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Sections of my Final Essay for my Philosophy of Education Class

         I believe the virtues of reciprocity, tolerance, and mutual respect need to be taught to students in society. This is because society is made up of many different groups of people that are interconnected and work together in society. Reciprocity is needed to determine what is fair and reasonable. According to Callan, author of Creating Citizens: Political Education and Liberal Democracy, “reasonable persons are predisposed sincerely to propose principles intended to fix the rules of fair cooperation with other” (Callan 25).  The virtue of reciprocity also gives one the capacity of realizing that it is not fair or reasonable to treat someone in a manner that they themselves would not like to be treated. Reciprocity is a necessary virtue in a pluralistic society since each member of the society will have their own beliefs and both parties will need to come to acceptance and mutual respect of each other when a conflict or disagreement arises. For one to have mutual respect for someone outside his or her community he or she needs to accept the burdens of judgment. To accept the burdens of judgment one needs to be humble about their own beliefs and needs to respect others’ beliefs (Callan 25).  In a society that supports everyone being autonomous and having their own ideas, the burdens of judgment would be necessary so that the reciprocity can function. The virtue of being tolerant is also needed since everyone in the society will have their own ideas and beliefs. Members of the society will need to learn to be tolerant to others’ beliefs since they will come across beliefs that are unlike theirs. People in society need to understand that other people have a different point of view then he or she does, and he or she needs to assume that the other person is reasonable. By teaching these virtues students will learn not to oppress other beliefs that are different from their own, since everyone’s beliefs and ideas are equal.

        Reasonable pluralism goes side by side with autonomy, since one needs to be free to have their own thoughts to be able to see another person’s perspective. An autonomous person is free to have their own ideals, thoughts and conceptions of what is good (Callan 155).  Someone whose thoughts and morals are subordinate to another person because of his or her power over them or molding of their character is not an autonomous person; he or she is ethically servile. Students need to be free to have their own opinions and thoughts. John Dewey in his writing Experience and Education explains that “a sound instinct which identifies freedom with power and frame purposes and to execute or carry into effect purposes so framed” (Dewey 67). Freedom allows one to do what he or she believes in. I believe students that are forced into believing what another person says is true will never fully come to accept that to be true. A classroom should be set up in a manner that cultivates the independence. To accomplish this, the teacher can encourage the students discuss their own ideas of a certain subject area and allow the students to further their study of content of their choice in that subject area. The teacher will need to guide their student to have the experiences needed to gain the information or virtues the teacher plans the student to take away. However, the teacher should not force their ideals on the student.

            In my vision of education a school would be structured in a manner that allows the students to be inquisitive and come to learning about the world and their beliefs through experience. I believe that being able to question and understand is two of the most valuable skills that a student should have.  Students should have the skill to be inquisitive; by questioning everything that does not seem right, or questioning what they want to know more about, they would come to a greater understanding of the world. Humans are able to find truth through their senses and experimentation, but they will never know if the truth they find is the actual truth. By being inquisitive and learning from firsthand experience the student will be able to gain a deeper understanding of the subject. A method that utilizes experiential learning is one that uses one’s own hands as a connection to the world. Mathew Crawford in his book Shop Class as Soul craft: An Inquiry to the Value of Work explains how “we are led to consider how the specifically human manner of being is lit up, as it were by man’s interaction with his world through his hands” (Crawford 64).  By experiencing an object with their hands one is learning through tactile sensory method. I have seen this method in use in an elementary math class by creating less or greater then values using M&M’s and in a science class where the students were asked to create simple machines. The students are able to learn through concrete examples that instead of abstract concepts, which can aid the student in coming to a deeper understanding of the concept.

