February 11, 2022

Read Out Loud?

4 Benefits (and more) of Reading like the Ancients

Dr. Sue Fisher at The Lukeion Project

    When was the last time you read out loud? If you have small children around you, you probably do this on a regular basis, but as those children get older and can read for themselves, this practice generally drifts away. Reading becomes a solitary affair, usually undertaken in silence except for the occasional sharing of a quip or a quote.

    For this reason, it often comes as a surprise to my students that it was the customary practice for the Greeks and Romans to read out loud. In the pre-technological world, recitations were common forms of entertainment and public speeches were an important part of civic life. Reading aloud was not just for public affairs, however. Reading out loud privately was a customary practice well into at least the 17th century.

    Today, however, reading out loud after childhood is associated with incapability. The image of a dim-witted gomerel attempting to sound out easily pronounced words is an image all too readily conjured up. Anyone who has enjoyed a well-narrated audible book, however, knows that literature in the hands of a skilled reader can enhance the text and bring that book to life in ways that simple reading often cannot.

    While the modern world does not always afford the time and place for reading aloud, there are both practical and esoteric advantages to be gained when one adopts this practice. 

 

Better Focus:

    When reading a difficult text or something that is not necessarily of deep interest, it is all too easy for our minds to wander off. Soundbite culture has only added to this problem. The practice of reading out loud is an easy remedy to this problem because it incorporates more than one sense to get the job done. Engaging your mouth and your ears along with your eyes and your brain makes it harder to lose attention. 

 

Better Speaking:

    Reading out loud forces the speaker to pronounce the words they are encountering. Science has shown that people recognize words in blocks rather than by syllable. This is what makes it easy to mix up words that begin and end the same way. When reading silently it is easy to identify the word as a block and quickly move on. A reader may not be able to pronounce those words gracefully if at all. Likewise, out loud reading forces a speaker to slow down, take pauses that allow for processing of the text, and also imbue the words with feeling. All of these practices are foundational for good public speaking. 

 

Better Appreciation:

    Some works are written to be heard as well as read. Imagine Dr. Martin Luther King’s I Have a Dream speech or Lewis Carrol’s Jabberwocky. You likely imagined them being spoken or heard rather than reading them. Impassioned words, meter, rhyme, and other literary devices all can be seen with the eyes but were created for the ears. This is where their interest lies, and they simply cannot be fully appreciated without being read out loud. 

 

Better Editing:

    Reading out loud is the simplest and most effective tool for editing your work. The very thing that keeps most of us from reading aloud, the fact that it slows you down, is the very thing that makes reading out loud such an effective tool for editing. Reading out loud provides an opportunity for the ears to hear what the eyes might miss. For instance, while reading aloud, a person naturally pauses in places and these pauses can be excellent indicators of where commas or periods are needed. Running out of breath is a good indicator that a sentence is a run-on and needs to be divided. Lack of clarity becomes more apparent. The list goes on and on. 

 

    While these are some of the practical, academic reasons for targeted out loud reading, there are some less measurable benefits as well. The greatest of these, in my opinion, is the opportunity it provides for camaraderie. Studies have shown that reading to children is as much about bonding and relationship as it is about the story and skills themselves. This is not something that disappears when people reach a certain age. Sharing a story, or an article, or a poem or a speech out loud provides opportunities for common experiences and discussions that strengthen relationships; the benefits of this, in turn, are immeasurable.

February 5, 2022

Why You Should Study the History of Math

 
By Dr. Kim Johnson with The Lukeion Project
(instructor /designer of  "Counting to Computers: Math from the Dawn of Time to the Digital Age")

In the mid 1300s a fad made its way around Italy. Mathematicians would challenge each other to “mathematical duels.” They would post problems for their opponents to solve, sometimes along with their solutions in coded poetry. The winners would get support and funding from rich patrons and the losers would descend into obscurity. One such contest between Fiore and Tartaglia involved a new method for solving the cubic. In order to win Tartaglia worked day and night to find Fiore’s method. Unfortunately, Fiore did not do the same and only knew his own method and no others.

Recall that the formula for solutions to quadratic equations of the form

use the quadratic formula,


 Giorlamo Cardano, a physician, philosopher, astrologer and mathematician, convinced Tartaglia to share his method and promised never to reveal it. Then Cardano figured out a more general method, and wanted to share it, but was blocked by his promises. Fortunately for Cardano, he realized that Fiore’s teacher, del Ferro, had actually figured out Tartaglia’s solution earlier. So Cardano shared del Ferro’s solution (which happened to be the same as the one he had promised not to reveal) along with his more general method. Tartaglia was upset, and eventually lost the duel which would have given him a professorship. He hated Cardano for the rest of his life.

