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The study of ancient history often reveals some fascinating anecdotes, mysterious happenings, and colorful characters. Some of these are not generally known.
Amsco’s Lingua Latina, Books I and II, by Professor John Traupman of St. Joseph’s University, deal with the Latin language and Roman history and culture. In Book I, Dr. Traupman describes a Roman of dubious character who was murdered in 52 B.C. Publius Claudius Pulcher (the Handsome) belonged to one of the most aristocratic families of the Roman Republic, the Claudii. One of his ancestors had built Rome’s first highway, the Via Appia, in 312 B.C. Nevertheless, he changed his name to Clodius in order to get political support from the common people, or plebians.
Clodius became a notorious gang leader. He and his followers terrorized the streets of Rome. (The Roman world, at that time, was ruled by the First Triumvirate of Julius Caesar, Pompey the Great, and Marcus Crassus. These three men brought stability and order to Rome and its provinces. However, they were intense rivals. Each sought an opportunity to eliminate the other two. The death of Crassus in battle against the Parthians ultimately led to civil war between Pompey and Caesar. Pompey lost his head and Caesar emerged as sole ruler of the Roman world.)
Clodius’ sister Clodia was called pulchra because of her great beauty. Like her brother, she lived a wild life, taking many lovers. Among them was the poet Catullus. Brother and sister were admired by some and feared by others. They were involved with the leading political figures of the late Republic.
Among Clodius’ many criminal activities was the affair of the mysteries of the Bona Dea in December 62 B.C. These mysteries were open only to women. Dressed as a woman, Clodius entered the house of Julius Caesar while the mysteries of the goddess were being celebrated. Upon discovery, a scandal erupted. Clodius was accused of attempting to carry on an affair with Pompeia, Casesar’s wife. Whether this was true or not, Caesar divorced Pompeia. Clodius was brought to trial, but avoided conviction by bribing the jury.
After the departure of Caesar for Gaul, Clodius and his gang became masters of Rome. Milo, a rival gang leader and politician, was a candidate for the consulship (Rome’s highest office) in 53 B.C. Clodius’ opposition led to street battles between armed bands of the two leaders. Milo’s gang was strong enough to hold Clodius in check.
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 Happy Tau Day, the most exciting math holiday you’ve yet to discover! Today, June 28th is 6/28, which contains in order the first three digits of tau (τ), the rival of math’s most popular irrational number, pi (π).
In 2001, Bob Palais wrote an article for The Mathematical Investigator called , “π is wrong!” In it, he insists that the choice of using π in our mathematical formulas for hundreds of years is no good. He argues that the use of τ would simplify many formulas and its derivation is much more intuitive. (Notice that the symbol resembles that for pi, but with one "leg" instead of two.)
The significance of our beloved irrational number π is that it is equal to the ratio of the circumference of any circle to its diameter--in notation, π = C/ d. However, the most defining characteristic of a circle is not its diameter but its radius. A circle is defined as the collection of points on a plane that are exactly the same distance, its radius, from a point, its center. Palais argues that intuition should direct us to the use of a more elegant Circle Constant, tau, where τ is the ratio of the circumference of a circle to its radius--in notation, τ = C/r.
Self-described “notorious mathematical propagandist” Michael Hartl takes the argument even further in his now-famous “ The Tau Manifesto,” which he published on Tau Day of 2010, exactly one year ago. He demonstrates with many adapted formulas that the factor of 2 is unnecessary if we incorporate it into the ratio itself. For instance, the periods of basic trigonometric functions f(x) = sin(x), and f(x) = cos(x), are in both cases 2π. Why not change them to tau instead? Palais and Hartl each list numerous other examples from calculus and physics, in which the factor of 2 is rendered obsolete by replacing 2π with τ.
The really intuitive part is revealed if you think of angle measure. How things are done now with π, a half turn of the circle is π radians, and a full turn is 2π radians. Should we adopt τ instead, τ radians would be a full turn, τ/2 radians a half turn, τ/4 radians a quarter turn, and so on.
There are, of course, instances where π appears un-doubled. For instance, the formula for area of a circle: A = πr 2. Hartl shows, in a mathematically sophisticated way, that the replacement of π by τ even in this instance is the more sound choice, since it is analogous to similar formulas in physics.
