15.4: RNA Processing in Eukaryotes
Skills to Develop
- Describe the different steps in RNA processing
- Understand the significance of exons, introns, and splicing
- Explain how tRNAs and rRNAs are processed
After transcription, eukaryotic pre-mRNAs must undergo several processing steps before they can be translated. Eukaryotic (and prokaryotic) tRNAs and rRNAs also undergo processing before they can function as components in the protein synthesis machinery.
mRNA Processing
The eukaryotic pre-mRNA undergoes extensive processing before it is ready to be translated. The additional steps involved in eukaryotic mRNA maturation create a molecule with a much longer half-life than a prokaryotic mRNA. Eukaryotic mRNAs last for several hours, whereas the typical E. coli mRNA lasts no more than five seconds.
Pre-mRNAs are first coated in RNA-stabilizing proteins; these protect the pre-mRNA from degradation while it is processed and exported out of the nucleus. The three most important steps of pre-mRNA processing are the addition of stabilizing and signaling factors at the 5' and 3' ends of the molecule, and the removal of intervening sequences that do not specify the appropriate amino acids. In rare cases, the mRNA transcript can be “edited” after it is transcribed.
Evolution Connection: RNA Editing in Trypanosomes
The trypanosomes are a group of protozoa that include the pathogen Trypanosoma brucei , which causes sleeping sickness in humans (Figure \(\PageIndex{1}\)). Trypanosomes, and virtually all other eukaryotes, have organelles called mitochondria that supply the cell with chemical energy. Mitochondria are organelles that express their own DNA and are believed to be the remnants of a symbiotic relationship between a eukaryote and an engulfed prokaryote. The mitochondrial DNA of trypanosomes exhibit an interesting exception to The Central Dogma: their pre-mRNAs do not have the correct information to specify a functional protein. Usually, this is because the mRNA is missing several U nucleotides. The cell performs an additional RNA processing step called RNA editing to remedy this.
Other genes in the mitochondrial genome encode 40- to 80-nucleotide guide RNAs. One or more of these molecules interacts by complementary base pairing with some of the nucleotides in the pre-mRNA transcript. However, the guide RNA has more A nucleotides than the pre-mRNA has U nucleotides to bind with. In these regions, the guide RNA loops out. The 3' ends of guide RNAs have a long poly-U tail, and these U bases are inserted in regions of the pre-mRNA transcript at which the guide RNAs are looped. This process is entirely mediated by RNA molecules. That is, guide RNAs—rather than proteins—serve as the catalysts in RNA editing.
RNA editing is not just a phenomenon of trypanosomes. In the mitochondria of some plants, almost all pre-mRNAs are edited. RNA editing has also been identified in mammals such as rats, rabbits, and even humans. What could be the evolutionary reason for this additional step in pre-mRNA processing? One possibility is that the mitochondria, being remnants of ancient prokaryotes, have an equally ancient RNA-based method for regulating gene expression. In support of this hypothesis, edits made to pre-mRNAs differ depending on cellular conditions. Although speculative, the process of RNA editing may be a holdover from a primordial time when RNA molecules, instead of proteins, were responsible for catalyzing reactions.
5' Capping
While the pre-mRNA is still being synthesized, a 7-methylguanosine cap is added to the 5' end of the growing transcript by a phosphate linkage. This moiety (functional group) protects the nascent mRNA from degradation. In addition, factors involved in protein synthesis recognize the cap to help initiate translation by ribosomes.
3' Poly-A Tail
Once elongation is complete, the pre-mRNA is cleaved by an endonuclease between an AAUAAA consensus sequence and a GU-rich sequence, leaving the AAUAAA sequence on the pre-mRNA. An enzyme called poly-A polymerase then adds a string of approximately 200 A residues, called the poly-A tail . This modification further protects the pre-mRNA from degradation and signals the export of the cellular factors that the transcript needs to the cytoplasm.
Pre-mRNA Splicing
Eukaryotic genes are composed of exons , which correspond to protein-coding sequences ( ex- on signifies that they are ex pressed), and int ervening sequences called introns ( int- ron denotes their int ervening role), which may be involved in gene regulation but are removed from the pre-mRNA during processing. Intron sequences in mRNA do not encode functional proteins.
The discovery of introns came as a surprise to researchers in the 1970s who expected that pre-mRNAs would specify protein sequences without further processing, as they had observed in prokaryotes. The genes of higher eukaryotes very often contain one or more introns. These regions may correspond to regulatory sequences; however, the biological significance of having many introns or having very long introns in a gene is unclear. It is possible that introns slow down gene expression because it takes longer to transcribe pre-mRNAs with lots of introns. Alternatively, introns may be nonfunctional sequence remnants left over from the fusion of ancient genes throughout evolution. This is supported by the fact that separate exons often encode separate protein subunits or domains. For the most part, the sequences of introns can be mutated without ultimately affecting the protein product.
All of a pre-mRNA’s introns must be completely and precisely removed before protein synthesis. If the process errs by even a single nucleotide, the reading frame of the rejoined exons would shift, and the resulting protein would be dysfunctional. The process of removing introns and reconnecting exons is called splicing (Figure \(\PageIndex{2}\)). Introns are removed and degraded while the pre-mRNA is still in the nucleus. Splicing occurs by a sequence-specific mechanism that ensures introns will be removed and exons rejoined with the accuracy and precision of a single nucleotide. The splicing of pre-mRNAs is conducted by complexes of proteins and RNA molecules called spliceosomes.
Art Connection
Errors in splicing are implicated in cancers and other human diseases. What kinds of mutations might lead to splicing errors? Think of different possible outcomes if splicing errors occur.
Note that more than 70 individual introns can be present, and each has to undergo the process of splicing—in addition to 5' capping and the addition of a poly-A tail—just to generate a single, translatable mRNA molecule.
Link to Learning
See how introns are removed during RNA splicing at this website .
Processing of tRNAs and rRNAs
The tRNAs and rRNAs are structural molecules that have roles in protein synthesis; however, these RNAs are not themselves translated. Pre-rRNAs are transcribed, processed, and assembled into ribosomes in the nucleolus. Pre-tRNAs are transcribed and processed in the nucleus and then released into the cytoplasm where they are linked to free amino acids for protein synthesis.
Most of the tRNAs and rRNAs in eukaryotes and prokaryotes are first transcribed as a long precursor molecule that spans multiple rRNAs or tRNAs. Enzymes then cleave the precursors into subunits corresponding to each structural RNA. Some of the bases of pre-rRNAs are methylated; that is, a –CH 3 moiety (methyl functional group) is added for stability. Pre-tRNA molecules also undergo methylation. As with pre-mRNAs, subunit excision occurs in eukaryotic pre-RNAs destined to become tRNAs or rRNAs.
Mature rRNAs make up approximately 50 percent of each ribosome. Some of a ribosome’s RNA molecules are purely structural, whereas others have catalytic or binding activities. Mature tRNAs take on a three-dimensional structure through intramolecular hydrogen bonding to position the amino acid binding site at one end and the anticodon at the other end (Figure \(\PageIndex{3}\)). The anticodon is a three-nucleotide sequence in a tRNA that interacts with an mRNA codon through complementary base pairing.
Summary
Eukaryotic pre-mRNAs are modified with a 5' methylguanosine cap and a poly-A tail. These structures protect the mature mRNA from degradation and help export it from the nucleus. Pre-mRNAs also undergo splicing, in which introns are removed and exons are reconnected with single-nucleotide accuracy. Only finished mRNAs that have undergone 5' capping, 3' polyadenylation, and intron splicing are exported from the nucleus to the cytoplasm. Pre-rRNAs and pre-tRNAs may be processed by intramolecular cleavage, splicing, methylation, and chemical conversion of nucleotides. Rarely, RNA editing is also performed to insert missing bases after an mRNA has been synthesized.
Art Connections
Figure \(\PageIndex{2}\): Errors in splicing are implicated in cancers and other human diseases. What kinds of mutations might lead to splicing errors? Think of different possible outcomes if splicing errors occur.
- Answer
-
Mutations in the spliceosome recognition sequence at each end of the intron, or in the proteins and RNAs that make up the spliceosome, may impair splicing. Mutations may also add new spliceosome recognition sites. Splicing errors could lead to introns being retained in spliced RNA, exons being excised, or changes in the location of the splice site.
Glossary
- 7-methylguanosine cap
- modification added to the 5' end of pre-mRNAs to protect mRNA from degradation and assist translation
- anticodon
- three-nucleotide sequence in a tRNA molecule that corresponds to an mRNA codon
- exon
- sequence present in protein-coding mRNA after completion of pre-mRNA splicing
- intron
- non–protein-coding intervening sequences that are spliced from mRNA during processing
- poly-A tail
- modification added to the 3' end of pre-mRNAs to protect mRNA from degradation and assist mRNA export from the nucleus
- RNA editing
- direct alteration of one or more nucleotides in an mRNA that has already been synthesized
- splicing
- process of removing introns and reconnecting exons in a pre-mRNA


Page 1.5: Rationalizing Expressions
Introduction
An algebraic expression may sometimes have a radical in the denominator (or numerator). In calculus, a helpful technique would be to get rid of the radical in the denominator (or numerator). The technique used to rid the expression of the radical is called rationalizing . We will first discuss the idea of rationalizing the denominator, followed by rationalizing the numerator.
What is Rationalizing a Denominator?
The idea of rationalizing a denominator makes a bit more sense if you consider the definition of “rationalize.” Recall that the numbers 5, \(\ \frac{1}{2}\), and \(\ 0.75\) are all known as rational numbers because they can each be expressed as a ratio of two integers (\(\ \frac{5}{1}\), \(\ \frac{1}{2}\), and \(\ \frac{3}{4}\) respectively). Some radicals are irrational numbers because they cannot be represented as a ratio of two integers. As a result, the point of rationalizing a denominator is to change the expression so that the denominator becomes a rational number.
Here are some examples of irrational and rational denominators.
| Irrational | Rational | |
| \(\ \frac{1}{\sqrt{2}}\) | = | \(\ \frac{\sqrt{2}}{2}\) |
| \(\ \frac{2+\sqrt{3}}{\sqrt{3}}\) | = | \(\ \frac{2 \sqrt{3}+3}{3}\) |
Now let’s examine how to get from irrational to rational denominators.
Rationalizing Denominators with One Term
Let’s start with the fraction \(\ \frac{1}{\sqrt{2}}\). Its denominator is \(\ \sqrt{2}\), an irrational number.
Notice that multiplying the fraction by 1 does not change the value and so equivalently, multiplying the fraction by \(\ \frac{\sqrt{2}}{\sqrt{2}}\) also does not change it's value. Allow us to now see what happens.
