contribute to this variance include historical experiences, cultural beliefs, socioeconomic status, language barriers , and access to health care. Historical experiences of discrimination, mistreatment, or disparities in health care can significantly impact an individual’s or a community’s trust in the health care system.
Factors Influencing Trust of the Health Care System
As discussed in Structural Racism and Systemic Inequities, certain cultural groups have experienced systemic injustices, leading to mistrust of the U.S. health care system. For instance, from 1932 to 1972, the U.S. Public Health Service conducted the Tuskegee Syphilis Study , deliberately misleading Black men about its purpose and withholding penicillin from them when it became available as a treatment. The study had a lasting impact on the Black community’s trust in health care providers and the health care system (CDC, 2022; Freimuth et al., 2001).
Negative stereotypes about certain groups of people have led these groups to mistrust government and institutions. For instance, those living in rural areas with low incomes have been stigmatized since the earliest colonial times. At that time, poor White colonists were viewed as unwanted vagrants who were not entitled to their rights and dignity as American citizens. Rural communities tend to be more skeptical of government and institutions. This is largely because these communities face numerous challenges in obtaining affordable, timely, and quality health care services. Such obstacles often stem from financial limitations, transportation issues, and differences in the quality of health care provided (Rural Health Information Hub, 2022).
Members of the LGBTQ+ community have also been subject to high rates of health care discrimination historically, ranging from harassment and humiliation to being turned away for care. For example, although the Affordable Care Act prohibits discrimination on the basis of sex, including pregnancy, sexual orientation, gender identity, and sex characteristics by federally funded health care providers (U.S. Department of Health and Human Services, 2021), nine U.S. states have laws that allow medical professionals to decline service to LGBTQ+ clients based on religious beliefs (Movement Advancement Project [MAP], 2023b). In 2023, 15 U.S. states banned some forms of best practice medical care for transgender youth, and nine states banned Medicaid from providing coverage for medically necessary health care for all transgender individuals (MAP, 2023a).
Other factors that result in clients’ distrust of the health care system include:
- The impact of cultural beliefs and values surrounding health and healing practices and how they affect an individual’s trust in the system. Certain cultural groups have traditional or spiritual healing practices that may not align with Western medicine, and it is crucial to respect and acknowledge these beliefs to establish trust.
- Communication difficulties and language barriers. Limited proficiency in the dominant language can make it difficult for individuals from specific cultural groups to effectively express their health concerns, understand medical information, or build rapport with health care providers.
- A lack of diversity and representation in the health care workforce hurts trust. When individuals from specific cultural groups do not see health care providers who share their cultural background or resemble them, it can lead to mistrust and a feeling of being misunderstood or disrespected.
Fostering Trust Through Cultural Responsiveness
Eradicating stereotypes and negative perceptions toward certain groups is a necessary step in establishing community trust in the health care industry. This can be achieved when nurses and other health care providers display an understanding of and respect for diverse cultural practices, beliefs, values, and ways of life. Doing so can enhance trust and strengthen the relationship between clients and health care providers.
To promote trust, the nurse can:
- Take steps to learn about the populations they serve (Association of Public Health Nursing [APHN], n.d.).
- Advocate for a workforce that reflects the diversity of the populations served (APHN, n.d.).
- Practice inclusiveness, listen to understand, and recognize the knowledge and power of each individual and group (APHN, n.d.).
- Role model and exemplify the principles of social justice (APHN, n.d.).
- Use effective communication and resolution strategies respectfully to address conflicts (APHN, n.d.).
- Establish community-engaged partnerships, including rural residents from historically marginalized groups (APHN, n.d.).
- Advocate for rural-centered health care delivery models (Lister & Joudrey, 2022).
- Practice with cultural sensitivity by developing a deep understanding of clients’ cultural backgrounds and their impact on health and healing (Seeleman et al., 2015).
Community support and advocacy efforts can play an important role in building trust. When marginalized populations have community organizations, leaders, or advocates actively addressing health disparities and advocating for equitable health care, it can help foster trust and engagement with the health care system.
Recall Nurse Sarah. She is organizing a community health fair to raise awareness about preventive health measures. She wants to ensure that community members feel comfortable and trust the information and services provided at the event. The box below presents actions that Sarah initiates to create an environment of trust.
When organizing a community health fair, Sarah takes the following actions to create an environment of trust.