An article in today’s BBC News paints the issue as a violent conflict, with pi detractors up in arms over a lifetime of educational betrayal, which seems to this mathematician something of a manufactured controversy. (I can imagine you'd be upset if you are the sort of mathematician that has memorized pi to the nth digit. If you are one of these folks, here's the start for your new parlor trick: reciting tau, 6.283185307...)
Is it worthwhile to switch to tau use, an
Till recently, I always thought of Ambrose Bierce as “that weird horror writer who disappeared into the woods without a trace.”
Actually, it wasn’t the woods. It was Mexico. In 1913, Bierce wanted an eyewitness view of the Mexican revolution, so he took off with the rebel troops. He was never seen or heard from again.
He was more than just a horror writer, but stories like “The Damned Thing” (1898) show he was one of the best. In “The Damned Thing,” a hunter is savagely killed and mutilated by an invisible animal. Another goodie is “A Diagnosis of Death” (1909), in which a skeptic is warned of his oncoming death by his doctor’s ghost.
Bierce was also a satirist. His The Devil’s Dictionary (1906), originally called The Cynic’s Word Book, contained definitions that crossed in common usage. (E.g., he defines cynic as “a blackguard whose faulty vision sees things as they are, not as they ought to be.”) His fierce literary criticism (Oscar Wilde hated him) and scathing view of life led people to call him “Bitter Bierce.”
“War,” he once said, “is God's way of teaching Americans geography.”
I was impressed by all the Civil War stories he wrote. The most famous was “An Occurrence at Owl Creek Bridge” (1890), which depicts a Confederate supporter who is about to be hanged at the bridge he tried to sabotage.
“Chickamauga” (1891), his most tragic war story, is from the point of view of a six-year-old boy, a Southern planter’s son. It starts out innocently enough, with the boy crudely making a wooden sword (that even his ex-soldier father doesn’t recognize!). He leaves the plantation and marches off to play “war games.”
In the woods, the boy gets lost, and falls asleep on the ground from sheer exhaustion. When he wakes up, he thinks he sees animals creeping through the woods. Actually, they’re mangled Union soldiers (the Battle of Chickamauga was one of the worst Union defeats in the Civil War), crawling away on hands and knees. Their pale, blood-streaked faces amuse the naïve boy, who’s reminded of circus clowns.
In one grisly part, the boy attempts to “play horsey” on one soldier’s back:
The man sank upon his breast, recovered, flung the small boy fiercely to the ground as an unbroken colt might have done, then turned upon him a face that lacked a lower jaw--from the upper teeth to the throat was a great red gap fringed with hanging shreds of flesh and splinters of bone. The unnatural prominence of nose, the absence of chin, the fierce eyes, gave this man the appearance of a great bird of prey crimsoned in throat and breast by the blood of its quarry. The man rose to his knees, the child to his feet. The man shook his fist at the child; the child, terrified at last, ran to a tree near by. . . .
In the distance, the sky is red. Surrounded by the wounded, crawling mob, the boy marches ahead, playing that he is their new leader (even turning to ma
Those who study modern China know that the Communist government struggles with the yearnings and demands of its 55 ethnic minorities. What immediately comes to mind are the calls from Tibetans for more autonomy, or independence itself, and the complaints of the Uyghur people concerning religious and political discrimination in Xinjiang, the the northwest part of China. The majority Han people have been moving into both Tibet and Xinjiang, thereby changing the native cultures there.
In the last few months, we have been hearing complaints from the Mongolian people in China. Mongols are upset that so many Han have moved into Inner Mongolia and disrupted their pastoral way of life. The Mongols have staged protests against the environmental damage that comes with settled agriculture, the strip-mining of coal, the building of highways, the damming of rivers, and the overgrazing of land.
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| Inner Mongolian grasslands |
Background. The Mongols and Han have a long history of interactions. The nomadic Mongols invaded China many times, attracted to the relative wealth of the more settled Chinese. In fact, the Mongols even ruled China from 1279 to 1368, setting up the Yuan dynasty with its capital at Tatu, which is present-day Beijing. The Yuan dynasty was known for its religious toleration, especially of Muslims, Daoists, and Buddhists. During Mongol rule, the country prospered because the Mongols encouraged foreign and domestic trade. Eventually, the Han Chinese became dissatisfied with Mongol rule and threw them out. Since then, the Han have dominated their Mongol neighbors. Now the Peoples Republic of China rules Inner Mongolia.