\(\ \frac{1}{\sqrt{2}} \cdot 1=\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{\sqrt{2 \cdot 2}}=\frac{\sqrt{2}}{\sqrt{4}}=\frac{\sqrt{2}}{2}\)
The denominator of the new fraction is no longer a radical (notice, however, that the numerator is).
So why choose to multiply \(\ \frac{1}{\sqrt{2}}\) by \(\ \frac{\sqrt{2}}{\sqrt{2}}\)? You knew that the square root of a number times itself will be a whole number. In algebraic terms, this idea is represented by \(\ \sqrt{x} \cdot \sqrt{x}=x\). Look back to the denominators in the multiplication of \(\ \frac{1}{\sqrt{2}} \cdot 1\). Do you see where \(\ \sqrt{2} \cdot \sqrt{2}=\sqrt{4}=2\)?
Here are some more examples. Notice how the value of the fraction is not changed at all; it is simply being multiplied by another name for 1.
Rationalize the denominator. \(\ \frac{2+\sqrt{3}}{\sqrt{3}}\)
Solution
| \(\ \frac{2+\sqrt{3}}{\sqrt{3}}\) | The denominator of this fraction is \(\ \sqrt{3}\). To make it into a rational number, multiply it by \(\ \sqrt{3}\), since \(\ \sqrt{3} \cdot \sqrt{3}=3\). |
| \(\ \frac{2+\sqrt{3}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}\) | Multiply the entire fraction by another name for 1, \(\ \frac{\sqrt{3}}{\sqrt{3}}\). |
| \(\ \frac{\sqrt{3}(2+\sqrt{3})}{\sqrt{3} \cdot \sqrt{3}}\) | |
| \(\ \frac{2 \sqrt{3}+\sqrt{3} \cdot \sqrt{3}}{\sqrt{9}}\) | Use the Distributive Property to multiply \(\ \sqrt{3}(2+\sqrt{3})\). |
| \(\ \frac{2 \sqrt{3}+\sqrt{9}}{\sqrt{9}}\) | Simplify the radicals, where possible. \(\ \sqrt{9}=3\). |
\(\ \frac{2+\sqrt{3}}{\sqrt{3}}=\frac{2 \sqrt{3}+3}{3}\)
You can use the same method to rationalize denominators to simplify fractions with radicals that contain a variable. As long as you multiply the original expression by another name for 1, you can eliminate a radical in the denominator without changing the value of the expression itself.
Rationalize the denominator. \(\ \frac{\sqrt{x}+\sqrt{y}}{\sqrt{x}}\), where \(\ x \neq 0\)
Solution
| \(\ \frac{\sqrt{x}+\sqrt{y}}{\sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}}\) | The denominator is \(\ \sqrt{x}\), so the entire expression can be multiplied by \(\ \frac{\sqrt{x}}{\sqrt{x}}\) to get rid of the radical in the denominator. |
| \(\ \frac{\sqrt{x}(\sqrt{x}+\sqrt{y})}{\sqrt{x} \cdot \sqrt{x}}\) | |
| \(\ \frac{\sqrt{x} \cdot \sqrt{x}+\sqrt{x} \cdot \sqrt{y}}{\sqrt{x} \cdot \sqrt{x}}\) | Use the Distributive Property. Simplify the radicals, where possible. Remember that \(\ \sqrt{x} \cdot \sqrt{x}=x\). |
\(\ \frac{\sqrt{x}+\sqrt{y}}{\sqrt{x}}=\frac{x+\sqrt{x y}}{x}\)
Rationalize the denominator and simplify. \(\ \sqrt{\frac{100 x}{11 y}}\), where \(\ y \neq 0\)
Solution
| \(\ \frac{\sqrt{100 x}}{\sqrt{11 y}}\) | Rewrite \(\ \sqrt{\frac{a}{b}}\) as \(\ \frac{\sqrt{a}}{\sqrt{b}}\). |
| \(\ \frac{\sqrt{100 x}}{\sqrt{11 y}} \cdot \frac{\sqrt{11 y}}{\sqrt{11 y}}\) | The denominator is \(\ \sqrt{11 y}\), so multiplying the entire expression by \(\ \frac{\sqrt{11 y}}{\sqrt{11 y}}\) will rationalize the denominator. |
| \(\ \frac{\sqrt{100 \cdot 11 x y}}{\sqrt{11 y} \cdot \sqrt{11 y}}\) | Multiply and simplify the radicals, where possible. |
| \(\ \frac{\sqrt{100} \cdot \sqrt{11 x y}}{\sqrt{11 y} \cdot \sqrt{11 y}}\) | 100 is a perfect square. Remember that \(\ \sqrt{100}=10\) and \(\ \sqrt{x} \cdot \sqrt{x}=x\). |
\(\ \sqrt{\frac{100 x}{11 y}}=\frac{10 \sqrt{11 x y}}{11 y}\)
Rationalize the denominator and simplify. \(\ \frac{3}{\sqrt{7}}\)
- \(\ \frac{3 \sqrt{7}}{\sqrt{7}}\)
- \(\ 3\)
- \(\ \frac{7 \sqrt{3}}{3}\)
- \(\ \frac{3 \sqrt{7}}{7}\)
- Answer
-
- Incorrect. After you rationalize a denominator, the denominator should not be in radical form. Try multiplying the fraction by \(\ \frac{\sqrt{7}}{\sqrt{7}}\). The correct answer is \(\ \frac{3 \sqrt{7}}{7}\).
- Incorrect. The process of rationalizing does not remove the denominator, it just changes the fraction so that the denominator is no longer a radical. Try multiplying the numerator and denominator by \(\ \frac{\sqrt{7}}{\sqrt{7}}\). The correct answer is \(\ \frac{3 \sqrt{7}}{7}\).
- Incorrect. You may have rationalized the fraction \(\ \frac{7}{\sqrt{3}}\) instead of \(\ \frac{3}{\sqrt{7}}\). Try multiplying the numerator and denominator by \(\ \frac{\sqrt{7}}{\sqrt{7}}\). The correct answer is \(\ \frac{3 \sqrt{7}}{7}\).
- Correct. To rationalize the denominator, multiply \(\ \frac{3}{\sqrt{7}}\) by \(\ \frac{\sqrt{7}}{\sqrt{7}}\). This will create an integer in the denominator, so the fraction will have been rationalized.
Rationalizing Denominators with Two Terms
Denominators do not always contain just one term, as shown in the previous examples. Sometimes, you will see expressions like \(\ \frac{3}{\sqrt{2}+3}\) where the denominator is composed of two terms, \(\ \sqrt{2}\) and \(\ +3\).
Unfortunately, you cannot rationalize these denominators the same way you rationalize single-term denominators. If you multiply \(\ \sqrt{2}+3\) by \(\ \sqrt{2}\), you get \(\ 2+3 \sqrt{2}\). The original \(\ \sqrt{2}\) is gone, but now the quantity \(\ 3 \sqrt{2}\) has appeared, but this is no better!
In order to rationalize this denominator, you want to square the radical term and somehow prevent the integer term from being multiplied by a radical. Is this possible?
It is possible, and you have already seen how to do it!
Recall that when binomials of the form \(\ (a+b)(a-b)\) are multiplied, the product is \(\ a^{2}-b^{2}\). So, for example, \(\ (x+3)(x-3)=x^{2}-3 x+3 x-9=x^{2}-9\); notice that the terms \(\ -3 x\) and \(\ +3 x\) combine to 0. Now for the connection to rationalizing denominators: what if you replaced \(\ x\) with \(\ \sqrt{2}\)?
Look at the examples below. Just as \(\ -3 x+3 x\) combines to 0 in the top example, \(\ -3 \sqrt{2}+3 \sqrt{2}\) combines to 0 in the bottom example.
\(\ \begin{array}{l}
(x+3)(x-3) \\
=x^{2}-3 x+3 x-9 \\
=x^{2}-9
\end{array}\)
\(\ \begin{array}{l}
(\sqrt{2}+3)(\sqrt{2}-3) \\
=(\sqrt{2})^{2}-3 \sqrt{2}+3 \sqrt{2}-9 \\
=(\sqrt{2})^{2}-9 \\
=2-9 \\
=-7
\end{array}\)
There you have it! Multiplying \(\ \sqrt{2}+3\) by \(\ \sqrt{2}-3\) removed one radical without adding another.
In this example, \(\ \sqrt{2}-3\) is known as a conjugate , and \(\ \sqrt{2}+3\) and \(\ \sqrt{2}-3\) are known as a conjugate pair . To find the conjugate of a binomial that includes radicals, change the sign of the second term to its opposite as shown in the table below.
| Term | Conjugate | Product |
| \(\ \sqrt{2}+3\) | \(\ \sqrt{2}-3\) | \(\ (\sqrt{2}+3)(\sqrt{2}-3)=(\sqrt{2})^{2}-(3)^{2}=2-9=-7\) |
| \(\ \sqrt{x}-5\) | \(\ \sqrt{x}+5\) | \(\ (\sqrt{x}-5)(\sqrt{x}+5)=(\sqrt{x})^{2}-(5)^{2}=x-25\) |
| \(\ 8-2 \sqrt{x}\) | \(\ 8+2 \sqrt{x}\) | \(\ (8-2 \sqrt{x})(8+2 \sqrt{x})=(8)^{2}-(2 \sqrt{x})^{2}=64-4 x\) |
| \(\ 1+\sqrt{x y}\) | \(\ 1-\sqrt{x y}\) | \(\ (1+\sqrt{x y})(1-\sqrt{x y})=(1)^{2}-(\sqrt{x y})^{2}=1-x y\) |
More generally, if a fraction has a denominator of the form \(a + b \sqrt{c} \), then the conjugate is \(a - b \sqrt{c} \) and vice-versa.
