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In accordance with his ambition to become a professional military officer in , Descartes joined, as a mercenary , the Protestant Dutch States Army in Breda under the command of Maurice of Nassau , [29] and undertook a formal study of military...
Martin's Day , while stationed in Neuburg an der Donau , Descartes shut himself in a room with an "oven" probably a cocklestove [40] to escape the cold. While within, he had three dreams, [41] and believed that a divine spirit revealed to him a new...
In , Cartesian philosophy was condemned at the University of Utrecht , and Descartes was obliged to flee to the Hague, settling in Egmond-Binnen. This edition was also dedicated to Princess Elisabeth. In the preface to the French edition , Descartes praised true philosophy as a means to attain wisdom. He identifies four ordinary sources to reach wisdom and finally says that there is a fifth, better and more secure, consisting in the search for first causes.
She was interested in and stimulated Descartes to publish the Passions of the Soul , a work based on his correspondence with Princess Elisabeth. There, Chanut and Descartes made observations with a Torricellian mercury barometer. Challenging Blaise Pascal , Descartes took the first set of barometric readings in Stockholm to see if atmospheric pressure could be used in forecasting the weather.
It soon became clear they did not like each other; she did not care for his mechanical philosophy , nor did he share her interest in Ancient Greek. By 15 January , Descartes had seen Christina only four or five times. On 1 February, he contracted pneumonia and died on 11 February. Pies has questioned this account, based on a letter by the Doctor van Wullen; however, Descartes had refused his treatment, and more arguments against its veracity have been raised since. His manuscripts came into the possession of Claude Clerselier , Chanut's brother-in-law, and "a devout Catholic who has begun the process of turning Descartes into a saint by cutting, adding and publishing his letters selectively. Thought cannot be separated from me, therefore, I exist Discourse on the Method and Principles of Philosophy.
Most notably, this is known as cogito ergo sum English: "I think, therefore I am". Descartes concluded, if he doubted, then something or someone must be doing the doubting; therefore, the very fact that he doubted proved his existence. Descartes concludes that he can be certain that he exists because he thinks. But in what form? He perceives his body through the use of the senses; however, these have previously been unreliable. So Descartes determines that the only indubitable knowledge is that he is a thinking thing.
Thinking is what he does, and his power must come from his essence. Descartes defines "thought" cogitatio as "what happens in me such that I am immediately conscious of it, insofar as I am conscious of it". Thinking is thus every activity of a person of which the person is immediately conscious. Known as Cartesian dualism or mind—body dualism , his theory on the separation between the mind and the body went on to influence subsequent Western philosophies. Humans are a union of mind and body; [86] thus Descartes's dualism embraced the idea that mind and body are distinct but closely joined.
While many contemporary readers of Descartes found the distinction between mind and body difficult to grasp, he thought it was entirely straightforward. Descartes employed the concept of modes, which are the ways in which substances exist. In Principles of Philosophy , Descartes explained, "we can clearly perceive a substance apart from the mode which we say differs from it, whereas we cannot, conversely, understand the mode apart from the substance".
To perceive a mode apart from its substance requires an intellectual abstraction, [87] which Descartes explained as follows: The intellectual abstraction consists in my turning my thought away from one part of the contents of this richer idea the better to apply it to the other part with greater attention. Thus, when I consider a shape without thinking of the substance or the extension whose shape it is, I make a mental abstraction. Thus, Descartes reasoned that God is distinct from humans, and the body and mind of a human are also distinct from one another.
But that the mind was utterly indivisible: because "when I consider the mind, or myself in so far as I am merely a thinking thing, I am unable to distinguish any part within myself; I understand myself to be something quite single and complete. Everything that happened, be it the motion of the stars or the growth of a tree , was supposedly explainable by a certain purpose, goal or end that worked its way out within nature.
