Category Archives: 2. Papers

You will be able to find here some of my essays about educational topics.

For a complete index of all papers click on the Papers Page located on the left hand side.

Critical Concepts and Attributes Paper, Mathematics

2009/09/14

Critical Concepts and Attributes Paper, Mathematics

Mathematics is a natural science that requires deep cognitive and logical thinking. Many people are afraid of complicated formulas and difficult-to-spot patterns. But I believe that everyone can know mathematics to the certain extent if he starts building on proper basis. We could compare it to the knowledge of building a house.

First, we have to know what materials to use. Bricks, concrete mixture, pillars, etc. are necessary to even start thinking about building something. Similarly, the knowledge of elementary number theory is necessary. One has to know the classification of numbers and basic math vocabulary.

Once we have realised what materials we have, the question arises: “How can we combine bricks with concrete in order to build?” The tools such as a shovel and a temperer are indeed required. The next step in mathematics is to start thinking how the numbers interact among themselves. Arithmetic is probably the oldest and the most elementary branch of mathematics. Nowadays, each single person has to know at least a little bit of basic number addition, subtraction, multiplication, division, exponentials, etc. This is the most important concept of mathematics with which we get familiar at early stages of infant development (adding objects in different games) and we use it persistently even after we retire (cooking meals).

Back to our construction idea, that is all we need to know to build a primitive one-storey hut. But knowing how to combine just bricks and concrete is not enough if we want to build a nice apartment house with several storeys, sewage conduit and so on. We would be so much better off if we could use some pillars, pipes and knew static principles so that nothing falls on our heads. And that is exactly what we need to follow in mathematics – building up on more and more complex ideas. Calculus, being the stairs from the main floor in our house, is undoubtedly one of them. Without calculus we could not proceed to other floors with different rooms of geometry, vectors, linear algebra, etc.

Yes, one could argue that there are other critical concepts to include but we have to be careful not to go too much into details. Remember, we are trying to build just a simple apartment house (which is better than a prehistoric hut), not a complicated gothic cathedral or hotel ‘a la Las Vegas’.

However, we have to keep on mind that the house is not going to build itself; we have to have a  form of labour included. A construction worker has to take each of the bricks manually and pile them up. Analogically, a passionate teacher frankly interested in mathematics needs to be present. If she is not satisfied about being in a classroom or she does not like the subject of mathematics, she is not going to be a great help to students. It is the same with placing a cook on the construction site – he might be skilled in cooking but if he prefers to work inside instead and if he does not want to learn new skills, he is not going to be constructing our house.

Furthermore, the teacher has to have developed logical thinking in a way that she knows connections among different branches of mathematics precisely. If there was a wall which fell while building the house, we would have wanted to have had employed a worker who known what the problem was, why it arose and how to fix it. It is not enough to memorize that we anchor each pillar in the ground; it is important to understand the idea behind stabilizing vertical objects.

Lastly, we want to have a worker who can see that there are many different ways to build a house, but there is only one, the most efficient way. A teacher needs to be open-minded and always fond of welcoming new ideas and solutions. It is certainly a turn off for a student of mathematics who thinks about a problem in a slightly bit different way and she hears that her solution is unquestionably wrong, instead of getting explanation why the other solution is more appropriate. In other words, the teacher needs to be flexible and react to specific needs of her students. Following a book word-to-word is no good if a book does not even think of certain situations. For example, a sudden rain on our construction site located in a desert is something we would have not anticipated at all (Would you keep building the house? Why not? And when yes?).

In conclusion, there are three preliminary theoretical concepts of mathematics and three attributes each teacher should have. But thinking of our example again, would it be possible to build the house quicker? Well, we have only one worker at the moment and he would sure welcome some extra help. A specialized team working on the same project is the goal in math education too; students should posses the same attributes as our teacher does. Though, it is the teacher’s responsibility to strike students’ interest, passion, open-minded approach and logical thinking about the subject.

Home Schooling

2009/04/08

Proposal for The Final Research Essay

Home schools. What exactly is the concept of home-schooling and how does such education work like? Frankly, I have no certain answer now as the topic is “a Spanish garden” for me. The first time I heard about home schools was only a couple of months ago when I arrived overseas. Having grown up in Eastern Europe, I encountered with just a proper public education and a few private schools. The concept of home-schooling, however, seems very interesting and researchable for me. What are some pros and cons of going through such education? Is it independence, or freedom to choose; or does such education isolate pupils from growing up in a social environment with peers?

I will try to investigate the answers for these and similar questions in my Researched Essay. I already know a bit about home-schooling system because I talked to a classmate of mine who has gone through one. I will try to interview her in a more precise manner and I will look for her personal opinion. I wonder how she perceives the differences in between her home school and a college where she studies at the moment.

Similarly, I will try to look up for a faculty member who has experiences with home schools, either from a learner or a teacher point of view (or both).

Moreover, an uncle of mine has just moved from Panama to Canada and he plans to educate his daughters in a home school. Why did his wife, a primary school teacher, and he make such a decision?

