{"content":{"sharePage":{"page":0,"digests":[{"id":"34051836","dateCreated":"1297405050","smartDate":"Feb 10, 2011","userCreated":{"username":"crystalgremillion","url":"https:\/\/www.wikispaces.com\/user\/view\/crystalgremillion","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"},"monitored":false,"locked":false,"links":{"self":"https:\/\/klam-emeralds.wikispaces.com\/share\/view\/34051836"},"dateDigested":1532763025,"startDate":null,"sharedType":"discussion","title":"Papert","description":"From the Papert article, what do many children think causes the wind? Why do such theories matter for Piaget? What might this mean for teaching?","replyPages":[{"page":0,"digests":[{"id":"34134636","body":"Children think that movement of objects causes the wind. However if we look further, this shows that many times when children are wrong, their thinking can be right. Piaget suggests that many times adults will just look on the surface of an answer and consider it wrong but if the answer is disected, they will find the answer to be "entirely sensible and coherent within the framework of the child's way of knowing". He goes on to suggest that if adults continue to tell the child that his answer is wrong, the child will eventually stop making their own theories. This idea is crucial to teaching because the ability to think deeper, enough to question ideas and formulate theories is a crucial tool in student success. If children can be motivated to continue making elaborate and sensible theories, they can use that tool of deeper thinking and questioning to further understand lessons.","dateCreated":"1297579884","smartDate":"Feb 12, 2011","userCreated":{"username":"HalaSiddiqui","url":"https:\/\/www.wikispaces.com\/user\/view\/HalaSiddiqui","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34169058","body":"In this article, when the child is asked about the cause of wind, they say that it is because of the trees, waving there arms. To me, this makes sense, because when you move your hand, or wave it, it produces wind, sort of. Piaget was interested in these theories because the way a child makes up their own theories gives a lot of information about the workings of their mind. It helps to see the reasoning behind the idea, and helps to figure out what the development process is with a young mind. From a teaching standpoint, this is important to know because just simply telling a child that their wrong every time makes them disinterested and makes them want to give up. The focus in teaching is not whether the child is right or wrong, it is about how they arrived at that answer and why they did. If everything was so black and white, people wouldn't learn a thing. A teacher needs to know the thinking process of the child in order to better understand how to help them learn.","dateCreated":"1297658252","smartDate":"Feb 13, 2011","userCreated":{"username":"admiller2","url":"https:\/\/www.wikispaces.com\/user\/view\/admiller2","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34170438","body":"According to this article, a child explains that trees cause wind because they "wave their arms" and on land, waves produce the wind. To Piaget, this is crucial because although the theories are sometimes bizarre, bizarre theories are often formulated by observations. It's not the result that is important here, rather the mental stimulation that drives it. Piaget believes that if these simple misconceptions were addressed, it would de-motivate a child's natural curiosity because no one wants to be confronted and told they are wrong.
