Dilations Essays - Dilation, Metric Geometry, Free Essays

Dilations Essays - Dilation, Metric Geometry, Free Essays Dilations Dilations in Math, Art, and Science Historically, dilations have been fundamentally indispensable in the development of cultures around the world. The Greeks for example, without dilations would have merely been a bunch of homeless philosophers instead of the brilliant architects they were. In this paper Ill discuss the uses and the history of dilations. Dilations have long been used in the world, both past and present. Early examples include Greek, Roman, and other ancient cultures using dilations to accomplish various complex engineering feats. Overseers would commonly sit a set distance from a construction site, and a pole of some sort with a fixed length was placed in front of them. Because of this layout, the engineers were allowed to see both length and height (if desired) of the specified building or construction. Artists also commonly utilized the use of simple dilations to make scaled and accurate artwork in the 1400 and 1500s. Even today, you see dilations in use. For instance, a picture of the globe, or a map of a particular area can be magnified many times, creating dilation (see the example on the visual board.) On a golf course, you might look at the flagpole at the end of the course to get a fairly accurate sense of the distance from you to the green. Common sense dictates that the smaller the 4 flag is in your perspective, the farther the golf hole is from you, and vice versa. Dilation Instructions: To perform a simple dilation, follow these instructions. Place one point, the size of a pencil tip, at any place on a piece of paper (preferably the near the middle to keep this simple.) Now, measure a compass width to approximately inch. Make a light circle surrounding your dilation origin (pencil dot; dilation center.) Place a dot at any place on that circle, and then exactly inch away from the dot you just made, draw another dot on the circle. After this, measure your compass width to approximately 1-inch wide. Draw another circle about your origin (original dot; pencil dot; dilation center.) Make a line that goes through both your origin, and one of your dots that are on the first inner circle. Do the same with the origin and the other dot on the first inner circle. Now, find the place where each line intersects the second circle and place a dot on those two places. Erase the inner and outer circles and the two lines and you have a dilation! Bibliography NA

Data Collection for Discrete Trials

Data Collection for Discrete Trials Discrete trial teaching is the basic instructional technique used in Applied Behavior Analysis. Once a specific skill is identified and operationalized, there are several ways to record success. Since trials are generally multiple probes of since skills, when you collect data you want your data to reflect several things: Correct responses, Non-responses, Incorrect responses, and Prompted responses. Usually, a goal is written in a way to name what each response will look like: John will touch a letter from a field of three.When presented with a colored sorting bear, Belinda will correctly place it on a plate of the matching colorWhen presented with a set of counters from 1 to 5, Mark will correctly count the counters. When you use a discrete trial teaching approach, you may want to create a program to teach a skill. Clearly, you will want to be shaping the behavior/skill you are teaching, starting with the antecedent skills. I.e., if the skill you are teaching is recognizing colors, you will want to start with a benchmark that asks the child to distinguish between two colors, in other words, John, touch red, from a field of two (say, red and blue.) Your program could be called Color Recognition, and would probably expand to all the primary colors, the secondary colors and finally the secondary colors, white, black and brown. In each of these cases, the child is asked to complete a discrete task (therefore, discrete trials) and the observer can easily record whether their response was Correct, Incorrect, Non-Responsive, or whether the child needed to be Prompted. You may want to record what level of prompting was required: physical, oral or gestural. You can use a record sheet to record these and plan how you will fade prompting. A Free Printable Record Sheet Use this free printable record sheet  to record five days of the particular task. You certainly dont need to record every day the child is in your classroom, but by providing you with five days, this worksheet is a little more accessible for those of you would like to keep a sheet a week for data collection. There is a space next to each p on each column that you can use to record what kind of prompt if you are using this form not only to record your trial by trial but also to fade prompting. At the bottom is also a place to keep percents. This form provides 20 spaces: you certainly only need to use as many trials as your student usually can attend to. Some low functioning students may only successfully complete 5 or 6 of the tasks. 10 is of course optimal, because you can quickly create a percent, and ten is a fairly decent representation of a students skills. Sometimes, however, students will resist doing more than 5, and building up the number of successful responses may be one of your goals: they may otherwise stop responding or respond with anything to get you to leave them alone. There are spaces at the bottom of each column for next to write when you are expanding your field (say, from three to four) or adding more numbers or letters in letter recognition. There is also a place for notes: perhaps you know the child didnt sleep well the night before (a note from Mom) or he or she was really distracted: you may want to record that in the notes, so you give the program another shot the next day. Hopefully, this data sheet provides you the flexibility you need to successfully record your students work.