5.5: Legendre Symbol
In this section, we define Legendre symbol which is a notation associated to quadratic residues and prove related theorems.
Definition: Legendre symbol
Let \(p\neq 2\) be a prime and \(a\) be an integer such that \(p\nmid a\). The Legendre symbol \(\left(\frac{a}{p}\right)\) is defined by
\[\left(\frac{a}{p}\right)=\left\{\begin{array}{lcr} \ 1 &\mbox{if a is a quadratic residue of p} \\ \ -1 &\mbox{if a is a quadratic nonresidue of p}. \\ \end{array}\right .\]
Notice that using the previous example, we see that
\[\begin{aligned} && \left(\frac{1}{7}\right)=\left(\frac{2}{7}\right)=\left(\frac{4}{7}\right)=1\\ && \left(\frac{3}{7}\right)=\left(\frac{5}{7}\right)=\left(\frac{6}{7}\right)=-1\end{aligned}\]
In the following theorem, we present a way to determine wether an integer is a quadratic residue of a prime.
Euler’s Criterion
Let \(p\neq 2\) be a prime and let \(a\) be a positive integer such that \(p\nmid a\). Then
\[\left(\frac{a}{p}\right)\equiv a^{\phi(p)/2}(mod \ p).\]
Assume that \(\left(\frac{a}{p}\right)=1\). Then the congruence \(x^2\equiv a(mod \ p)\) has a solution say \(x=x'\). According to Fermat’s theorem, we see that
\[a^{\phi(p)/2}=((x')^2)^{\phi(p)/2}\equiv 1(mod\ p).\]
Now if \(\left(\frac{a}{p}\right)=-1\), then \(x^2\equiv a(mod \ p)\) is not solvable. Thus by Theorem 26, we have that for each integer k with \((k,p)=1\) there is an integer \(l\) such that \(kl\equiv a(mod \ p)\). Notice that \(i\neq j\) since \(x^2\equiv a(mod \ p)\) has no solutions. Thus we can couple the integers \(1,2,...,p-1\) into \((p-1)/2\) pairs, each has product \(a\). Multiplying these pairs together, we find out that
\[(p-1)!\equiv a^{\phi(p)/2}(mod \ p).\]
Using Wilson’s Theorem , we get \[\left(\frac{a}{p}\right)=-1\equiv a^{(p-1)/2}(mod \ p).\]
Let \(p=13\) and \(a=3\). Then \(\left(\frac{3}{13}\right)=-1\equiv 3^{6}(mod \ 13).\)
We now prove some properties of Legendre symbol.
Let \(p\neq 2\) be a prime. Let \(a\) and \(b\) be integers such that \(p\nmid a\), \(p\nmid b\) and \(p\mid (a-b)\) then \[\left(\frac{a}{p}\right)=\left(\frac{b}{p}\right).\]
Since \(p\mid (a-b)\), then \(x^2\equiv a(mod \ p)\) has a solution if and only if \(x^2\equiv b(mod \ p)\) has a solution. Hence \[\left(\frac{a}{p}\right)=\left(\frac{b}{p}\right)\]
Let \(p\neq 2\) be a prime. Let \(a\) and \(b\) be integers such that \(p\nmid a\), \(p\nmid b\) then \[\left(\frac{a}{p}\right)\left(\frac{b}{p}\right)=\left(\frac{ab}{p}\right)\]
By Euler’s criterion, we have \[\left(\frac{a}{p}\right)\equiv a^{\phi(p)/2}(mod \ p)\] and \[\left(\frac{b}{p}\right)\equiv b^{\phi(p)/2}(mod \ p).\] Thus we get \[\left(\frac{a}{p}\right)\left(\frac{b}{p}\right) \equiv (ab)^{\phi(p)/2}\equiv \left(\frac{ab}{p}\right)(mod \ p).\] We now show when is \(-1\) a quadratic residue of a prime \(p\).

By Euler’s criterion, we know that \[\left(\frac{a}{p}\right)=(-1)^{\phi(p)/2}(mod \ p)\] If \(4\mid (p-1)\), then \(p=4m+1\) for some integer \(m\) and thus we get \[(-1)^{\phi(p)/2}=(-1)^{2m}=1.\] and if \(4\mid (p-3)\), then \(p=4m+3\) for some integer \(m\) and we also get \[(-1)^{\phi(p)/2}=(-1)^{2m+1}=-1.\]
We now determine when \(2\) is a quadratic residue of a prime \(p\).
For every odd prime \(p\) we have
\[\left(\frac{2}{p}\right)=\left\{\begin{array}{lcr} \ 1 &{\mbox{if}\ p\equiv \pm1(mod \ 8)} \\ \ -1 &{\mbox{if}\ p\equiv \pm 3(mod \ 8)}. \\ \end{array}\right .\]
 Multiplying all these equations we get,
\[2.4.6...(p-1)\equiv \left(\frac{p-1}{2}\right)!(-1)^{1+2+...+(p-1)/2} \ \ \ (mod \ p).\]
This gives us
\[2^{(p-1)/2}\left(\frac{p-1}{2}\right)! \equiv \left(\frac{p-1}{2}\right)!(-1)^{(p^2-1)/8} (mod \ p).\]
Now notice that \(\left(\frac{p-1}{2}\right)!\not\equiv 0(mod \ p)\) and thus we get
\[2^{(p-1)/2}\equiv (-1)^{(p^2-1)/8}(mod \ p).\]
Note also that by Euler’s criterion, we get
\[2^{\phi(p)/2}\equiv \left(\frac{2}{p}\right)(mod \ p),\]
and since each member is 1 or -1 the two members are equal.
We now present an important lemma that determines whether an integer is a quadratic residue of a prime or not.
Gauss’s Lemma
Let \(p\neq 2\) be a prime and \(a\) a relatively prime integer to \(p\). If \(k\) counts the number of least positive residues of the integers \(a, 2a,...,((p-1)/2)a\) that are greater than \(p/2\), then
\[\left(\frac{a}{p}\right)=(-1)^k.\]
Let \(m_1,m_2,...,m_s\) be those integers greater than \(p/2\) in the set of the least positive residues of the integers \(a, 2a,...,((p-1)/2)a\) and let \(n_1,n_2,...,n_t\) be those less than \(p/2\). We now show that
\[p-m_1,p-m_2,...,p-m_k,p-n_1,p-n_2,...,p-n_t\]
are precisely the integers \[1,2,...,(p-1)/2,\] in the same order.
So we shall show that no two integers of these are congruent modulo \(p\), because there are exactly \((p-1)/2\) numbers in the set, and all are positive integers less than or equal to \((p-1)/2\). Notice that \(m_i\not\equiv m_j (\mod \ p)\) for all \(i\neq j\) and \(n_i\not\equiv n_j (\mod \ p)\) for all \(i\neq j\). If any of these congruences fail, then we will have that \(r\equiv s(mod \ p)\) assuming that \(ra\equiv sa(mod \ p)\). Also any of the integers \(p-m_i\) can be congruent to any of the \(n_i\)’s. Because if such congruence holds, then we have \(ra\equiv p-sa(mod \ p)\), so that \(ra\equiv -sa(mod \ p)\). Because \(p\nmid a\), this implies that \(r\equiv -s(mod \ p)\), which is impossible. We conclude that
\[\prod_{i=1}^k(p-m_i)\prod_{i=1}^tn_i\equiv \left(\frac{p-1}{2}\right)!(mod \ p),\]
which implies
\[(-1)^sm_1m_2...(p-m_k)n_1n_2...n_t\equiv \left(\frac{p-1}{2}\right)!(mod \ p),\]
Simplifying, we get
\[m_1m_2...(p-m_k)n_1n_2...n_t\equiv a.2a...((p-1)/2)= a^{(p-1)/2}((p-1)/2)!( mod \ p).\]
As a result, we have that
\[a^{(p-1)/2}((p-1)/2)!\equiv ((p-1)/2)!(mod \ p)\]
Note that since \((p,((p-1)/2)!)=1\), we get
\[(-1)^ka^{(p-1)/2}\equiv 1(mod \ p).\]
Thus we get
\[a^{(p-1)/2}\equiv(-1)^k(mod \ p).\]
Using Euler’s criterion, the result follows.
To find \(\left(\frac{5}{13}\right)\) using Gauss’s lemma, we calculate
\[\sum_{i=1}^6[5i/13]=[5/13]+[10/13]+[15/13]+[20/13]+[25/13]+[30/13]=5\] Thus we get \(\left(\frac{5}{13}\right)=(-1)^5=-1\).
Exercises
- Find all quadratic residues of 3
- Find all quadratic residues of 19.
- Find the value of Legendre symbol \(\left(\frac{j}{7}\right)\) for \(j=1,2,3,4,5,6\).
- Evaluate the Legendre symbol \(\left(\frac{7}{11}\right)\) by using Euler’s criterion.
- Let \(a\) and \(b\) be integers not divisible by \(p\). Show that either one or all three of the integers \(a,b\) and \(ab\) are quadratic residues of \(p\).
- Let \(p\) be a prime and \(a\) be a quadratic residue of \(p\). Show that if \(p\equiv 1(mod \ 4)\), then \(-a\) is also a quadratic residue of \(p\), whereas if \(p\equiv 3(mod \ 4)\), then \(-a\) is a quadratic nonresidue of \(p\).
- Show that if \(p\) is an odd prime and a is an integer not divisible by \(p\) then \(\left(\frac{a^2}{p}\right)=1\).
Contributors and Attributions
-
Dr. Wissam Raji, Ph.D., of the American University in Beirut. His work was selected by the Saylor Foundation’s Open Textbook Challenge for public release under a Creative Commons Attribution ( CC BY ) license.


3.1: Introduction
The Atmosphere
The atmosphere , the gaseous layer that surrounds the earth, formed over four billion years ago and is held in place by the attractive forces of gravity. During the evolution of the solid earth, volcanic eruptions released gases into the developing atmosphere. Assuming the outgasing was similar to that of modern volcanoes, the gases released included: water vapor (H2O), carbon monoxide (CO), carbon dioxide (CO2), hydrochloric acid (HCl), methane (CH4), ammonia (NH3), nitrogen (N2) and sulfur gases. The atmosphere was reducing because there was no free oxygen. Most of the hydrogen and helium that outgassed would have eventually escaped into outer space due to the inability of the earth's gravity to hold on to their small masses. There may have also been significant contributions of volatiles from the massive meteoritic bombardments known to have occurred early in the earth's history.
Water vapor in the atmosphere condensed and rained down, eventually forming lakes and oceans. The oceans provided homes for the earliest organisms which were probably similar to cyanobacteria. Oxygen was released into the atmosphere by these early organisms, and carbon became sequestered in sedimentary rocks. This led to our current oxidizing atmosphere, which is mostly comprised of nitrogen (roughly 78 percent) and oxygen (roughly 21 percent) with 0.9% argon (Ar) and 0.04% carbon dioxide (CO 2 ). The atmosphere also contains highly variable concentrations of water vapor, which can range from only 0.01% in frigid winter air in the Arctic to 5% in warm, humid, tropical air. The atmosphere also contains several gases in trace amounts, such as helium, neon, methane and nitrous oxide. One very important trace gas is ozone (O 3 ), which absorbs harmful UV radiation from the sun.
