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Computer Simulations  
  
1403   01:50 صباحاً   date: 6-1-2016
Author : Alessi, Stephen M., and Stanley R. Trollip
Book or Source : Multimedia for Learning: Methods and Development
Page and Part : ...


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In simulations, people are confronted with real-life situations and can take risks without having to suffer the consequences of failure. People can experiment with dangerous chemicals on the computer screen, for example, and not be in danger from the actual chemicals. With laboratory simulations, there is no expensive lab equipment to buy and students do not have to wait as long for the results of an experiment. Simulations save time and money, reduce risks, and work well as aids in decision-making.

A simulation is an abstraction or imitation of a real-life situation or process. Computers can be used to simulate complicated processes such as the spread of a virus throughout a city, the long-term effects of urban renewal, or the economy of an entire country. In simulations, participants usually play a role in which they interact with other people or with elements of the simulated environment. A business management simulation, for example, might put participants into the role of executive of a mythical corporation, provide them with information about the corporation, and ask them to negotiate a new labor contract with a union bargaining team.

A well-designed simulation models the elements most important to the objective of the simulation, and it informs the participants about elements that have been simplified or eliminated. A complicated simulation might be too time-consuming for the intended audience, whereas an over-simplified simulation may fail completely to communicate its intended point.

One particular value of simulations is that they implement the problem based learning method as directly and clearly as possible. In problem-based learning, one is taught to understand principles by being given a problem situation. Most simulations attempt to immerse participants in a problem.

Through simulations, participants are offered a laboratory in areas such as the social sciences and human relations as well as in areas related to the physical sciences, where laboratories have long been taken for granted. The great advantage of simulated immersion in a topic is that individuals are more likely to be able to apply to real life what they have practiced in simulated circumstances.

This raises the issue of the degree of realism captured by a simulation.

Simulations can vary greatly in the extent to which they fully reflect the realities of the situation they are intended to model. A common defect in poorly designed simulations is an overemphasis on chance factors in determining outcomes. Because many of the processes in the real world depend at least partly on  random events, a successful simulation includes an appropriate amount of random numbers to help best replicate a real-life situation.

Benefits of Simulations

Simulations typically have four main advantages over more conventional media and methodologies such as books, lectures, or tutorials:

(1) simulations tend to be more motivating;

(2) simulations enhance transfer of learning;

(3) simulations are usually more efficient; and

(4) simulations are one of the most flexible methodologies, applicable to all phases of instruction and adaptable to different educational philosophies.

It is well known and not surprising that simulations enhance motivation. Participants are expected to be more motivated by active involvement in a situation than by passive observation. Trying to fly a simulated airplane, for example, is more exciting than reading about flying. Trying to diagnose and treat a simulated patient is more exciting than attending a lecture about it.

Several motivational elements can found in most simulations, including fantasy, challenge, and relevance. Realistic fantasy (imagining oneself in an interesting activity) is a part of most simulations and is a function of the simulation storyline or scenario. Simulations that increase in difficulty as the participant progresses offer challenge as a motivation. Most learners consider simulations more relevant to their learning than lectures, books, or other passive methods, because they are engaging in the activity rather than just reading or hearing about it.

Many simulations include  gaming techniques. These simulations are particularly popular in business education because the competition inherent in games is also a factor in the real world of business, including competetion among firms, between management and labor, or among salespeople.

Such simulation games have the potential to be more motivating than more conventional instruction, such as lectures and reading assignments.

“Transfer of learning” refers to whether skills or knowledge learned in one situation are successfully applied in other situations. Simulations have good transfer of learning if what was learned during the simulation results in improved performance in the real situation. For example, a gardening simulation—in which one manipulates soil acidity, the exposure to sunlight, and the amount of watering—would have a better transfer of learning than reading a gardening book. The simulation gives one practice in gardening and the opportunity to try out different combinations of conditions and care.

The book, however, only provides information and hints on how to so.

The term “transfer of learning” is often used in reference to quite different ideas. The term “near transfer” refers to applying what is learned to very similar circumstances. The term “far transfer” refers to applying what is learned to somewhat different circumstances, or generalization of what is learned. Simulations can be designed to optimize either type of transfer.

The idea of transfer of learning can be taken a step farther. Not only can one measure how effectively knowledge, skill, or information transfer from one situation to another, but one can also measure how efficient the initial learning experience is with respect to the transfer. This is best illustrated with a hypothetical example.

Suppose a teacher has two different classes for one chemistry course.

The teacher gives one class a series of interesting and informative lectures dealing with a specific laboratory procedure. In the other class, the teacher provides a computer program with the same information and includes a simulation of the laboratory. On completing their respective forms of instruction, each class of chemistry students performs the procedure in a real laboratory. Both classes perform well on the actual laboratory experiment.

On the basis of this information one could conclude that both instructional methods have the same transfer of learning.

However, if the lecture series took 10 hours and the average time to complete the simulation required only 5 hours, one might conclude that the simulation was more time efficient. That is, more transfer occurred per unit of learning time with the simulation than with the lectures. Although simulations do not guarantee time efficiency, there is evidence that well-designed simulations do foster it.