Aristotle called this the "final cause," and these final causes were indispensable for explaining the ways nature operated. Descartes' theory of dualism supports the distinction between traditional Aristotelian science and the new science of Kepler and Galileo, which denied the role of a divine power and "final causes" in its attempts to explain nature. Descartes' dualism provided the philosophical rationale for the latter by expelling the final cause from the physical universe or res extensa in favor of the mind or res cogitans. Therefore, while Cartesian dualism paved the way for modern physics , it also held the door open for religious beliefs about the immortality of the soul. A human was, according to Descartes, a composite entity of mind and body.
Descartes gave priority to the mind and argued that the mind could exist without the body, but the body could not exist without the mind. In Meditations, Descartes even argues that while the mind is a substance, the body is composed only of "accidents". If this were not so, I, who am nothing but a thinking thing, would not feel pain when the body was hurt, but would perceive the damage purely by the intellect, just as a sailor perceives by sight if anything in his ship is broken. It was this theory of innate knowledge that later led philosopher John Locke — to combat the theory of empiricism , which held that all knowledge is acquired through experience. These animal spirits were believed to be light and roaming fluids circulating rapidly around the nervous system between the brain and the muscles, and served as a metaphor for feelings, like being in high or bad spirit.
These animal spirits were believed to affect the human soul, or passions of the soul. Descartes distinguished six basic passions: wonder, love, hatred, desire, joy and sadness. All of these passions, he argued, represented different combinations of the original spirit, and influenced the soul to will or want certain actions. He argued, for example, that fear is a passion that moves the soul to generate a response in the body. In line with his dualist teachings on the separation between the soul and the body, he hypothesized that some part of the brain served as a connector between the soul and the body and singled out the pineal gland as connector.
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When you score your answers to the review questions, always count up and record how many you got right. Every problem is worth one point unless otherwise stated. You may grant partial credit for a multi-part problem. I wanted to give you one important reminder before you begin. Many of your lessons below have an internet link for you to click on. When you go to the different internet pages for your lessons, please DO NOT click on anything else on that page except what the directions tell you to. DO NOT click on any advertisements or games. DO NOT click on anything that takes you to a different website. Just stay focused on your lesson and then close that window and you should be right back here for the next lesson.
What is geometry? Read the intro on the first page and then click on A and B. On each page, do the interactive activity. Complete part C, folding paper. Follow the directions. Remember that when we say something is 2D or 3D, the D stands for dimensional. A 2D object has two dimensions: height and width. A 3D object has three dimensions: height, width and depth. Read, do the review queue questions, check your answers at the bottom of the page, go through the examples and solutions carefully. This site requires you to set up a free account. This is the end of your work for this course for your first day. Scroll down to the review questions and do the first five. Check your answers. Lesson 3 Complete this page on definitions and proof. Click the expandable links at the bottom, read through the sections, work the sample problems: Understanding Definitions watch the video in this section , Dividing Polygons…, Triangles…, Notes, Solutions.
Whenever it gives you a postulate, or a theorem, write it down. You should make a list of them. Check your Geometry 1. Lesson 4 Read and watch about line segments. Read the directions carefully each lesson. Record your score out of Chance for 1 point of extra credit. Lesson 5 Do the review queue problems. Read through the material and try the examples. Stop when it gives you a link to an animation for constructing with a protractor. Angles and Measurement 1. Scroll down to the end of the lesson in order to check your answers. Record your score as a 5, minus 1 point for each incorrect answer. Do the review queue and work through the examples. Check your review queue answers by scrolling to the bottom.