Rationalize the denominator and simplify. \(\ \frac{5-\sqrt{7}}{3+\sqrt{5}}\)
Solution
| \(\ \frac{5-\sqrt{7}}{3+\sqrt{5}} \cdot \frac{3-\sqrt{5}}{3-\sqrt{5}}\) | Find the conjugate of \(\ 3+\sqrt{5}\). Then multiply the entire expression by \(\ \frac{3-\sqrt{5}}{3-\sqrt{5}}\). |
| \(\ \frac{(5-\sqrt{7})(3-\sqrt{5})}{(3+\sqrt{5})(3-\sqrt{5})}\) | |
| \(\ \frac{5 \cdot 3-5 \sqrt{5}-3 \sqrt{7}+\sqrt{7} \cdot \sqrt{5}}{3 \cdot 3-3 \sqrt{5}+3 \sqrt{5}-\sqrt{5} \cdot \sqrt{5}}\) | Use the Distributive Property to multiply the binomials in the numerator and denominator. |
| \(\ \frac{15-5 \sqrt{5}-3 \sqrt{7}+\sqrt{35}}{9-3 \sqrt{5}+3 \sqrt{5}-\sqrt{25}}\) | Since you multiplied by the conjugate of the denominator, the radical terms in the denominator will combine to 0. |
|
\(\ \begin{array}{l}
\frac{15-5 \sqrt{5}-3 \sqrt{7}+\sqrt{35}}{9-\sqrt{25}} \\ \frac{15-5 \sqrt{5}-3 \sqrt{7}+\sqrt{35}}{9-5} \end{array}\) |
Simplify radicals where possible. |
\(\ \frac{5-\sqrt{7}}{3+\sqrt{5}}=\frac{15-5 \sqrt{5}-3 \sqrt{7}+\sqrt{35}}{4}\)
Rationalize the denominator and simplify. \(\ \frac{\sqrt{x}}{\sqrt{x}+2}\)
Solution
| \(\ \frac{\sqrt{x}}{\sqrt{x}+2} \cdot \frac{\sqrt{x}-2}{\sqrt{x}-2}\) | Find the conjugate of \(\ \sqrt{x}+2\). Then multiply the numerator and denominator by \(\ \frac{\sqrt{x}-2}{\sqrt{x}-2}\). |
| \(\ \frac{\sqrt{x}(\sqrt{x}-2)}{(\sqrt{x}+2)(\sqrt{x}-2)}\) | |
| \(\ \frac{\sqrt{x} \cdot \sqrt{x}-2 \sqrt{x}}{\sqrt{x} \cdot \sqrt{x}-2 \sqrt{x}+2 \sqrt{x}-2 \cdot 2}\) | Use the Distributive Property to multiply the binomials in the numerator and denominator. |
| \(\ \frac{\sqrt{x} \cdot \sqrt{x}-2 \sqrt{x}}{\sqrt{x} \cdot \sqrt{x}-2 \sqrt{x}+2 \sqrt{x}-4}\) |
Simplify. Remember that \(\ \sqrt{x} \cdot \sqrt{x}=x\). Since you multiplied by the conjugate of the denominator, the radical terms in the denominator will combine to 0. |
\(\ \frac{\sqrt{x}}{\sqrt{x}+2}=\frac{x-2 \sqrt{x}}{x-4}\)
One word of caution: this method will work for binomials that include a square root, but not for binomials with roots greater than 2. This is because squaring a root that has an index greater than 2 does not remove the root, as shown below.
\(\ \begin{array}{l}
(\sqrt[3]{10}+5)(\sqrt[3]{10}-5) \\
=(\sqrt[3]{10})^{2}-5 \sqrt[3]{10}+5 \sqrt[3]{10}-25 \\
=(\sqrt[3]{10})^{2}-25 \\
=\sqrt[3]{100}-25
\end{array}\)
\(\ \sqrt[3]{100}\) cannot be simplified any further, since its prime factors are \(\ 2 \cdot 2 \cdot 5 \cdot 5\). There are no cubed numbers to pull out! Multiplying \(\ \sqrt[3]{10}+5\) by its conjugate does not result in a radical-free expression.
Identify the conjugate of the denominator. \(\ \frac{x+2}{\sqrt{2 x}-7}\)
- \(\ \sqrt{2 x}+7\)
- \(\ \sqrt{2 x}-7\)
- \(\ 2 x+\sqrt{7}\)
- \(\ (2 x)^{2}+7\)
- Answer
-
- Correct. The conjugate will be the binomial that, when multiplied by the denominator, eliminates the radical. The conjugate is \(\ \sqrt{2 x}+7\).
- Incorrect. The denominator is not the conjugate. Look for the binomial that, when multiplied by the denominator, eliminates the radical. The correct answer is \(\ \sqrt{2 x}+7\).
- Incorrect. Multiplying the denominator by \(\ 2 x+\sqrt{7}\) will not remove the radical. Look for the binomial that follows the pattern \(\ (a+b)(a-b)=a^{2}-b^{2}\). The correct answer is \(\ \sqrt{2 x}+7\).
- Incorrect. Multiplying the denominator by \(\ (2 x)^{2}+7\) will not remove the radical. Look for the binomial that follows the pattern \(\ (a+b)(a-b)=a^{2}-b^{2}\). The correct answer is \(\ \sqrt{2 x}+7\).
Rationalizing The Numerator
The process of rationalizing the numerator is extremely similar to that of rationalizing the denominator.
Rationalize the numerator: \[ \frac{\sqrt{4+h}-2}{h} \nonumber\ \] You may assume that \(h \neq 0 \).
- Answer
-
\begin{align*} \frac{\sqrt{4+h}-2}{h} &= \frac{\sqrt{4+h}-2}{h} \times \frac{\sqrt{4+h}+2}{\sqrt{4+h}+2} \\ &= \frac{1}{\sqrt{4+h}+2} \end{align*}
Rationalize the numerator: \[ \frac{\sqrt{t^2+9}-3}{t} \nonumber\ \] You may assume that \(t \neq 0 \).
- Answer
-
\[ \frac{\sqrt{t^2+9}-3}{t} = \frac{\sqrt{t^2+9}-3}{t} \times \frac{\sqrt{t^2+9}+3}{\sqrt{t^2+9}+3} = \frac{t}{\sqrt{t^2+9}+3} \nonumber\ \]


32.5: The Nurse’s Role in Emergency Preparedness and Disaster Response
By the end of this section, you should be able to:
- Explain the nurse’s role in emergency preparedness, disaster response, and disaster recovery.
- Compare the stages of disaster to the nursing process.
- Describe disaster triage.
Community health nurses are well positioned to respond in times of disaster and maintain a constant role across the disaster cycle of preparedness and national planning framework (APHN, 2014). From emergency preparedness to disaster recovery , they work with individuals, families, the community, and local administrators to promote health and well-being and to prevent illness (Siva & Prema, 2018). Community health nurses are not only acute-care providers or first responders, but they also maintain a long-term focus on a healthy community during the disaster phases. Their knowledge of and skills in epidemiology , determinants of health , community mapping , risk assessment , disease surveillance , community resources, health teaching, and mass education make them effective members of the disaster management team. Their relationships with and intimate knowledge of how people in the community will respond to a crisis and what resources they may use or benefit from make them trusted health care professionals during times of uncertainty (APHN, 2014; Siva & Prema, 2018).
As discussed, emergency preparedness is an essential role for the community health nurse. Having a workable plan that can be implemented in an immediate response to a disaster is critical. Community health nurses should be ready to expand their role in nonroutine practice areas during the response to a mass casualty event. The competencies expected of the community health nurse include emergency readiness and response and ensure the nurse’s ability to understand and execute the necessary skills and behaviors in the event of an incident (International Council of Nurses, 2019). Table 32.11 lists disaster competencies for the general professional nurse, or nurses who have completed undergraduate nursing education programs. The competencies fall within eight disaster management domains.
| Domain | Competency |
|---|---|
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Stages of Disaster Response and Recovery
When communities face a disaster, the success of the response and recovery depends on a common, interoperable approach to sharing resources, coordinating and managing incidents, and communicating information (Homeland Security, 2019). The National Response Framework (NRF) provides foundational emergency management guidelines for response (Homeland Security, 2019). The National Incident Management System (NIMS) was developed by the Department of Homeland Security in 2004 within the NRF to establish a standardized set of processes and procedures that guides emergency responders at all levels of government organizations, nongovernmental organizations, and the private sector to conduct response operations (FEMA, 2017). The NRF and NIMS identify key roles and responsibilities at each stage of disaster response. The NRF can be partially or fully implemented when there is a threat or hazard, a significant event is anticipated, or in response to an incident (Homeland Security, 2019).
Disaster response and recovery occurs in stages that occur sequentially as the incident develops. These stages are grouped by activities with a common purpose so that emergency response is well organized and sequenced through specific intervals of an incident (HHS, 2012).
- Stage 1: Incident Recognition —A rapid assessment of the situation is completed, and the organization decides that emergency-related support and response is needed.
- Stage 2: Initial Notification and Activation —Initial notification and activation occur simultaneously. Appropriate organizations within the response system are notified of the incident. Urgent information is provided about the incident, and guidance is provided about the actions the community should take. Activation determines the response level to the incident and activates the emergency response procedures.
- Stage 3: Mobilization —This is the movement of the organization from a state of inactivity or baseline operations to the required response level.
- Stage 4: Incident Operations —This refers to all actions that address the response objectives following activation (other than mobilization and demobilization). The actions in this stage may be further divided into “initial” (or “immediate”) and “ongoing” categories.
- Stage 5: Demobilization —This stage addresses the transition of resources from response activities back to baseline operations. Demobilization procedures are triggered as response objectives are achieved and resources are relieved of incident responsibilities.
- Stage 6: Transition to Recovery and Return to Readiness —This stage is a return to a state of readiness for the next emergency.
The Nursing Process Applied to Disaster Response and Recovery
Public health nurses bring critical expertise to each phase of a disaster: mitigation, preparedness, response, and recovery. The practice of public health nursing is often more visible and better understood by the general public during the response and recovery phases, but their contribution is just as vital in the mitigation and preparedness phases, although probably underutilized. The increased involvement of public health nurses in disaster planning and response begins with their understanding of the comprehensive scope and standards of practice and follows with their striving to achieve individual competencies to better collaborate with others and contribute to emergency preparedness and response (Jakeway et al., 2008). Table 32.12 shows the phases of the disaster management cycle and provides examples of the nurse’s role in relation to the nursing process.
| Disaster Phase | Assessment and Analysis | Planning | Implementation | Evaluation |
|---|---|---|---|---|
| Mitigation and Preparedness |
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| Response |
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| Recovery |
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Mass Casualty Triage Systems
Response to mass casualty event s often involves more victims than responding caregivers, requiring responders to sort victims categorically based on the degree of injury. Triaging during a mass casualty event is a dynamic process that requires disaster preparedness training. Medical responders to a mass casualty must triage victims differently than when caring for clients in a controlled setting, sorting victims based on severity of injury rather than treatment of injuries. This may seem counterintuitive to normal prehospital protocols. The goal of triage systems used in mass casualty events is to do the greatest good for the greatest number of people given limited available health care resources (Clarkson & Williams, 2023). Treatment during field triage is minimal, with the goal of moving clients away from the incident and toward resources that offer more comprehensive care. Victims should be reassessed and may be recategorized based on changes in their clinical status. The triage process should focus on clients’ rapid assessment and quick movement (Clarkson & Williams, 2023).