Transparent and clear communication:
Sarah shares information about the health fair, its purpose, and what community members can expect with community members and partners. She provides details about the services, workshops, and resources available and openly addresses any concerns or questions.
Cultural sensitivity and inclusivity:
Recognizing the diversity within the community, Sarah takes steps to ensure cultural sensitivity and inclusivity by involving representatives from various cultural groups in the planning process to ensure that the health fair addresses the needs and preferences of different communities. Sarah tries incorporating diverse perspectives, languages, and cultural practices into the event.
Building relationships and partnerships:
Sarah actively builds relationships with community leaders, organizations, and concerned parties. She collaborates with local community-based organizations, faith-based groups, and other agencies to establish partnerships that can enhance the credibility and reach of the health fair. Sarah engages these partners in the planning and implementation to ensure community ownership and involvement.
Active listening and empathy:
Sarah listens attentively to community members’ concerns, feedback, and suggestions. She demonstrates empathy by validating their experiences and emotions. Sarah encourages open dialogue, creates a safe space for sharing, and assures community members that their voices are valued and will be considered.
Confidentiality and privacy protection:
Sarah ensures that all personal health information is treated with confidentiality. She explains to community members how their data will be managed and stored, assuring them that their information will only be used for the intended purposes and in compliance with relevant privacy laws and regulations.
Professional competence and integrity:
Sarah maintains high professional competence and integrity in her work. She stays current with the latest evidence-based practices, research, and guidelines in public health. Sarah provides accurate and reliable information, avoiding misinformation or bias that could undermine trust. She follows ethical guidelines and acts in the best interest of the community.
Sarah’s actions foster an environment of trust within the public health department and its community. She prioritizes open communication, cultural sensitivity, and inclusivity while maintaining professionalism and integrity. Her efforts are instrumental in strengthening relationships, promoting community engagement, and ultimately, improving health outcomes. Such interactions build trust over time. Sarah knows that earning and maintaining trust involves cultivating humility and demonstrating her commitment to culturally responsive care through her actions, words, and consistent efforts. Sarah’s approach involves ongoing self-reflection, a commitment to learning, and a deep appreciation for the diversity within her community. Through these efforts, she fosters sensitivity and humility and contributes to creating a culturally responsive and inclusive health care environment.
Taking Action to Promote Cultural Humility
To create an inclusive, equitable health care environment, nurses should establish goals that encourage cultural humility. It is essential to review and assess these goals frequently, to ensure they align with ongoing growth and development in these areas. Display the goals in a prominent location and replace accomplished goals with new ones. Here are some suggestions for setting these goals:
- Expand cultural awareness : Make it a goal to learn more about different cultures, including their beliefs, values, practices, and health care disparities. This can involve reading books, attending cultural competency workshops or webinars, and conversing with people from different cultural backgrounds.
- Improve cross-cultural communication skills: Set a goal to actively listen, use appropriate language and tone, and be mindful of nonverbal cues. Practice empathetic and nonjudgmental listening to understand clients’ unique cultural perspectives better.
- Reflect on biases and assumptions: Regularly reflect on personal biases, assumptions, and stereotypes that may impact one’s interactions with clients from different cultures. Seek to challenge and unlearn these biases through self-reflection, self-education, and feedback from colleagues or mentors.
- Seek cultural immersion experiences: Actively engage in cultural immersion experiences to deepen one’s understanding of different cultures. This can involve participating in community events, volunteering with diverse populations, or undertaking cultural exchange programs.
- Foster self-awareness: Enhance self-awareness regarding one’s cultural identity and how it influences interactions with others. Explore one’s cultural background, values, and beliefs to better understand one’s cultural perspective and how it may differ from others.
- Build cross-cultural relationships: Seek opportunities to interact and build meaningful relationships with people from different cultural backgrounds within and outside the health care setting.
- Promote cultural competence in practice policies: Advocate for integrating cultural competence into a health care organization’s policies and practices. Suggest implementing cultural assessment tools, providing staff cultural competence training, and promoting a diverse and inclusive work environment.
- Engage in ongoing education: Commit to learning and professional development related to cultural competence. Stay informed about emerging research, best practices, and evolving cultural dynamics. Attend conferences, seminars, or online courses to expand knowledge and skills in providing culturally sensitive care.
Now that you have explored the concepts of cultural competence and cultural humility, it is time to develop an action plan.