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\nThis perhaps means that children may not be ready for constructive criticism in certain areas. To me, this means that although children may not be ready for scientific explanation, they are still ready for mathematical explanation (counting, addition etc) and language studies (reading, writing). Children at young ages believe Santa Claus is plausible. It is more important to their young minds to think, than to be correct.","dateCreated":"1297662908","smartDate":"Feb 13, 2011","userCreated":{"username":"Caseyb.crittenden","url":"https:\/\/www.wikispaces.com\/user\/view\/Caseyb.crittenden","imageUrl":"https:\/\/www.wikispaces.com\/user\/pic\/1296425910\/Caseyb.crittenden-lg.jpg"}},{"id":"34170732","body":"Children think that trees and waves make wind. To us, it seems silly because most of us know that wind is caused by air flowing from high pressure to low pressure. However, to Piaget, their answers are very significant because it gives us access to children\u2019s mind. He believes that \u201cthe key to human knowledge might be discovered by observing how the child\u2019s mind develops\u201d (Papert). It\u2019s not important whether the answer is right or wrong, it is the thinking processes behind an answer that he cares about. It shows that children are already having the ability to reason and form their own hypothesis. What might this mean for teaching? Instead of beating down their own natural way of learning with hard facts, teacher should utilize it and be the person to guide it toward the right direction. Teachers should not discourage their reasoning; they should encourage it.","dateCreated":"1297664265","smartDate":"Feb 13, 2011","userCreated":{"username":"TuyenN","url":"https:\/\/www.wikispaces.com\/user\/view\/TuyenN","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34173772","body":"According to the article,many children think, winds are caused by movement of trees in the land and the waves in the sea. Piaget values these theories because it shows the child's thought behind the answer. Piaget says, "Children have real understanding only of that which they invent themselves, and each time that we try to teach them something too quickly, we keep them from reinventing it themselves." When it comes to teaching teachers must understand that children build knowledge on their own therefore the must encourage the student to develop their own theories rather than feeding them with facts and not just judge the student by an answer but also question the reason behind it.","dateCreated":"1297680995","smartDate":"Feb 14, 2011","userCreated":{"username":"Ebbybaby","url":"https:\/\/www.wikispaces.com\/user\/view\/Ebbybaby","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34232278","body":"I'm glad that we're all agreeing on this subject matter. This is a response to everyone's post. We all see that the child's ability to form hypotheses that although not scientifically accurate, are still somewhat based on logic. As teachers, we are to encourage their thinking, yet be critical at times. I'd like to pose another question. How can teachers inspire this independent thought and teach correct information?
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\nI believe that one way to encourage this level of thinking would be to ask children general questions such as why the wind blows for a homework assignment before a new lesson plan. The children wouldn't have to look up much if any for the assignment. There are of course classes where this would be foolish, but it could be applied on an elementary level.","dateCreated":"1297737383","smartDate":"Feb 14, 2011","userCreated":{"username":"Caseyb.crittenden","url":"https:\/\/www.wikispaces.com\/user\/view\/Caseyb.crittenden","imageUrl":"https:\/\/www.wikispaces.com\/user\/pic\/1296425910\/Caseyb.crittenden-lg.jpg"}},{"id":"34276034","body":"In response to Casey, I agree with what you say about how children can still learn about math and language. However, I think that we can teach them about science too. Teachers should do a better job at encouraging kids to discover the world around them by doing a lot more inductive lessons. That way we could lead them to the right direction and preserve or even improve their critical thinking.","dateCreated":"1297798728","smartDate":"Feb 15, 2011","userCreated":{"username":"TuyenN","url":"https:\/\/www.wikispaces.com\/user\/view\/TuyenN","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34306582","body":"Casey
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\nindependent thought is really important to the students creativety. a way we can move away from this wrong\/right answer way of thinking is by placing creativety as a requirement on lesson plans and rubrics. my world history teacher use to save a place in the rubric for creativety so that we were forced to do something out of the norm. She wouldnt give us ideas like so many teachers do, this forced us all to do really different things and to this point I remember some of the topics we learned.","dateCreated":"1297821182","smartDate":"Feb 15, 2011","userCreated":{"username":"HalaSiddiqui","url":"https:\/\/www.wikispaces.com\/user\/view\/HalaSiddiqui","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34314144","body":"Casey