There are several triage systems used worldwide. The algorithms are similar and have a tightly structured approach. The following sections discuss the most common triage systems.
START Triage
The Simple Triage And Rapid Treatment (START) method was developed in 1983 by Hoag Hospital and Newport Beach Fire Department staff in California for rescuers with basic first-aid skills. START is the most widely used triage system in the United States for mass casualty incidents (Clarkson & Williams, 2023). START assesses the victim’s ability to obey commands, respiratory rate, and radial pulse or capillary refill.
The START triage system uses a color-coded tag method to categorize clients based on the severity of the injury and to guide transport. Triage tags allow responders to sort victims quickly and indicate the level of treatment needed efficiently. These colors are universally recognized and correspond to a predetermined set of physical assessment findings, so responders have a standardized way to tag victims. Red indicates that the person has a life-threatening injury that requires immediate treatment; yellow indicates that the person has a serious injury that can tolerate delayed treatment, and green indicates that the person has minor injuries and is considered “walking wounded.” The color black is used for those already deceased or imminently expected to expire. Figure 32.7 shows the decision tree for tagging victims based on assessment findings. Once victims are triaged and tagged, they should be moved to designated areas that serve as treatment and loading zones for transport to higher levels of care.
SALT Triage
The Sort, Assess, Life-saving Interventions, and Triage/treatment (SALT) system is similar to the START system; however, it is more comprehensive and adds simple life-saving interventions during field triage (Clarkson & Williams, 2023).
- SORT: Sort the walking, waving, and still. The responder asks all victims at the scene to walk to a designated casualty collection area if possible and wave an arm or leg if they need help. Those who cannot move or follow commands should be assessed first.
- ASSESSMENT: Assessment and lifesaving interventions occur concurrently. Upon assessment of a victim with life-threatening injuries, the responder should intervene.
- LIFE-SAVING INTERVENTIONS: If not time-intensive, simple techniques such as controlling major hemorrhages, opening airways, needle decompression, and auto-injector antidotes should be performed. Once the intervention is performed, the responder should assign a color-coded tag similar to the START system and move on to the next victim.
- TREATMENT AND TRANSPORT: Once tagged, victims are moved to the designated casualty collection point for transport by emergency management services to higher levels of care.
This video gives an overview of how the START Triage algorithm is used during field triage.
Watch the video, and then respond to the following questions.
- How does the nurse provide rapid assessment using START triage?
- How should the nurse tag a client who passes all tests? How should a nurse tag a client who fails one test?
- What interventions do victims tagged as immediate receive?
JumpSTART
JumpSTART is a modification to the START system to assess and triage pediatric victims up to 8 years old. This method considers the difference in normal respiratory rates for children up to age 8. If the child’s age is unknown, the responder should look for underarm hair in males or breast development in females as an indicator of adult age (Clarkson & Williams, 2022).
The differences in this algorithm include:
- If a child is apneic with a pulse, open the airway and provide five rescue breaths. If breathing resumes, tag them as immediate (red). If apnea continues after five rescue breaths, they are given an expectant (black) tag.
- Normal respiratory rates are more than 15 or less than 45. If respirations fall outside this range, tag them as immediate (red).
- Neurological assessment is performed using the mnemonic AVPU (alert, responds to verbal stimuli, responds to painful stimuli, and unresponsive). Victims with abnormal posturing to painful stimuli or who are unresponsive are assigned an immediate (red) tag designation.
Read the scenario, and then answer the questions that follow based on all the case information provided in the chapter thus far. This case study is a follow-up to Case Study Part A.
A major hurricane makes landfall in Juanita’s community, causing widespread damage, loss of electricity, flooding, and mass injury. The community activates the hurricane disaster plan and mobilizes the emergency response team. Juanita is dispatched with the first wave of emergency responders to assist in client triage on-scene. She tags victims using the START method for adults and JumpSTART for children and provides lifesaving interventions to red-tagged victims prior to moving them for transport.
The following day Juanita works at a shelter receiving community members displaced from their homes. She finishes set-up of the temporary health center, organizes and tracks supplies, assesses community members as they enter the shelter, and provides interventions to prevent communicable disease such as setting up handwashing stations, monitoring for signs of infection, and providing clean clothing, food, and water.
3. What action should Juanita complete prior to on-scene triage?
- Confirm victim transport has arrived
- Activate the Incident Command center
- Ensure the scene is safe
- Provide report to the emergency room
4. What finding will Juanita expect when assessing community members entering the shelter?
- Malnutrition
- Stress
- Communicable disease
- Confusion


11.7: Medical Specialists, Diagnostic Testing, and Procedures Related to the Lymphatic and Immune Systems
Medical Specialists
Immunology (im-yŭ-NOL-ŏ-jē) is the study of disorders of the immune system. An immunologist (ĭm-ū-NŎL-ō-jĭst) is a physician who specializes in the study and treatment of immune system disorders.
An allergist (AL-ĕr-jist) is a physician who specializes in the study and treatment of allergies.
Read more about careers in allergy and immunology on the American Academy of Allergy Asthma and Immunology’s Careers web page .
Diagnostic Testing
Lymph Node Biopsy
During a lymph node biopsy, lymph node tissue is removed for examination under a microscope by a pathologist to diagnose medical conditions like infection or cancer. There are different types of lymph node biopsies, including the following [1] :
- Needle biopsy (NĒ-dĭl BĪ-ŏp-sē): After applying local anesthesia, a radiologist inserts a needle into a lymph node using ultrasound or CT scan to find the node.
- Laparoscopic lymph node biopsy (lăp-ăr-ŏ-SKŎ-pĭk limf nōd BĪ-ŏp-sē): After the patient is placed under general anesthesia, a small tube with a light and camera is inserted through a small incision. One or more other incisions will also be made for the insertion of tools to locate and remove the lymph node.
- Open lymph node biopsy (Ō-pĕn limf nōd BĪ-ŏp-sē): Surgery is performed to remove all or part of a lymph node, typically performed if the lymph node is large enough to be felt on physical exam.
- Sentinel lymph node biopsy (SĔN-tĭ-nĕl limf nōd BĪ-ŏp-sē): For some cancers, a sentinel lymph node biopsy is performed to find the best lymph nodes to biopsy. A tiny amount of a radioactive tracer or dye is injected in the area of the tumor. The tracer or dye flows into the nearest lymph nodes, the first lymph nodes to which a cancer may spread. These lymph nodes, called the sentinel nodes, are removed and analyzed.
Skin Testing for Allergies
Skin testing for allergies is performed by an immunologist or allergist to identify allergens in Type I hypersensitivity. In skin testing, allergen extracts are injected into the patient’s epidermal layer of the skin. The development of a wheal at the site of injection indicates a positive result. Based on the test results, individuals should avoid allergens that trigger a Type I hypersensitivity reaction. See Figure 11.11 [2] for an image of allergy testing with wheals indicating positive responses to an allergen.
Tissue Typing
Tissue typing (TĬSH-ū tī-pĭng) ensures that an organ from a donor will be compatible with its recipient. The process starts with identifying the unique human leukocyte antigens (hyū-măn lū-kō-sīt ĂN-tĭ-jĕnz) (HLAs) for the organ donor and recipient, either from blood or tissue. HLAs are an important part of the immune system’s response to foreign substances and act as a barcode to distinguish “self” from “non-self” — the latter resulting in rejection of the transplanted organ. [3]
To date, more than 35,000 variations of the HLA protein have been identified. This makes it extremely difficult to find HLA-matched donors for transplant recipients. Half of a person’s antigens are inherited from their mother and half from their father, so the more similar the antigen patterns are from two people, the more likely it is that those people are related. Identical twins have the same pattern, and brothers and sisters have a 1-in-4 chance of having an identical match. [4]
Procedures Related to the Lymphatic and Immune System
Splenectomy
Splenectomy (splĕ-NĔK-tŏ-mē) refers to surgical removal of a diseased or damaged spleen. Because of the important role the spleen plays in the immune system, individuals who have had a splenectomy are at increased risk of infection for the remainder of their lives.
Tonsillectomy
The tonsils help protect against infections. However, abnormally large tonsils may be removed if they contribute to recurrent cases of tonsillitis (tŏn-sĭl-Ī-tĭs) or breathing problems, especially at night. During a tonsillectomy (tŏn-sĭl-ĔK-tŏ-mē), the patient is placed under general anesthesia and the tonsils are removed by a surgeon. The adenoid, located behind the nasal cavity, may also be removed during this surgery and is referred to as an adenoidectomy (ăd-ĕ-noid-ĔK-tŏ-mē). [5]
- Medline Plus. (2022). Lymph node biopsy. https://medlineplus.gov/ency/article/003933.htm ↵
- “ Another_allergy_skin_testing.jpg ” by Ismael Olea is licensed under CC BY 4.0 ↵
- Brunk-Young, J. (2021, April 30). What is tissue typing for transplant? The Ohio State University Wexner Medical Center. https://wexnermedical.osu.edu/blog/tissue-typing ↵
- Brunk-Young, J. (2021, April 30). What is tissue typing for transplant ? The Ohio State University Wexner Medical Center. https://wexnermedical.osu.edu/blog/tissue-typing ↵
- Medline Plus. (2023). Tonsillectomy . https://medlineplus.gov/ency/article/003013.htm ↵


6.12: Stressors in Middle Childhood
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- Lumen Learning
Learning Outcomes
- Examine short term-and long term consequences of divorce on children
- Describe issues regarding sexual abuse and children
Family Life
During middle childhood, children spend less time with parents and more time with peers. Parents may have to modify their approach to parenting to accommodate the child’s growing independence. Authoritative parenting which uses reason and joint decision-making whenever possible may be the most effective approach (Berk, 2007). A more harsh form of parenting, authoritarian parenting, uses strict discipline and focuses on obedience. Asian-American, African-American, and Mexican-American parents are more likely than European-Americans to use an authoritarian style of parenting. Children raised in authoritative households tend to be confident, successful, and happy (Chao, 2001; Stewart and Bond, 2002).
Family Tasks
One of the ways to assess the quality of family life is to consider the tasks of families.
Berger (2005) lists five family functions:
- Providing food, clothing and shelter
- Encouraging Learning
- Developing self-esteem
- Nurturing friendships with peers
- Providing harmony and stability
Notice that in addition to providing food, shelter, and clothing, families are responsible for helping the child learn, relate to others, and have a confident sense of self. The family provides a harmonious and stable environment for living. A good home environment is one in which the child’s physical, cognitive, emotional, and social needs are adequately met. Sometimes families emphasize physical needs, but ignore cognitive or emotional needs. Other times, families pay close attention to physical needs and academic requirements, but may fail to nurture the child’s friendships with peers or guide the child toward developing healthy relationships. Parents might want to consider how it feels to live in the household. Is it stressful and conflict-ridden? Is it a place where family members enjoy being?