The earth's atmosphere extends outward to about 1,000 kilometers where it transitions to interplanetary space. However, most of the mass of the atmosphere (greater than 99 percent) is located within the first 40 kilometers. On average, the total weight of the atmospheric mass exerts a pressure at sea level of around 1.0 × 10 5 pascals (Pa; or one atmosphere), which is equivalent to 1.0 kg per cm 2 . The density of the atmospheric mass is much greater close to the surface and decreases rapidly with increasing altitude. The vertical temperature profile of the atmosphere is variable and depends upon the types of radiation that affect each atmospheric layer. This, in turn, depends upon the chemical composition of that layer (mostly involving trace gases). Based on these factors, the atmosphere can be divided into four distinct layers: the troposphere, stratosphere, mesosphere, and thermosphere (Figure \(\PageIndex{1}\)). The boundaries of the layers are inexact because they may vary over time and space. Beyond the atmosphere is outer space, an immeasurably vast region where the Earth exerts no detectable chemical or thermal influences.
Figure \(\PageIndex{1}\): The layers of the atmosphere. the toposphere is the closest to the Earth's surface (0-12 km). Next, is the stratosphere (12-50 km), mesophere (50-80 km), and thermosphere (80+ km). The outermost layer (the exosphere) is not shown. Ground-level ozone in the troposphere is a form of air pollution, but the ozone layer in the stratosphere helps filter UV rays. Image by GFDL ( CC-BY-SA ).
The troposphere (or lower atmosphere) contains 85-90% of the atmospheric mass and extends from the surface to an altitude of 8-20 km. It is thinner at high latitudes, and thicker at equatorial latitudes, but also varies seasonally, at any place being thicker during the summer than in the winter. Because convective air currents (winds) are common in the troposphere (the name troposphere means “region of mixing”) it is sometimes referred to as the “weather layer.” The troposphere contains the largest percentage of the mass of the atmosphere relative to the other layers. It also contains some 99 percent of the total water vapor of the atmosphere. The temperature of the troposphere is warm (roughly 17º C) near the surface of the earth. This is due to the absorption of infrared radiation from the surface by water vapor and other greenhouse gases (e.g. carbon dioxide, nitrous oxide and methane) in the troposphere. The concentration of these gases decreases with altitude, and therefore, the heating effect is greatest near the surface. The temperature in the troposphere decreases at a rate of roughly 6.5º C per kilometer of altitude. The temperature at its upper boundary is very cold (roughly -60º C). Water vapor evaporated from the earth's surface condenses in the cooler upper regions of the troposphere and falls back to the surface as rain. Dust and pollutants injected into the troposphere become well mixed in the layer, but are eventually washed out by rainfall. The troposphere is therefore self cleaning. A narrow zone at the top of the troposphere is called the tropopause . It effectively separates the underlying troposphere and the overlying stratosphere. The temperature in the tropopause is relatively constant. Strong eastward winds, known as the jet stream , also occur here.
The stratosphere extends from the troposphere to as high as about 50 km, depending on the season and latitude. Within the stratosphere there are few convective air currents. The temperature profile of the stratosphere is quite different from that of the troposphere. The temperature remains relatively constant up to roughly 25 kilometers and then gradually increases up to the upper boundary of the layer. The amount of water vapor in the stratosphere is very low, so it is not an important factor in the temperature regulation of the layer. Instead, it is ozone (O3) that causes the observed temperature inversion. Most of the ozone in the atmosphere is contained in a layer of the stratosphere from roughly 20 to 30 kilometers. This ozone layer absorbs solar energy in the form of ultraviolet radiation (UV), and the energy is ultimately dissipated as heat in the stratosphere. This heat leads to the rise in temperature. Stratospheric ozone is also very important for living organisms on the surface of the earth as it protects them by absorbing most of the harmful UV radiation from the sun. The upper boundary of the stratosphere is known as the stratopause , which is marked by a sudden decrease in temperature.
The third layer in the earth's atmosphere is called the mesosphere . It extends from the stratopause (about 50 kilometers) to roughly 85 kilometers above the earth's surface. Because the mesosphere has negligible amounts of water vapor and ozone for generating heat, the temperature drops across this layer. It is warmed from the bottom by the stratosphere. The air is very thin in this region with a density about 1/1000 that of the surface. With increasing altitude this layer becomes increasingly dominated by lighter gases, and in the outer reaches, the remaining gases become stratified by molecular weight.
The fourth layer, the thermosphere , extends outward from about 85 kilometers to about 600 kilometers. Its upper boundary is ill defined. The temperature in the thermosphere increases with altitude, up to 1500º C or more. The high temperatures are the result of absorption of intense solar radiation by the last remaining oxygen molecules. The temperature can vary substantially depending upon the level of solar activity. The lower region of the thermosphere (up to about 550 kilometers) is also known as the ionosphere . Because of the high temperatures in this region, gas particles become ionized. The ionosphere is important because it reflects radio waves from the earth's surface, allowing long-distance radio communication. The visual atmospheric phenomenon known as the northern lights also occurs in this region. The outer region of the atmosphere is known as the exosphere . The exosphere represents the final transition between the atmosphere and interplanetary space. It extends about 1000 kilometers and contains mainly helium and hydrogen. Most satellites operate in this region.
Climate and Weather
A common misconception about global climate change is that a specific weather event occurring in a particular region (for example, a very cool week in June in central Indiana) is evidence of global climate change. However, a cold week in June is a weather-related event and not a climate-related one. These misconceptions often arise because of confusion over the terms climate and weather.
Climate refers to the long-term, predictable atmospheric conditions of a specific area. The climate of a biome is characterized by having consistent temperature and annual rainfall ranges. Climate does not address the amount of rain that fell on one particular day in a biome or the colder-than-average temperatures that occurred on one day. Climate scientists often average over decades to determine climate in a given location.
In contrast, weather refers to the conditions of the atmosphere during a short period of time. Weather forecasts are usually made for 48-hour cycles. Long-range weather forecasts are available but can be unreliable.
To better understand the difference between climate and weather, imagine that you are planning an outdoor event in northern Wisconsin. You would be thinking about climate when you plan the event in the summer rather than the winter because you have long-term knowledge that any given Saturday in the months of May to August would be a better choice for an outdoor event in Wisconsin than any given Saturday in January. However, you cannot determine the specific day that the event should be held on because it is difficult to accurately predict the weather on a specific day. Climate can be considered “average” weather.
What is Climate Change?
Climate change refers to any significant change in the measures of climate lasting for an extended period of time. In other words, climate change includes major changes in temperature, precipitation, or wind patterns, among other effects, that occur over several decades or longer.
Contributors and Attributions
Modified by Kyle Whittinghill, Melissa Ha, and Rachel Schleiger from the following sources:
-
Connie Rye (East Mississippi Community College), Robert Wise (University of Wisconsin, Oshkosh), Vladimir Jurukovski (Suffolk County Community College), Jean DeSaix (University of North Carolina at Chapel Hill), Jung Choi (Georgia Institute of Technology), Yael Avissar (Rhode Island College) among other contributing authors. Original content by OpenStax (CC BY 4.0; Download for free at<EMAIL_ADDRESS>).
- Kyle Whittinghill (University of Pittsburgh)
- Contributed by Melissa Ha and Rachel Schleiger Faculty (Biological Sciences) at Yuba College & Butte College
- Climate and the Effects of Global Climate Change from General Biology by OpenStax (licensed under CC-BY )
- Climate Change from Environmental Biology by Matthew R. Fisher (licensed under CC-BY )
- Carbon Cycle from Biology by John W. Kimball (licensed under CC-BY )
- The Physical World from Environmental Science: A Canadian Perspective by Bill Freedman
- Essentials of Environmental Science by Kamala Doršner is licensed under CC BY 4.0
- The Atmosphere from AP Environmental Science by University of California College Prep accessed through CNX.


6.3 Patterns in Life History Traits
The types of trade-offs illustrated in the previous section result in many species exhibiting particular groupings of life history traits that have complementary trade-offs. In this section, we will consider two examples of these groupings, r -selected species and K -selected species . The terms r and K are components of the population growth equation, which is discussed in detail in the Population Growth and Dynamics section. Table 6.3.1 shows traits, characteristics, and representative examples of species that are highly r -selected and species that are highly K -selected. These two categories represent two ends of a continuum, and so not all species are considered either r- selected or K -selected; instead some species (as we will discuss below) may fall in the middle of the continuum (and be neither r -selected nor K -selected) or have traits at each of the continuum (and so, in a sense be both r -selected and K -selected).
Recall the trade-off related to offspring size and number. We discussed that a larger individual offspring has a higher likelihood of succeeding, but that more numerous (and therefore smaller) offspring represent more 'chances' at successful maturation. Offspring size (especially in traits such as egg or seed size) directly relates to parental investment in offspring, though parental investment can also involve care as the offspring matures. Consider the bison ( Bison bison ) and European grass frog ( Rana temporaria ) discussed previously, and included again below. A female bison may produce one (or, rarely, two) calves in each annual reproductive event. The female carries the offspring within its own body, nourishing and protecting it, for a gestation period of ~283 days. Calves are nourished solely by milk produced by the female bison for approximately 7 months, and even after weaning remain near their mother for protection and care for an additional five months. Because of this care and support, a large proportion of calves born in a given year generally survive to maturity. Conversely, a female Rana temporaria , lays up to 2,000 eggs per reproductive event and clusters them together in a mass (Figure 6.3.1C), which she does not tend or protect or nourish. The only parental care provided by the female in this case, is the nourishment contained within the egg when it is laid. Consequently, the eggs are vulnerable to predators, pathogens, and environmental stressors (such as the pool drying out) and experience a high degree of mortality before hatching into tadpoles. These two species illustrate the differences in reproductive strategies between r- selected ( Rana temporaria ) and K- selected ( Bison bison ) species.
They differences in offspring number and size and degree of parental care result in different survival patterns throughout the developmental stages of individuals. Species with Type I survivorship curves have high offspring survival and a large proportion of individuals survive to adulthood and reproductive maturity. The highest degree of mortality occurs in advanced adult age groups. Type I survivorship curves are therefore characteristic of K-selected species.Type III survivorship curves exhibit significant juvenile mortality such that the majority of offspring never reach sexual maturity. Type III survivorship curves are characteristic of r-selected species. Type II survivorship curves exhibit relatively constant survivorship and mortality throughout different age groups and therefore are not r- selected or K- selected, but instead somewhat in the middle of the continuum between the two.