            The teacher would also need to teach with a method that is conducive for students to deeply understand a subject and is not based on memorization. Lessons with objectives that are based on the higher level on the Blooms Taxonomy (applying, analyzing, evaluating, and creating) emphasize meaning, rather than memorization. Teachers should utilize these methods of teaching since it will aid the students in being engaged and active learners. These methods will also help the student gain the reasoning behind the subject and will be more able to reflect on why a concept is how it is.  In a lesson I taught I utilized the applying method in teaching about the voting process. I had the student fill out pretend voter registration forms, make I.D’s and fill out mock ballots after they researched the platforms of the two candidates. By teaching this lesson in a manner that used a higher level of the Blooms Taxonomy the students were well equipped to explain how one votes and the students were engaged throughout the entire lesson.

            The manner in which a school is set up in can affect the way students are able to learn virtues. I believe that a common school approach over a separate school approach would need to be taken for students to be able to learn these virtues.  A common school is defined as a school that is open to all, hospitable to all reasonable beliefs, and represents the cultural diversity of the society (Callan 164). In common schools students are able to interact and get to know people in the society that are different from them and part of different communities.  A separate school is different from a common since it only welcomes members of a particular group in the society and its educational outcomes vary by the particular group (Callan 164).  Callan explains that “When a dialogical setting excludes diverse voices as a separate school must do by welcoming only those who adhere to its separate educational aims, we are compelled to create imaginary interlocutors if we are to practice reasonableness” (Callan 177). In a separate school the students will not be around others from different communities in their society, so the students will not be able interact with people that have different beliefs or ideals than they do. This will cause the students in a separate school to not have as great an opportunity to gain the virtues of reciprocity, mutual respect and tolerance. Callan states that teaching these virtues to students should “affirm the importance of respecting the many different ways of life individuals permissibly choose within the framework of free institutions, even when those differences divide them at the deepest levels of identity” (Callan 14).

            I believe that the school should be set up in a manner that encourages ordinary conversations between students. Dialogue is an essential means of developing care for others which is an important part of civic virtue. These dialogs should hone intrapersonal reasoning, which will strengthen relationships and build confidence and self-esteem (Callan 203).  To truly understand one persons or a community of people’s point of view and to be open and understanding of their ideas you need to have known someone and have had a social relationship with someone with that point of view. Common schools are an ideal place for this kind of interaction to happen since all different people from a multitude of different communities come together in one place to learn.

A story of a Revelutionary War hero, Sybil Ludington (The Girl who Outrode Paul Revere)

        A community can be a group of people big or small, a million miles apart or just next-door, but all having some aspects in common. These communities can be drastically altered by an event that changes or threatens the function of these communities.  In the American Revolutionary War the American settlers were trying to gain their independence from Britain, which affected the community of the American colonists. On April 26, 1777 when the British army marched into Danbury, Connecticut and started to burn the city, the people that lived in Danbury and the Hudson Valley were in danger of being destroyed (Danbury Historic Society).  One of the members in the community was Sybil Ludington, who stood up to save her community from being destroyed.  The community of American Patriots, and Sybil Ludington’s bravery directly aided in saving the Hudson Valley and Danbury from the British in 1777. Still to this day, one can learn from this community’s patriotism.

            The residents that lived in the southeastern part of the Hudson Valley, New York, into Danbury, Connecticut felt strongly about their country and community breaking free from the British rule. The Southeastern Hudson Valley, especially the counties of Dutchess, Putnam and the Danbury area in the seventeen hundreds was an area of small towns that were interconnected by trade and easily accessible to each other.  The interconnections of the towns meant that the townspeople in the community knew and relied on each other. The article “Sybil Ludington” by the Patterson historic society, describes the Hudson Valley area as a home to the Seventh Dutchess County Militia. This militia had four hundred volunteers and was under the instruction of Col. Henry Ludington. The volunteers were scattered throughout the Hudson valley (Historic Society of Patterson). The militia demonstrated the values of the community, since many of its residents were volunteers.