Family Change: Divorce
A lot of attention has been given to the impact of divorce on the life of children. The assumption has been that divorce has a strong, negative impact on the child and that single-parent families are deficient in some way. Research suggests 75-80 percent of children and adults who experience divorce suffer no long term effects (Hetherington & Kelly, 2002). Children of divorce and children who have not experienced divorce are more similar than different (Hetherington & Kelly, 2002).
Mintz (2004) suggests that the alarmist view of divorce was due in part to the newness of divorce when rates in the United States began to climb in the late 1970s. Adults reacting to the change grew up in the 1950s when rates were low. As divorce has become more common and there is less stigma associated with divorce, this view has changed somewhat. Social scientists have operated from the divorce as deficit model emphasizing the problems of being from a “broken home” (Seccombe &Warner, 2004). More recently, a more objective view of divorce, repartnering, and remarriage indicates that divorce, remarriage, and life in stepfamilies can have a variety of effects. The exaggeration of the negative consequences of divorce has left the majority of those who do well hidden and subjected them to unnecessary stigma and social disapproval (Hetherington & Kelly, 2002).
The tasks of families listed above are functions that can be fulfilled in a variety of family types-not just intact, two-parent households. Harmony and stability can be achieved in many family forms and when it is disrupted, either through divorce, or efforts to blend families, or any other circumstances, the child suffers (Hetherington & Kelly, 2002).
Factors Affecting the Impact of Divorce
As you look at the consequences (both pro and con) of divorce and remarriage on children, keep these family functions in mind. Some negative consequences are a result of financial hardship rather than divorce per se (Drexler, 2005). Some positive consequences reflect improvements in meeting these functions. For instance, we have learned that a positive self-esteem comes in part from a belief in the self and one’s abilities rather than merely being complimented by others. In single-parent homes, children may be given more opportunity to discover their own abilities and gain independence that fosters self-esteem. If divorce leads to fighting between the parents and the child is included in these arguments, the self-esteem may suffer.
The impact of divorce on children depends on a number of factors. The degree of conflict prior to the divorce plays a role. If the divorce means a reduction in tensions, the child may feel relief. If the parents have kept their conflicts hidden, the announcement of a divorce can come as a shock and be met with enormous resentment. Another factor that has an great impact on the child concerns financial hardships they may suffer, especially if financial support is inadequate. Another difficult situation for children of divorce is the position they are put into if the parents continue to argue and fight-especially if they bring the children into those arguments.
Short-term consequences : In roughly the first year following divorce, children may exhibit some of these short-term effects:
- Grief over losses suffered . The child will grieve the loss of the parent they no longer see as frequently. The child may also grieve about other family members that are no longer available. Grief sometimes comes in the form of sadness, but it can also be experienced as anger or withdrawal. Preschool-aged boys may act out aggressively while the same aged girls may become more quiet and withdrawn. Older children may feel depressed.
- Reduced Standard of Living . Very often, divorce means a change in the amount of money coming into the household. Children experience in new constraints on spending or entertainment. School-aged children, especially, may notice that they can no longer have toys, clothing, or other items to which they’ve grown accustomed, or it may mean that there is less eating out or cancelling satellite television, and so on. The custodial parent may experience stress at not being able to rely on child support payments or having the same level of income as before. This can affect decisions regarding healthcare, vacations, rents, mortgages and other expenditures. The stress can result in less happiness and relaxation in the home. The parent who has to take on more work may also be less available to the children.
- Adjusting to Transitions . Children may also have to adjust to other changes accompanying a divorce. The divorce might mean moving to a new home and changing schools or friends. It might mean leaving a neighborhood that has meant a lot to them as well.
Long-Term consequences : The following are some effects found after the first year of a divorce:
- Economic/Occupational Status . One of the most commonly cited long-term effects of divorce is that children of divorce may have lower levels of education or occupational status. This may be a consequence of lower income and resources for funding education rather than to divorce per se. In those households where economic hardship does not occur, there may be no impact on education or occupational status (Drexler, 2005).
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Improved Relationships with the Custodial Parent
(usually the mother): The majority of custodial parents are mothers (approximately 80.4 percent) and
19.6 percent of custodial parents are fathers, [1] Shared custody is on the rise, however, and shows promising social, academic, and psychological results for the children. [2] Children from single-parent families talk to their mothers more often than children of two-parent families (McLanahan and Sandefur, 1994). Most children of divorce lead happy, well-adjusted lives and develop stronger, positive relationships with their custodial parent (Seccombe and Warner, 2004). In a study of college-age respondents, Arditti (1999) found that increasing closeness and a movement toward more democratic parenting styles was experienced. Others have also found that relationships between mothers and children become closer and stronger (Guttman, 1993) and suggest that greater equality and less rigid parenting is beneficial after divorce (Steward, Copeland, Chester, Malley, and Barenbaum, 1997). - Greater emotional independence in sons . Drexler (2005) notes that sons who are raised by mothers only develop an emotional sensitivity to others that is beneficial in relationships.
- Feeling more anxious in their own love relationships. Children of divorce may feel more anxious about their own relationships as adults. This may reflect a fear of divorce if things go wrong, or it may be a result of setting higher expectations for their own relationships.
- Adjustment of the custodial parent . Furstenberg and Cherlin (1991) believe that the primary factor influencing the way that children adjust to divorce is the way the custodial parent adjusts to the divorce. If that parent is adjusting well, the children will benefit. This may explain a good deal of the variation we find in children of divorce. Adults going though divorce should consider good self-care as beneficial to the children-not as self-indulgent.
- Mental health issues : Some studies suggest that anxiety and depression that are common in children and adults within the first year of divorce may actually not resolve. A 15 year study by Bohman, Låftman, Päären, Jonsson (2017) ( https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5370459/ ) suggests that parental separation significantly increases the risk for depression 15 years later when depression rates were compared to matched controls. In fact, the risk of depression was related more strongly with parental conflict and parental separation than it was with parental depression!
 The median age for sexual abuse is 8 or 9 years for both boys and girls (Finkelhor et. al. 1990).    In each of these cases, the child is exploited by an older person without regard for the child’s developmental immaturity and inability to understand the sexual behavior (Steele, 1986).
Although rates of sexual abuse are higher for girls than for boys, boys may be less likely to report abuse because of the cultural expectation that boys should be able to take care of themselves and because of the stigma attached to homosexual encounters (Finkelhor et. al. 1990). Girls are more likely to be victims of incest and boys are more likely to be abused by someone outside the family. Sexual abuse can create feelings of self-blame, betrayal, and feelings of shame and guilt (Valente, 2005). Sexual abuse is particularly damaging when the perpetrator is someone the child trusts. Victims of sexual abuse may suffer from depression, anxiety, problems with intimacy, and suicide (Valente, 2005). Sexual abuse has additional impacts as well.
 The concept of false self-training (Davis, 1999) refers to holding a child to adult standards while denying the child’s developmental needs. Sexual abuse is just one example of false self-training. Children are held to adult standards of desirableness and sexuality while their level of cognitive, psychological, and emotional immaturity is ignored. Consider how confusing it might be for a 9-year-old girl who has physically matured early to be thought of as a potential sex partner. Her cognitive, psychological, and emotional state do not equip her to make decisions about sexuality or, perhaps, to know that she can say no to sexual advances. She may feel like a 9-year-old in all ways and be embarrassed and ashamed of her physical development. Girls who mature early have problems with low self-esteem because of the failure of others (family members, teachers, ministers, peers, advertisers, and others) to recognize and respect their developmental needs. Overall, youth are more likely to be victimized because they do not have control over their contact with offenders (parents, babysitters, etc.) and have no means of escape (Finkelhor and Dzuiba-Leatherman, in Davis, 1999).
Glossary
- false self-training
- holding a child to adult standards while denying the child’s developmental needs
- Wolf, Jennifer. The Single Parent Statistics Based on Census Data. Verywell Family. Retrieved from https://www.verywellfamily.com/single-parent-census-data-2997668<EMAIL_ADDRESS>- Warshak, Richard (2017). After divorce, shared parenting is best for children’s health and development . Stat. Retrieved from https://www.statnews.com/2017/05/26/divorce-shared-parenting-children-health/<EMAIL_ADDRESS>Contributors and Attributions
- Modification, adaptation, and original content. Authored by : Stephanie Loalada for Lumen Learning. Provided by : Lumen Learning. License : CC BY: Attribution
- Psyc 200 Lifespan Psychology. Authored by : Laura Overstreet. Located at : http://opencourselibrary.org/econ-201/ . License : CC BY: Attribution
- Sexual Abuse. Provided by : Wikipedia. Located at : https://en.Wikipedia.org/wiki/Child_sexual_abuse . License : CC BY-SA: Attribution-ShareAlike
- Three friends. Authored by : Peter Griffin. Provided by : Needpix. Located at : https://www.needpix.com/photo/download/1328232/people-girls-girlfriends-happy-friends-youngpeople-pre-teens-youngsters-three-friends . License : Public Domain: No Known Copyright


6.6: Issues of Social Justice in the Early Childhood Classroom
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- Krischa Esquivel, Emily Elam, Jennifer Paris, & Maricela Tafoya
- College of the Canyons
Social justice and bias (implicit and explicit) have recently become key terms in the field of early care and education, but have been researched for many years. Dissecting biases can often lead straight to imbalances in social justice which include inequity in education, access to resources including food and healthcare, and in areas early educators see as vital to development such as play.
The Disappearance of Play
In early education, we have been taught that play is a child’s work. Children learn about the world through play, practice social norms including role-playing, learn how to negotiate, use their imagination and release stress, develop fine and gross motor skills and misdirected energy. Yet as we look at early education centers who are located in lower socioeconomic communities, play can be little to none. Often times it can be used as a reward and given, or a punishment and taken away. Schools that serve impoverished communities may mistakenly eliminate play and replace it with more formal, structured instructional time, believing this will help children learn. This ignores the facts that children are fully engaged when playing, developing self -regulation through movement and choice, social-emotional skills by negotiating and building ideas together, and practicing what works in language. (K. Esquivel, 2019)
“Free play should not be seen as a “reward” for young children’s hard work - play is the work of a young child. Early childhood educators must use play as a tool for cognitive and social-emotional growth.” Young children need play in order to develop full, healthy lives. It gives them a unique way to engage with language and build literacy skills. It builds their knowledge as they solve problems, interact with concepts, and test their hypotheses. “Children build resilience, confidence, physical abilities, and relational skills as they engage in play with meaning.”