As the types of survivorship curves illustrate, r -selection and K -selection exist on a continuum, not as discrete groupings. Some organisms are somewhat in the middle. For example, many medium-sized mammals and birds might fall in this area. Organisms in the middle of the continuum are neither quite large nor small, have middling life spans and rates of growth, produce moderate numbers offspring in which they invest a moderate amount of resources and parental care. Many also exhibit a Type II survivorship curve.
Additionally, other organisms seem to exist at both ends of the continuum, exhibiting some highly r -selected traits, and other highly K -selected traits. For example, leatherback sea turtles (Fig 6.3.3) are among the largest and longest-lived reptiles, with average weight in excess of 1,000 pounds (454 kg) and average life spans estimated at 50-100 years, both of which would indicate K -selection. In reproduction, however, female leatherbacks lay around 110 eggs, do not tend or protect the nest and do not return to care for nestlings once they hatch. The small size of hatchlings makes them highly vulnerable to predation until they reach a sufficiently safe size, producing a Type III survivorship curve. These traits indicate r -selection. Species such as leatherback sea turtles are therefore difficult to categorize on the r to K continuum.
Image Credits
- https://commons.wikimedia.org/wiki/F..._FWS_18383.jpg
- https://commons.wikimedia.org/wiki/F...Bison_head.png
- https://commons.wikimedia.org/wiki/File:Thresher.jpg
- https://commons.wikimedia.org/wiki/F...lion_clock.jpg
- https://commons.wikimedia.org/wiki/File:Fly_06086.JPG
- https://commons.wikimedia.org/wiki/F...pia_gialla.jpg
- https://commons.wikimedia.org/wiki/F...201136370).jpg
- https://commons.wikimedia.org/wiki/F..._auf_Stein.jpg
- https://commons.wikimedia.org/wiki/F...raria.eggs.jpg
- https://commons.wikimedia.org/wiki/F...665415746).jpg
- https://commons.wikimedia.org/wiki/F...550717549).jpg
- https://commons.wikimedia.org/wiki/F...ach,_Aruba.jpg
- https://commons.wikimedia.org/wiki/F...alcoyunque.jpg


8.1: Sage Exercises
Create the (binary) Golay code with the
codes.GolayCode()
constructor. Read the documentation to be sure you build the binary version (not ternary), and do not build the extended version (which is the default).
- Use Sage methods to compute the length, dimension and minimum distance of the code.
- How many errors can this code detect? How many can it correct?
- Find a nonzero codeword and introduce three errors by adding a vector with three 1's (your choice) to create a received message. Show that the message is decoded properly.
- Recycle your choices from the previous part, but now add one more error. Does the new received message get decoded properly?
One technique for improving the characteristics of a code is to add an overall parity-check bit, much like the lone parity-check bit of the ASCII code described in Example \(8.3\). Such codes are referred to as the extended version of the original.
-
Construct the (binary) Golay code and obtain the parity-check matrix. Use Sage commands to enlarge this matrix to create a new parity check matrix that has an additional overall parity-check bit. You may find the matrix methods
.augment()
and.stack()
useful, as well as the constructorszero_vector()
andones_matrix()
(remembering that we specify the binary entries as being from the fieldGF(2)
.)Create the extended code by supplying your enlarged parity-check matrix to the
codes.from_parity_check_matrix()
constructor and compute the length, dimension and minimum distance of the extended code. - How are the properties of this new code better? At what cost?
-
Now create the extended (binary) Golay code with the Sage constructor
codes.GolayCode()
and the correct keyword to obtain the extended version. With luck, the sorted lists of your codewords and Sage's codewords will be equal. If not, the linear code method.is_permutation_equivalent()
should returnTrue
to indicate that your code and Sage's are just rearrangements of each other.
Note:
This problem is on holiday (as of Sage \(6.7\)), while some buggy Sage code for the minimum distance of a Hamming code gets sorted out. The
r = 2
case produces an error message and for
r > 5
the computation of the minimum distance has become intolerably slow. So it is a bit harder to make a reasonable conjecture from just \(3\) cases.
The dual of an \((n,k)\) block code is formed as all the set of all binary vectors which are orthogonal to every vector of the original code. Exercise 8.6.25 describes this construction and asks about some of its properties.
You can construct the dual of a code in Sage with the
.dual_code()
method. Construct the binary Hamming codes, and their duals, with the parameter
r
ranging from
2
to
5
, inclusive. Build a table with six columns (perhaps employing the
html.table()
function) that lists \(r\text{,}\) the length of the codes, the dimensions of the original and the dual, and the minimum distances of the orginal and the dual.
Conjecture formulas for the dimension and minimum distance of the dual of the Hamming code as expressions in the parameter \(r\text{.}\)
A code with minimum distance \(d\) is called perfect if every possible vector is within Hamming distance \((d-1)/2\) of some codeword. If we expand our notion of geometry to account for the Hamming distance as the metric, then we can speak of a sphere of radius \(r\) around a vector (or codeword. For a code of length \(n\text{,}\) such a sphere will contain
\[ 1 + {n\choose 1} + {n\choose 2} + \cdots + {n\choose r} \nonumber \]
vectors within in it. For a perfect code, the spheres of radius \(d\) centered at the codewords of the code will exactly partition the entire set of all possible vectors. (This is the connection that means that coding theory meshes with sphere packing problems.)
A consequence of a code of dimension \(k\) being perfect is that
\[ 2^k\left({n\choose 0} + {n\choose 1} + {n\choose 2} + \cdots + {n\choose \frac{d-1}{2}}\right) = 2^n \nonumber \]
Conversely, if a code has minimum distance \(d\) and the condition above is true, then the code is perfect.
Write a Python function, named
is_perfect()
which accepts a linear code as input and returns
True
or
False
. Demonstrate your function by checking that the (binary) Golay code is perfect, and then use a loop to verify that the (binary) Hamming codes are perfect for all lengths below \(32\text{.}\)


7.5: Distribution of Sample Proportions (2 of 6)
Learning Objectives
- Describe the sampling distribution for sample proportions and use it to identify unusual (and more common) sample results.
Recall that our goal is to create a probability model that describes the long-run behavior of proportions from random samples. Previously, we used a simulation to collect a few random samples to get acquainted with making a distribution of sample proportions. We randomly selected 25 students at a time from a population of part-time college students that is 60% female. In the next example, we predict what happens in the long run when we select many, many random samples of 25 students at a time from this population. Then we watch a simulation to see if our predictions are correct.
Example
Predicting the Behavior of Sample Proportions
Based on our intuition and what we observed with the simulation, we might expect the following about the distribution of sample proportions that come from a population where p = 0.60:
Center: Some sample proportions will be on the low side – such as 0.52 or 0.56 – and others will be on the high side – such as 0.64 or 0.68. It is reasonable to expect all the sample proportions in repeated random samples to average out to the underlying population proportion, 0.6. In other words, the mean of the distribution of sample proportions should be p .
Spread: For samples of 25, we expect sample proportions of females not to stray too far from the population proportion 0.6. Sample proportions lower than 0.44 or higher than 0.72 will be unusual. Previously, we took smaller random samples of 8 and observed more variability in the sample proportions. We therefore think that sample size plays a role in the spread of the distribution of sample proportions. Smaller samples may be less accurate and more variable than larger samples.
Shape: Sample proportions closest to 0.6 will be most common, and sample proportions far from 0.6 in either direction will be progressively less likely. In other words, the shape of the distribution of sample proportions may be somewhat bell-shaped.
Now we use a simulation to collect numerous samples to see what happens in the long run. We use the simulation to check whether our intuition about the center, spread, and shape of the distribution of sample proportions is right.
At this point, we have a good sense of what happens as we take random samples from a population. Our simulation suggests that our initial intuition about the shape and center of the distribution of sample proportions is correct.
Now we use another simulation to help us think more precisely about the variability we expect to see in the sample proportions. Our intuition tells us that larger samples will better approximate the population, so we might expect less variability in large samples. In the next walk-through, we use a simulation to investigate this idea. After that walk-through, we tie these ideas to more formal theory about the probability model for the long-run behavior of proportions from random samples.
We are now ready to use what we have observed to develop a formal probability model to describe the behavior of sample proportions. First, let’s return to the original question that prompted our investigation of sample proportions.
We based our investigation on the prediction that 60% of part-time college students will be female. In our investigation, we asked, How much could the sample proportion vary from a population proportion of 0.60 for us to feel confident in our prediction?
We don’t expect a sample proportion to be exactly equal to the population proportion. But how much error seems reasonable?
We now see that the answer to this question depends on the size of the sample.
- If we select a random sample of 25 students, the distribution of sample proportions has a standard deviation of about 0.1. We can see that most sample proportions fall within 2 standard deviations of 0.60. Therefore, we might decide that 2 × 0.10 = 0.20 is a reasonable margin of error, so a sample proportion between 0.40 and 0.80 is not surprising if 0.60 of all part-time college students are female.
- If we select a random sample of 100 students, the distribution of sample proportions has less variability. It has a standard deviation of about 0.05. Again we see that most sample proportions fall within 2 standard deviations of 0.60, so we might decide that 2 × 0.05 = 0.10 is a reasonable amount of error for these larger samples. For a sample of 100 students, then, a sample proportion between 0.50 and 0.70 is not surprising if 0.60 of all part-time college students are female.
We discuss this idea further in “Introduction to Statistical Inference” in this unit.
Contributors and Attributions
- Concepts in Statistics. Provided by : Open Learning Initiative. Located at : http://oli.cmu.edu . License : CC BY: Attribution


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1.2.1: Relations as Sets
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A relation \(R\) on a set \(A\) is a way of relating elements of \(A\). We write \(Rxy\) if the relation holds between \(x\) and \(y\). Formally, we can consider \(R\) as the sets of pairs \(\langle x,y \rangle \in A^2\) such that \(Rxy\).
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1.2.2: Philosophical Reflections
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We define relations as certain sets. What is such a definition doing?
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1.2.3: Special Properties of Relations
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A relation \(R\) is reflexive if everything is \(R\)-related to itself; symmetric, if with \(Rxy\) also \(Ryx\) holds for any \(x\) and \(y\); and transitive if \(Rxy\) and \(Ryz\) guarantees \(Rxz\).
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1.2.4: Equivalence Relations
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A relation that is reflexive, symmetric, and transitive is called an equivalence relation.
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1.2.5: Orders
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A relation which is both reflexive and transitive is called a preorder. A preorder which is also anti-symmetric is called a partial order. A partial order which is also connected is called a linear order.
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1.2.6: Graphs
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Every relation \(R\) on a set \(X\) can be seen as a directed graph \(\langle X, R \rangle\).
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1.2.7: Operations on Relations
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Since relations are sets (of pairs), they can be operated on as sets (e.g., we can form the union and intersection of relations). We can also chain them together (relative product \(R \mid S\)). If we form the relative product of \(R\) with itself arbitrarily many times we get the transitive closure \(R^+\) of \(R\).