This area was a key part in the American Revolution. In the book Glory, Passion and Principle by historian Melissa Bohrer points out that the southeastern Hudson valley was the “most direct route between Connecticut and the long Island Sound” (Bohrer6).  This demonstrates that this area was crucial for the Continental Army. “It was the most dangerous to defend: sandwiched on both sides of deep woods” (Bohrer6). The topography was very rural, rugged, densely covered with trees, and very difficult to navigate. The article “American Revolution in Danbury” by the Danbury Museum and Historical Society explains to readers that the many goods needed by the continental army were stored in Danbury. “There were about 3000 barrels of pork, more than 1000 barrels of flour, several hundred barrels of beef, 1600 tent, 2000 bushels of grain, besides many other valuable articles” (Danbury Museum and Historical Society). The surplus of goods made the community an asset for the Continental Army. The British army also had knowledge of the wealth of this community, and as a result this lead to the British’s attack on Danbury.

When the British army threatened the area, Sybil took lead to help her community to fight back. On April 26, 1777 the British forces of two-thousand men marched into Danbury to burn the town down and destroy the military stores. This was done as a way to prevent the Continental army from using the supplies (Danbury Museum and Historical Society).  Fear spread throughout the community. When a messenger rode to Col. Henry Ludington’s house in the Hudson Valley and told him the news that the British were invading Danbury, Col. Ludington’s oldest daughter Sybil volunteered herself to take the perilous journey to warn the community. Sybil, who was only sixteen, went out on horseback to round her father’s men who were scattered in the southeastern Hudson Valley, to save Danbury. Sybil rode on her horse for forty miles around the area sounding the alarm (Historic Paterson, New York). According to Sybil Ludington a Call to Arms by V.T Dacquino, a local historian, “Key people in each village heard her banging on their shutters and, in turn, alerted the local contingent while she rode on to compete her mission” (Dacquino 30). Dacquino explains that she rode on rough terrain at night in the pouring rain and at one point in her journey she needed to hide from British loyalists who were crossing her path (Dacquino 30).  One can see that the community had to work together to sound the alarm and to gather together the Seventh Dutchess County Militia to meet at Col. Henry Ludington’s headquarters.

The British tried hard, but the Community of American Patriots in the Hudson Valley and Danbury would not let anyone destroy their community and their dream. After Sybil Ludington completed her mission, the Seventh Dutchess County Militia gathered and marched into Danbury. Dacquino described them as, “A motley company, some without arms, some half-dressed, but all filled with a certain berserk rage. They were short of ammunition and outnumber three to one” (Dacquino 30). Even though this community was unequipped they fought with a will that came from within.  According to Dacquino, they fought the British by firing behind trees, fences, and stone walls from all angles. The Continental troops of Bethel, Connecticut, and Peekskill, New York, who had been alerted of the burning of Danbury by other dispatchers from the Continental Army, together with the Col. Ludington’s troops forced the British to retreat and abandoning their plains of invading Dutchess, and Putnam County (Dacquino 32). With the help of Sybil Ludington and troops from Bethel and Peekskill the Seventh Dutchess County Militia was able to keep the British from destroying Danbury.

Sybil Ludington’s passion for her community can teach people how just one person’s actions can make a difference in a community.  Sybil was raised in this community seeing her father fight in what he believed in; the right to have a free country. With the attitude of believing in the need to be free constantly around her, she felt that it was her duty to protect what her community believed in. What Sybil Ludington did was dangerous, but in the end she knew that she could not let the British destroy her community and her community’s dream of freedom. Sybil was only a sixteen year old girl, but her age did not stop her from saving her community. Anyone can do this, stand up for what they and their community believe in. One does not need to go so far as to risk their lives, like Sybil Ludington did; all they need is to be advocates for their community and stand up to obstacles that will challenge or threaten what their community believes in.

Together as one, the bravery of the American Patriots, like Sybil Ludington, were able to overcome the forces of the British. This community acted together to shape and secure their future so they could evolve into the community that it is today. Community brings people together in hard times and in good times; people of a community will be there for each other in times of need. When ones passion comes from within one will do anything to be certain that their community will survive. Community does not shape the dreams of its people; it is the dreams of its people that shape the community.