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\nI think debates and projects that requires critical thinking are one way to get the students to think independently. This way we get to understand the students thoughts. Allowing the student to present these project also gives opportunity for other students to share their thoughts, and as a teacher we can correct any misconception that comes along the way too. These methods encourage independent thinking.","dateCreated":"1297827498","smartDate":"Feb 15, 2011","userCreated":{"username":"Ebbybaby","url":"https:\/\/www.wikispaces.com\/user\/view\/Ebbybaby","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}}],"more":0}]},{"id":"34051742","dateCreated":"1297404697","smartDate":"Feb 10, 2011","userCreated":{"username":"crystalgremillion","url":"https:\/\/www.wikispaces.com\/user\/view\/crystalgremillion","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"},"monitored":false,"locked":false,"links":{"self":"https:\/\/klam-emeralds.wikispaces.com\/share\/view\/34051742"},"dateDigested":1532763026,"startDate":null,"sharedType":"discussion","title":"Gardner - Intelligence","description":"Piaget suggests 4 stages of cognitive development. How do you know when a person has moved from Stage 3 to Stage 4? Let\u2019s assume that there could be a Stage 5. What would be the characteristics of people in Stage 5? How would that be different from Stage 4?","replyPages":[{"page":0,"digests":[{"id":"34135068","body":"In stage 3, a child can perform and undo mental operations that are based on concrete objects. However a stage 4 is not limited by concrete objects, the child is comfortable thinking about concepts, theories, and ideas as basis of mental operations. Piaget's four stages are built upon one another so a stage 5 would be built upon the abilities of a stage 4. However, it would be different from stage four because it would make the seemingly complete and full stage incomplete or limited. The biggest characteristic of people in stage 5 would be the age group. Stage 4 stops at teenagers so stage 5 would be composed of adults and ideas on brain functionality that makes them so different. As was pointed out in the article, not many genius' or inventors have been teenagers so what characteristic trait apart form maturity do the teenagers lack and adults have.","dateCreated":"1297583275","smartDate":"Feb 12, 2011","userCreated":{"username":"HalaSiddiqui","url":"https:\/\/www.wikispaces.com\/user\/view\/HalaSiddiqui","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34167594","body":"A person in stage three has moved to the forth stage when they are able to think about the world in theoretical terms. This means that they no longer rely on the need to have a concrete object, they can now make postulates about the world in using ideas, theories, and concepts that cannot be tested or measured in any reasonable way. They can come up with hypothetical situations. People in stage three will not be able to deal with the complexity of these kinds of themes. Some one moving on to stage five would have to of obtained some even higher level of thought beyond the theme of theories and concepts. They would probably be at the level of high school graduate more or less, going on into old age.","dateCreated":"1297655399","smartDate":"Feb 13, 2011","userCreated":{"username":"admiller2","url":"https:\/\/www.wikispaces.com\/user\/view\/admiller2","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34170214","body":"A child in stage 3 is characterized as being capable of concrete operations. This name is given because a child in this stage can understand how to reach and prove a conclusion that is based on concrete objects. However, a their thinking is somewhat limited to a 1 variable system. A child in stage 4 is characterized as being capable of formal operations. They still share a similar thought process to a child in stage 3, but they are able to understand the concept of multiple variables. They have become much more aware of the world around them (a teenager pays much more attention while riding in a car than does a stage 2 child, also possibly due to becoming drivers).
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\nSince stages seem to be affected by schooling, a stage 5 would likely refer to someone who has undergone post-high school schooling. Someone wouldn't become a stage 5 thinker once they enter college (it could even arise while in high school in some cases), or necessarily ever in college. Many cases where a child had proved to become a next level thinker was done in a science laboratory. Not to sound like an elitist, but post high school math\/science classes force students to think on higher levels. Understanding science increases understanding of the world around you, which is also another indicator of higher level cognitive development.","dateCreated":"1297662049","smartDate":"Feb 13, 2011","userCreated":{"username":"Caseyb.crittenden","url":"https:\/\/www.wikispaces.com\/user\/view\/Caseyb.crittenden","imageUrl":"https:\/\/www.wikispaces.com\/user\/pic\/1296425910\/Caseyb.crittenden-lg.jpg"}},{"id":"34171778","body":"According to Piaget suggestion, children in third stage develop an ability to think conceptually. During this time, children gain a better understanding of mental operations. Children begin thinking logically about concrete events, but have difficulty understanding abstract or hypothetical concepts. On the other hand children in forth stage do not need a physical abject to make rational judgments. In this stage, children do not have a difficulty using deductive logic, which involves using a general principle to determine the outcome of a specific topic or event. I think stage five would be different then stage four because children age would be different from stage four. I believe High School and college level student should count in stage five because their ability of thinking is more advance level.","dateCreated":"1297668696","smartDate":"Feb 13, 2011","userCreated":{"username":"RAHIMMOMIN","url":"https:\/\/www.wikispaces.com\/user\/view\/RAHIMMOMIN","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34173326","body":"Stage 3 children can see from a perspective of a different person like picture mentally of an object from someone's else viewpoint, and can also perform mentally reversing mental operation. But it is difficult for these children to understand theoretical concepts therefore they can only apply one variable to a given concept from the two that are in conflict. Unlike stage 3 children a person from stage 4 usually in their adolescence have the ability to develop new theories when two variables are in conflict, They can comfortably think about thoughts ideas and concepts.