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Review findings from the learning activities conducted in the previous sections:
- Cultural Competence Self-Evaluation Checklist
- Social Identity Wheel
- Inventory of Values, Beliefs, and Cultural Heritage
- How to Deal with Unconscious Bias
- Implicit Bias
- Project READY is a program funded by the Institute of Museum and Library Services focused on racial equity and culturally sustaining pedagogy. Use this template from Project READY: Reimagining Equity & Access for Diverse Youth to set three goals for becoming culturally competent and practicing cultural humility: one short-term goal that you can accomplish immediately, one medium-term goal that you can accomplish over the next several months, and one long-term goal that you can accomplish over the next year.


16.10.3: Figuring for Yourself
Figuring for Yourself
Estimate the amount of mass that is converted to energy when a proton combines with a deuterium nucleus to form 3 He.
30.
How much energy is released when a proton combines with a deuterium nucleus to produce 3 He?
31.
The Sun converts kg of mass to energy every second. How many years would it take the Sun to convert a mass equal to the mass of Earth to energy?
32.
Assume that the mass of the Sun is 75% hydrogen and that all of this mass could be converted to energy according to Einstein’s equation E = mc 2 . How much total energy could the Sun generate? If m is in kg and c is in m/s, then E will be expressed in J. (The mass of the Sun is given in Appendix E.)
33.
In fact, the conversion of mass to energy in the Sun is not 100% efficient. As we have seen in the text, the conversion of four hydrogen atoms to one helium atom results in the conversion of about 0.02862 times the mass of a proton to energy. How much energy in joules does one such reaction produce? (See Appendix E for the mass of the hydrogen atom, which, for all practical purposes, is the mass of a proton.)
34.
Now suppose that all of the hydrogen atoms in the Sun were converted into helium. How much total energy would be produced? (To calculate the answer, you will have to estimate how many hydrogen atoms are in the Sun. This will give you good practice with scientific notation, since the numbers involved are very large! See Appendix C for a review of scientific notation.)
35.
Models of the Sun indicate that only about 10% of the total hydrogen in the Sun will participate in nuclear reactions, since it is only the hydrogen in the central regions that is at a high enough temperature. Use the total energy radiated per second by the Sun, watts, alongside the exercises and information given here to estimate the lifetime of the Sun. (Hint: Make sure you keep track of the units: if the luminosity is the energy radiated per second, your answer will also be in seconds. You should convert the answer to something more meaningful, such as years.)
36.
Show that the statement in the text is correct: namely, that roughly 600 million tons of hydrogen must be converted to helium in the Sun each second to explain its energy output. (Hint: Recall Einstein’s most famous formula, and remember that for each kg of hydrogen, 0.0071 kg of mass is converted into energy.) How long will it be before 10% of the hydrogen is converted into helium? Does this answer agree with the lifetime you calculated in Exercise 16.35?
37.
Every second, the Sun converts 4 million tons of matter to energy. How long will it take the Sun to reduce its mass by 1% (the mass of the Sun is kg)? Compare your answer with the lifetime of the Sun so far.
38.
Raymond Davis Jr.’s neutrino detector contained approximately 10 30 chlorine atoms. During his experiment, he found that one neutrino reacted with a chlorine atom to produce one argon atom each day.
- How many days would he have to run the experiment for 1% of his tank to be filled with argon atoms?
- Convert your answer from A. into years.
- Compare this answer to the age of the universe, which is approximately 14 billion years .
- What does this tell you about how frequently neutrinos interact with matter?


12.4: Hemispheric Distribution
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After having dealt with how knowledge is stored in the brain, we now turn to the question of whether the brain is specialised and, if it is specialised, which functions are located where and which knowledge is present in which hemisphere. These questions can be subsumed under the topic “hemispheric specialisation” or “lateralisation of processing” which looks at the differences in processing between the two hemispheres of the human brain.
Differences between the hemispheres can be traced back to as long as 3.5 million years ago. Evidence for this are fossils of australopithecines (which is an ancient ancestor of homo sapiens). Because differences have been present for so long and survived the selective pressure they must be useful in some way for our cognitive processes.
Differences in Anatomy and Chemistry
Although at first glance the two hemispheres look identical, they differ in in various ways.
Concerning the anatomy, some areas are larger and the tissue contains more dendritic spines in one hemisphere than in the other. An example of this is what used to be called “Broca’s area” in the left hemisphere. This area which is –among other things- important for speech production shows greater branching in the left hemisphere than in the respective right hemisphere area. Because of the left hemisphere’s importance for language, with which we will deal later, one can conclude that anatomical differences have consequences for lateralisation in function.