And lastly, I will of course research written resources which can be found in a library or on the internet. I expect to gain a valid insight to the topic of home-schooling. My research question is not specified uniquely right now but I will narrow down the field of concentration once I get more information. I am really curious!

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2009/05/07

Home schools: what and why are they?

Homeschooling is an educational system many people have heard about but do not know about in details. It is an alternative option to  common public and private schooling. Since home schools are not officially legal in my home country (Slovakia, Europe), I heard the concept of being educated in an informal setting only a few months ago when I arrived in the US. A classmate of mine went through such an educational system in Pennsylvania and she became one of my main research sources. What are general characteristics of the homeschooling system and people preferring it; and why did home schools originate, became successful and become chosen as a valid educational option? I came to the conclusion that home schools are an upcoming phenomenon:

-a.)   of education with no formal setting publicized in 1970´s;

-b.)   maximizing flexibility and relevancy of topics;

-c.)   usually chosen by privileged families with different family structure;

-d.)   mainly based on family, academic and religious reasons;

-e.)   soon to become a legitimate institutional idea worldwide.

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a.) What the concept is and when it was publicized:

Home schooling is an educational system where students are taught in no formal setting. It can start in young pre-school age as kindergarten or also in late middle school age. The concept was strongly promoted by an American educator, John Holt, in the 1970´s.  He argued that “there is the proper base for exploration of the world which we call learning or education. Home would be the best base no matter how good the schools were.”  He believed that similarly as cubs in the nature, human beings should not be taught in large institutions grouped with peers of the same age but individually in their homes on exploration bases instead. John Holt established GWS (Growing Without Schooling) magazine, which has helped home schooling families for decades.

In like manner, Michedolene Hogan co-authored Unique Parenting, a website where she promotes ideas of Socialization and the Case against Formal Schooling. She thought: “the best foundation for learning occurs in the home. In this case ‘learning’ refers not only to academic knowledge but also to an understanding of the world. Only in the home can children learn to be sociable and be properly prepared for the social environment. The proper atmosphere is in the home. The value system that will shape all other behaviours is learned in the home. The paradigm for learning how to honour and respect authority is found in the home.”  Therefore, she believed that “the best place for children to learn how to be part of their community physically and spiritually is the home”.

Apparently, homeschooling students learn at home most of the time. But not only are they taught by their parents (facilitators) and tutors, they also learn by conversation, reading, playing, outside class volunteering, online tools and topical themes. The idea is to have an individual approach which assures the child´s interest in a topic. Studies have advocated that a child retains 45% more information simply by studying through thematic units with individual interest.  For example, a family relative of my case study was diagnosed born deaf and the whole family, suddenly, had a new aspect to learn about in their lives. They altered the curriculum, included unit studies about deafness, explored backgrounds of the disability, and learned the sign language. They managed to use the time flexibly for their own benefit; we say that the relevancy of the topic yielded the base for successful learning.

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b.) How the system works:

As said in the example above, flexibility and relevancy of the topic were maximized. It is recognizable that such students have school highly integrated in their lives. They can choose to study certain subjects in depth (e.g. the sign language case) or omit certain topics if they consider them irrelevant. Unless aspiring to a career in physics, a farmer from Idaho in his high-school years does not necessarily have to be introduced to Einstein´s Theory of Relativity, he can spend more time getting familiar with the mechanics of tractors instead.

Homeschool students usually utilize local libraries and low cost community resources. However, the chief source is the human interaction and practical learning. Surveys like Homeschooling in the United States: 2003 have shown that only a quarter of homeschoolers use public school books.  Once a student decides to take the education to her own hands, she does not want to follow a standard guide; she wants to gain perspective from various resources. Searching for her own resources teaches her independence. This characteristic is shared across all types of homeschooling.

There is no single homeschooling type to be described specifically though, since the system includes various methods also found in private schools (i.e. Montessori, Waldorf). In general, home schools utilize the eclectic approach of mixed themes: art, history, mathematics, science, theology, ‘flora or fauna’ or ‘American slavery or ancient Rome’. Moreover, different states have individual laws for the system. For example, California requires official teaching credentials from anyone teaching at home (since 2008), and that should virtually assure the quality of education and absorption of knowledge. California does not require any official statement or exam to be passed on the end of an academic year.

On the other hand, Pennsylvania offers free textbooks from public schools, requires 180 self-scheduled school days and, beginning the 3rd grade, asks to keep a portfolio with a logbook that are checked on the end of a usual academic year. Then an evaluator writes a letter to a superintendent, either approving or prohibiting further home school education.

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c.) Who chooses home schooling:

It is important to recognize a historical parallel of home schools. Education in Middle-Aged Europe (early 16th to late 18th century) was not compulsory and only privileged families could afford private tutors. Otherwise, everybody was educated either at home or in a community by mutual sharing of knowledge. After the Theresian School Reform of 1774 in Early-Modern Europe, education became compulsory and public.  However, the first public schools were communal and students were taught in joined classes. Multiple grades were taught at the same time and grade classification became common only in the early 20th century. Up until then, students were mixed in different age groups and could explore the world in a more natural way.