A Recent Novel. By coincidence, this spring I read a novel about the Han and the Mongolians in Inner Mongolia. Wolf Totem by Jiang Rong tells the tale of Chen Zhen, a Chinese Han who travels there in the 1960s during the Cultural Revolution and falls in love with the traditional Mongol way of life. He and two other Han young people work and live in a community that raises cattle, sheep, and horses on the steppe. While there, Chen learns from a local wise man of Mongolian lore and spritual life and the important place that wolves play in both.
Every year I wait to see them. I saw my first one of 2011 on June 14, at dusk. It was just one lonely firefly, signaling its presence near a bunch of parked cars. For me it was an exciting moment. I am not even sure why. I just love the sight of these glowing insects; they mean summer is here. Their renewed presence means the species has survived yet another year and still exists to tell me it is June. But they are not really flies. So what are they?
Fireflies are actually winged beetles. The 2,000 species of fireflies that exist are found in temperate and tropical habitats around the world. They are also known as lightning bugs and even as glowworms (particularly in their larval phase) and they have these names because of their “conspicuous crepuscular use of bioluminescence to attract mates or prey” (per Wikipedia). In other words, they emit light at twilight to communicate with other insects. The light is produced by a chemical reaction that occurs within a special organ in their lower abdomen. Each species has its own pattern of light flashing to find mates.
Most firefly species are active at night, when their flashing light can be readily spotted. Some species of fireflies are active during the day, but they tend not to be luminescent. However, all firefly larvae glow, presumably as a way to warn would-be predators of their nasty chemical taste. As adults, the light usually signals a willingness to meet and mate. At least one species uses its flashing light for a different – and deceptive – purpose. The female of this type mimics the mating flashes of other fireflies; when a hopeful male responds, he ends up being dinner, not a mate. So much for a “light” dinner!
Of course, I am not the only person who loves watching these bugs. There is a magic to watching children run through a field trying to capture fireflies. Professional institutions are also dedicated to the study of fireflies. The Museum of Science in Boston teams up with university researchers to study firefly sightings each year. Volunteers around the country help them count fireflies as a way of tracking their numbers. It seems that their population has been decreasing, and this could be due to environmental influences. There is even the Kumejima Firefly Museum in Okinawa, Japan, that is dedicated to this amazing insect. The museum celebrates the fact that there are seven species of firefly thriving on Kumejima because of the island’s clean ecosystem.
So, the next time you see some bug flying near you, please don’t reach out to swat it. Just keep an eye on it and you may be rewarded by the glow of a bioluminescent love signal.
Carol
Social Education, the official journal of the National Council for Social Studies, recently published a lesson plan on Starbucks. The lesson plan is great, as it analyzes American culture and consumerism through an analysis of Starbucks. It also inspired me to think of an interdisciplinary project that social studies and science teachers could co-teach on Ethos water.
 Ethos water is owned by Starbucks and sold in their stores. Branding itself as a responsible company, Ethos claims its mission is to help bring clean drinking water to children throughout the world. A 20-ounce bottle of Ethos water costs $1.80. Out of the $1.80 paid for each bottle of Ethos water, Starbucks will donate $.05 toward their mission. According to the article in Social Education, “they are charging customers 15 to 20 percent more than other companies . . . in other words, they charge customers to feel good about themselves.” Interviewing, an important skill for budding social scientists, could be used to determine why people are buying an overpriced bottle of water. Is it because of the “clean water” mission? Is it out of convenience? Is it for another reason altogether?
As an entry point into this project, science and social studies teachers can use the debate over whether or not Ethos does more harm than good. Students could research which regions of the world are in need of clean drinking water, and the political and environmental issues that create that need. Students could also investigate the environmental impact of drinking bottled water, as well as issues regarding tap water versus bottled water. For instance, if students determine that tap water is safer than bottled water, they could argue for drinking tap water and donating the saved money to help bring clean drinking water to “dehydrated communities.” Another student might research statistics on charitable donations and determine that people who are saving money by drinking tap water would just buy something else rather than donating their savings. In that case, Ethos is invaluable, as the donation is built into the purchase. 
Editorial writing is another skill that could be incorporated into this project. Students could write an editorial to support or discredit Ethos. Of course, these editorials could be published in a class blog instead of a traditional paper. Then students would read each other’s opinions, include relevant links, and comment on their peers’ work.