Lesson 8 Go through this quick review on finding midpoints. Scroll down, down, down and do these review questions: , evens 20 — If you want to try them, you can get a point of extra credit for any challenge question you get right. Lesson 9 Review angle measurement. Do the review queue and read through the lesson, doing the examples. Always write down theorems and postulates. Angle Pairs Check your answers. As always, record your score as a 5, minus 1 point for each incorrect answer. Lesson 10 Scroll down, down, down and do these review questions: 1- 15, 16 — 30 even. There are 23 problems. Angle Pairs Check your Geometry 1. Lesson 11 Do the review queue and read the lesson. Work through the examples. Stop after you have looked through the classifying shapes chart. Lesson 12 Review polygons. Scroll down, down, down and do the review questions. The last one is optional, for extra credit. Lesson
An important component of the Systemic Initiatives was the aggressive distribution of NCTM aligned curricula for classroom use. The NCTM Standards were vague as to mathematical content, but specific in its support of constructivist pedagogy, the criterion that mattered most to the NSF. It should be noted that the Systemic Initiatives sometimes promoted curricula not on the list above, such as College Preparatory Mathematics, a high school program, and MathLand, a K-6 curriculum. Most notable in this regard was the NSF's funding of a "reform calculus" book, often referred to as "Harvard Calculus," that relied heavily on calculators and discovery work by the students, and minimized the level of high school algebra required for the program. For example, an NSF sponsored organization created in called, "The K Mathematics Curriculum Center," had a mission statement "to support school districts as they build an effective mathematics education program using curriculum materials developed in response to the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards for School Mathematics.
K education collectively was a multi-billion dollar operation and the huge budgets alone gave public education an inertia that would be hard to overcome. Even though the millions of dollars at its disposal made the EHR budget large in absolute terms, it was miniscule relative to the combined budgets of the school systems that the NSF sought to reform. It would not be easy to effect major changes in K mathematics and science education without access to greater resources. To some extent private foundations contributed to the goal of implementing the NCTM Standards through teacher training programs for the curricula supported the by the NSF, and in other ways.
Others such as the W. Keck Foundation and Bank of America contributed as well. However, the NSF itself found ingenious ways to increase its influence. The strategy was to use small grants to leverage major changes in states and school districts. The catalytic nature of the USI-led reform obligates systemwide policy and fiscal resources to embrace standards-based instruction and create conditions for helping assorted expenditures to become organized and used in a single-purpose direction. Yet, the LASI project exerted almost complete control over mathematics and science education in the district. In addition to Title II funds, LASI gained control of the school district's television station and its ten science and technology centers.
According to Luther Williams' July Summary update, "[LASI] accountability became the framework for a major policy initiative establishing benchmarks and standards in all subject areas for the entire school system. All four sets of standards were adopted by the school district in The Los Angeles School district math standards were so weak and vague that they were a source of controversy. One typical standard, without any sort of elaboration, asked students to "make connections among related mathematical concepts and apply these concepts to other content areas and the world of work. The word "triangle" did not even appear in the standards at any grade level. By design, trigonometry and all Algebra II topics were completely missing. This plan was not carried out because of the adoption of a new set of mathematics standards by the state of California in December At a meeting of the LAUSD school board on May 2, , it was revealed that fewer than three percent of elementary schools in the district were using California state approved mathematics programs.
El Paso, Texas serves as an example. El Paso is geographically removed from other U. This made the effectiveness of the K and university programs easier to assess. It also made the entire education system easier to control. During the s, the K education system in El Paso was highly coordinated and focused on implementing constructivist math and science education programs. For this reason, it became a model center for educators from other parts of the country to visit and study. Dana Center in Austin. The El Paso Collaborative for Academic Excellence created a confidential student evaluation questionnaire to monitor teaching methods used in high school math classrooms in all of EL Paso's public high schools.
How often do YOU show that you understand a solution to a problem by explaining it in writing? How often do YOU use math in science and science in math? How often do YOU use hand calculators or computers to analyze data or solve problems? Yet, in spite of the low funding, the Texas SSI "provides leadership for a vast array of agency partnerships, and influences all aspects of education in Texas. Curricula, instructional practices, textbooks, assessment, professional development of teachers, teacher evaluation, teacher certification, and preservice teacher education all now fall under the purview of the Texas SSI.
The mathematics books and curricula that parents of school children resisted shared some general features. Those programs typically failed to develop fundamental arithmetic and algebra skills. Elementary school programs encouraged students to invent their own arithmetic algorithms, while discouraging the use of the superior standard algorithms for addition, subtraction, multiplication, and division. Calculator use was encouraged to excess, and in some cases calculators were even incorporated into kindergarten lesson plans. Student discovery group work was the preferred mode of learning, sometimes exclusively, and the guidelines for discovery projects were at best inefficient and often aimless.
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