Neurochemistry is another domain the hemispheres differ in: The left hemisphere is dominated by the neurotransmitter dopamine, whereas the right hemisphere shows higher concentrations of norepinephrine. Theories suggest that modules specialised on cognitive processes are distributed over the brain according to the neurotransmitter needed. Thus, a cognitive function relying on dopamine would be located in the left hemisphere.
The Corpus Callosum
The two hemispheres are interconnected via the corpus callosum, the major cortical connection. With its 250 million nerve fibres it is like an Autobahn for neural data connecting the two hemispheres. There are in fact smaller connections between the hemispheres but these are little paths in comparison. All detailed higher order information must pass through the corpus callosum when being transferred from one hemisphere to the other. The transfer time, which can be measured with ERP, lies between 5 and 20 ms.
Historic Approaches
Hemispheric specialisation has been of interest since the days of Paul Broca and Karl Wernicke, who discovered the importance of the left hemisphere for speech in the 1860s. Broca examined a number of patients who could not produce speech but whose understanding of language was not severed, whereas Wernicke examined patients who suffered the opposite symptoms (i.e. who could produce speech but did not understand anything). Both Broca and Wernicke found that their patients’ brains had damage to distinct areas of the left hemisphere.
Because in these days language was seen as the cognitive process superior to all other processes, the left hemisphere was believed to be superior to the right which was expressed in the “cerebral dominance theory” developed by J.H. Jackson. The right hemisphere was seen as a “spare tire [...] having few functions of its own” (Banich, S.94). This view was not challenged until the 1930s. In this decade and the following, research dramatically changed this picture. Of special importance for showing the role of the right hemisphere was Sperry, who conducted several experiments in 1974 for which he won the Nobel Prize in Medicine and Physiology in 1981.
Experiments with Split-Brain Patients
Sperry’s experiments took place with people who suffered a condition called “split brain syndrome” because they underwent a commissurotomy . In a commissurotomy the corpus callosum is sectioned so that communication between the hemispheres becomes severed in these patients. With his pioneering experiments, Sperry wanted to find out whether the left hemisphere really plays such an important role in speech processing as suggested by Broca and Wernicke.
Sperry used different experimental designs in his studies, but the basic assumption behind all experiments of this type was that perceptual information received at one side of the body is processed in the contra-lateral hemisphere of the brain. In one of the experiments the subjects had to recognise objects by touching it with merely one hand, while being blindfolded. He then asked the patients to name the object they felt and found that people could not name it when touching it with the left hand (which is linked to the right hemisphere). The question that arose was whether this inability was due to a possible function of the right hemisphere as “spare tire” or due to something else. Sperry now changed the design of his experiment so that patients now had to show that they recognised the objects by using it the right way. For example, if they recognised a pencil they would use it to write. With this changed design, no difference in performance between both hands were found.
In a different experiment conducted by Sperry et al. the patients were shown the word sky to one visual field and scraper to the other. They now had to draw the whole word they had seen with one hand. The patients were not able to synthesise this to skyscraper , instead they draw a scraper overlapped by some cloud. Thus it was concluded that each hemisphere took control of the hand to draw what it had seen.
Experiments with Patients with other Brain-Lesions
There have been other experiments conducted to gain more knowledge about hemispheric specialisation. They were conducted with epileptic individuals who were about to receive surgery where parts of one of their hemispheres was going to be removed. Before the surgery started it was important to find out which hemisphere is responsible for speech in this individual. This was done using the Wada-technique , where barbiturate is injected into one of the arteries supplying the brain with blood. Shortly after the injection, the contra-lateral side of the body is paralysed. If the person is now still able to speak, the doped hemisphere of the brain is not responsible for speech production in this individual. With the results of this technique it could be estimated that 95\% of all adult right-handers use their left hemisphere for speech.
 Because of this, it is possible that their brains are not typical or have received damage to other areas during the surgery. Also, these studies have been performed with very limited numbers of subjects, so the statistical reliability might not be high.
Experiments with Neurologically Intact Individuals
In addition to experiments with brain-severed patients, studies with neurologically intact individuals have been conducted to measure perceptual asymmetries. These are usually performed with one of three methods: Namely the “divided visual field technique”, “dichaptic presentation” and “dichotic presentation”. Each of them again has as basic assumption the fact that perceptual information received at one side of the body is processed in the contra-lateral hemisphere.