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1.2.8: Summary
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2.6: Verbos reflexivos con emociones
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Objetivos
Recognize reflexive verbs that refer to emotions
Reflexive verbs that refer to emotions.
As we learned in the beginning of the chapter, in reflexive verbs the subject does the action to him/her/itself. But there are some reflexive verbs in Spanish that use the reflexive pronoun to show how one is feeling, especially the onset of an emotional or physical state. These are often expressed in English with “to get” + adjective; be very careful not to translate such English idioms literally! Use the reflexive verb instead. Below are common reflexive emotional verbs and their non-reflexive (transitive) forms for comparison:
Reciprocal verbs
Reciprocal verbs are used to talk about actions that people do to each other. Reciprocal verbs are formed by the combination of a reflexive pronoun and a verb, very similar to the reflexive verbs. Since reciprocal actions always involve two or more people, only plural pronouns are considered reciprocal:
1a persona plural:
nos
(
to, for, from, or off ourselves / each other
)
2a persona plural:
os
(
to, for, from, or off yourselves / each other
)
3a persona plural:
se
(
to, for, from, or off themselves, yourselves / each other
)
Reciprocal or Reflexive
Sentences with reciprocal actions sometimes look just like sentences with reflexive actions. To differentiate a reflexive action from a reciprocal action, the use of expressions such as “el uno al otro”, “uno a otro”, “mutuamente”, “recíprocamente”, “entre sí”, etc. can be added to a phrase to show that the subjects are performing the action on each other. All these expressions can be roughly translated as “each other”, “one another”, or “mutually”.
To specify that an action is reflexive, we can use phrases like “a sí mismo” ( to him/herself ) or “a sí mismos” ( to themselves ).
For example:
- Se aman mutuamente. ( They love one another. )
- Los narcisistas se aman a sí mismos. ( Narcissists love themselves. )
- Se miran a sí mismos en el espejo. ( They look at themselves in the mirror. )
- Se miran el uno al otro por la ventana. ( They look at each other through the window. )
List of Common Reciprocal Verbs
In English you would not need to emphasize that the two people are doing the action together because it is already implied. Therefore, in Spanish try to think about verbs that involve two people and remember that you may need the reflexive pronouns. Below you’ll find a list of verbs that are commonly used to talk about reciprocal actions.
- Abrazarse ( to hug each other )
- Ayudarse ( to help each other )
- Besarse ( to kiss each other )
- Casarse ( to marry each other )
- Conocerse ( to know each other )
- Despedirse ( to say goodbye to each other )
- Divorciarse ( to divorce each other )
- Mirarse ( to look at each other )
- Pelearse ( to fight with each other )
- Reunirse ( to get together )
- Turnarse ( to take turns )


6.8: Music of Hector Berlioz
Hector Berlioz (b. 1803-1869) was born in France in La Côte-Saint-André, Isère near Grenoble. His father was a wealthy doctor and planned on Hector’s pur- suing the profession of a physician. At the age of eighteen, Hector was sent to study medicine in Paris. Music at the Conservatory and at the Opera, however, became the focus of his attention. A year later, his family grew alarmed when they realized that the young student had decided to study music instead of medicine.
At this time, Paris was in a Romantic revolution. Berlioz found himself in in the company of novelist Victor Hugo and painter Delacroix. No longer receiving financial support from his parents, the young Berlioz sang in the theater choruses, performed musical chores, and gave music lessons. As a young student, Berlioz was amazed and intrigued by the works of Beethoven. Berlioz also developed interest in Shakespeare, whose popularity in Paris had recently increased with the performance of his plays by a visiting British troupe. Hector became impassioned for the Shakespearean characters of Ophelia and Juliet as they were portrayed by the alluring actress Harriet Smithson. Berlioz became obsessed with the young actress and also overwhelmed by sadness due to her lack of interest in him as a suitor. Berlioz became known for his violent mood swings, a condition known today as manic depression.
In 1830, Berlioz earned his first recognition for his musical gift when he won the much sought-after Prix de Rome. This highly-esteemed award provided him a stipend and the opportunity to work and live in Paris, thus providing Berlioz with the chance to complete his most famous work, the Symphonie Fastastique , that year.
Upon his return to Rome, he began his intense courtship of Harriet Smithson. Both her family and his vehemently opposed their relationship. Several violent and arduous situations occurred, one of which involved Berlioz’s unsuccessfully attempting suicide. After recovering from this attempt, Hector married Harriet. Once the previously unattainable matrimonial goal had been attained, Berlioz’s passion somewhat cooled, and he discovered that it was Harriet’s Shakespearean roles that she performed, rather than Harriet herself, that really intrigued him. The first year of their marriage was the most fruitful for him musically. By the time he was forty, he had composed most of his famous works. Bitter from giving up her acting career for marriage, Harriet became an alcoholic. The two separated in 1841 Berlioz then married his long time mistress Marie Recio, an attractive but average singer who demanded to perform in his concerts.
To supplement his income during his career, Berlioz turned to writing as a music critic, producing a steady stream of articles and reviews. He successfully utilized this vocation as a way to support his own works by persuading the audience to accept and appreciate them. His critical writing also helped to educate audiences so they could understand his complex and innovative pieces. As a prose writer, Berlioz wrote The Treatise on Modern Instrumentation and Orchestration. He also wrote ‘ Les Soirées de l’Orchestre’ (Evenings with the Orchestra), a compilation of his articles on musical life in nineteenth-century France, and an autobiography entitled Mémoires. Later in life, he conducted his music in all the capitals of Europe, with the exception of Paris. It was one location where the public would not accept his work; the Paris public would read his reviews and learn to welcome lesser composers, but they would not accept Berlioz’s music. As over the years Berlioz saw his own works neglected by the public of Paris while they cheered and supported others, he became disgusted and bitter from the neglect. His last final work composed to gain acceptance by the Parisian audiences was the opera Béatrice et Bénédict with his own libretto based upon Shakespeare’s Much Ado about Nothing . But the Parisian public did not appreciate it. After this final effort, the disillusioned and embittered Berlioz composed no more in his seven remaining years, dying rejected and tormented at the age of sixty-six. Only after his death would France appreciate his achievements.
His operas include Benvenuto Cellini , Le Troyens (to hear and view an excerpt, go to the link on www.52composers.com/berlioz.html) , Béatrice et Bénédict, Les francs-juges (incomplete), Grande Messe des morts (Requiem) (to view and hear the tuba mirum from the Requiem, go to the link found at www.52composers.com/ berlioz.html) , La damnation de Faust, Te Deum, and L’enfance du Christ .
His major orchestral compositions include Symphonie fantastique (to hear the fifth movement, go to the link on www.52composers.com/berlioz.ht- ml) , Harold en Italie, Romeo et Juliette (to hear and view an excerpt, go to the link on www.52composers.com/berlioz.html) , The Corsair, King Lear, and Grande symphonie funèbre et triomphale. Berlioz is credited for changing the modern sound of orchestras.
Berlioz’s Symphonie fantastique is important for several reasons: it is a pro- gram symphony, it incorporates an idée fixe (a recurring theme representing an ideology or person that provides continuity through a musical work), and it con- tains five movements rather than the four of most symphonies.
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Listening Guide For audio, go to: https://www.youtube.com/watch?v=l7chHNocFAc Performed by The BBC Philharmonic Orchestra, conducted by Yan Pascal Tortelier |
| Composer: Hector Berlioz |
| Composition: Symphonie Fantastique, Op.14: 1st movement Reveries – Passions |
| Date: 1830 |
| Genre: Symphony, First movement |
| Form: Sonata form |
| Performing Forces: large Romantic symphony orchestra |
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What we want you to remember about this composition:
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Other things to listen for: • Berlioz is known for being one of the greatest orchestrators of all time. He even wrote the first comprehensive book on orchestration. He always thought in terms of the exact sound (tone or timbre) of the orchestra and the mixture of individual sounds to blend through orchestration. He gave very detailed instructions to the conductor and individual performers in regards to articulations and how he wanted them to play. Listen to the subtleties and nuance of the performance. Berlioz left little up to chance since he was so thorough in his compositions. |
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Timing |
Music Measure (Bar) Numbers |
Form, Melody, and Texture |
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00:12 |
3-6 |
The introductory four-bar phrase played by the violin one forms the basis for the following three phrases to bar sixteen, most of the music being played on muted strings. Here the composer portrays both depression and elation. fig 6.10.1 |
| 1:45 | 17-71 | The key changes from C major to Eb major to C minor and finally arriving to C major with a cadence in measure 62 |
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5:30 |
72-111 |
Exposition-Allegro
[Subject/
idée fixe
, bars 72-111]
fig 6.10.2 |
| 6:33 | 133-149 | Transition section that provides rising tension in the approach to the dominant. |
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6:47 |
150-166a |
Second subject introduced and established in the key of G major at measure 160. See Music insert 3 for second subject notation. [Second Subject found in bars 160-166] fig 6.10.3 |
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8:36 |
167-228 |
Development Section—this section includes recapitulations and further developments. Two new motifs (musical segments) are featured in this section of the first movement. The first has become known as the “sigh motif.” This motif musically represents the sighing figure of a long note followed by a shorter note. See music insert 4 for sighing motif notation. fig 6.10.4 [Sigh motif notations, measure 87.] The second motif has become known as the “heart beat motif.” It is heard as a pair of detached pulses/quavers. These are brought out dynamically (volume emphasis) and represent heartbeats. See music insert 5 for heart- beat motif notation. fig 6.10.5 [Heartbeat motif notations, measure seventy-eight] |
| 9:33 | 232-278 | Recapitulation in the dominant key of G major |
| 10:20 | 278- 311 | Transitional Passage to upcoming second subject |
| 10:51 | 311-329 | Second subject resolving fortissimo in C major |
| 11:50 | 358-409 | Further development section continues and gradually increased tension setting up next unison section. |
| 12:40 | 410-439 | The full orchestra plays the first subject in C major |
| 13:08 | 440-474 | Further orchestral build up |
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13:43 |
475-526 |
Coda section: The final chords musically representing the consolation of religion ending with a plagal cadence (traditional Amen progression/ending). |


16.5: XVI Glossary
Dry Powder Inhaler (DPI): An inhaler with medication provided in a powder form that is inhaled from the mouth into the lungs using a quick breath to activate the medication and move it into the lungs. An example of a DPI is tiotropium (Spiriva).
Innunction: A medication that is massaged or rubbed into the skin.
Metered Dose Inhaler (MDI): An inhaler that provides a mist of medication that is inhaled through the mouth into the lungs. An example of an MDI is albuterol. Optimal administration is achieved with a spacer attached to the inhaler.
Small-volume nebulizers: Devices that provide a fine mist using oxygen or compressed air to transport the medication from a nebulizer cup into the mouth and into the lungs as the patient breathes normally through a mask or pipe device.
