Geometry Question

 

It is well known that reflection on past work is a valuable learning tool. Thus, the portfolio is to provide you with an opportunity to systematically reflect on and consolidate your thinking and reasoning. The portfolio is also valuable for me, your teacher, because it gives me insight into your progress and accomplishments that is difficult to obtain in other forms of assessments.

To begin, go over all of your work in this course. This includes problems done in class, problems done for homework, and any other related work that you have done outside of class. From this body of work, select five “entries” to showcase your progress and accomplishments. Typically an entry will be a particular problem that, for you, represent important personal progress or accomplishment. Consider selecting entries that highlight your creativity or inventiveness, your mathematical growth, your new insights into what makes for powerful learning or teaching, the value of mathematically interacting and communicating with others, your ability to connect ideas/concepts, your deep understanding of concepts, your ability to model with mathematics, reason mathematically, or even the nature of mathematics itself. Each entry is to include your original response(s) and any revisions or additions that you would like to add. It is not mandatory that you revise or add to your original solution. However, sometimes it is helpful to revise or add to earlier work to showcase your progress and growth.

Each entry is to include a rationale statement that explains why you selected this entry. Explain the significance of the entry for you, personally (as described above). Use first person in your rationale statement. Each rationale statement should be on a separate piece of paper and placed in front of the respective entry. Length of the rationale statement will typically be 150 to 200 words.

Portfolio structure

Cover sheet
Table of contents (list of five entries with some label that identifies the problem(s). For example, Entry 1: What is straight on the sphere)
Rationale statement 1
Entry 1
Rationale statement 2
Entry 2
Rationale statement 3
Entry 3
Rationale statement 4
Entry 4
Rationale statement 5
Entry 5

 

 

 

Sample Solution

ee will”. Leaving aside Locke’s own discourse on the state of nature, we try to make a new argument for “restricting free will” from our point of view. Locke believes that it is possible for people to restrict their own free will on the premise that family is the typical representative in an environment of undegraded benevolence. “In the early days of the establishment of the government, the number of the state was not much different from that of the family, nor was the number of laws much different from that of the family; since the rulers cared for them for their happiness like their fathers, the rule of the government was almost entirely privileged.” Locke introduced “privilege” here and linked privilege with benevolence. “Privilege is a kind of power to act for the benefit of the public according to discretion without legal provisions, sometimes even in violation of the law.” (The Treatise of Government (Part Two): P102) Kant believes that this kind of rule is absolute. “If a government is based on the principle of benevolence to the people as a father does to his children, that is to say, a father’s government, the subjects here are forced to adopt a passive attitude just as they can’t tell what is really good or bad for their children, so that they can only expect the head of state’s happiness. Judgment, and if the head of state is willing to do so, only his goodwill is expected; such a government is the greatest authoritarianism imaginable.” (Volume 8 of Kant’s Complete Works: Papers after 1781: P294) We do not quote Kant’s statement that Kant supports Locke, but that Kant also opposes Hobbes. Locke believes that human happiness can only be measured by external public welfare. Kant denies this, which is the fundamental difference between them. But the source of Kant’s refutation of Hobbes may be related to Locke. In short, when the benevolent family finally degenerates, it is necessary to restrict power, because the father-like leader is no longer the father, he has no inherent motive for benevolence to benefit the public, on the contrary, he may infringe on public welfare. Benevolence is the internal means of restricting power. Since this internal means has failed, it is necessary to restrict power through external means. Legislative power and law enforcement power should be separated. Locke himself logically disintegrated patriarchy by refuting the Theocracy of monarchy, which not only made the disintegration of patriarchy a historical process, but also a logical argument. So far, politics is only related to one kind of morality, that is, secular morality and public welfare, which is also the focus of Locke’s argument. But when he retains God, he also retains the morality of faith. Although God no longer exercises the power to punish those who violate secular morality, he still exercises the power to punish those who violate beliefs. It can be seen as Locke defending the church, or as Locke’s unwillingness to drive God out of People’s lives so easily.

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