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Summer is almost officially here. Bravo for hot weather, cool watermelon, ice cream, and if you are lucky, some great trips. Parents and students are happy that school is finished. However, studies find that students lose significant math and literacy skills during their summer vacation. So, make sure to encourage your children to keep reading this summer.
 Amsco’s La Gran Aventura de Alejandro by Abby Kanter is a great start. This reader gives students in the early stages of learning Spanish the pleasurable experience of reading simple material of significant value in language and culture.
The book tells the story of Alejandro, a young Mexican boy who goes on vacation with his family to Spain. While seeing the sights, Alejandro, who is a courageous individual, walks away from his family momentarily to help a little girl. Later on, he meets the girl’s mother. To thank him for his help, the woman gives him a ring that will allow him to embark on a great adventure.
 While having fun, this book will help students keep up with their Spanish during their free time. Enjoy the summer!
I wonder how many times students have been directed to complete a table for homework or on an exam. Chemists have an incomplete table that they are trying to complete: the Periodic Table of the Elements, or the Periodic Table, for short. Uranium, element number 92 is the last naturally occurring element in the Periodic Table. Elements beyond number 92, called the transuranium elements, have all been produced in laboratories. The first transuranium element, neptunium (#93) was produced in 1940 at the University of California, Berkeley, by Edwin McMillan and Phillip Abelson by exposing uranium oxide to neutrons from a cyclotron. The last one, copernicium (#112) was officially recognized in 2009.
On June 6, 2011, the Joint Working Party on the Discovery of Elements of the International Union of Pure and Applied Chemistry ( IUPAC) and the International Union of Pure and Applied Physics ( IUPAP) announced the addition of two new elements to the Periodic Table—element 114 and element 116. For now, element 114 is called ununquadium and element 116 is called ununhexium. These names are based on their atomic numbers. By officially acknowledging the collaboration between researchers from Lawrence-Livermore National Laboratory in California and Russia’s Joint Institute for Nuclear Research in Dubna, these researchers will get to suggest names for the new elements. The names will go through a review process before being adopted and the elements will be assigned a symbol by the IUPAC Council.
Scientists produced these elements by bombarding curium (#96) atoms with calcium (#20) nuclei. In a few milliseconds, element 116 decays into element 114 which lasts about half a second before decaying into copernicium (#112). In other experiments element 114 was produced by bombarding plutonium (#94) with calcium nuclei. Notice that 96 + 20 = 116 and 94 + 20 = 114.
There are three more elements waiting to be recognized: 113, 115, and 118. According to IUPAC, “Review of the claims associated with elements 113, 115, and 118 are at this time not conclusive and evidences have not met the criteria for discovery.” As soon as I hear anything more, I will let you know.
Flag Day! What's that? On this day in 1777, the Second Continental Congress adopted the stars and stripes as the nation's flag. In 1916, President Wilson officially proclaimed June 14 to be Flag Day. Since then, it has been a day to commemorate the American flag. Consider it a warm up for Independence Day.
Like apple pie, the bald eagle, and Lady Liberty, the flag symbolizes our nation: it is a visible sign of invisible things. Look at the pictures in the collection that follows and for each ask yourself the question, "What does the flag represent here?" Share your answers by writing a comment below.
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 Summer is upon us. We all know that.
The big question is… What will we read? While on the beach; in the car heading towards a vacation destination; on a plane; sitting on that park bench; or in bed at night, when the cicadas are singing and the breeze is warm… What will you be reading? Me? Oh. Well, thanks for asking: Lawrence Durrell’s Alexandria Quartet
Legson Kayira’s I Will Try Kenzaburo Oe’s Rouse Up O Young Men of the New Age! Richard Wright’s Native Son Norman Mailer’s An American Dream Arthur C. Clarke's Rendezvous with Rama A collection of poetry by Walt Whitman And my favorite to-be-read-aloud-to-friends-at-a-picnic book: Lewis Carroll’s Alice in Wonderland and Through the Looking Glass
We are very proud to have received the HOMEEducators Resource Directory Seal of Approval! How did we earn this honor? The same qualities that have established Amsco as a classroom favorite, also make us a go-to resource for secondary-level homeschoolers.
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One of the things that has always bothered me about the Common Core Curriculum is the idea of teaching for "understanding." On the surface, this seems like a term that is so vague that it is almost useless. How do you know when a student understands? Then I started to read Adding It Up: Helping Children Learn Mathematics—the CCSS borrows freely from this report.