Highly simplified picture of the visual pathway.
The divided visual field technique is based on the fact that the visual field can be divided into the right (RVF) and left visual field (LVF). Each visual field is processed independently from the other in the contra-lateral hemisphere. The divided visual field technique includes two different experimental designs: The experimenter can present one picture in just one of the visual fields and then let the subject respond to this stimulus. The other possibility involves showing two different pictures in each visual field.
A problem that can occur using the visual field technique is that the stimulus must be presented for less than 200 ms because this is how long the eyes can look at one point without shifting of the visual field.
In the dichaptic presentation technique the subject is presented two objects at the same time in each hand. (c.f. Sperry’s experiments)
The dichotic presentation technique enables researchers to study the processing of auditory information. Here, different information is presented simultaneously to each ear. Experiments with these techniques found that a sensory stimulus is processed 20 to 100 ms faster when it is initially directed to the specialised hemisphere for that task and the response is 10% more accurate.
Explanations for this include three hypotheses, namely the direct access theory , the callosal relay model and the activating-orienting model . The direct access theory assumes that information is processed in that hemisphere to which it is initially directed. This may result in less accurate responses, if the initial hemisphere is the unspecialised hemisphere. The Callosal relay model states that information if initially directed to the wrong hemisphere is transferred to the specialised hemisphere over the corpus callosum. This transfer is time-consuming and is the reason for loss of information during transfer. The activating-orienting model assumes that a given input activates the specialised hemisphere. This activation then places additional attention on the contra-lateral side of the activated hemisphere, “making perceptual information on that side even more salient”. (Banich)
Common Results
All the experiments mentioned above have some basic findings in common: The left hemisphere is superior at verbal tasks such as the processing of speech, speech production and recognition of letters whereas the right hemisphere excels at non-verbal tasks such as face recognition or tasks that involve spatial skills such as line orientation, or distinguishing different pitches of sound. This is evidence against the cerebral dominance theory which appointed the right hemisphere to be a spare tire! In fact both hemispheres are distinct and outclass at different tasks, and neither one can be omitted without this having high impact on cognitive performance.
Although the hemispheres are so distinct and are experts at their assigned functions, they also have limited abilities in performing the tasks for which the other hemisphere is specialised. In the picture above is an overview which hemisphere gives raise to what ability.
Differences in Processing
Experiment on local and global processing with patients with left- or right-hemisphere damage
There are two sets of approaches to the question of hemispheric specialisation. One set of theories is about the topic by asking the question “What tasks is each hemisphere specialised for?”. Theories that belong to this set, assign the different levels of ability to process sensory information to the different levels of abilities for higher cognitive skills. One theory that belongs to this set is the “spatial frequency hypothesis”. This hypothesis states that the left hemisphere is important for fine detail analysis and high spatial frequency in visual images whereas the right hemisphere is important for low spatial frequency. We have pursued this approach above.
The other approach does not focus on what type of information is processed by each hemisphere but rather on how each hemisphere processes information. This set of theories assumes that the left hemisphere processes information in an analytic, detail- and function-focused way and that it places more importance on temporal relations between information, whereas the right hemisphere is believed to go about the processing of information in a holistic way, focusing on spatial relations and on appearance rather than on function.
The picture above shows an exemplary response to different target stimuli in an experiment on global and local processing with patients who suffer right- or left-hemisphere damage. Patients with damage to the right hemisphere often suffer a lack of attention to the global form, but recognise details with no problem. For patients with left-hemisphere-damage this is true the other way around. This experiment supports the assumption that the hemispheres differ in the way they process information.
Interaction of the Hemispheres
Why is the transfer between the hemispheres needed at all if the hemispheres are so distinct concerning functioning, anatomy, chemistry and the transfer results in degrading of quality of information and takes time? The reason is that the hemispheres, although so different, do interact. This interaction has important advantages because as studies by Banich and Belger have shown it may “enhance the overall processing capacity under high demand conditions” (Banich). (Under low demand conditions the transfer does not make as much sense because the cost of transferring the information to the other hemisphere are higher than the advantages of parallel processing.)
