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  • Decomposition

  • The late Stanford University Professor Georgelya once said, "If you can't solve a problem,

  • then there is an easier problem you can solve: find it." This advice can be applied to any

  • problem by identifying easier to solve smaller problems within larger ones--decomposition.

  • For example, consider this ridiculous problem--how would you go about eating an elephant? The

  • answer? One mouthful at a time! This goofy analogy actually provides great insight into

  • the first step of problem solving through Computational Thinking. Big, complex problems

  • are comprised of smaller, and more easily solved subproblems or tasks. The process/strategy

  • of logically identifying these smaller problems and determining how to use the combined solutions

  • to solve the bigger problem is called decomposition.

  • The process of focusing on how a problem breaks into parts is called analysis. In contrast,

  • rebuilding or focus on how the parts come back together is called synthesis.

  • When a problem is broken down into smaller parts, these parts may be addressed simultaneously,

  • or in parallel. Organizing and multitasking to work on several smaller problems is called

  • parallelization. Parallelization is something you practice when you are cooking multiple

  • dishes at the same time Depending on the problem, these smaller parts

  • may need to be addressed in a certain order, or sequentially.

  • Let’s start out with a visual example of decomposition. Here is a necklace made of

  • red beads, blue beads and thread, each with a different cost. The problem: determine the

  • total cost to construct this 24-inch necklace. Think for a minute. How do you set up this

  • problem? What information do you need?

  • Without even thinking much you have likely already decomposed the problem into subproblems.

  • Since the materials all have different costs and are used in different amounts, an analysis

  • of this problem leads us to the conclusion that calculating the cost for each type of

  • material and then adding those answers together is the logical way to approach the problem.

  • Solving each of those subproblems is an example of parallelization.

  • We will return to this necklace example throughout the course to learn about each step in the

  • Computational Thinking process.

  • The process of decomposition in the previous example is reminiscent of solving word problems

  • from math classes in our past. It involves thinking about how to solve the problem, translating

  • from the language of words into the language of math and numbers, breaking it down logically

  • and eventually solving it.

  • Math problems often utilize decomposition. Here is an example of a 6th grade Common Core

  • Math standard that incorporates decomposition.

  • The following examples show how decomposition might work for other kinds of practical, everyday

  • problems that aren’t represented by numbers. For example:

  • How does a bicycle work? By breaking down the bicycle into components and their functions

  • (such as gears, chain, pedals and brakes) and learning about how each works independently

  • first, and then together, one can understand how the more complex machine operates.

  • The same is true for a car, plane or boat. • How does the human body work? A very complicated

  • question, but when we learn about the human body we focus on one system at a time - respiratory,

  • circulatory, digestive, skeletal and muscular - and then think about how they interact with

  • each other. • What happened at a crime scene? Police

  • and detectives are careful to observe an entire crime scene, but they have procedures for

  • in-depth examination of all the details (blood spatter, position of bodies, fingerprints,

  • fibers and other clues) to piece together the most likely scenario for what occurred.

  • Composing a song--musicians think in terms of parts as they are writing music. There

  • are different roles for different instruments. Some play the bass beat, while others provide

  • the melody or harmony. All the parts work together to create a whole.

  • Creating an app. The idea of building an app may be a daunting challenge if you

  • aren’t a computer programmer. However, anyone can work through the process of decomposition

  • for creating an app by thinking about what your app will do, what it will look like,

  • how you want the user to move through the screens and how much it will cost.

  • Writing for an English classthe process of writing a paper involves outlining, or

  • breaking the idea for your paper into logical parts. When asked to analyze a poem you focus

  • on the poem as a whole, but also meter, rhyme, imagery, structure, tone, diction and meaning

  • individually.