The last advantage of simulation is its flexibility. Simulations can satisfy more than one of the four phases of instruction. In fact, they usually satisfy at least two: either initially presenting material and guiding the learner through it (Phases 1 and 2) or guiding the learner through previously learned material and providing practice with it (Phases 2 and 3).

When simulations do provide initial instruction, they frequently do so by the scientific discovery learning or experimentation approach. Most other repetitive simulations are examples of this. Not all simulations teach in this way, however. Some provide extensive help or tutorial components that learners may access at any time and according to their own choice.

A simulation about road signs and driving laws might introduce the signs and rules, guide the learner in their use, and provide practice by letting the learner use the simulation over and over until familiar with the laws. Many simulations have this characteristic. If used once, the simulation presents information and guides the learner in its acquisition. If used repeatedly, it takes on the characteristics of a drill, and, like a drill, some

simulations require the participant to continue until proficiency is demonstrated.

Spreadsheet Simulations

When one thinks of simulation software, one often thinks of expensive, complex software. But simulations that demonstrate manipulation of one or more variables can be created using only a spreadsheet. Spreadsheet simulations allow one to manipulate a variable and see the resulting numerical change or change in a graph.

For example, a man on Earth weighing 160 pounds will have a different weight on Earth’s moon or on another planet. This concept may  be difficult to imagine. Using a spreadsheet, however, one can create realistic examples and problems to help understand and apply the concept of gravity.

A spreadsheet simulation can be used to teach students how to make predictions based on the rules or laws they have discovered. For example,  students can use atmospheric data to predict the weather or use  demographic and historical voting data to predict the results of an election. Students have even used spreadsheet simulations to determine the probability of winning the largest bingo prize.

Spreadsheet simulations can also be used to explore mathematical relationships. One can create a spreadsheet to both calculate and plot the relationship between an unknown (x) and its coefficient and constants. As the values change, the equation is solved for (x), and the relationships between the coefficient, constants, and x are displayed in a graph that is automatically updated with each change.

Spreadsheets are useful for teaching math concepts such as surface area and volume problems and  polynomial problems. Teachers can also use spreadsheets to teach math concepts in classes such as economics.

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Reference

Alessi, Stephen M., and Stanley R. Trollip. Multimedia for Learning: Methods and  Development, 3rd ed. Boston: Allyn and Bacon, 2001.

Koetke, Walter J. Scholastic Computers & Math: Problem Solving with Basic. New York: Scholastic, 1986.

Morrison, Gary R., Deborah L. Lowther, and Lisa DeMeulle.  Integrating Computer Technology into the Classroom. Upper Saddle River, NJ: Merrill, 1999.

Sharp, Vicki. Computer Education for Teachers, 3rd ed. Boston: McGraw-Hill, 1999.

 




الجبر أحد الفروع الرئيسية في الرياضيات، حيث إن التمكن من الرياضيات يعتمد على الفهم السليم للجبر. ويستخدم المهندسون والعلماء الجبر يومياً، وتعول المشاريع التجارية والصناعية على الجبر لحل الكثير من المعضلات التي تتعرض لها. ونظراً لأهمية الجبر في الحياة العصرية فإنه يدرّس في المدارس والجامعات في جميع أنحاء العالم. ويُعجب الكثير من الدارسين للجبر بقدرته وفائدته الكبيرتين، إذ باستخدام الجبر يمكن للمرء أن يحل كثيرًا من المسائل التي يتعذر حلها باستخدام الحساب فقط.وجاء اسمه من كتاب عالم الرياضيات والفلك والرحالة محمد بن موسى الخورازمي.


يعتبر علم المثلثات Trigonometry علماً عربياً ، فرياضيو العرب فضلوا علم المثلثات عن علم الفلك كأنهما علمين متداخلين ، ونظموه تنظيماً فيه لكثير من الدقة ، وقد كان اليونان يستعملون وتر CORDE ضعف القوسي قياس الزوايا ، فاستعاض رياضيو العرب عن الوتر بالجيب SINUS فأنت هذه الاستعاضة إلى تسهيل كثير من الاعمال الرياضية.

تعتبر المعادلات التفاضلية خير وسيلة لوصف معظم المـسائل الهندسـية والرياضـية والعلمية على حد سواء، إذ يتضح ذلك جليا في وصف عمليات انتقال الحرارة، جريان الموائـع، الحركة الموجية، الدوائر الإلكترونية فضلاً عن استخدامها في مسائل الهياكل الإنشائية والوصف الرياضي للتفاعلات الكيميائية.
ففي في الرياضيات, يطلق اسم المعادلات التفاضلية على المعادلات التي تحوي مشتقات و تفاضلات لبعض الدوال الرياضية و تظهر فيها بشكل متغيرات المعادلة . و يكون الهدف من حل هذه المعادلات هو إيجاد هذه الدوال الرياضية التي تحقق مشتقات هذه المعادلات.