Even though this “mathematical dueling” was exciting, dramatic, and expanded the horizons of what was known mathematically, the practice only lasted a few years. What happened? Why don’t we still engage in mathematical duels today? The change didn’t come because we are so much smarter than the historical mathematicians. Things changed because we have different tools than they did. These days we are solving different problems than they did.

We have better tools.

    Because we have the benefit of tools based on thousands of years of mathematical creativity, things which were difficult to the historical mathematician are literally child’s play to us. The reason that algebra is taught in middle school or early high school rather than being the crowning glory of the life’s work of mathematician has to do with the progression from rhetorical algebra to symbolic algebra. In the beginning of mathematics, every single problem was a word problem. The ancient mathematicians simply lacked symbols. By the 1200s, rhetorical algebra evolved to syncopated algebra, a mix of words with a few symbols thrown in. Finally, in the 16th and 17th centuries Francois Viete (a code-master with the French government) and Rene Descartes were among the mathematicians developed the standard symbology we use today.

    The ancient mathematicians didn’t even have the most useful of symbols, the number zero, until the Hindu mathematicians developed it in the 600s and it was exported around the world by the Arabs (which is why we use Hindu-Arabic numbers). Even then, most European mathematicians used Roman numerals until the 1200s and Liber Abaci by Fibonacci popularized the idea. Although many people,  including a Pope, believed zero and the place value system were useful, they did not become universal until much later. When you try to divide MCMDLXXXII by DCXIV, the ease of the place value system becomes obvious. In most cases, the tools that have been developed make computations much easier for us than they were for our predecessors.
 

We are solving different problems.

    Part of the reason the historical mathematicians didn’t have the same tools as we do is because they were not solving the same types of problems. For example, when algebra was introduced by the Arabs, it was developed for solving specific problems including those relating to inheritance. The mathematicians in India used their work to imagine and build altars of various sizes and shapes. The Romans, whose contribution to mathematics was once summed up as “Cicero finding the tomb of Archimedes,” were interested in solving problems only when they were practical. A problem from one of their texts, for example, talks about “the shortest way across a river when there is an army on the other side.” Babylonians were interested in keeping track of goods and astronomy. Egyptians were interested in the area of plots of land for taxes as well as a calendar for computing the flooding of the Nile. Enlightenment mathematicians were interested in solving problems related to how planets moved.

    There have been dice games and other games of chance available for millennia. Only since the 1300s have these been analyzed mathematically. Cardano, mentioned above, put himself through medical school by gambling since his father wouldn’t pay. He redeemed himself, however, by analyzing the games of chance he played and thus inventing the field of combinatorics and probability. Why had no one developed these methods before? They believed that the results of the roll were the results of favor from the gods. Why look for mathematics in something that was divinely ordained?

    Even though the Babylonians had developed the beginnings of the concept of zero, the Greeks had real trouble with even the idea of zero. The void was meaningless to them, and so in part they never developed zero. The Hindu mathematicians had no such philosophical barrier, and so they could use the powerful tool to solve difficult problems.

We are different people.

    Finally, the mathematicians of the past had unique personalities that led to their discoveries. It helps to understand Cantor and infinity when we understand his mental health. We can understand the development of the calculus in a new way when we know about Newton and how he saw the world vs. Leibnitz and his view of the world---and how Euler brought them all together. Some mathematicians, like Fermat and Mersenne, were extremely interested in communication and collaboration. Some, like Sophie Germain or Carl Gauss, overcame terrible obstacles. Others, like the Bernoulli family and Euler, seemed destined to study math. Still others pursued mathematics as a side passion, like John Napier, a Scottish laird who studied theology and incidentally invented the logarithm. The personalities of the mathematicians themselves work their way into their mathematical discoveries.

    For all these reasons---the tools, problems and personalities of historical mathematics---we should look at the history of mathematics in order to understand the mathematics itself. These historical mathematicians were not stupid, they were merely coming from a different perspective. When we understand their various perspectives, our own perspective broadens and our progress in mathematics becomes richer.