Topical medications: Medications administered via the skin or mucous membranes for direct local action, as well as for systemic effects.
Transdermal route: Patches or disks applied to the skin that deliver medication over an extended period of time.


7.5: Language in Middle Childhood
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Learning Objectives
By the end of this section, you will be able to:
- Identify milestones in language development in middle childhood
- Discuss the benefits and challenges facing multilingual speakers and learners
Eight-year-old Troy’s aunt has noticed that his vocabulary has grown considerably, and that she can now have detailed conversations with him about his day as well as about his hopes and dreams. He still makes some grammatical errors when he’s speaking, but they are becoming less frequent. He’s also starting to love puns and knock-knock jokes, which makes conversations with him so much more fun. And he loves sharing that he can count to ten in Spanish, French, and Mandarin—all thanks to a new initiative in his elementary school to expose children to world languages at an earlier age.
Language skills continue to develop during middle childhood, which is when children become much more effective communicators, both verbally and nonverbally. In this section, you’ll explore some of the major milestones they achieve before considering the benefits and challenges of multilingualism in middle childhood.
Language Milestones
By middle childhood children can easily express their thoughts and engage in full conversations, but language is complicated and continues to develop throughout childhood. There are significant increases in vocabulary and children continue to learn grammatical rules. They also learn that language changes when communicating with people in different social contexts (adults versus peers, for example). Children also make great strides in their reading abilities during middle childhood, which will become one of the major ways in which they learn as they get older. Facets of language development that improve in middle childhood including vocabulary and grammar, pragmatic skills, and reading skills.
Vocabulary and Grammar
Vocabulary increases dramatically in middle childhood and is associated with other developmental outcomes. Vocabulary is important for reading as well as for language processing (Li et al., 2021). Children with larger vocabulary sizes are also better at describing and recognizing emotions (Beck et al., 2012).
As children get older, they become more aware of the qualities of language and can think about and evaluate language, a skill known as metalinguistic awareness (Simard & Gutiérrez, 2017). For example, in addition to mastering new words, children begin to learn that many words have similar meanings and can refer to the same object or action, such as animal and mammal. They also begin to understand that one word can have multiple meanings. For example, duck can refer to an animal or an action. This new ability is one of the reasons children begin to appreciate humor, puns, and eventually sarcasm. For example, in the preceding vignette, Troy loves jokes. He might enjoy one like this: “What did Baby Corn say to Mama Corn? Answer: Where is Popcorn?”
What fuels the vocabulary explosion seen during middle childhood? Certainly, our everyday experiences are important for introducing us to specific words. Learning vocabulary is closely tied to reading , too, as well as to socioeconomic status (Van der Kleij et al., 2022). Children from lower socioeconomic statuses tend to be exposed to less language with less diverse vocabulary, which has consequences for vocabulary development and for reading (Lervåg et al., 2019). Vocabulary has also been shown to grow significantly during the school year but less so during summer holidays, particularly among low SES children (Van der Kleij et al., 2022).
More grammatical rules become familiar during middle childhood. Children begin studying the parts of language and sentence structure as one element of their formal schooling . They also begin to understand more complex grammar, such as passive voice (“The baby is being fed”) and conditional sentences (“If I had been home, I would have finished my chores”). For English-speaking children, grasping these more complex grammatical structures depends on gaining more experience with and exposure to sophisticated language and sentence structure. Thus, it takes longer to master these types of sentences than sentences that use active voice (“The baby is eating”). However, in other cultures that use more passive-voice sentences, children understand and use the passive voice earlier. For example, in Northern East Cree, a language spoken by Indigenous peoples in Canada, children use the passive voice much earlier than do children who are speaking English (Henke et al., 2024).
Pragmatics
As children get older, they continue to learn to change their speech in response to the needs of the listener. As discussed in 5.4 Language in Early Childhood, pragmatics is the way we use language in different social contexts, and a useful tool for developing social relationships with others. It requires understanding 1) how to use language for different functions such as requesting something, telling a story, or conveying knowledge, 2) how to use written language differently across contexts such as text messages versus emails or writing an essay for school, 3) how to change language to meet the needs of listeners as different as a grandparent and a friend, or to speak up in a noisy room, and 4) the “hidden” rules of conversation such as taking turns and using eye contact, body gestures, and facial expressions. The use of pragmatics during middle childhood also includes code-switching , which refers to using more than one form of language within a single conversation. Although it is often seen among multilingual speakers, children may also code switch when alternating between speech used in different social contexts such as speaking differently to peers versus teachers. For example, if you are talking to a peer you might use more casual language and slang, but quickly switch to more formal language when a teacher calls on you.
Although many children are able learn pragmatics through everyday social interactions, those with certain developmental disabilities may struggle to do so. For example, one study found that children with ADHD scored lower on a pragmatic language assessment than typically developing children, but higher than children with a developmental language disorder (Vassiliu et al., 2023). For example, a child with ADHD might sometimes have difficulty with language pragmatics by frequently interrupting others during conversations or speaking too loudly in a quieter space, which could be distracting or disruptive to peers.
Reading
Learning to read and write is a significant milestone for middle childhood. The fundamentals needed for reading—such as spoken language, an understanding of the alphabet and the sounds each letter makes, and the knowledge that spoken sounds correspond to written words—begins during infancy and early childhood. But it is during middle childhood that children coordinate these skills and begin to read (Figure 7.19). Unlike many other developmental skills, reading does not come naturally to most children. In fact, only 5 percent of children learn to read without help (Willingham, 2015). Reading requires explicit teaching as well as practice. The teaching of reading to children has been approached in several ways. The ongoing debate regarding which method is most effective is often referred to as the “reading wars” (Castles et al., 2018).
There are two primary approaches to teaching reading. The phonics approach helps children understand how to translate letters into sounds and then put those individual sounds together to create words. In essence, children are taught how to sound out words. Unlike many languages, however, English has more sounds (44) than letters (26) which makes learning to read it more difficult (Kerestes et al., 2024). For example, the letter C can make more than one sound including the /k/ sound as in “car” or the /s/ sound as in ‘pencil’. Even more confusing is that C can make both sounds within one word such as ‘council.’
A second approach to teaching reading, the whole-language approach , focuses on teaching reading in natural contexts such as books rather than focusing on the sounds that make up words. Since the early 2000s, many schools have adopted a balanced literacy approach , intending to blend the best elements of the phonics-based and whole-language methods. In addition to sounding out words phonetically, the balanced approach teaches students to recognize core words (often referred to as “sight words” in schools) like “they” or “and” as a single word rather than a collection of letters. Phonics is included based on research showing that phonics and phonemic awareness, the ability to identify and manipulate the individual sounds in words, are both important predictors of reading skills (Faris, 2023). In fact, children who have received instruction on phonics score significantly better on standardized tests of reading (National Early Literacy Panel, 2008). Recent research has also shown that a balanced literacy approach is effective for teaching English language learners (Mirhosseini & Sharif, 2022). 3
Despite this intense focus on how to teach reading, by fourth grade only 32 percent of U.S. children are proficient readers (National Assessment of Educational Progress, 2023). Unfortunately, school closures related to the COVID-19 pandemic resulted in a lower rate of proficient readers in elementary school and the negative impact was worse for students from lower socioeconomic backgrounds as well as for English learners and students with disabilities (Relyea et al., 2023). 4 Difficulties learning to read are associated with later challenges in mental health, academic achievement, and vocations (Hendren et al., 2018). Children who are struggling with academic achievement, including reading, are more likely to drop out of school (Lowder et al., 2022). Many continue to have difficulty reading as adults. In fact, about 23 percent of U.S. adults lack literacy skills which is defined by the Program for the International Assessment of Adult Competencies as “the ability to understand, evaluate, use and engage with written texts to participate in society, to achieve one’s goals, and to develop one’s knowledge and potential” (p. 61, OECD 2013). Compare this to other countries, such as Costa Rica, where only 4 percent of the population does not have literacy skills.
Intersections and Contexts: How Much Did COVID School Closures Set Students Back?
COVID-19 school closures had a significant impact on student learning. The pivot to remote learning negatively impacted student academic performance and many students did not perform at grade level on standardized assessment for both mathematics and reading both during the closures or after schools reopened (Colvin et al., 2022; Cortés-Albornoz et al., 2023). Furthermore, the loss of learning was worse for children living in lower SES families (Moscoviz & Evans, 2022). For example, low-income families had less access to devices and to reliable internet (Francis & Weller, 2022). In low-income households with several school-aged children, students were often forced to share a single device. As a result, many children from lower SES families were forced to drop out of school or received less learning time (Zagalaz-Sánchez et al., 2021).
The pandemic also increased stressors more for lower-income families with many households experiencing unemployment or underemployment that led to food and housing insecurity and increases in parental depression and anxiety (Fahle et al., 2023). All these factors may have impacted the mental health of children and their parents’ ability to help them with schoolwork. Finally, the pandemic increased social isolation in children due to the major disruptions that happened to daily life and activities (Fahle et el., 2023).
As a result of all these factors, research studies have reported larger losses in learning among children attending schools with higher levels of poverty than among children in lower poverty schools (Kuhfeld et al., 2022). 5 It will likely take years to fully recover from this loss of learnings and will require schools to make significant investments in student learning over several years (Fahle et al., 2023).
Multilingualism
Many children around the world grow up in multilingual households, where more than one language is spoken. In the United States, approximately 26 percent of children are multilingual, a relatively low rate compared to other areas such as Singapore (90 percent), Europe (67 percent), and Canada (55 percent) although multilingualism is increasing in the United States (Luk, 2017; Wu et al., 2020). It varies quite a bit from state to state, with California having the highest rates at 43 percent and West Virginia the lowest, around 2 percent (Annie E. Casey Foundation, 2018). U.S. multilingual children speak a total of more than 100 different languages, but approximately 75 percent speak Spanish and English (Dietrich & Hernandez, 2022).
Thus, in many parts of the United States, multiple languages may be spoken by the children in a single classroom. Even more challenging for teachers is the wide range of abilities among these children. While some may speak more than one language well and may have homes that are multilingual, others may not speak English as well as the language they speak at home. Others may be losing competence in their home language as they become more competent in the language spoken at school (Tse, 2001). Still others may view English as being more important for the future success than their first or home language and, thus, may be less likely to use the latter regularly (Mohamed, 2020).
Children who are multilingual must become adept at regularly switching between languages (Tulloch & Erika, 2023), a speech style called multilingual code-switching (or translanguaging). Multilingual code-switching requires competency in at least two languages and is associated with strongly identifying with two cultures (Yim & Clément, et al., 2021). While some children learn multiple languages at the same time beginning at birth, others may learn one language in their early years and then add a second. In this case it takes longer to master the second language than it does if both languages are learned at the same time (Paradis, 2023).