As per Adding It Up, conceptual understanding is about making connections and organizing ideas. Students need to learn how to represent situations in different ways and know how different representations can be useful for different purposes. In particular, students need to explore similarities and differences among various representations. Students need to learn why ideas are important.
Let's look at some examples of varying difficulty. - As per standard A.SSE.4, students are supposed to understand that the polynomials form a system similar to the integers. You can teach for understanding by having students explore the similarities and differences among addition, subtraction, and multiplication with integers and polynomials. In particular, students can see whether or not the usual properties of numbers hold for polynomials—commutativity, associativity, etc.
- As per standard 6.RP.2, students need to understand the concept of unit rate. You can teach for understanding by emphasizing unit rates in different real-world contexts. For example, speed as a rate, cost per item as a rate, etc.
- As per standard 8.F.1, students are supposed to understand the concept of a function. Again, you can teach for understanding by emphasizing the different ways that functions can be represented—symbolic, numerical (table), and graphical. For example, you can give a problem that asks students to compare two functions—one represented symbolically and the other by a graph. You can also teach for understanding by talking about the importance of functions in modern society—namely, how functions are a fundamental part of computers.
A healthy brain can be taught a new word in less than 15 minutes, according to scientists. This discovery will deprive many students of their excuse for not studying a foreign language.
Cambridge neuroscientists found that all you need to do is to listen to a word 160 times over a span of 15 minutes. The secret is just hearing a word repeatedly. After that, the brain will have formed a completely new network of neurons specifically tasked with remembering that word.
Dr. Yury Shtyrov and his team reached this conclusion after placing electrodes on the heads of 16 healthy volunteers to monitor their brain activity. They recorded the pulses generated when the subjects listened to a familiar word. Then the volunteers were made to listen to a made-up word, over and over again. Initially, the brain had to make an effort to recognize the new word. However, after 160 repetitions over 14 minutes, the new memory traces were "virtually indistinguishable" from those of the already familiar word, said Dr. Shtyrov.
I guess that hearing a word 160 times does not seem like a particularly amusing way to learn a language, but at least it gives one hope that becoming comfortably proficient in a foreign language is possible.
This research gives us a hint of the importance of recycling content throughout lessons when you are teaching a foreign language. It is not a secret that the more you see or hear something, the more you will remember it. On the other hand, maybe the key to retaining information is to forget that you are trying to learn it in the first place.
Now that summer is around the corner, I’m starting to miss the beach. And I don’t mean any beach, certainly not in the United States. I’m talking about a tropical beach, with white sand and coconut and sea-grape trees for shade. I’m talking about Balneario La Monserrate, better known as Luquillo Beach. It is located about 15 miles (45 minutes) east of San Juan. As a kid, I used to go there quite often (it was 30 minutes away from my house). It is a crescent of fine sand, with various types of mature trees. And behind this beach is the rain forest—it’s picture perfect.
The balneario (public beach resort) has been designated a “blue flag beach.” This means it meets very high standards (water quality, facilities, management, etc.). The beach itself is wide, so there is ample room to pick your favorite spot. If you are melanin challenged, you may look for a shady spot because you will burn in a New York minute. Luquillo Beach is very popular with locals and tourists alike, and it can get incredibly crowded. An alternative spot for snorkeling enthusiasts, Playa Azul (Blue Beach), is a few minutes away. La Pared (The Wall) and La Selva (The Jungle) offer good medium-range surfing waves, if you’re interested in that kind of action.
3 Comments on It's Time For Fun In The Sun, last added: 6/22/2011
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Once upon a time, there was a very evil man named Heinrich Himmler. During the period of the Third Reich– 1933–1945, Himmler had the title of Reichfuhrer SS. As head of the SS (Schutzstaffel), Hitler’s private army, and the Gestapo, Himmler was the most feared man in Europe. During the Holocaust, six million Jews and nine million other Europeans were murdered on his orders. It was he who directed the work of the concentration camps and the roving action groups that carried out the work of genocide. In order to begin to understand the mind of Himmler and the homicidal maniacs who worked with him, the basics of Nazi racial theories must be examined. Hitler, Himmler, and the other Nazi leaders preached the superiority of the German race. Those of pure Aryan descent were ein herrenvolk, a master race whose destiny it was to rule the world. Non-Aryans were untermenschen, racial inferiors, who must serve the master race. It all became quite involved, with an Institute for Racial Study, charts, graphs, racial purity tests, genealogical studies, etc. Eventually, all the peoples of the world were placed into racial categories, ranked in order of their proximity to the pure Aryans. By killing off racial inferiors, either immediately, or by working them to death, the Nazis would create a better world, based upon the principles of racial superiority. Such beliefs motivated them to do all sorts of things, such as naming their Japanese allies honorary Aryans during World War II (1939–1945).