\nAssuming there is stage 5 i think the people in the fifth stage would be college students with the ability to analyze different concepts and to critically think.","dateCreated":"1297677708","smartDate":"Feb 14, 2011","userCreated":{"username":"Ebbybaby","url":"https:\/\/www.wikispaces.com\/user\/view\/Ebbybaby","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34178380","body":"In the third stage, the concretes operations stage, children begin to construct schemes that let them decenter their thinking. In other words they are able to attend two or more dimensions of a stimulus at the same time. This enables them to understand reversibility and conservation. Children at this stage are able to apply logical operations only to problems that can be tested in real life. In the fourth stage, the formal operational stage, children\/teenagers uses schemes to apply logical thinking to a series of hypothetical propositions. In order for them to move from the third to the fourth stage, children must construct a scheme that allows them to coordinate present reality with other possible realities. If there\u2019s a stage five, young adults are able to apply logical thinking with consideration of extraneous factors to a series of hypothetical propositions. In stage four, they are able to construct an imaginary reality that is linked to present reality. However, they display a type of thinking that Piaget called na\u00efve idealisms. Meaning their plays always work out the ways that they wanted to. Stage five would be different because they would be able to calculating in other factors that can change the outcome of their hypothetical propositions.","dateCreated":"1297692267","smartDate":"Feb 14, 2011","userCreated":{"username":"TuyenN","url":"https:\/\/www.wikispaces.com\/user\/view\/TuyenN","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34311494","body":"Casey,
\nI also think that science\/math is a great start to higher level thinking. The fields of math and science explain so many things about the world that we live in, and there are so many things still unexplainable as of now. The more we know, the more that we can ultimately do with that information, and the better we can be.","dateCreated":"1297824750","smartDate":"Feb 15, 2011","userCreated":{"username":"admiller2","url":"https:\/\/www.wikispaces.com\/user\/view\/admiller2","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34327100","body":"Hala
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\nI think there is more than just maturity in adults that make them different from a teenagers way of thinking. because this would mean that the older you get the better you think but this may not be the case always","dateCreated":"1297864106","smartDate":"Feb 16, 2011","userCreated":{"username":"Ebbybaby","url":"https:\/\/www.wikispaces.com\/user\/view\/Ebbybaby","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}}],"more":0}]},{"id":"34051678","dateCreated":"1297404468","smartDate":"Feb 10, 2011","userCreated":{"username":"crystalgremillion","url":"https:\/\/www.wikispaces.com\/user\/view\/crystalgremillion","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"},"monitored":false,"locked":false,"links":{"self":"https:\/\/klam-emeralds.wikispaces.com\/share\/view\/34051678"},"dateDigested":1532763027,"startDate":null,"sharedType":"discussion","title":"Gardner - Cognitive Science","description":"Describe assimilation and accommodation. Provide an example of each from personal experience.","replyPages":[{"page":0,"digests":[{"id":"34128914","body":"The words "assimilation" and "accommodation" are very often being related to Piaget's theory of cognitive development. According to his theory, the way in which human knowledge develops is primarily through the process of organizing. In other words, experiences are grouped; we use specific experiences in the past to make inferences to new experiences. Piaget uses the word \u201cassimilation\u201d to refer to \u201cthe process of new objects, experiences, and information are incorporated into existing schemes\u201d (Wood 316). There are many instances when I used accommodation. When I was little, I was always amazed at how balloons can float in the air. So one day my mom blew up for me a big red balloon. I was so excited because I expected it to float and that it would fly away if I let go of the string. One the other hand, the word \u201caccommodation\u201d is