Nowadays, families who recognize the benefits of social interaction with individuals at various ages decide to provide homeschooling for their children. But as it was with European private tutors, home schooling asks for a stronger financial background. There has to be at least one stable income. Statistical studies have shown that four fifths of homeschooling families have two white parents, while one half of such families has a non-working parent at home.

Furthermore, more than a half of all homeschooling mothers and fathers finished at least a bachelor degree of post-secondary education.  They are well educated themselves and they are willing to take a risk of being responsible for their children’s education. It is also common that a parent is a professional teacher. Then he does not necessary have to sacrifice his career for the sake of spending more time at home; he can fulfill his desire to teach and spend more time with children, thence strengthening the family bonds too.

Homeschooling families have usually closer relationships and tend to function well on mutual understanding and cooperation basis. If a child knows a topic, let´s say basic multiplication in math, she can tutor her siblings. The family structure of such families is different from those of regular ones.

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d.) Why they choose so and what the effect is:

There are numerous reasons why people choose homeschooling. One of the most common ones is the religion. Parents do not agree with what is being taught in schools and therefore they want to preserve certain beliefs in children’s minds. This is, however, a dangerous approach because of its outcome. If children are supposed to interact with the rest of the world, they will sooner or later find out what other people think; the reason of homeschooling will have not been achieved anyway. And if the children are supposed to stay in a closed community, they may keep the beliefs; but the risk of potential development of religious and social extremism and parallel societies will have occurred. That is, however, highly undesirable in these days of social and intra-cultural tension. Homeschooling should be chosen from different reasons instead.

The other most common reason is the academic one originating from the idea that parents can give better education to a child at home. Especially in rural and suburban locations of the western USA, public schools are unreachable and their quality is low. Parents judge that the academic failure of schoolchildren is caused by pressure played on children in schools and they correctly believe that they can do a better job on their own. Academic Statistics on Homeschooling have shown that homeschoolers outperform their peers at standardized tests.  Moreover, studies have shown that “homeschoolers have a more positive self-concept than their schooled peers; they are more likely to have friends of different ages and to be free of the cliquish, exclusive behaviour so common in school.” Homeschoolers are actively involved in community actions, creative and sport clubs and therefore the worry of social isolation caused by studying at home is groundless.

Lastly, the third main reason is the family reason. There are families who travel a lot due to work expectations and there are also families who would like to preserve cultural heritage, mostly by providing a bilingual education. For example, an English-Spanish family of my Canadian uncle has moved back to francophone Montreal from Panama lately and they want to keep providing education to the children in Spanish as a main language. Furthermore, the quality and safety of public schools there is not what they desire. Since my aunt is a teacher, they are strongly considering the home schooling option.

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e.) What can we expect in the future:

The USA has the highest percentage of homeschoolers comparing to other countries. The boom of homeschooling happened in 1970´s in the US. While there were only 15,000 such students in 1970, there were 500,000 already in 1990.  Similarly, student body from 1999 of 850,000 homeschoolers expanded onto 1.1 million homeschoolers in 2003.  In 4 years, that was a significant increase from 1.7% onto 2.2% of total US student population. It is estimated that there were around 2 million homeschoolers after another 3 years (in 2006), i.e. circa 4%. It is notable that so far rare homeschooling is becoming more and more popular these days and the trend will remain in the following years.

Considering the facts that home schools are illegal in most of the parts of the world and they are legal only in a few mostly western countries (USA, Canada, UK, France, etc.) where they are successful and popular among a specific population group, we can expect that more countries will look into the alternative option of education in upcoming decades. In conclusion, homeschooling will then become a legit institution worldwide similarly as public and private schools are now.

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RESOURCES:

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-interview:

Thanks to Olivia Grugan who found her 1h of time on Sunday, May 3, 2009.

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-books:

Collins J.B., Taylor K.L.: Early modern Europe: issues and interpretations. Oxford: Wiley-Blackwell, 2006 (ISBN 0-631-22893-4).

Bauman K., Home Schooling in the United States Trends and Characteristics. Washington, D.C.: U.S. Census Bureau, Population Division, 2001.

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-digital publications:

http://permanent.access.gpo.gov/lps17744/www.ed.gov/offices/oeri/sai/
homeschool/homeschoolers.pdf
http://www.austega.com/gifted/articles/Hogan_Againstformalschooling.htm
http://www.bropay.net
http://www.en.wikipedia.org/wiki/Homeschooling
http://www.en.wikipedia.org/wiki/Homeschooling_in_the_United_States
http://www.en.wikipedia.org/wiki/John_Caldwell_Holt
http://www.epaa.asu.edu/epaa/v7n8
http://www.ezinearticles.com/?expert_bio=Michedolene_Hogan
http://www.holtgws.com/faqabouthomescho.html#What%20is%20Holt%20GWS
http://www.hslda.org/docs/nche/000010/200410250.asp
http://www.nces.ed.gov/pubs2006/homeschool/index.asp
http://www.nces.ed.gov/pubs2006/2006042.pdf
http://www.thehomeschoolmom.com/teacherslounge/styles/unitstudymethod.php
http://www.uniqueparenting.com/