In the summer of 1935, Himmler founded the Ahnenerbe, an organization devoted to the study of German ancestral heritage. The organization was intended to give scientific credibility to Nazi racial theories and to strengthen German nationalism. Its mission was to investigate German history and mythology, using as their principal tools the disciplines of archeology and anthropology. The Ahnenerbe’s most important task was to investigate the origins and spread of the Aryan race. It was in pursuit of this task that Himmler ordered the Nazi expedition to Tibet (1938–1939). Five Ahnenerbe scientists, all SS officers, aided by Indian and Tibetan guides and porters, suffered considerable hardships making their way through Indian monsoons and freezing Himalayan passes before entering Tibet and spending two months in the area around the capital city, Lhasa. Tibet was a strange place to search for the origins of the tall, blond, blue-eyed Aryans of Germanic mythology. However, scientists of the 19th and early 20th centuries believed that the highland plateau of Tibet was a likely place in which to find evidence of human origins and evolution. There the superior Aryans originated, aided in their cultural development by survivors of the lost continent of Atlantis.
The leader of the expedition was 28-year-old Ernst Shafer. A respected scientist who had studied zoology and geology at Gottingen University, Shafer had gai
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| Cynthia enjoys tea and crumpets. |
If I could’ve chosen my own name, what would it be?
Not Cynthia. It seems so formal, so tea and crumpets. Cindy is OK, though it sounds blond, and I’m a brunette. All the other Cindys I grew up with were blonds. But as adults, not all Cynthias are stuffed shirts.
In fiction, certain names conjure up stereotypical images. We expect Buffy to be a bubbly cheerleader and Rebel or Snake to be bikers. If we’re wrong, and Buffy winds up being the dental hygienist, we might feel tricked.
According to T.L. Cooper’s “Naming Characters in Fiction,” names create relationships between the characters and readers. Names show how the characters feel about themselves. And nicknames clue you in on how they feel about each other. In two of my own stories, minor characters named “Madman” and “Sorehead” told you these stories were set in a challenging, dysfunctional world.
Also in Cooper’s article was a list of Don’ts, to be aware of, when naming your characters. For one thing, you can’t use the same name for two different characters. It creates total confusion. (I mean, why would you even want to use the same name, unless they’re father and son? Then you could call them William and Billy.)
Also a no-no is using names that begin with the same letter (like Gary and Greg) or that are too similar, period (like Gary and Gerry). It’s also a hassle when your character has no name (“the big-nosed girl,” “the red-headed guy”). Trust me, it’s hard to keep up with that. If a character figures largely enough in my story, I come up with a name.
Jack Oceano’s “Five Tips for Naming Your Characters in Fiction” helps us when we’re stumped.
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Uh-oh, it’s that time of the year again, I thought. It’s time for students to start planning for the next academic year. And I don’t mean what clothes, shoes, and accessories you’re planning on wearing. Remember all the vocabulary you learnt in your foreign-language class? How about those pesky grammar rules? If you answered “yes,” congratulations! If you answered, “no,” you need to get to work; but don’t worry: there are plenty of Amsco books to help you review and get ready for this year’s challenges. Amsco foreign-languages workbooks aim to provide students with a concise and systematic review of the essential elements of the target language. Abundant and varied communicative exercises help students master each grammar topic. These workbooks are designed so that each chapter is complete in itself. The chapters may be used in any order, according to the student’s individual needs. Explanations are clear and concise, and are followed by numerous examples. There is a great variety of exercises that provide both communicative and written practice. Check out some our offerings: Spanish First Year Spanish Two Years Spanish Three Years Spanish Four Years French First Year French Two Years French Three Years French Four Years Italian First Italian Two And Three Years And there are many more. I’m sure you will find something that suits you. Good luck!
The problem was in the 2-point, or short answer free response, portion of the exam, testing the learning standard that demands students “determine the inverse of a function and use composition to justify the result.” 
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Very interesting! Now we know why we had all that snow. Well researched and written.