Link to Learning
Some people are unsure about how to handle themselves in unfamiliar social situations and will feel intimidated. Others can easily maneuver in any social situation and blend in easily because they understand how to code switch. Watch this TED Talk about code-switching by Katelynn Duggins to learn more.
The Impact of Multilingualism on Development
Recent research suggests that any disadvantages associated with being bilingual are erased by its numerous advantages (Dentella et al., 2024). These include better executive functioning, memory, selective attention, and analytical reasoning (Nguyen et al., 2023; Planckaert et al., 2023). For example, children who speak multiple languages have better cognitive control because they must inhibit one language while they use another. They also have better metalinguistic skills than children who only speak one language. For example, children who are bilingual can understand grammatical rules more easily than children who speak a single language. There are also social benefits to multilingualism, such as being able to participate in diverse communities (Djonov, 2019).
Link to Learning
What are the advantages to having a bilingual (or multilingual) brain? Watch this TED Talk by Educator Mia Nacamulli about how our brains benefit from knowing more than one language to learn more.
There are some challenges associated with multilingualism. Some children may have smaller vocabularies in both languages than children who only speak a single language (Bialystok & Feng, 2011). They may also have difficulties maintaining the language they speak at home. For example, some studies have shown that children who were multilingual before five years of age often ended up speaking only the dominant language of the country in which they lived by the time they were 5 years old (Verdon et al., 2014). However, the children of parents who encourage their children to be bilingual have more positive language outcomes than other multilingual children (Mak et al., 2023).
Approaches to Multilingualism in the Classroom
There is a long debate about how best to teach English to multilingual children who are English Language Learners (ELL), meaning they are not yet proficient in English by the time they start school. Several different strategies exist (ALİSOY, 2024). One consists of immersion program s, which teach all academic subjects in English. These programs are associated with an increased loss of the native language. Another strategy is to begin instruction in the primary language of the student and gradually add in instruction in English. These programs are referred to as developmental bilingual program s.
Programs between immersion and developmental bilingual programs are English as a Second Language (ESL) and two-way immersion programs. In ESL programs, all non-English speaking students are taught in a single classroom. Children often spend part of their day learning English in specific ESL classrooms, but there is no accommodation for their native language in other academic classes. In two-way immersion program s, instruction occurs equally in two languages (Collier & Thomas, 2017). Since both languages are valued equally, students feel their cultural heritage is respected. They have also been found to have enhanced self-esteem and to retain their native language better than students in other types of bilingual programs (Pedrone, 2018).
Two-way immersion programs are more effective than immersion programs for the successful learning of English (Linholm-Leary, 2011). However, two-way immersion programs are not universally accepted. Some research has suggested that there may not be positive impacts for all core academic subjects such as mathematics, reading, and science (Steele et al., 2017) and that it there are racial disparities for access to schools that offer this approach to language learning (Flores & Garcia, 2017). In addition, these programs are less common than immersion programs because they require teachers who are highly skilled and fluent in both languages. Two-way immersion is also not practical in schools in which multiple other languages are spoken besides English. Ultimately, the specific method applied often depends on the goals of the school. If the primary goal is to assimilate children into U.S. society and culture, the school will likely use an immersion approach. If the goal is to encourage multiculturalism, the two-way immersion approach is more likely to be effective.
Second Language Education
Children tend to learn new languages more easily than adults (Ghasemi & Hashemi, 2011). This may be partly because they are more willing to use the language without fear of making errors or because their brains have more neural plasticity or flexibility (Birdsong, 2017). In addition, non-native speakers who learned a language before the age of 10 are often difficult to distinguish from a native speaker of that language (Ghasemi & Hashemi, 2011). For this reason, childhood is often referred to as a critical period for the acquisition of a second language (Birdsong, 2017). Even adolescents up to age 17 or 18 can learn the grammar structure of a new language more easily than adults (Hartshorne et al., 2018).
Despite the clear research showing that children can learn a new language much more easily than they will be able to do so later in life, children often do not begin learning a new language in school until adolescence—if at all. In fact, only about 20 percent of children in the United States learn a second language during school (Stein-Smith, 2019). This is very different than in other countries where learning a second language is prioritized. For example, in most European countries, learning a second language is required and students begin learning another language in school between 6 and 9 years of age (Pew Research Center, 2018; Devlin, 2018) (Figure 7.20).
Taken together, the human ability to learn multiple languages shows how adaptable and resilient the human brain is. The fact that children do such learning with more ease is another example illustrating a sensitive period in lifespan development.
References
Alisoy, H. Effective strategies in primary second language education. Preprints 2024, Article<PHONE_NUMBER>. https://doi.org/10.20944/preprints202401.0330.v1
Annie E. Casey Foundation (2018). The number of bilingual kids in America continues to risk. https://www.aecf.org/blog/the-number...tinues-to-rise . Retrieved March 18, 2024.
Beck, L., Kumschick, I. R., Eid, M., & Klann-Delius, G. (2012). Relationship between language competence and emotional competence in middle childhood. Emotion, 12 (3), 503–514. doi.org/10.1037/a0026320
Bialystok, E. & Feng, X. (2011). Language proficiency and its implications for monolingual and bilingual children. In Durgunoglu, A. Y. & Goldenberg, C. (eds), Language and literacy development in bilingual settings , 121–38. New York: Guilford.
Birdsong D. (2017). Critical periods. In: Aronoff M, editor. Oxford Bibliographies in Linguistics. New York: Oxford University Press; 2017. http://dx.doi.org/10.1093/obo/9780199772810-0139
Castles, A., Rastle, K., & Nation, K. (2018). Ending the reading wars: reading acquisition from novice to expert. Psychological Science in the Public Interest, 19, 5–51. doi.org/10.1177/1529100618772271
Collier, V. P., and W. P. Thomas. (2017). “Validating the power of bilingual schooling: Thirty-two years of large–scale, longitudinal research.” Annual Review of Applied Linguistics 37: 203–217. https://doi.org/10.1017/S0267190517000034
Colvin M.K. (Molly), Reesman J., & Glen T. The impact of COVID-19 related educational disruption on children and adolescents: an interim data summary and commentary on ten considerations for neuropsychological practice. The Clinical Neuropsychologist. 2022; 36: 45–71. doi.org/10.1080/13854046.2021.1970230
Cortés-Albornoz, M. C., Ramírez-Guerrero, S., García-Guáqueta, D. P., Vélez-Van-Meerbeke, A., & Talero-Gutiérrez, C. (2023). Effects of remote learning during COVID-19 lockdown on children's learning abilities and school performance: A systematic review. International Journal of Educational Development , 101 , Article 102835. https://doi.org/10.1016/j.ijedudev.2023.102835
Dentella, V., Masullo, C., & Leivada, E. (2024) Bilingual disadvantages are systematically compensated by bilingual advantages across tasks and populations. Scientific Reports, 14 , Article 2107. https://doi.org/10.1038/s41598-024-52417-5
Devlin, K. (2018). Most European students are learning a foreign language in school while Americans lag. Pew Research Center. https://www.pewresearch.org/short-re...americans-lag/
Dietrcih, S. & Hernandez, E. (2022). Nearly 68 million people spoke a language other than English at home in 2019. https://www.census.gov/library/stori...ed-states.html
Djonov, E. (2019). Bilingualism and multilingualism in early childhood education (Australia). Bloomsbury Education and Childhood Studies , 2019 . https://doi.org/10.5040/9781350996298.0010
Fahle, E.M., Kane, T.J., Patterson, T., Reardon, S.F., Staiger, D.O., & Stuart, E. A. (2023). School district and community factors associated with learning loss during the COVID-19 pandemic. https://cepr.harvard.edu/sites/hwpi....osses_5.23.pdf
Faris, A. S. (2023). The effectiveness of phonics approach in teaching reading. IJECA (International Journal of Education and Curriculum Application) , 1 (1), 11–15. https://doi.org/10.31764/ijeca.v0i0.1981
Flores, N., & García, O. (2017). A critical review of bilingual education in the United States: From basements and pride to boutiques and profit. Annual Review of Applied Linguistics , 37 , 14–29. https://doi.org/10.1017/S0267190517000162
Francis, D. V., & Weller, C. E. (2022). Economic inequality, the digital divide, and remote learning during COVID-19. The Review of Black Political Economy , 49 (1), 41-60. doi.org/10.1177/00346446211017797
Ghasemi, B. & Hashemi, M. (2011). Foreign language learning during childhood. Social and Behavioral Sciences, 28, 872–876. https://doi.org/10.1016/j.sbspro.2011.11.160
Hartshorne, J. K., Tenenbaum, J. B., & Pinker, S. (2018). A critical period for second language acquisition: Evidence from 2/3 million English speakers. Cognition , 177 , 263-277. https://doi.org/10.1016/j.cognition.2018.04.007
Hendren, R. L., Haft, S. L., Black, J. M., White, N. C., & Hoeft, F. (2018). Recognizing psychiatric comorbidity with reading disorders. Frontiers in Psychiatry , 9 , Article 101. https://doi.org/10.3389/fpsyt.2018.00101
Henke, R. E., Brittain, J., Deen, K. U., & Acton, S. (2024). The acquisition of the passive voice in Northern East Cree. First Language , 44 (1), 44–37. doi.org/10.1177/01427237231198758
Kerestes, G., Hjelmquist, E., Veisson, M. & Siegel, L.S. (2024). The importance of fluence in reading: A comparison of English, Swedish, Croation and Estonian. Reading Psychology. doi.org/10.1080/02702711.2024.2319576
Kuhfeld, M., Soland, J., & Lewis, K. (2022). Test Score Patterns Across Three COVID-19-Impacted School Years. Educational Researcher, 51 (7), 500–506. doi.org/10.3102/0013189X221109178
Lervåg A., Dolean D., Tincas I., & Melby-Lervåg M. (2019). Socioeconomic background, nonverbal IQ and school absence affects the development of vocabulary and reading comprehension in children living in severe poverty. Developmental Science, 22 (5), Article e12858. doi.org/10.1111/desc.12858
Li, L., Zhu, D., & Wu, X. (2021). The effects of vocabulary breadth and depth on reading comprehension in middle childhood: The mediator role of listening comprehension. Reading & Writing Quarterly , 37 (4), 336-347. doi.org/10.1080/10573569.2020.1809585
Lindholm-Leary, K. (2011). Student outcomes in Chinese two-way immersion programs: Language proficiency, academic achievement, and student attitudes. In D. J. Tedick, D. Christian, & T. W. Fortune (Eds.), Immersion education, : Practices, policies, possibilities (pp. 81–103). https://doi.org/10.21832/9781847694041-008
Lowder, Christopher, Chris O’Brien, Dawson Hancock, Jeremy Hachen, and & Chuang Wang. "High school success: A learning strategies intervention to reduce drop-out rates." The Urban Review 54, no. 4 (2022): 509–530. https://doi.org/10.1007/s11256-021-00624-z
Luk, G. (2017). Bilingualism. In B. Hopkins, Geangu, & S. Linkenauger (Eds.), The Cambridge Encyclopedia of Child Development , 2nd ed. (pp. 385–391). Cambridge, UK: Cambridge University Press. https://doi.org/10.1017/9781316216491.062
Mak, E., N. Nichiporuk Vanni, X. Yang, M. Lara, Q. Zhou, and Y. Uchikoshi. (2023). “Parental perceptions of bilingualism and home language vocabulary: Young bilingual children from low-income immigrant Mexican American and Chinese American Families.” Frontiers in Psychology, 14 . https://doi.org/10.3389/fpsyg.2023.1059298 .