 

Tips for Understaning fractions

Fractions are a difficult concept for many students to grasp. Students often see fractions as an abstract concept that is nonsensical if the students do not receive proper instruction on understanding the meaning of fractions.

            Partitioning and iteration fractions are tools to aid understanding of the meaning of fractions and aids operating on fractions.  Partitioning according to the article “consists of creating smaller, equal-sized amounts from a larger amount” (Siebert, Gaskin).  This means one takes a whole or larger amount and cuts/partitions that amount into equal sized pieces from that one amount. Iterating consists of “making copies of a smaller amount and combine them to create a larger amount” (Siebert, Gaskin).  This means that one takes a smaller amount and makes exacts copies of that amount to create a larger amount. For example, one makes four copies of ¼ to make a whole. Partitioning and iterating can be used with any fraction even if the numerator of the fraction is more than one. Both partitioning and iterating is needed when working with fractions since “without partitioning, the creation of smaller, equal-sized larger pieces is difficult; without iteration, the creation of larger pieces from smaller ones is difficult” (Siebert, Gaskin).    

            Partitioning and iterating can be a useful tool for understanding operations with fractions, such as multiplication. When one multiplies fractions he or she needs to be aware that “multiplication requires finding the total amount of ones that are in a certain number of groups of a certain size” (Siebert, Gaskin). Partitioning is needed to split the fraction into equal pieces of the group that is being multiplied by and then finding the ones. Iterating can be used to justify the answer.

            For students to be able to understand fractions they need to see that the numerator and the denominator are not whole numbers.  A commonly used term when teaching fractions is “out of”.  This term is confusing and creates an image where the numerator and the denominator are just whole numbers. Also the term “out of” does not indicate the relationship of the parts to the whole, this is why educators should not use the “out of” term when teaching fractions. Terms like “cut evenly”, “separate into equal parts”, and “making copies” should be used instead to indicate partitioning and iterating.

            Fractions can be a confusing concept for many students, but with the appropriate language use and the proper images of fractions students will be able to have a greater understanding of fractions. The use of partitioning and iterating can give students the proper image of fractions and help students to multiply, add, subtract, and divide fractions since it is giving students an image that does not depend on whole numbers.

My Mathematics Story

            I would describe my experience with math in grade school through high school as a love hate relationship. There were points in my experience in math where I was ahead of the class, there were points where I did not grasp the concept being taught, and there were points where I did not even want to try.

            In third grade I remember have the greatest trouble with my multiplication tables. This trouble with multiplication was my lowest point in math and also my greatest struggle. My teacher would have us memorize the multiplication tables and then take a quiz every morning for a month where we needed to answer one-hundred multiplication problems in a small amount of time. I had an extreme amount of trouble memorizing then multiplication tables my parents would sit me down on the kitchen table and have me recite the multiplication table and I was not allowed to pause to think. I felt like having to recite the multiplication table was a form of punishment I was intensely discouraged because I just did not know the answer. My parents also had me try to teach the multiplication tables to my brother to have me better understand how it worked. This method just ended with my brother who was in kindergarten knowing and understanding the multiplication table better than me and was able able to recite the whole multiplication table perfectly.  Still to this day I have not overcome my trouble with doing multiplication and to make up for the knowledge I do not know I use a calculator. From third till eighth grade I really disliked math because of this trouble and did not believe I was good at math even though other than multiplication I was good at it. I remember in fourth and fifth grade not even paying attention to the teacher when he taught because of my dislike for math. I believe I felt that I could not be good at math since I did not know my multiplication table and so much was based of multiplication.