slightly different. Accommodation is the term Piaget uses for \u201cthe mental process of modifying existing schemes and creating new ones to incorporate new objects, events, experiences, and information\u201d (Wood 316). So let us go back to the balloon example that I gave earlier. When I let go of the balloon that my mom just gave me, I was very confused to find that it was gently falling down instead of floating upward. So then I began to categorize balloon into two kinds: ones that float and ones that don\u2019t.","dateCreated":"1297559362","smartDate":"Feb 12, 2011","userCreated":{"username":"TuyenN","url":"https:\/\/www.wikispaces.com\/user\/view\/TuyenN","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34134488","body":"Assimilation is fitting new observations into old knowlegde, "existing schemas". I use to use this a lot when I was tring to memorize a concept. Instead of rote-memorization, which I was never good at, I would try to fit the new knowlegde into my old experiences. Accommodation is almost like the opposite of Assimilation, it is when you change old ideas or knowledge to fit into new experiences or knowledge. When I was younger I saw my cousin doing his calculus homework and what stuck out to me were the letters. I remember trully believing that there was a formula to adding and subtracting letters just as there was for numbers. Later I changed my incorrect beliefs when my I was introduced to pre-algerbra and I learned that the letters represent a number.","dateCreated":"1297578541","smartDate":"Feb 12, 2011","userCreated":{"username":"HalaSiddiqui","url":"https:\/\/www.wikispaces.com\/user\/view\/HalaSiddiqui","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34149182","body":"Assimilation and accommodation in this context refer to cognitive development of the human brain. Assimilation refers to the mind's ability to process new information and experiences and relating and grouping them with previous knowledge. Accommodation refers to sculpting of pre-existing knowledge with relation to new information and experiences. They are both crucial for the mind to be able to process new information with no corruption of pre-existing or new knowledge.
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\nA personal experience I have had with accommodation and assimilation is when I first learned about negative numbers. My mind fitted the concept of negative numbers with respect to positive numbers through assimilation. My mind then used accommodation when I began to relate algebraic operations (addition, subtraction etc) to negative numbers as well. The only thing that really changed for me was the number line.","dateCreated":"1297630137","smartDate":"Feb 13, 2011","userCreated":{"username":"Caseyb.crittenden","url":"https:\/\/www.wikispaces.com\/user\/view\/Caseyb.crittenden","imageUrl":"https:\/\/www.wikispaces.com\/user\/pic\/1296425910\/Caseyb.crittenden-lg.jpg"}},{"id":"34168156","body":" Assimilation and accommodation both refer to the minds ability to learn things about its surrounding environment. Assimilation happens when you take something from the environment and take it in to be a part of an already existing scheme, or network, in your brain. Accommodation is sort of the reverse of this action, where you conform your idea, an existing scheme, in order to adjust to something that is influencing you in your environment.
\n A good example of this that I could think of off the top of my head is studying. Studying is a scheme that already exists, something I practice for all of my classes, taking in new information and building more complex schemes. Studying would be assimilation. An example of accommodation would be when I study a little harder for my K&L or chemistry class because a normal amount of study time is not adequate! In studying for these two classes more, I have conformed to the environment, and have modified myself to do so.","dateCreated":"1297656372","smartDate":"Feb 13, 2011","userCreated":{"username":"admiller2","url":"https:\/\/www.wikispaces.com\/user\/view\/admiller2","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34174128","body":"Assimilation and accommodation are the terms given by Piaget for the process by which we learn things. Assimilation is the process where we add things from the external environment to our existing knowledge. An example for assimilation would be learning harmony for a song I already know.