The two hemispheres can interact over the corpus callosum in different ways. This is measured by first computing performance of each hemisphere individually and then measuring the overall performance of the whole brain. In some tasks one hemisphere may dominate the other in the overall performance, so the overall performance is as good or bad as the performance of one of the single hemispheres. What's surprising is that the dominating hemisphere may very well be the one that is less specialised, so here is another example of a situation where parallel processing is less effective than processing in just one half of the brain.
Another way of how the hemispheres interact is that overall processing is an average of performance of the two individual hemispheres.
The third, most surprising way the hemispheres can interact is that when performing a task together the hemispheres behave totally different than when performing the same task individually. This can be compared to social behavior of people: Individuals behave different in groups than they would when being by themselves.
Individual Factors Influencing Lateralisation
After having looked at hemispheric specialisation from a general point of view, we now want to focus on differences between individuals concerning hemispheric specialisation. Aspects that may have an impact on lateralisation might be age, gender or handed-ness.
Age could be one factor which decides in how far each hemisphere is used at specific tasks. Researchers have suggested that lateralisation develops with age until puberty. Thus infants should not have functionally-lateralised brains. Here are four pieces of evidence that speak against this hypothesis:
Infants already show the same brain anatomy as adults. This means the brain of a new born is already lateralised. Following the hypothesis that anatomy is linked to function this means that lateralisation is not developed at a later period in life.
Differences in perceptual asymmetries that means superior performance at processing verbal vs. non- verbal material in the different hemispheres cannot be observed in children aged 5 to 13, i.e. children aged 5 process the material the same way 13 year olds do.
Experiments with 1-week-old infants showed that they responded with increased interest to verbal material when this was presented to the right ear than when presented to the left ear and increased interest to non-verbal material when presented to the left ear. The infants’ interest was hereby measured by the frequency of soother sucking.
Although children who underwent hemispherectomy (the surgical removal of one hemisphere) do develop the cognitive skills of the missing hemisphere (in contrast to adults or adolescents who can only partly compensate for missing brain parts), they do not develop these skills to the same extent as a child with hemispherectomy of the other hemisphere. For example: A child whose right hemisphere has been removed will develop spatial skills but not to the extent that a child whose left hemisphere has been removed, and thus still possesses the right hemisphere.
Handedness is another factor that might influence brain lateralisation. There is statistical evidence that left-handers have a different brain organisation than right-handers. 10% of the population is left-handed. Whereas 95% of the right-handed people process verbal material in a superior manner in the left-hemisphere, there is no such a high figure for verbal superiority of one hemisphere in left-handers: 70% of the left-handers process verbal material in the left-hemisphere, 15% process verbal material in the right hemisphere (the functions of the hemispheres are simply switched around), and the remaining 15% are not lateralised, meaning that they process language in both hemispheres. Thus as a group, left-handers seem to be less lateralised. However a single left-handed-individual can be just as lateralised as the average right-hander.
Gender is also an aspect that is believed to have impact on the hemispheric specialisation. In animal studies, it was found that hormones create brain differences between the genders that are related to reproductional functions. In humans it is hard to determine to which extent it is really hormones that cause differences and to which extent it is culture and schooling that are responsible.
One brain area for which a difference between the genders was observed is the corpus callosum. Although one study found that the c.c. is larger in women than in men these results could not be replicated. Instead it was found that the posterior part of the c.c. is more bulbous in women than in men. This might however be related to the fact that the average woman has a smaller brain than the average man and thus the bulbousness of the posterior section of the c.c. might be related to brain size and not to gender.
In experiments that measure performance in various tasks between the genders the cultural aspect is of great importance because men and women might use different problem solving strategies due to schooling.
Summary
Although the two hemispheres look like each other’s mirror images at first glance, this impression is misleading. Taking a closer look, the hemispheres not only differ in their conformation and chemistry, but most importantly in their function. Although both hemispheres can perform all basic cognitive tasks, there exists a specialisation for specific cognitive demands. In most people, the left hemisphere is an expert at verbal tasks, whereas the right hemisphere has superior abilities in non-verbal tasks. Despite the functional distinctness the hemispheres communicate with each other via the corpus callosum.
This fact has been utilised by Sperry’s experiments with split-brain-patients. These are outstanding among other experiments measuring perceptual asymmetries because they were the first experiments to refute the hemispheric dominance theory and received recognition through the Nobel Prize for Medicine and Physiology.
Individual factors such as age, gender or handed-ness have no or very little impact on hemispheric functioning.