  • As you can see, decomposition is a critical skill for solving complicated problems. Decomposition

  • is a relatively simple concept, but each problem will have different variables and decomposition

  • will need to be approached in different ways. It is critical to understand that to effectively

  • use Computational Thinking students must be able to logically break down a problem on

  • their own. It’s not enough to show some examples and assume your students understand,

  • students must practice breaking down increasingly complex problems to learn how to apply this

  • skill on their own and incorporate it into their process of thinking. Students need to

  • be responsible for their own learning, individually or in small groups, rather than just shown

  • examples of decomposition.

  • In introducing students to the idea of decomposing a problem, start with something very simple,

  • for example, how to clean your teeth. The goal is not to list the steps in brushing

  • teeth, but the components involved in solving the problem, for example:

  • What tools and materials will you use to clean your teeth?

  • What methods and actions will you use to clean your teeth, and for how long?

  • Links to several excellent existing activities that can be done in the classroom to reinforce

  • decomposition, analysis, synthesis and parallelization skills are provided along with this video.

  • A few are introduced here. These activities are meant to be challenging. When you finish

  • watching the video, please take the time to explore these links and choose some to try

  • out with your students, either individually or in small groups. Because every problem

  • is different, the more exposure to different ways of thinking about decomposition the better

  • students will become at putting the skill into practice. Also, remember that in many

  • cases there is no one right answer about how to decompose a problem. Be open and discuss

  • studentstrain of thought.

  • Bee-Bot is a simple game for very young children to start to understand programming. Although

  • geared toward children younger than Middle and High School, Bee-Bot can be used as a

  • visual example to explain and practice decomposition. The goal in the Bee-Bot game is to move the

  • bee from its starting point to the flower by inputting instructions using the arrow

  • keys. The Bee-Bot only performs one instruction at a time, but can remember and perform a

  • series of many. As the student adds steps, they are listed across the top of the screen--a

  • decomposition of their larger set of instructions. When they clickgothe steps are highlighted

  • as they are performed, allowing students to see where they may have made a mistake. At

  • this point in the course this allow students to play with this game through trial and error.

  • Point out how it keeps track of steps and how this is an example of decomposition of

  • the problem. Students will likely find the first few levels easy and learn how the program

  • works and then, since the complexity of the route increases by level, they will be challenged

  • and likely find the decomposed steps to be very useful. We will return to Bee-Bot again

  • later in the training.

  • The activity Colour by Number: Image Representation provides opportunity for both synthesis and

  • analysis in decomposition. Students follow basic instructions to fill in squares on graph

  • paper that collectively form a recognizable image, an example of synthesis. Then, students

  • analyze a recognizable image into squares and create instructions for their classmates.

  • The process here is similar how pixels on a computer work.

  • Google: Divide and ConquerSearching for the Token

  • Dividing and conquering is a different method of decomposition that can make a complex problem

  • much simpler. Strategic yes/no questions allow for up to half of the complexity of the problem

  • to be removed through process of elimination. In Searching for the Token students hide a

  • token of some sort in one of their pockets or desks. The instructor then asks yes/no

  • questions to determine who has the token. Instead of questions such asdoes Alice

  • have the token?” oris the person with the token wearing a blue shirt?” a much

  • more efficient decomposition method is to divide the room in half and ask if the token

  • is on the right side. In one question you will determine in which half of the room the

  • token is hiding. Your second question can divide the appropriate side of the room in

  • half again, and so on, until you find the token--it won’t take long! Students should

  • take turns practicing finding the token to get a good handle on the concept of divide

  • and conquer.

  • Another method to encourage efficient, strategic thinking in decomposition is to have students

  • buy” a question using candy--the goal is to keep (and eat) as much candy as possible.

  • This is demonstrated in the activity Searching Algorithms and could be used during Searching

  • for the Token.

  • To reinforce the concept of divide and conquer decomposition students can explore the silly

  • Santa’s Dirty SockseBook where savvy elves use divide and conquer to efficiently

  • locate Santa’s dirty socks amid a sea of packages on Christmas Eve.

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

  • to check your understanding.

Decomposition

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B1 中級

計算思維。分解 (Computational Thinking: Decomposition)

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    Chris Lyu 發佈於 2021 年 01 月 14 日
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