January 28, 2022

4 Things to Improve High School Writing

Time to Transition to the Academic Style

By Randee Baty at The Lukeion Project

    There are many kinds of writing in the world. There is journalism, blogging, creative writing, creative non-fiction, personal narratives, informational reports, poetry, diaries, the list can go on and on. Many students start in the elementary years writing stories, book reports, and informational papers. Those are strong ways to get a child used to putting words and thoughts on paper. However, there comes a time for all students when they must learn the skill of academic writing.

    Academic writing is what is going to be required of students as they begin their more rigorous high school classes and their college classes. This is an objective, structured, third-person style of writing that is not taught in younger grades. It can be a challenge for some students at first. They are used to being told that colorful adjectives and adverbs are good, which they are, but not in academic writing. They are accustomed to giving their opinions, which is good, but not in academic writing. They are comfortable with being told that using their imagination is good, which it is, but academic writing uses the imagination in a different way.

    Taking on this challenge should begin by 8th or 9th grade. Unless they are specifically taking creative writing classes or enjoying personal writing time, creative writing skills will not be used much in class after this point. It was a great gateway to writing, but –at least for now— creative writing will be more of a hobby or stress-reducer.

    At this point, what a student thinks or feels about a subject or topic becomes less important than what they can give evidence for and what they can discuss analytically. Some students are shocked to realize that most high school teachers and professors do not much care what the student thinks about the topic they are studying or assigned to write about. Those instructors will expect to see well-written thesis statements that are back up by evidence rather than opinion. How a student feels about something will matter little. What a student can provide evidence to support is everything. Instructors will normally start expecting academic writing from their students as they mature through high school and move to college level work.

    Academic writing is how one scholar, the student, talks to another scholar, their professor. Academic writing has certain conventions that those professors assume will be used, such as formatting the paper according to specific guidelines, writing in a third-person point of view, staying in a formal, academic tone, using source citation, and creating an argument that they can support with evidence in a clear, logical manner.

    For some parents, this is the point where they become uncomfortable judging their student’s writing because it may have been many years since they did this type of writing themselves. They are unsure how to help their student master this skill and how to judge whether the student is becoming a strong academic writer or not. Here are some of the guidelines to help parents know if their student is on track to become a strong academic writer as they must in rigorous high school classes and in a good college.

Formatting is Key

    Formatting is far more important than most students believe. Professors are going to ask most commonly for MLA or APA formatting. If they ask for it, the student must know what is being asked for and provide it. The professor will not ask for it if they are not going to grade on the student’s ability to format their paper in that style. The best guide to both styles is in the Purdue Owl. Their information is usually easier to use than the style guides provided by the organizations that write these styles. Formatting matters, and students must learn to employ it well whether they understand why or not.

Be Clear

    Academic writing uses few adjectives or adverbs, modifiers, or intensifiers. While students may have learned to use these extensively to create imaginative stories, they are not used any more than necessary in academic writing. Scholarly writing is clear and straight to the point without unnecessary words. Getting to the point as quickly and clearly as possible is how academic writing is done. Clarity is valued above technique. If modifiers or intensifiers are required, then the writer did not use the correct word to begin with. Common modifiers are not necessary but are just a habit of the author, such as using the word “very.” Eliminating unnecessary modifiers will make writing more powerful and concise.

 Be Concise

    To go along with the previous point, academic writing is concise. Complex thoughts must be expressed in the simplest way with the fewest words possible. If you have read academic articles or papers that feel like you are wading through mud, you know why concision is a desired quality of academic writing. Do not pad the paper, do not add fluff, and do not use any words that are not needed to convey the intended meaning. Cut ruthlessly!

Be Precise

    Academic writing is specific. Some students think this contradicts the idea of using few adjectives and adverbs, but it does not. Being specific refers to giving the necessary details and using the precise word that conveys the intended meaning. It means saying “rose” instead of “flower.” It means saying “Paris” instead of “the city.” It means giving specific quantities instead of vague generalities. Specificity is what makes writing interesting. I had a student draft a paper over a surgery she had, but by the end of the paper, I had no idea what the surgery was for. After using my feedback to revise her paper, I still had no idea what the surgery was for. Having read two versions of the paper, I had still had no idea if the surgery was on her hand, foot, head, or where it was. That lack of specificity made the paper not only uninteresting to read, but ineffective in conveying the information she wanted me to know. Be as specific as possible.

    Most parents should have their student take some classes in academic writing to help them learn how to write arguments, use research sources, and put together strong introductions and conclusions. Parents can give the students a good start by working on some of these aspects of their student’s writing earlier rather than later and then encouraging the jump from creative pieces to analytical writing by early high school.

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