Play is increasingly being pushed out of children’s daily lives, in spite of the advocacy for play from researchers, psychologists, and early childhood educators. “The issue of missing play in schools is essential for educators to address as children continue to grow in stressful situations, requiring the unique supports that development through play offers. Children who experience a play-based early education are empowered as confident people with tools for healthy development in every area of their lives. Play is a tool that educators must use to honor children’s needs as they learn and grow.” [82]
Inequitable Access to Play as Curriculum
As we discuss the types of curriculums used in more affluent schools, we will see the vast difference on how play is welcomed, nurtured, appreciated and viewed as a necessity. We also know children from more affluent communities tend to have less behavior related challenges, more impulse control, and greater use of language which shows a direct correlation to the increased play that is received and valued.
As the next generation of early care and education educators, there is a need to be cognizant of the social justice issue rooted in play, while also acknowledging the biases which may be linked to children playing. Some of these biases are:
- Play is a waste of time
- “Those” children are already too wild and get more wild when they play
- Children are to be seen and not heard
- “Those” children are already behind and need to be learning not playing
Understanding why a family or school pushes back on children’s play is an important first step towards change and delivering information and moving towards changing imbalances. Diverse cultures place differing value on play. Not all families will understand or agree with the importance of play for young children in early childhood education programs.
A disparity in materials purchased can also be noted and rooted in the feelings of certain groups being less deserving and/or not taking care of nice materials. As professionals, we know fancy materials are not needed, rather the upkeep of an inviting, clean environment and quality interactions using materials that are in good repair and rotated frequently to maintain engagement. Additionally, providing the ‘basics’ are needed such as:
- Various building materials
- Various art materials including writing
- Various books that are culturally relevant to those in the class
- Outdoor space with ways to practice fine and gross motor skills
Appropriate classroom materials including how to design high quality environments can be found in Early Childhood Environment Rating Scale (ECERS-R) for preschoolers or Infant/Toddler Environment Rating Scale (ITERS-R) for infants and toddlers. Additionally, there are separate tools used for family child care centers, Family Child Care Environment Rating Scale, Revised Edition (FCCERS-R) and for programs that serve out-of-school programs, School-Age Care Environment Rating Scale (SACERS).
Differences in Food and Mealtimes
Meal practices vary based not only on family culture, but differences can be seen based on the location of the early education center. Schools located in more affluent areas have a tendency to get more fresh foods and homemade meals by default vs the opposite in other communities who receive packaged or processed foods.
Many programs are understanding the value in children having access to fresh foods including fruits and vegetables and are adjusting their practices and budgets accordingly. Families are also understanding the negative effects on children’s growth and development along with the immediate effects on their child’s behavior due to various dyes found in many foods (K. Esquivel, 2019).
In addition to the food served, meal time practices also vary. Meal times are most beneficial when they are enjoyable, not rushed, and filled with back and forth conversations that allow for children to socialize and practice social norms. Having family style meals (where the food is on the table and children serve themselves) allows for children to practice their fine and gross motor skills and leads to children trying a variety of foods they may not typically be exposed to. Educators must consider the possibility of push back because of family traditions, food scarcity, socializing at the table only being for adults and eating all things given is a must.
As you work with families who exhibit meal time traits that do not align with best practice, strategies discussed in Chapter 14 may be helpful. One strategy is starting a conversation with the family, while encouraging the child to take a more active role in their meals is a useful tool. There is a fine line between respecting the family culture and their wishes, and perpetuating social injustices that can be linked to socioeconomic differences (K. Esquivel, 2019).
It is also important to note that the use of food as a play material is a topic that families and early child educators may have strong feelings about. For some, especially those who have experienced food insecurity (not knowing where their next meal was coming from), it may be considered wasteful to use food for play instead of nourishing people. Programs may choose to implement a policy to respect the views and the values behind them.
Biased Response to Children’s Behavior
Developing a culturally responsive understanding of child development is imperative to ensure child behaviors are not categorized as negative when they are actually rooted in race, ethnicity, and/or gender. Educators must acknowledge that goals and beliefs about children’s development vary across different cultural contexts (the cultural context of the many adults in the child’s life: parents/caregivers, extended family, practitioners, teachers).
The behavior of children of color, particularly Black, Latino and Native American boys, is often mislabeled as challenging and negative. Boys from these groups are singled out more often for displaying the same behaviors as and withheld from more opportunities than their white peers. They are suspended at much higher rates, even from preschool and are more harshly labeled as being aggressive, loud and disrespectful.
Boys of color are seen as much older than their actual age, thereby having expectations being placed on them well beyond their ability. Research has shown that implicit bias, the unconscious beliefs each of us possesses about specific groups, plays a large role in the negative connotation given to typical child behaviors. [83]
In his experimental study, Dr. Gilliam asked early educators to watch a video of children in a classroom and press a button each time they saw a “behavior that may become a potential challenge”.  In reality, the video had no challenging behaviors in it. Using an eye tracking device, the research team measured where teachers were looking on the screen. Findings revealed that teachers spent significantly more time looking at the Black boy in the video, than any other child.
This research may shed some light on the stubborn disparities we see in expulsion and suspension practices. If early educators are scrutinizing black boys more, looking at them more, expecting more challenging behavior from them- we may expect they may find it, or in some cases think they’ve found it, even if objectively it is not there.
When the federal government published its own data on preschool suspensions for the first time, the results were remarkably similar.  New Federal data released just this year, again, show that the numbers haven’t moved. While black children make up 19% of enrollment, they make up 47% of suspensions. This year’s data also reveal that black girls make up 20% of the female preschool population, but 54% of all preschool girls suspended.
Of course, when we see such pervasive and long lasting disparities, many of us consider the possibility of bias in the system. Dr. Gilliam’s research is important because it provides us with data that explicitly finds implicit bias in the educators and directors who work in our early childhood programs. While it is exceedingly disturbing that bias, which is pervasive across all systems, is also present in our early childhood programs, it is not surprising.
All of us have biases- no matter what our profession, no matter where we live, or where we’re from.  In fact, research shows that while explicit bias has decreased in our country over time, implicit bias has remained stable. And it is instilled in us at very early ages. [84]


1.10.4: Gibbs Energies- Equilibrium and Spontaneous Change
The Gibbs energy of a closed system at temperature \(\mathrm{T}\) is related to the enthalpy \(\mathrm{H}\) using equation (a) [1].
\[\mathrm{G}=\mathrm{H}-\mathrm{T} \, \mathrm{S} \nonumber \]
The differential change in Gibbs energy at constant temperature is related to the change in enthalpy \(\mathrm{dH}\) using equation (b).
\[\mathrm{dG}=\mathrm{dH}-\mathrm{T} \, \mathrm{dS} \nonumber \]
For a process taking place in a closed system involving a change from state I to state II, the change in Gibbs energy is given by equation (c).
\[\Delta \mathrm{G}=\Delta \mathrm{H}-\mathrm{T} \, \Delta \mathrm{S} \nonumber \]
The latter equation signals how changes in enthalpy and entropy determine the change in Gibbs energy. A given closed system at temperature \(\mathrm{T}\) and pressure \(\mathrm{p}\) is prepared using \(\mathrm{n}_{1}\) moles of solvent (water) and \(\mathrm{n}_{\mathrm{j}}\) moles of solute \(j\). The system is at equilibrium such that the composition/organisation is represented by \(\xi^{\mathrm{eq}\) and the affinity for spontaneous change is zero. We summarise this state of affairs as follows.
\[\mathrm{G}^{e q}=\mathrm{G}^{\mathrm{eq}}\left[\mathrm{T}, \mathrm{p}, \mathrm{n}_{1}, \mathrm{n}_{\mathrm{j}}, \xi^{\mathrm{eq}}, \mathrm{A}=0\right] \nonumber \]
In a plot of \(\mathrm{G}\) against \(\xi\) (at fixed \(\mathrm{T}\) and \(\mathrm{p}\)) the Gibbs energy is a minimum at \(\xi^{\mathrm{eq}}\) [2]. The enthalpy \(\mathrm{H}^{\mathrm{eq}}\) of the equilibrium state can be represented in a similar fashion.
\[\mathrm{H}^{e q}=\mathrm{H}^{e q}\left[\mathrm{~T}, \mathrm{p}, \mathrm{n}_{1}, \mathrm{n}_{\mathrm{j}}, \xi^{\mathrm{eq}}, \mathrm{A}=0\right] \nonumber \]
However it is unlikely that \(\mathrm{H}^{\mathrm{eq}}\) at \(\xi^{\mathrm{eq}}\) corresponds to a minimum in enthalpy \(\mathrm{H}\) when \(\mathrm{H}\) is plotted as a function of \(\xi\). A similar comment applies to the entropy \(\mathrm{S}^{\mathrm{eq}}\);
\[\mathrm{S}^{\mathrm{eq}}=\mathrm{S}^{\mathrm{eq}}\left[\mathrm{T}, \mathrm{p}, \mathrm{n}_{1}, \mathrm{n}_{\mathrm{j}}, \xi^{\mathrm{eq}}, \mathrm{A}=0\right] \nonumber \]
However taken together \(\mathrm{H}^{\mathrm{eq}}\) and \(\mathrm{S}^{\mathrm{eq}}\) produce the minimum in \(\mathrm{G}\) at \(\mathrm{G}^{\mathrm{eq}}\).
\[\mathrm{G}^{\mathrm{eq}}=\mathrm{H}^{\mathrm{eq}}-\mathrm{T} \, \mathrm{S}^{\mathrm{eq}} \nonumber \]
In summary; at thermodynamic equilibrium
- \(\mathrm{A}\) is zero,
- \(\mathrm{G}\) is a minimum and
- the rate of change of composition/organisation \(\mathrm{d}\xi/\mathrm{dt}\) is zero.