\nAccommodation is the process where our minds modifies the knowledge according to the external environment. An example for accommodation would be singing according to the key the music is played.","dateCreated":"1297682451","smartDate":"Feb 14, 2011","userCreated":{"username":"Ebbybaby","url":"https:\/\/www.wikispaces.com\/user\/view\/Ebbybaby","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34186422","body":"In response to Hala, according to Piaget assimilation is the process of the brain that creates new schemes for new experiences; it does not change schemes that already exist. I think you are mistaking it for cognitive psychology with their information-processing theory.","dateCreated":"1297698940","smartDate":"Feb 14, 2011","userCreated":{"username":"TuyenN","url":"https:\/\/www.wikispaces.com\/user\/view\/TuyenN","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34310632","body":"Tuyen, I'm going to have to disagree with you on the assimilation idea. Assimilation is the idea that you treat aspects of your environment in a way, so that they can become part of an already existing scheme.","dateCreated":"1297824087","smartDate":"Feb 15, 2011","userCreated":{"username":"admiller2","url":"https:\/\/www.wikispaces.com\/user\/view\/admiller2","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}}],"more":0}]},{"id":"34051456","dateCreated":"1297403664","smartDate":"Feb 10, 2011","userCreated":{"username":"crystalgremillion","url":"https:\/\/www.wikispaces.com\/user\/view\/crystalgremillion","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"},"monitored":false,"locked":false,"links":{"self":"https:\/\/klam-emeralds.wikispaces.com\/share\/view\/34051456"},"dateDigested":1532763028,"startDate":null,"sharedType":"discussion","title":"Driver","description":"Piaget believed that formal thought develops at 12 years of age, but other researchers have suggested that it actually develops much later. Identify some characteristics of formal thought. Do you think it is possible to teach subjects such as physics and calculus to students who have not yet developed formal thought processes?","replyPages":[{"page":0,"digests":[{"id":"34134088","body":"The basic characteristic of formal thought is the ability to manipulate propositions. Through formal thought, the child can manipulate and think about many variables while questioning the relivance of each variable. With these characteristics of formal thought in mind, I do not believe that teachers can successfully teach physics and\/or calculus to children who have not developed formal thought processes. Calculus and Physics are similar in that both subjects deal with manipulation of multiple variables. One example is setting up an integration problem and solving it. From my experience in calculus, just the task of setting up the intergal range for an integration problem requires some deeper thought that would only be seen in formal thought processes.","dateCreated":"1297576108","smartDate":"Feb 12, 2011","userCreated":{"username":"HalaSiddiqui","url":"https:\/\/www.wikispaces.com\/user\/view\/HalaSiddiqui","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34138760","body":"The formal operations stage of Piaget\u2019s stages of cognitive development is characterized by "the ability to apply logical thinking to abstract problems and hypothetical situations\u201d (Wood 322). Since physics and calculus require the application of logical thinking to a series of hypothetical propositions, it would be very difficult to teach these subjects to students who have not yet developed formal thought processes. Let\u2019s look at one of the mean-value theorem and applications problems. Suppose that the function f is defined for all x, is it possible for f to satisfy f(x) > 0, f\u2019(x) < 0, and f\u2019\u2019(x) < 0 for all x? The way that I would solve this problem is by reasoning out: if f\u201d(x) < 0 and f\u2019(x) < 0 for all x, then f(x) < f\u2019(0)x + f(0) when the domain is (0, \u221e). This means that f(x) would have to be -\u221e as x\u2192\u221e. This does not satisfy the first condition, therefore the answer is no. As shown above, calculus requires a very complex logical reasoning, so it would not make sense to students without formal thought processes.","dateCreated":"1297609029","smartDate":"Feb 13, 2011","userCreated":{"username":"TuyenN","url":"https:\/\/www.wikispaces.com\/user\/view\/TuyenN","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34170762","body":"Several features of formal thought include a child's ability to use "hypothetico-deductive" reasoning, and concepts of proportions. At this stage, a child can understand more complex scientific principles such as density. A step above concrete operations, a child can understand multiple variables within a system.
