“Mathematics and Learning”

What subject should be learned first?  The question rightly troubles anyone who’s interest is in education.  Of course, young children often must learn in a very basic and rote fashion, applying their apt memorization skills to simple tasks that will serve them very well in later years when they go one to apply such knowledge to more complex topics.  However, when the time comes to designing curricula, an important question must be answered for older students, namely “What is most important first topic in these students’s education?”

An argument can be made for the use of mathematics as a tool for teaching students how to reason more clearly.  This is not because mathematics is the basis of all knowledge.  Indeed not.  There are many important subjects including not only the humanities like poetry and history but sciences like biology and physiology too.   These topics are not strictly speaking mathematical in nature, even though mathematics can be used in it in many ways.

Our minds are best geared for learning things that we can sense, things that are visible and tangible.  Although mathematics is abstract, it can begin with this kind of sense derived experience.  Beginning with simple everyday examples, children can be taught the more abstract and difficult skills that must be learned for the sake of the development of mathematical skills.  In the process of learning these topics, the children will begin to learn important rules about reasoning.  He or she will learn how several propositions can serve as the basis for conclusions.  They will learn how certain properties are related to various geometric figures and arithmetical rules.  Although much of this will be memorized at first, with time, they will have the opportunity to see that human reasoning in mathematical subjects is orderly and logical.  On the basis of such “logical experience,” young learners can then begin to be taught the rules of logic that they have been using all along.  As the medievals used to say, they could go from logica utens, logic used in other subjects, to logica docens logic taught, as a unique, and separate subject.

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If the team would have spent more time in the weight room, they would have been better prepared to face the massive offensive line of Ridgely High.

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After he went to the grocery store, Frank stops at the hardware store to pick up some nails.

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Before I took the exam, I purchased several preparation manuals containing both practice tests and review exercises.

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Billy gone to the ocean once before in his life.

Josh suffered from a fear of dogs since he is a little boy. He would shiver in his boots thinking of a dog barking at him, biting him, or that could chase him. He had never met a single dog he liked. The scarier dog he had ever seen was Mr. Green’s dog, whom he had to pass every day. On his way to school. This dog barked so loudly it made Josh’s hairs stand on end.

She said that there was no need to be afraid. Josh’s mom told him that dogs only barked because they were excited to see him. She told him that he just needed to be confident and not act afraid of this dogs’ barking, and speak in a reassuring tone. Then the dog would quiet down and act more friendly.

Josh felt that neither confidence or a reassuring tone would make any difference. He didn’t think he would ever get over his fear. However, one day he had enough. Barking for hours, he realized the dog was bored and just needed a friend. He wasn’t sure if his mother’s advice would prove true? Hiding his fear, he approached the dog and spoke to it in a reassuring tone. To his surprise, the dog wagged it’s tail and quieted down right away. 

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Josh suffered from a fear of dogs ever since he is a little boy. He would shiver in his boots thinking of a dog barking at him, biting him, or that could chase him. He had never met a single dog he liked. The scarier dog he had ever seen was Mr. Green’s dog, whom he had to pass every day. On his way to school. This dog barked so loudly it made Josh’s hairs stand on end.

She said that there was no need to be afraid. Josh’s mom told him that dogs only barked because they were excited to see him. She told him that he just needed to be confident and not act afraid of this dogs’ barking, and speak in a reassuring tone. Then the dog would quiet down and act more friendly.

Josh felt that neither confidence or a reassuring tone would make any difference. He didn’t think he would ever get over his fear. However, one day he had enough. Barking for hours, he realized the dog was bored and just needed a friend. He wasn’t sure if his mother’s advice would prove true? Hiding his fear, he approached the dog and spoke to it in a reassuring tone. To his surprise, the dog wagged it’s tail and quieted down right away. 

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[1] Some people are excited, some people are just annoyed. [2] Being called to jury duty can inspire a range of different emotions. [3] Unsure how long the trial will take, a call to jury duty can be stressful for people who can’t afford to miss work or school.

Some people will be making attempts to get out of jury duty. However, most will still need to serve. Fortunately, many cases are settled before going to trial and is not uncommon for trials to just last only one day. Either way, once you have served on a jury, you won’t have to do it again for a while!

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“Justice and Parents”

We tend to think of justice as a matter of strict equality.  For example if someone wants to buy an item, they are understandably expected to pay an amount that is roughly equal to its value.  Likewise, when a law declares that the penalty for speeding is $150, it is considered just that one who breaks this law pays the fine.  However, justice can also pertain to matters that are beyond mere equality.

An obvious example of this is the case of the relationship between children and their parents.  Unlike the cases discussed earlier, children will have had little opportunity to repay they’re parents for all that they have done for them.  Technically speaking, strict “equality” would require the child to give birth to the parents.  This is an absurd thing to suggest.  Similarly absurd is the suggestion that children should directly repay the rearing offered by parents.  Once again, strict equality cannot occur in the child-parent relationship.

However, there is a kind of justice between children and his or her parents.  For example, when a parent ages and is in need of assistance, if the adult child can provide assistance but refuses to do so.  This is a kind of injustice to the parents.  On a more positive note.  For example, an adult child might send his parents on a cruise in memory of their anniversary.  Such an action would be a kind of “justice” done to the parents—at least in that it recognizes the immense debt that is owed by the child to the parents in question.

In these (and many other cases), justice is less about equality than it is about paying what one can pay.  That is, in such cases, both justice or injustice is determined by worthiness that surpasses mere equality.  This kind of justice could be called justice above justice.  That is, it is a kind of justice that surpasses the “normal” justice of equality.  Such acts of “justice above justice” ensure that society does not become reduced to the cold calculation of equality but, instead, has the warmth of true affection and loving gratitude.

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Over winter break, our AP Spanish class took a trip to South America to practice the language and learn more about different Spanish-speaking cultures.  Before we left, every student had to get their vaccinations for yellow fever and typhoid. Our first stop was Bolivia. When we landed at El Alto airport the highest in the world, we could see the city of La Paz sprawling up the hillsides in the shadow of the Andes.   The first day in La Paz, we went to the Witches’s Market, run by local yatiri. The yatiri are medical practitioners who perform healing rituals in they’re communities. At the market, we saw dried frogs, llama fetuses, herbs, and seeds, used in various rituals. After we visited La Paz, we traveled to Cochabamba.  Cochabamba is Bolivia’s culinary capital, with delicious specialties such as salteñas and rellenos. In Cochabamba, we also climbed 1400 steps to see the Cristo de La Concordia statue, the tallest of it’s kind in South America. Next, we visited the salt flats of Uyuni.  Several lagoons dotted the high desert landscape, some of who were full of flamingos!

On our way out of Bolivia, we stopped at Lake Titicaca on the Peruvian border. Because the lake’s elevation is over 12,000 feet, some of my classmates experienced a bit of altitude sickness.  Despite the altitude sickness, everyone said they loved seeing the beautiful scenery and visiting the mysterious “floating islands” made of reeds.   When we crossed the border into Peru, one of my classmates thought she had lost her passport. I would of had a panic attack! She ended up finding it buried in a pocket of her backpack and we were on our way. 

My favorite part of Peru was our trek to the ancient Incan ruins of Machu Picchu. We spent four days hiking in the Andes on a trail to the ruins. Our guides, whom spoke Spanish, English, and Quechua, were very knowledgeable about the history, flora, and fauna in the region.  Upon waking up the next morning, a beautiful sunrise greeted us and cast the mountains in its soft pink glow. After we explored the ruins, we took a train ride back to Cuzco.  The next day, we flew to Lima and prepared to return home. I was sad to leave, but I know I would be back some day!

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