The latter condition emerges from the conclusion that this rate is zero if there is no affinity for change. For a given system at defined \(\mathrm{T}\) and \(\mathrm{p}\), the state for which \(\mathrm{G}\) is a minimum is unique [3]. Indeed if this was not the case, chemistry would be a very difficult subject. In a given spontaneous chemical reaction proceeds until the composition/organisation reaches \(\xi^{\mathrm{eq}}\). In other words the Gibbs energy is the important thermodynamic potential, certainly forming the basis of treatments of chemical reactions in closed systems at fixed \(\mathrm{T}\) and \(\mathrm{p}\) [4]. However a word of caution is in order. The Gibbs energy of a system differs from the thermodynamic energy \(\mathrm{U}\). In fact the Gibbs energy is a somewhat contrived property but aimed at a description of closed systems at fixed \(\mathrm{T}\) and \(\mathrm{p}\). Nevertheless the Gibbs energy can be given practical significance. We consider a system at equilibrium (i.e. \(\mathrm{A} = 0\)) at temperature \(\mathrm{T}\) and pressure \(\mathrm{p}\) where in this state (state I) the Gibbs energy is \(\mathrm{G}[\mathrm{I}]\). The system is displaced by a change in pressure to a neighbouring equilibrium state (at constant \(\mathrm{T}\)). The equilibrium isothermal dependence of Gibbs energy \(\mathrm{G}[\mathrm{I}]\) on pressure equals the volume of the system, \(\mathrm{V}[\mathrm{I}]\) [5].
\[V=\left[\frac{\partial G}{\partial p}\right]_{T, A=0} \nonumber \]
In other words we may not know the Gibbs energy of a system (in fact never know) at least we know that the pressure dependence is the volume which we can readily measure. The isobaric dependence of \(\mathrm{G}[\mathrm{I}]\) on temperature for an equilibrium displacement yields the entropy.
\[\mathrm{S}=-\left[\frac{\partial \mathrm{G}}{\partial \mathrm{T}}\right]_{\mathrm{p}, \mathrm{A}=0} \nonumber \]
Four key points can be made.
- The equilibrium state for a system at constant \(\mathrm{T}\) and \(\mathrm{p}\) corresponds to a minimum in Gibbs energy.
- The minimum in Gibbs energy of a given system is unique.
- In the non-equilibrium, there is no direct relationship between the gradient \((\partial \mathrm{G} / \partial \xi)\) and the rate of spontaneous change, \((\partial \xi / \partial t)\).
- The equilibrium state is stable; \((\partial \mathrm{A} / \partial \xi)<0\) at \(\xi^{\mathrm{eq}}\) [6].
Footnotes
[1]
\[\begin{aligned}
&\mathrm{G}=[\mathrm{J}] ; \mathrm{T} \, \mathrm{S}=[\mathrm{K}] \,\left[\mathrm{J} \mathrm{K}^{-1}\right]=[\mathrm{J}] ; \mathrm{p} \, \mathrm{V}=\left[\mathrm{N} \mathrm{m}^{-2}\right] \,\left[\mathrm{m}^{3}\right]=[\mathrm{N} \mathrm{m}]=[\mathrm{J}] \\
&\mathrm{A} \, \xi=\left[\mathrm{J} \mathrm{mol}^{-1}\right] \,[\mathrm{mol}]=[\mathrm{J}]
\end{aligned} \nonumber \]
[2] See for example
- G. Willis and D. Ball, J. Chem. Educ.,1984, 61 , 173, and
- P. L. Corio, J. Phys. Chem.,1983, 87 , 2416.
[3] This point is discussed in the monograph, F. Van Zeggeren and S. H. Story, The Computation of Chemical Equilibria, Cambridge University Press, 1970.
[4] The dependence of rate of reaction on composition is described using the law of mass action and rate constants. The law of mass action is in these terms, extrathermodynamic , meaning that the law does not follow from the first and second laws.
[5] For completeness we consider the case where in equilibrium state [I] at \(\xi^{\mathrm{eq}}[\mathrm{I}]\), the system is displaced by a change to a neighbouring state having the same composition/organisation, \(\xi[\mathrm{I}]\); i.e. the system is ‘frozen’. The isothermal dependence of \(\mathrm{G}[\mathrm{I}]\) on pressure at constant composition equals the volume. Thus, \(\mathrm{V}[\mathrm{I}]=\left[\frac{\partial \mathrm{G}}{\partial \mathrm{p}}\right]_{\mathrm{T}, \xi[\mathrm{I}]}\) Similarly, \(\mathrm{S}[\mathrm{I}]=-\left[\frac{\partial \mathrm{G}}{\partial \mathrm{T}}\right]_{\mathrm{p}, \xi[\mathrm{I}]}\)
The identities of \(\mathrm{S}\) and \(\mathrm{V}\) at constant ‘\(\mathrm{A}=0\)’ and at \(\xi^{\mathrm{eq}}[\mathrm{I}]\) arise from the fact that \(\mathrm{V}\) and \(\mathrm{S}\) are strong state variables.
[6] Consider a simple cup in which we have placed (delicately) a steel ball near the top edge.
- We release the ball, the ball rolls down and the ball gathers speed.
- At the bottom of the cup the speed of the ball is a maximum (i.e. maximum in kinetic energy) where the potential energy is a minimum.
- The ball continues through the bottom of the cup and rises to the opposite edge.
- The ball slows down and then changes direction, falling back to the bottom of the cup.
- If the surface of the cup is perfectly smooth ( i.e. no energy lost to friction), the ball oscillates about the bottom of the well of the cup. This mechanical model is not correct for chemical reactions in closed systems. In fact the rate of the chemical reaction decreases as a system approaches the minimum in Gibbs energy.


5.13: Video- Ocean Basins
This video provides an introduction to the Wilson cycle, a theory that describes the lifecycle of the ocean basin:
As you can see, it is very common for oceans to form and then disappear. Continental rifting plays a key role in the formation of an ocean. But how did the oceans form in the first place? Watch the following video for some current theories:
The low lying areas mentioned in the video are the ocean floors. Oceanic crust is basalt and continental crust is composed granite. Basalt is heavier so when they both rest on the top of the mantle, oceanic crust sinks lower forming a basin for the water to drain into.
Contributors and Attributions
- Authored by : Kimberly Schulte and Lumen Learning. Provided by : Lumen Learning. License : CC BY: Attribution
- Geology: Wilson Cycle. Authored by : mitartemis. Located at : https://youtu.be/I_q3sAcuzIY . License : All Rights Reserved . License Terms : Standard YouTube License
- Earth the Biography: Oceans. Authored by : National Geographic. Located at : https://youtu.be/hwVU0-2Qnso . License : All Rights Reserved . License Terms : Standard YouTube License


3.1: Inductive Arguments and Statistical Generalizations
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As we saw in chapter 1 (section 1.8), an inductive argument is an argument whose conclusion is supposed to follow from its premises with a high level of probability, rather than with certainty. This means that although it is possible that the conclusion doesn’t follow from its premises, it is unlikely that this is the case. We said that inductive arguments are “defeasible,” meaning that we could turn a strong inductive argument into a weak inductive argument simply by adding further premises to the argument. In contrast, deductive arguments that are valid can never be made invalid by adding further premises. Recall our “Tweets” argument:
- Tweets is a healthy, normally functioning bird
- Most healthy, normally functioning birds fly
- Therefore, Tweets probably flies
Without knowing anything else about Tweets, it is a good bet that Tweets flies. However, if we were to add that Tweets is 6 ft. tall and can run 30 mph, then it is no longer a good bet that Tweets can fly (since in this case Tweets is likely an ostrich and therefore can’t fly). The second premise, “most healthy, normally functioning birds fly,” is a statistical generalization. Statistical generalizations are generalizations arrived at by empirical observations of certain regularities. Statistical generalizations can be either universal or partial. Universal generalizations assert that all members (i.e., 100%) of a certain class have a certain feature, whereas partial generalizations assert that most or some percentage of members of a class have a certain feature. For example, the claim that “67.5% of all prisoners released from prison are rearrested within three years” is a partial generalization that is much more precise than simply saying that “most prisoners released from prison are rearrested within three years.” In contrast, the claim that “all prisoners released from prison are rearrested within three years” is a universal generalization. As we can see from these examples, deductive arguments typically use universal statistical generalizations whereas inductive arguments typically use partial statistical generalizations. Since statistical generalizations are often crucial premises in both deductive and inductive arguments, being able to evaluate when a statistical generalization is good or bad is crucial for being able to evaluate arguments. What we are doing in evaluating statistical generalizations is determining whether the premise in our argument is true (or at least well-supported by the evidence). For example, consider the following inductive argument, whose premise is a (partial) statistical generalization:
- 70% of voters say they will vote for candidate X
- Therefore, candidate X will probably win the election
This is an inductive argument because even if the premise is true, the conclusion could still be false (for example, an opponent of candidate X could systematically kill or intimidate those voters who intend to vote for candidate X so that very few of them will actually vote). Furthermore, it is clear that the argument is intended to be inductive because the conclusion contains the word “probably,” which clearly indicates that an inductive, rather than deductive, inference is intended. Remember that in evaluating arguments we want to know about the strength of the inference from the premises to the conclusion, but we also want to know whether the premise is true! We can assess whether or not a statistical generalization is true by considering whether the statistical generalization meets certain conditions. There are two conditions that any statistical generalization must meet in order for the generalization to be deemed “good.”
1.
Adequate sample size
: the sample size must be large enough to support the generalization.
2.
Non-biased sample
: the sample must not be biased.
A sample is simply a portion of a population. A population is the totality of members of some specified set of objects or events.   A good statistical generalization is one in which the sample is representative of the population. When a sample is representative, the characteristics of the sample match the characteristics of the population at large. For example, my method of sampling cars and trucks that drive down my street would be a good method as long as the proportion of trucks to cars that drove down my street between 12-2 pm matched the proportion of trucks to cars that drove down my street during the whole day. If for some reason the number of trucks that drove down my street from 12-2 pm was much higher than the average for the whole day, my sample would not be representative of the population I was trying to generalize about (i.e., the total number of cars and trucks that drove down my street in a day). The “adequate sample size” condition and the “non-biased sample” condition are ways of making sure that a sample is representative. In the rest of this section, we will explain each of these conditions in turn.
It is perhaps easiest to illustrate these two conditions by considering what is wrong with statistical generalizations that fail to meet one or more of these conditions. First, consider a case in which the sample size is too small (and thus the adequate sample size condition is not met).  If I were to try to generalize from that sample, then I would have to say that only cars (and no trucks) drive down my street.  Taking this sample to be representative would be like going to Flagstaff, AZ for one day and saying that since it rained there on that day, it must rain every day in Flagstaff. Inferring to such a generalization is an informal fallacy called “hasty generalization.” One commits the fallacy of hasty generalization when one infers a statistical generalization (either universal or partial) about a population from too few instances of that population. Hasty generalization fallacies are very common in everyday discourse, as when a person gives just one example of a phenomenon occurring and implicitly treats that one case as sufficient evidence for a generalization. This works especially well when fear or practical interests are involved. For example, Jones and Smith are talking about the relative quality of Fords versus Chevys and Jones tells Smith about his uncle’s Ford, which broke down numerous times within the first year of owning it. Jones then says that Fords are just unreliable and that that is why he would never buy one. The generalization, which is here ambiguous between a universal generalization (i.e., all Fords are unreliable) and a partial generalization (i.e., most/many Fords are unreliable), is not supported by just one case, however convinced Smith might be after hearing the anecdote about Jones’s uncle’s Ford.