            In eighth grade I my experience in math really peaked.  I had a really great math teacher who was really approachable and when I asked a question I was not fearful that I was wrong. During this year we were learning algebra and I really excelled in this area. I remember the teacher telling me that I was doing really well with the algebra, which made my confidence level with math go up. I remember being confident to go up to the board and solve problems and explaining to the class how I go to the answer. It was the first time I accepted that I was good at math. I believe in eighth grade I had a turning point in math, this was due to my math teacher instructing in a way that was based less on memorization and had more emphasis on learning why we would go about solving a math problem in a certain way. My teacher also made an effort for every concept we covered in that math class to relate what we were learning to the real world. This increased my understanding in mathematics and also gave me problem solving tools. Another turning point I had during eighth grade was being allowed to use a calculator. By being allowed to use a calculator my trouble with the multiplication table did not hinder me anymore and I my knowledge was able to grow instead of being held back.

            In the future I see my relationship with mathematics growing. I want to try to familiarize myself was the math concepts that I have forgotten. I also want to teach math in a way similar to how my eighth grade math teacher taught, where more emphasis is put on understanding then memorizing. A negative future in mathematics for me would me one where I am become afraid of teaching math because of the challenges it might bring. Also I am fearful of teaching my students in a way that does not that does not benefit my students understanding of math and makes my students hate math.

 

                 

This week I assisted sixth grade students with their lab write up for the Science Fair. I was working with a group of sixth grade students on a project that tested if ice cubes melted at different speeds in different liquids. One of the girls in the group had been absent for a couple of science class periods and was behind in understanding what she needed to do for the lab write up and when the classroom teacher came around to help her the teacher asked the other student in the group to catch her up to speed. I noticed by having the peer explain to her what she needed to do helped the student understand what was already done, but did not help her understand what she needed to do next. I realized that the student who was not absent was going to write up the lab and do the next steps of the project with her partner just watching.  At this point I stepped in and asked the other group member what was the next steps in the write up of the lab report were and how can we split those steps so her partner had something to do. I learned from this experience that when a teacher has students working in groups they needed to make sure that every student in the group is on task and knows the tasks that they are responsible for in the group or the proper amount of work may not get done.

Today I was in a sixth grade science class to help the students write up and prepare their science experiments for the science fair. I was able to work one on one with a student developing his experiment on static electricity. While working with this student I realized how important it is to ask questions to the student that will make the student think about what they need to do, rather than tell the student what needs to be done. This occurred when the student was writing their procedure and one of the steps they wrote was not clear. I asked the student “If someone was replicating your experiment would they be able to do it exactly how you did it?” The student then saw how their step was not as clear as it could be. I then explained how if someone was repeating their experiment and did one step differently they could get different result.

Last Monday my Math Methods class went into a nursery school to work with the four year old class. We went into the class to see where the students were developmentally at with math. To do this my math methods class divided up into groups of two and prepared developmentally challenging activities to do with the four year olds . My partner and I prepared two activities in one activity the students needed to copy the pattern we made with the shape titles and then make their own pattern. In the second activity the students had to determine which pile of small and large hearts had more hearts in it. I observed that the students were challenged in both activities.

            In the first activity I found that the students were able to copy the pattern that my partner or I set up for them. When I asked the students what shape came next they were tentative to answer or gave the wrong answer, but when I prompted them by repeating out loud the pattern and reminding them to look at the how the pattern repeated before they were able to give the right answer. When I asked one of the students to make his own pattern he had difficulty with this and just randomly put the shape tiles together to make a shape. When I asked this to another student she was able to make her own pattern that repeated three times and when I asked her where her pattern repeated she was able to answer correctly. With my second activity I had two piles of hearts one pile had 10 small hearts and the other pile had 10 large hearts. When I asked the students which pile had more hearts in it half the students I asked said the pile with the larger hearts and the other half of the students said the pile with the smaller hearts. I then had the students count the number of hearts in each pile. When the students were counting the hearts they had trouble separating the hearts they had already counted with the hearts they did not count and I had to aide them by separating the hearts that the counted. The students were surprised to see that both piles had the same amount of hearts.
 Going into nursery school gave me a perspective to see where the students at four years old were developmentally at. It also gave me as a future teacher a prospective of where I would need to give more explanation when I teach these math concepts.