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  • Abstraction and Pattern Generalization

  • Abstraction in Computational Thinking allows for the creation of a more generalized model

  • of the complex problem being solved. Abstractionlets one object stand for manyand

  • allows us to deal with complexity and scale. Using what you learned by recognizing patterns,

  • relevant variables can be identified, grouped and generalized (described with less detail)

  • so that they define the main ideas of a problem.

  • The key to abstraction is to be able to identify and filter out or ignore the details not necessary

  • to solve the problem. From there, a model (equation, image, word, simulation, etc.)

  • can be developed to represent all the important variables. A variable is a name that can be

  • associated with a value. Variables have changing values and can be represented by a number,

  • letter, word, blank or image. Often, the value of one variable will determine, or be dependent

  • upon, another. In these examples, you can see how the value of the second variable,

  • or input, is dependent on the value of the first variable or input. Abstraction allows

  • you to create a generic representation of a problem.

  • Pattern generalizationis creating models, rules, principles, or theories of observed

  • patterns to test predicted outcomesIn other words, Pattern generalization is figuring

  • out the right relationship between the abstracted variables to accurately represent the problem.

  • Recognizing patterns as we did in the last video is critical, as patterns are almost

  • always where generalizations begin. What an abstraction looks like depends on

  • the type of problem being solved. Here are some abstractions across different areas and

  • problem types:

  • Science Examples of abstractions in science include

  • simplified models of the water cycle, nitrogen cycle, rock cycle, etc. Classification of

  • living things can also be considered abstraction--we use words like mammal to generalize groups

  • of animals, or marine organisms to generalize life in the ocean. In Chemistry the periodic

  • table is an abstract diagram representing lots of information about much of human knowledge

  • relating to earth’s materials.

  • Math Most of mathematics involves abstraction.

  • Even something as simple as a triangle is an abstraction of points, lines and angles.

  • Art In his painting Three Musicians Pablo Picasso’s

  • abstract shapes and colors come together to form a picture that we recognize as three

  • individuals playing instruments.

  • English When we learn a language, we learn about how

  • different parts of speech come together to form a sentence. Here is an abstraction of

  • a basic sentence structure in English.

  • Subject (person or thing) + action/occurrence/state of being + object (person or thing)

  • OR

  • Noun + verb + noun

  • For example: Susie ate pie.

  • The dog ran home.

  • Mad Libs are another example of abstraction. Instead of specific nouns, verbs and adjectives,

  • a blank is given where any noun, verb or adjective can be placed. The result is grammatically

  • correct sentences with some pretty silly meanings!

  • Universal symbols Every day we encounter familiar symbols that

  • are so commonplace in our lives we rarely notice them. However, these abstractions truly

  • dolet one object stand for many”. See if you know what message each of these symbols

  • represents.

  • Let’s start by using abstraction with a familiar problem. We previously decomposed

  • the problem into three smaller subproblems to be added together and identified the patterns

  • between how those subproblems can be solved. The subproblems are:

  • Cost of red beads x number of red beads Cost of blue beads x number of blue beads

  • Cost of thread x length of thread

  • We can now use abstraction to simplify the problem even further into one repeatable operation:

  • Material cost x material quantity The variables are

  • 1. The cost for each type of material 2. The quantity of each material

  • Through abstraction we have created one operation that can be used to determine the cost of

  • each of the three materials. In the final video we will return to this problem and discuss

  • an algorithm for solving the entire problem. Abstraction helps us to create models related

  • to a problem that can work for large quantities and ranges of data. Suppose you wanted to

  • calculate how much it would cost to make a 10 foot garland out of red beads and thread,

  • or calculate the cost to create 250 necklaces, or calculate how many 24 inch necklaces using

  • an alternating pattern of 3 red beads and 3 blue beads could be made for a certain budget?

  • The abstract operations you have designed can help you do that. Your abstract operations

  • can make it easy to model or calculate different options.

  • Other examples of abstraction being used to create models that allow testing of different

  • variables and situations include:

  • Learning about gravity and acceleration using a physical model (a ramp and ball) at a very

  • young age, in a lab as a middle school or high school student using graphing to model

  • changing variables, or as an engineer. Let’s continue with another example from

  • the last video, the Make a Monster example. In the last section we listed patterns or

  • similarities that the different monsters had in common. Here is what we found:

  • What do all the monsters have in common? • The all have a head

  • They all have eyesThey all have a nose

  • They all have a mouthTwo have ears

  • We know from looking at the pictures that there are several options for different head

  • shapes, eyes, noses, mouths and ears (including no ears). Using abstraction, we now want to

  • modify these statements so they could describe the qualities of any monster. For example,

  • This monster has a blank head. This monster has blank eyes.

  • This monster has a blank nose. This monster has blank ears.

  • This monster has a blank mouth.

  • In this case, the variables are as follows:

  • Heads: Zombus, Franken and Happy And eyes, ears, noses and mouth: Vegitas,

  • Wackus and Spritem

  • If a monster doesn’t have one of these features, we can call that InHideum.

  • In the last video we will learn how to take this abstraction and use it to give instructions

  • to another person to recreate any monster! Here are some other examples that you can

  • use in your classroom to practice abstraction: A Dichotomous Key provides a process for identifying

  • something based on its features. This can be an animal, plant or candy--the process

  • is the same! Like in Make a Monster, in this activity the student is responsible for abstracting

  • the characteristics of several different types or varieties of something--in this case candy.

  • By organizing those abstractions into a dichotomous key, they create a tool that can be used by

  • others for identification purposes. As mentioned earlier, Mad Libs are created

  • through abstraction of a sentence. Mad Libs can be done on paper, such as in the activity

  • Mad Glibs from studio.code.org, or they can be generated online.

  • In this activity students first go from specific to general, by carefully describing an everyday

  • object using general terms so that someone who didn’t know what it was could understand.

  • Students then trade descriptions and try to figure out what each other was describing.

  • Working with tangrams involves abstracting geometric patterns--using shapes to create

  • other recognizable shapes. This becomes a game at GeoShapes on National Geographic Kids.

  • Challenge your studentswho can solve the tangrams problems the fastest?

  • When you have finished watching this video, don’t forget to complete the quick self-evaluation

  • to check your understanding.

Abstraction and Pattern Generalization

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計算思維。抽象和模式概括 (Computational Thinking: Abstraction and Pattern Generalization)

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    Chris Lyu 發佈於 2021 年 01 月 14 日
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