Mirhosseini, S. & Sharif, N. (2022). Phonics vs. whole language in teaching EFL to young learners: A micro-ethnographic study. Interdisciplinary Studies in English Language Teaching. iselt.journals.umz.ac.ir/art...e01859f4df.pdf
Mohamed, N. (2020). First Language Loss and Negative Attitudes Towards Dhivehi Among Young Maldivians: Is the English-First Educational Policy to Blame?. TESOL Quarterly, 54 (3), 743–772. doi.org/10.1002/tesq.591
Moscoviz, L., & Evans, D. K. (2022). Learning loss and student dropouts during the COVID-19 pandemic: A review of the evidence two years after schools shut down [Working Paper 609]. Center for Global Development. https://www.cgdev.org/sites/default/...-two-years.pdf
National Assessment of Educational Progress (2023). An overview of NAEP. Washington, D.C.: National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. nces.ed.gov/nationsreportcard/about/https:// nces.ed.gov/nationsreportcard/readings/states/achievement/?grade=4
National Early Literacy Panel (2008). Developing Early Literacy. Retrieved at Developing EarlyLiteracy: Report of the National Early Literacy Panel (ed.gov) on March 13, 2024. https://lincs.ed.gov/publications/pd...LPReport09.pdf
Nguyen, M. V., Hutchison, L. A., Norvell, G., Mead, D. L., & Winsler, A. (2023). Degree of bilingualism and executive function in early childhood. Language and Cognition , 1–23. https://doi.org/10.1017/langcog.2023.46
OECD (2013). OECD Skills Outlook 2013: First results from the survey of adult skills. OECD iLibrary . doi.org/10.1787/9789264204256-en
OECD (2016). Survey of Adult Skills, OECD Publishing. doi.org/10.1787/9789264258075-en
Paradis, J. (2023). Sources of individual differences in the dual language development of heritage bilinguals. Journal of Child Language, 50(4), 793–817. https://doi.org/10.1017/S0305000922000708
Pedrone, J. D. (2018). The effect of two-way immersion on students' attitudes toward education, other cultures, and self-esteem . Liberty University. https://digitalcommons.liberty.edu/c...ntext=doctoral
Pew Research Center (2018). Most European students are learning a foreign language in school while Americans lag. https://www.pewresearch.org/short-re...s-are-learning
Planckaert, N., Duyck, W., & Woumans, E. (2023). Is there a cognitive advantage in inhibition and switching for bilingual children? A systematic review. Frontiers in Psychology , 14 , Article 1191816. https://doi.org/10.3389/fpsyg.2023.1191816
Relyea, J. E., Rich, P., Kim, J. S., & Gilbert, J. B. (2023). The COVID-19 impact on reading achievement growth of Grade 3-5 students in a US urban school district: variation across student characteristics and instructional modalities. Reading and Writing , 36 (2), 317–346. https://doi.org/10.1007/s11145-022-10387-y
Simard, D., & Gutiérrez, X. (2017). The study of metalinguistic constructs in second language acquisition research. The Routledge Handbook of Language Awareness
Steele, J., R. O. Slater, G. Zamarro, T. Miller, J. Li, S. Burkhauser, & M. Bacon. (2017). “Effects of dual–language immersion programs on student achievement: Evidence from lottery data.” American Educational Research Journal 54. files.eric.ed.gov/fulltext/E...6.pdf(1S):282S–306S.
Stein-Smith, K. (2019). Rethinking the role of languages in the US: Toward a more diverse cultural identity. Journal of Language Teaching and Research , 10 (3), 403-411. https://www.academypublication.com/i...ol10/03/01.pdf
Tse, L. (2001). Resisting and reversing language shift: Heritage-language resilience among U.S. native biliterates. Harvard Educational Review, 71(4) , 676–709. doi.org/10.17763/haer.71.4.ku752mj536413336
Tulloch, M. K., & Erika, H. O. F. F. (2023). Filling lexical gaps and more: code-switching for the power of expression by young bilinguals. Journal of Child Language , 50 (4), 981–1004. https://doi.org/10.1017/S0305000922000307
Van der Kleij, S.W., Burgess, A.P., Ricketts, J., & Shapiro, L.R. (2022). Tracking vocabulary and reading growth in children from lower and higher socioeconomic backgrounds during the transition from primary to secondary education. Child Development, 94(1), 357–366. doi.org/10.1111/cdev.13862
Vassiliu, C., Mouzaki, A., Antoniou, F., Ralli, A. M., Diamanti, V., Papaioannou, S., & Katsos, N. (2023). Development of structural and pragmatic language skills in children with attention-deficit/hyperactivity disorder. Communication Disorders Quarterly , 44 (4), 207–218. doi.org/10.1177/15257401221114062
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Zagalaz-Sánchez M.L., Cachón-Zagalaz J., Arufe-Giráldez V., Sanmiguel-Rodríguez A., & González-Valero G. Influence of the characteristics of the house and place of residence in the daily educational activities of children during the period of COVID-19 confinement. Heliyon. 2021:7. https://doi.org/10.1016/j.heliyon.2021.e06392


16.19: Cancer and Gene Regulation - Altered Gene Expression in Cancer
- Describe how cancer is caused by uncontrolled cell growth
Cancer: Disease of Altered Gene Expression
Cancer can be described as a disease of altered gene expression. There are many proteins that are turned on or off (gene activation or gene silencing) that dramatically alter the overall activity of the cell. A gene that is not normally expressed in that cell can be switched on and expressed at high levels. This can be the result of gene mutation or changes in gene regulation ( epigenetic, transcription, post-transcription, translation, or post-translation).
Changes in epigenetic regulation, transcription, RNA stability, protein translation, and post-translational control can be detected in cancer. While these changes do not occur simultaneously in one cancer, changes at each of these levels can be detected when observing cancer at different sites in different individuals. Therefore, changes in histone acetylation (epigenetic modification that leads to gene silencing), activation of transcription factors by phosphorylation, increased RNA stability, increased translational control, and protein modification can all be detected at some point in various cancer cells. Scientists are working to understand the common changes that give rise to certain types of cancer or how a modification might be exploited to destroy a tumor cell.
Tumor Suppressor Genes, Oncogenes, and Cancer
In normal cells, some genes function to prevent excess, inappropriate cell growth. These are tumor suppressor genes, which are active in normal cells to prevent uncontrolled cell growth. There are many tumor suppressor genes in cells, but the one most studied is p53, which is mutated in over 50 percent of all cancer types. The p53 protein itself functions as a transcription factor. It can bind to sites in the promoters of genes to initiate transcription. Therefore, the mutation of p53 in cancer will dramatically alter the transcriptional activity of its target genes.
Another type of gene often deregulated in cancers are proto-oncogenes which are positive cell-cycle regulators. When mutated, proto-oncogenes can become oncogenes and cause cancer. Overexpression of the oncogene can lead to uncontrolled cell growth because oncogenes can alter transcriptional activity, stability, or protein translation of another gene that directly or indirectly controls cell growth. An example of an oncogene involved in cancer is a protein called myc. Myc is a transcription factor that is aberrantly activated in Burkett’s Lymphoma, a cancer of the lymph system. Overexpression of myc transforms normal B cells into cancerous cells that continue to grow uncontrollably. High B-cell numbers can result in tumors that can interfere with normal bodily function. Patients with Burkett’s lymphoma can develop tumors on their jaw or in their mouth that interfere with the ability to eat.
Key Points
- Cancer results from a gene that is not normally expressed in a cell, but is switched on and expressed at high levels due to mutations or alterations in gene regulation.
- Alterations in histone acetylation, activation of transcription factors, increased RNA stability, increased translational control, and protein modification are all observed in cancer cells.
- Tumor suppressor genes, active in normal cells, work to prevent uncontrolled cell growth.
- Proto- oncogenes, which are positive cell-cycle regulators, can become oncogenes and cause cancer when mutated.
Key Terms
- oncogene : any gene that contributes to the conversion of a normal cell into a cancerous cell when mutated or expressed at high levels
- proto-oncogene : a gene that promotes the specialization and division of normal cells that becomes an oncogene following mutation
- cancer : a disease in which the cells of a tissue undergo uncontrolled (and often rapid) proliferation


16.2: Contextualizing Precarious Creativity
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- Michael Keane
- University of California Press
The notion of precarity and the neologism precariat have emerged in academia over the past decade to account for the way the labor market is reorganizing in many developed economies in response to flexible forms of capitalism; for instance, an increasing number of jobs are listed as casual without fixed incomes or benefits. Skills learned in schools and universities, such as reading and theorizing, are losing value in occupations that rely on on-the job learning. 4 When this argument is extended to art, design, and media sectors, we are informed of the condition of “precarious creativity.” On the surface, this coinage conjures up a dark side to creativity. In contrast to a wide-ranging consensus among educators, psychologists, and business leaders that creativity is positive and aspirational, there are now negative externalities to consider, among which is the apparently transient nature of employment in many creative sectors. Many scholars opt to use precarity as a corrective to euphoric claims associated with the creative economy, particularly that it is expanding globally and generating more meaningful jobs. 5
When used to refer to cultural and creative labor, precarity normally picks up on the employment insecurity of workers in industry sectors affected by technological convergence—for instance, music, film and TV production, online games, and design—rather than those providing lower-level service jobs in the same industries. 6 Of course, creative work itself is difficult to define, and it is beyond the scope of this essay to investigate gradations of creative labor intensity. What can be argued, however, is that creative products and services sold to consumer markets are generally produced by people with specifically acquired skill sets. My own research into media parks and creative clusters in China identified that 95 percent of creative workers had tertiary degrees, mostly undergraduate (54 percent). 7 Moreover, such technical and managerial skills can be easily learned or transferred when businesses move offshore, particularly when R&D sharing is part of the market entry equation. 8 For instance, AnnaLee Saxenian has characterized the migration of the Taiwanese integrated circuit (IC) supply chain to Shanghai in the early 1990s as “perhaps the greatest transfer of managerial and technical skills in human history.” 9
In China, where the nation’s capital stock has accumulated largely by virtue of “sweat industries,” the discourse of creativity juxtaposes productivity gains and labor market transformation. It promises a way to lift masses of people out of polluting, repetition-based industries and move them into value-adding service sectors while at the same time revitalizing domestic cultural and content industries by making them internationally successful; it offers what might be termed “cultural soft power” dividends. 10 Indeed, gains in expertise and innovation in new media sectors, which are less burdened by regulation, are assisting the Chinese government in its mission to extend the nation’s soft power internationally. The key factor is knowledge—or more specifically, know-how. The concept of know-how is by now fairly well entrenched in management literature. In speaking of China, moreover, it is worthwhile noting the epistemological distinction between knowledge-that and knowledge-how , as elaborated by Gilbert Ryle in the 1940s. 11 Knowledge-that constitutes propositional knowledge, things that we know about the world. Ryle believed that knowing-how is a “higher-grade disposition,” associated with “abilities and propensities” as well as “capacities, habits, liabilities and bents.” 12
Many view the challenge in terms of “catching up” with and learning from advanced soft-power nations in terms of acquiring more know-how. While the Chinese government is reluctant to openly identify such “know-how-rich” nations, there is no doubt that most practitioners in the creative industries target Western developed economies as well as Japan and South Korea. These have become China’s “soft power competitors.” 13 The acquisition of foreign know-how, in addition to codified intellectual knowledge (knowledge-that), readily obtainable from reports and scholarship, offers a key that can unlock secrets of innovation.