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\nI think it is completely possible to teach a student a calculus or physics before they reach formal operations. However, I believe that their learning at this point would be limited to memorizing equations and some very simple algebraic manipulation. I do not think that a concrete operations student could understand those subjects enough to apply their concepts to reality. Until a student is capable of working with multiple variables, their success in advanced math and science coursed will be a fraction of that compared to said student well into stage 4.","dateCreated":"1297664438","smartDate":"Feb 13, 2011","userCreated":{"username":"Caseyb.crittenden","url":"https:\/\/www.wikispaces.com\/user\/view\/Caseyb.crittenden","imageUrl":"https:\/\/www.wikispaces.com\/user\/pic\/1296425910\/Caseyb.crittenden-lg.jpg"}},{"id":"34172296","body":"I believe it is possible to teach subject such as physics and calculus to students who have not yet developed formal thought processes because before formal thought processes students enter into concrete operational stage in this stage students have the ability to master most types of conservationexperiments, and begins to understand reversibility. Concreat operational stage comes before formal though process during this stage, the child begins to reason logically, and organizethoughts coherently. However, they can only think about acutal physicalobjects, they can also handle abstract reasoning.","dateCreated":"1297671583","smartDate":"Feb 14, 2011","userCreated":{"username":"RAHIMMOMIN","url":"https:\/\/www.wikispaces.com\/user\/view\/RAHIMMOMIN","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34174770","body":"Characteristics of formal thoughts include; the ability to manipulate proposition, combination of multiple variables can be thought, certain variable can be controlled in experiment. differentiation of relevant and irrelevant factors during test procedure. It is possible to teach physics and calculus for students who have not developed formal thought processes because topics like proportionality can be thought in context of the lessons. Since knowledge is build upon allowing them to understand and develop the theories will also help them learn better.","dateCreated":"1297685987","smartDate":"Feb 14, 2011","userCreated":{"username":"Ebbybaby","url":"https:\/\/www.wikispaces.com\/user\/view\/Ebbybaby","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"34295058","body":"Hala,
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\nI agree with what you're saying and how students who are not yet in stage 4 of cognitive development would likely struggle with calculus and\/or physics. That being said, there are people who are well into stage 4 who have trouble grasping those concepts. Although I feel it would be very difficult to expect a stage 3 student to comprehend calculus, I do believe that it is possible to teach students so effectively to develop thought processes characteristic of a stage 4 learner earlier than naturally expected.","dateCreated":"1297812969","smartDate":"Feb 15, 2011","userCreated":{"username":"Caseyb.crittenden","url":"https:\/\/www.wikispaces.com\/user\/view\/Caseyb.crittenden","imageUrl":"https:\/\/www.wikispaces.com\/user\/pic\/1296425910\/Caseyb.crittenden-lg.jpg"}},{"id":"34305690","body":"Casey
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\nFor the majority stage 3 students calculus would be a struggle. However, I do see your point that it would not be impossible. It could be possible to teach students effectively to develop thought process characteristic of stage 4 learner earlier.","dateCreated":"1297820524","smartDate":"Feb 15, 2011","userCreated":{"username":"HalaSiddiqui","url":"https:\/\/www.wikispaces.com\/user\/view\/HalaSiddiqui","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}}],"more":0}]}],"more":false},"comments":[]},"http":{"code":200,"status":"OK"},"redirectUrl":null,"javascript":null,"notices":{"warning":[],"error":[],"info":[],"success":[]}}