The non-biased sample condition may not be met even when the adequate sample size condition is met. For example, suppose that I count all the cars on my street for a three hour period from 11-2 pm during a weekday. Let’s assume that counting for three hours straight give us an adequate sample size. However, suppose that during those hours (lunch hours) there is a much higher proportion of trucks to cars, since (let’s suppose) many work trucks are coming to and from worksites during those lunch hours. If that were the case, then my sample, although large enough, would not be representative because it would be biased. In particular, the number of trucks to cars in the sample would be higher than in the overall population, which would make the sample unrepresentative of the population (and hence biased).
Another good way of illustrating sampling bias is by considering polls. So consider candidate X who is running for elected office and who strongly supports gun rights and is the candidate of choice of the NRA. Suppose an organization runs a poll to determine how candidate X is faring against candidate Y, who is actively anti gun rights. But suppose that the way the organization administers the poll is by polling subscribers to the magazine, Field and Stream. Suppose the poll returned over 5000 responses, which, let’s suppose, is an adequate sample size and out of those responses, 89% favored candidate X. If the organization were to take that sample to support the statistical generalization that “most voters are in favor of candidate X” then they would have made a mistake. If you know anything about the magazine Field and Stream, it should be obvious why. Field and Stream is a magazine whose subscribers who would tend to own guns and support gun rights. Thus we would expect that subscribers to that magazine would have a much higher percentage of gun rights activists than would the general population, to which the poll is attempting to generalize. But in this case, the sample would be unrepresentative and biased and thus the poll would be useless. Although the sample would allow us to generalize to the population, “Field and Stream subscribers,” it would not allow us to generalize to the population at large.
Let’s consider one more example of a sampling bias. Suppose candidate X were running in a district in which there was a high proportion of elderly voters. Suppose that candidate X favored policies that elderly voters were against. For example, suppose candidate X favors slashing Medicare funding to reduce the budget deficit, whereas candidate Y favored maintaining or increasing support to Medicare. Along comes an organization who is interested in polling voters to determine which candidate is favored in the district. Suppose that the organization chooses to administer the poll via text message and that the results of the poll show that 75% of the voters favor candidate X. Can you see what’s wrong with the poll—why it is biased? You probably recognize that this polling method will not produce a representative sample because elderly voters are much less likely to use cell phones and text messaging and so the poll will leave out the responses of these elderly voters (who, we’ve assumed make up a large segment of the population). Thus, the sample will be biased and unrepresentative of the target population. As a result, any attempt to generalize to the general population would be extremely ill-advised.
Before ending this section, we should consider one other source of bias, which is a bias in the polling questionnaire itself (what statisticians call the “instrument”). Suppose that a poll is trying to determine how much a population favors organic food products. We can imagine the questionnaire containing a choice like the following:
Which do you prefer?
- products that are expensive and have no FDA proven advantage over the less expensive products
- products that are inexpensive and have no FDA proven disadvantage over more expensive products
Because of the phrasing of the options, it seems clear that many people will choose option “b.” Although the two options do accurately describe the difference between organic and non-organic products, option “b” sounds much more desirable than option “a.” The phrasing of the options is biased insofar as “a” is a stand-in for “organic” and “b” is stand-in for “non-organic.” Even people who favor organic products may be more inclined to choose option “b” here. Thus, the poll would not be representative because the responses would be skewed by the biased phrasing of the options. Here is another example with the same point:
Which do you favor?
- Preserving a citizen’s constitutional right to bear arms
- Leaving honest citizens defenseless against armed criminals
Again, because option “b” sounds so bad and “a” sounds more attractive, those responding to a poll with this question might be inclined to choose “a” even if they don’t really support gun rights. This is another example of how bias can creep into a statistical generalization through a biased way of asking a question.
Random sampling is a common sampling method that attempts to avoid any kinds of sampling bias by making selection of individuals for the sample a matter of random chance (i.e., anyone in the population is as likely as anyone else to be chosen for the sample). The basic justification behind the method of random sampling is that if the sample is truly random (i.e., anyone in the population is as likely as anyone else to be chosen for the sample), then the sample will be representative. The trick for any random sampling technique is to find a way of selecting individuals for the sample that doesn’t create any kind of bias. A common method used to select individuals for a random sample (for example, by Gallup polls) is to call people on either their landline or cell phones. Since most voting Americans have either a landline or a cell phone, this is a good way of ensuring that every American has an equal chance of being included in the sample. Next, a random number generating computer program selects numbers to dial. In this way, organizations like Gallup are able to get something close to a random sample and are able to represent the whole U.S. population with a sample size as small as 1000 (with a margin of error of +/- 4). As technology and social factors change, random sampling techniques have to be updated. For example, although Gallup used to call only landlines, eventually this method became biased because many people no longer owned landlines, but only cell phones. If some new kind of technology replaces cell phones and landlines, then Gallup will have to adjust the way it obtains a sample in order to reflect the changing social reality.
Exercise
What kinds of problems, if any, do the following statistical generalizations have? If there is a problem with the generalization, specify which of the two conditions (adequate sample size, non-biased sample) are not met. Some generalizations may have multiple problems. If so, specify all of the problems you see with the generalization.
1. Bob, from Silverton, CO drives a 4x4 pickup truck, so most people from Silverton, CO drive 4x4 pickup trucks.
2. Tom counts and categorizes birds that land in the tree in his backyard every morning from 5:00-5:20 am. He counts mostly morning doves and generalizes, “most birds that land in my tree in the morning are morning doves.”
3. Tom counts and categorizes birds that land in the tree in his backyard every morning from 5:00-6:00 am. He counts mostly morning doves and generalizes, “most birds that land in my tree during the 24-hour day are morning doves.”
4. Tom counts and categorizes birds that land in the tree in his backyard every day from 5:00-6:00 am, from 11:00-12:00 pm, and from 5:00-6:00 pm. He counts mostly morning doves and generalizes, “most birds that land in my tree during the 24-hour day are morning doves.”
5. Tom counts and categorizes birds that land in the tree in his backyard every evening from 10:00-11:00 pm. He counts mostly owls and generalizes, “most birds that land in my tree throughout the 24-hour day are owls.”
6. Tom counts and categorizes birds that land in the tree in his backyard every evening from 10:00-11:00 pm and from 2:00-3:00 am. He counts mostly owls and generalizes, “most birds that land in my tree throughout the night are owls.”
7. A poll administered to 10,000 registered voters who were home- owners showed that 90% supported a policy to slash Medicaid funding and decrease property taxes. Therefore, 90% of voters support a policy to slash Medicaid funding.
8. A telephone poll administered by a computer randomly generating numbers to call, found that 68% of Americans in the sample of 2000 were in favor of legalizing recreational marijuana use. Thus, almost 70% of Americans favor legalizing recreation marijuana use.
9. A randomized telephone poll in the United States asked respondents whether they supported a) a policy that allows killing innocent children in the womb or b) a policy that saves the lives of innocent children in the womb. The results showed that 69% of respondents choose option “b” over option “a.” The generalization was made that “most Americans favor a policy that disallows abortion.”
10. Steve’s first rock and roll concert was an Ani Difranco concert, in which most of the concert-goers were women with feminist political slogans written on their t-shirts. Steve makes the generalization that “most rock and roll concert-goers are women who are feminists.” He then applies this generalization to the next concert he attends (Tom Petty) and is greatly surprised by what he finds.
11. A high school principal conducts a survey of how satisfied students are with his high school by asking students in detention to fill out a satisfaction survey. Generalizing from that sample, he infers that 79% of students are dissatisfied with their high school experience. He is surprised and saddened by the result.
12. After having attended numerous Pistons home games over 20 years, Alice cannot remember a time when she didn’t see ticket scalpers selling tickets outside the stadium. She generalizes that there are always scalpers at every Pistons home game.
13. After having attended numerous Pistons home games over 20 years, Alice cannot remember a time when she didn’t see ticket scalpers selling tickets outside the stadium. She generalizes that there are ticket scalpers at every NBA game.
14. After having attended numerous Pistons home games over 20 years, Alice cannot remember a time when she didn’t see ticket scalpers selling tickets outside the stadium. She generalizes that there are ticket scalpers at every sporting event.
15. Bob once ordered a hamburger from Burger King and got violently ill shortly after he ate it. From now on, he never eats at Burger King because he fears he will get food poisoning.


12.4: Summary
12.1 Preconception Conditions Affecting Pregnancy
A high-risk pregnancy is one in which the pregnant person and fetus are at increased risk for adverse health outcomes during pregnancy. Extremes in maternal age place a pregnancy at risk, so preconception and pregnancy management should be tailored to individual patient age and health status. Nutritional imbalances from overnutrition or undernutrition require specific nutritional interventions and monitoring during preconception and pregnancy to prevent anemia and other complications. Certain conditions, such as migrant farm work, undocumented immigration status, substance misuse, and homelessness require specialized management and psychosocial support. Preexisting medical conditions, such as hypertension, diabetes, and thyroid disorders, should be managed closely prior to and after conception with an interdisciplinary care team. The nurse provides education about health concerns and treatment regimens, encourages compliance with ordered medications and tests, coordinates access to social services or specialist care, and supports patients dealing with the stress of a high-risk pregnancy.
12.2 Conditions Limited to Pregnancy
The physiologic changes that occur during pregnancy can lead to complications that impair maternal-fetal health. The first trimester is a critical time for fetal development, so conditions that develop during this period can significantly compromise fetal health. Abortions and pregnancy loss more commonly occur during the first trimester as well. During the first trimester, patients begin to experience early signs of pregnancy and will often attend their first prenatal visit. This prenatal visit is critical for the evaluation of maternal-fetal health and sets the stage for care during pregnancy.
As the fetus and uterus continue to grow, the pregnant person’s body accommodates the additional physiologic changes that take place during the second trimester. Complications such as cervical insufficiency and preterm labor can lead to early deliveries and adverse outcomes. Patients who are at high risk for complications will be monitored closely with more frequent prenatal visits and serial diagnostic tests. The fetus grows the fastest during the third trimester as the patient’s body prepares for labor. Patients should be monitored closely for signs of fetal distress, preterm labor, preeclampsia, hemorrhage, and other complications. Early detection and prompt management of these conditions can decrease the risk of adverse outcomes for both the pregnant person and the fetus.
Nurses play a key role in monitoring the pregnant person and fetus in antepartum units and in clinics and private practice. Nurses perform nonstress tests (NSTs) and analyze fetal monitor strips, educate the pregnant person on the importance of fetal movement counts, and provide supportive care to decrease the stress of a high-risk pregnancy.