For a Chinese person, the chance to work in a foreign company may be the means of acquiring both crucial know-how and know-that. But how long the worker stays with a company depends on salary, job satisfaction, and career expectations. The inclination to change occupations can be explained in terms of “compensating differentials,” that is, the coexistence of monetary and nonmonetary elements of employment. 14 People undertake jobs for a variety of reasons: in many creative industries, some work for less or work long hours because they enjoy the work they are doing and the people they associate with. Moreover, in a market like China, where there are plenty of job openings in new media sectors, workers can experience significant mobility. Taking knowledge gained, including IP, elsewhere is therefore another variant of precarious creativity. In short, the Chinese government hopes that the transfer of international knowledge together with an understanding of markets and consumer preferences might contribute to the rise of Chinese media influence. Whether this rise signals the receding influence of international media in China is a moot point.


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2.E: Atoms, Molecules, and Ions- Homework
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Last updated
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Save as PDF
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For Chapter 2 you MUST know:
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The names and symbols for elements 1-36
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Know the polyatomic Ions. You MUST know ammonium (\(\ce{NH4+}\)), acetate ( \(\ce{CH_3COO^-}\)), carbonate ( \(\ce{CO_3^{2-}}\)), hydroxide ( \(\ce{OH^-}\)), nitrate ( \(\ce{NO_3^-}\)), phosphate ( \(\ce{PO_4^{3-}}\)), and sulfate ( \(\ce{SO_4^{2-}}\)).
Turn in your answers for the following questions - show your work
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How many protons, neutrons and electrons are present in one atom of the following:
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1
H
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2
H
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3
H
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79
Br
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81
Br
1
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262
Bh
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What is the Atomic Weight of chlorine given that:
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The exact mass of
35
Cl is 34.9689 and the relative abundance is 75.53%
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The exact mass of
37
Cl is 36.9659 and the relative abundance is 24.47%
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Is this the answer that you expected?
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What is the Atomic Weight of ruthenium given the following information from WebElements, www.webelements.com. Is this the answer that you expected?
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Isotope Abundance Exact Mass
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96
Ru 5.54% 95.907599
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98
Ru 1.87% 97.905287
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99
Ru 12.76% 98.9059389
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100
Ru 12.60% 99.9042192
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101
Ru 17.06%<PHONE_NUMBER>
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102
Ru 31.55%<PHONE_NUMBER>
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104
Ru 18.62% 103.905424
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For the following molecules; write the chemical formula.
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carbon dioxide
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iron (II) chloride
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dinitrogen pentoxide
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iron (III) sulfate
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Name the following compounds.
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KI
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CaF
2
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Cu
2
SO
4
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N
2
O
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LiOH
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Give the chemical formula (or atomic symbol) and charge for the following ions:
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sulfate
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sulfite
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nitrate
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chloride
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nitride
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acetate
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carbonate
The Following Questions are for your practice - Do Not Turn In. They include answers so you can check your work
Atomic Structure and Symbolism
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Write the symbol for each of the following ions:
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the ion with a 1+ charge, atomic number 55, and mass number 133
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the ion with atomic number 15, mass number 31, and a 3− charge
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Answer A
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133
Cs
+
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Answer B
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31
P
3
−
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Give the number of protons, electrons, and neutrons in neutral atoms of each of the following isotopes:
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\(\ce{^7_3Li}\)
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\(\ce{^{125}_{52}Te}\)
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Answer A
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3 protons, 3 electrons, 4 neutrons
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Answer B
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52 protons, 52 electrons, 73 neutrons
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Write the molecular and empirical formulas of the following compounds:
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>
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Answer A
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molecular CO
2
, empirical CO
2
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Answer B
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molecular C
2
H
2
, empirical CH
The Periodic Table
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Using the periodic table, classify each of the following elements as a metal or a nonmetal, and then further classify each as a main-group (representative) element, transition metal, or inner transition metal:
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uranium
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bromine
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gold
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americium
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Answer A
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metal, inner transition metal
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Answer B
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nonmetal, representative element
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Answer C
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metal, transition metal
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Answer D
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metal, inner transition metal
Molecular and Ionic Compounds
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Using the periodic table, predict whether the following chlorides are ionic or covalent: (a) KCl, (b) NCl
3
, (c) ICl, and (d) PCl
5
.
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Answer A
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ionic
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Answer B
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covalent
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Answer C
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covalent
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Answer D
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covalent
Chemical Nomenclature
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Name the following compounds:
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CsCl
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BaO
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K
2
S
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Answer A
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cesium chloride
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Answer B
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barium oxide
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Answer C
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potassium sulfide
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Write the formulas of the following compounds:
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rubidium bromide
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magnesium selenide
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calcium chloride
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Answer A
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RbBr
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Answer B
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MgSe
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Answer C
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CaCl
2
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Write the formulas of the following compounds
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chlorine dioxide
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dinitrogen tetraoxide
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potassium phosphide
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silver(I) sulfide
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Answer A
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ClO
2
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Answer B
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N
2
O
4
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Answer C
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K
3
P
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Answer D
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Ag
2
S
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Each of the following compounds contains a metal that can exhibit more than one ionic charge. Name these compounds:
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Cr
2
O
3
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FeCl
2
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CrO
3
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Answer A
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chromium(III) oxide
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Answer B
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iron(II) chloride
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Answer C
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chromium(VI) oxide


4.2.3A: Theories of Socialization
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Socialization is the means by which human infants begin to acquire the skills necessary to perform as functioning members of their society.
Learning Objectives
- Discuss the different types and theories of socialization
Key Points
- Group socialization is the theory that an individual’s peer groups, rather than parental figures, influences his or her personality and behavior in adulthood.
- Gender socialization refers to the learning of behavior and attitudes considered appropriate for a given sex.
- Cultural socialization refers to parenting practices that teach children about their racial history or heritage and, sometimes, is referred to as pride development.
- Sigmund Freud proposed that the human psyche could be divided into three parts: Id, ego, and super-ego.
- Piaget’s theory of cognitive development is a comprehensive theory about the nature and development of human intelligence.
- Positive Adult Development is one of the four major forms of adult developmental study that can be identified. The other three forms are directionless change, stasis, and decline.
Key Terms
- socialization : The process of learning one’s culture and how to live within it.
“Socialization” is a term used by sociologists, social psychologists, anthropologists, political scientists, and educationalists to refer to the lifelong process of inheriting and disseminating norms, customs, and ideologies, providing an individual with the skills and habits necessary for participating within his or her own society. Socialization is thus “the means by which social and cultural continuity are attained.”
Socialization is the means by which human infants begin to acquire the skills necessary to perform as a functioning member of their society and is the most influential learning process one can experience. Unlike other living species, whose behavior is biologically set, humans need social experiences to learn their culture and to survive. Although cultural variability manifests in the actions, customs, and behaviors of whole social groups, the most fundamental expression of culture is found at the individual level. This expression can only occur after an individual has been socialized by his or her parents, family, extended family, and extended social networks.
The looking-glass self is a social psychological concept, created by Charles Horton Cooley in 1902, stating that a person’s self grows out of society’s interpersonal interactions and the perceptions of others. The term refers to people shaping themselves based on other people’s perception, which leads people to reinforce other people’s perspectives on themselves. People shape themselves based on what other people perceive and confirm other people’s opinion on themselves.
George Herbert Mead developed a theory of social behaviorism to explain how social experience develops an individual’s personality. Mead’s central concept is the self: the part of an individual’s personality composed of self-awareness and self-image. Mead claimed that the self is not there at birth, rather, it is developed with social experience.
Sigmund Freud was an Austrian neurologist who founded the discipline of psychoanalysis, a clinical method for treating psychopathology through dialogue between a patient and a psychoanalyst. In his later work, Freud proposed that the human psyche could be divided into three parts: Id, ego, and super-ego. The id is the completely unconscious, impulsive, child-like portion of the psyche that operates on the “pleasure principle” and is the source of basic impulses and drives; it seeks immediate pleasure and gratification. The ego acts according to the reality principle (i.e., it seeks to please the id’s drive in realistic ways that will benefit in the long term rather than bringing grief). Finally, the super-ego aims for perfection. It comprises that organized part of the personality structure, mainly but not entirely unconscious that includes the individual’s ego ideals, spiritual goals, and the psychic agency that criticizes and prohibits his or her drives, fantasies, feelings, and actions.
Different Forms of Socialization
Group socialization is the theory that an individual’s peer groups, rather than parental figures, influences his or her personality and behavior in adulthood. Adolescents spend more time with peers than with parents. Therefore, peer groups have stronger correlations with personality development than parental figures do. For example, twin brothers, whose genetic makeup are identical, will differ in personality because they have different groups of friends, not necessarily because their parents raised them differently.
Gender socialization Henslin (1999) contends that “an important part of socialization is the learning of culturally defined gender roles ” (p. 76). Gender socialization refers to the learning of behavior and attitudes considered appropriate for a given sex. Boys learn to be boys, and girls learn to be girls. This “learning” happens by way of many different agents of socialization. The family is certainly important in reinforcing gender roles, but so are one’s friends, school, work, and the mass media. Gender roles are reinforced through “countless subtle and not so subtle ways,” said Henslin (1999, p. 76).
Cultural socialization refers to parenting practices that teach children about their racial history or heritage and, sometimes, is referred to as “pride development. ” Preparation for bias refers to parenting practices focused on preparing children to be aware of, and cope with, discrimination. Promotion of mistrust refers to the parenting practices of socializing children to be wary of people from other races. Egalitarianism refers to socializing children with the belief that all people are equal and should be treated with a common humanity.