Directions: Read this article, and Writing in Mathematics. At the end of this paper are instructions for writing a paper.
The Design Cycle
The Design Cycle is the problem solving method that you have been using, unconsciously, for years. In the past you most likely used the George Polya method of problem solving without knowing it. The Polya method is normally taught as: Read, Plan, Solve, and Check by elementary and middle school teachers. Below is the Wikipedia take on Polya.
George Pólya's 1945 book How to Solve It (ISBN 0-691-08097-6) is a small volume describing methods of problem-solving. It suggests the following steps when solving a mathematical problem:
- First, you have to understand the problem. What is asked? What is given?
- After understanding, then make a plan.
- Carry out the plan.
- Look back on your work. How could it be better?
Objectives
The design cycle is a model and it is intended to be the central tool to help students to create and evaluate solutions in response to challenges. The MYP technology design cycle consist of four major stages—note how the Polya method has four steps that are basically the same. The Design Cycle is more general in its approach and is the standard methodology used by software “shops,” and industry.
Below are the four steps adapted from International Baccalaureate Organization.
Investigate
Identify the problem to be solved. At the end of the course, students should be able to:
- Evaluate the importance of the problem for life, society, and the environment
- Outline the design brief.
Formulate a design specification. At the end of the course, students should be able to:
- List the specific requirements that must be met by the product/solution.
- Design tests to evaluate the product/solution against the design specification.
Plan
Students design the product/solution. At the end of the course, students should be able to:
- Generate several feasible designs that meet the design specification
- Evaluate the designs against the design specification
- Select one design and justify its choice.
Students plan the product/solution. At the end of the course, students should be able to:
- Construct a plan to create the product/solution that has a series of logical steps (Learn how to write a heuristic/algorithm via Writing in Mathematics.)
- Construct a plan to create the product/solution that makes effective use of resources and time
- Evaluate the plan and justify any modifications to the design.
Create
Students use appropriate techniques and equipment. At the end of the course, students should be able to:
- Use a range of appropriate techniques and equipment competently (Photoshop, Dreamweaver, Flash, Fireworks, MS Office, iMovie, and Audacity.)
- Ensure a safe working environment for themselves and others.
Students follow the plan. At the end of the course, students should be able to:
- Follow the plan to produce the product/solution
- Evaluate the plan and justify any changes to the plan (when necessary.)
Students create the product/solution. At the end of the course, students should be able to:
- Create a product/solution of appropriate quality.
Evaluate
Students evaluate the product/solution. At the end of the course, they should be able to:
- Carry out tests to evaluate the product/solution against the design specification
- Evaluate the success of the product/solution in an objective manner based on testing, their own views and the views of the intended user
- Evaluate the impact of the product/solution on individuals and on society
- Explain how the product/solution could be improved.
Students evaluate their use of the design cycle. At the end of the course, students should be able to:
- Evaluate their performance at each stage of the design cycle
- Suggest ways in which their performance could be improved.
Compare and Contrast: The Design Cycle vs. Polya's Method
Notice how the Design Cycle has four steps: Investigate, Plan, Create, and Evaluate. Now contrast these four steps with the four-steps of Polya’s method: Read, Plan, Solve, and Check. They are merely synonyms. Furthermore, when we actually delve into the meaning of each stage, and the definitions used in the Design Cycle and by Polya then it is evident that there really is no difference between the two problem solving methods. The only difference is in the intended application that the problem solving method targets. The Design Cycle is a heuristic which makes it applicable for solving any type of problem: math, science, automotive, relationships, etc. The Polya method targets one set of problems only: mathematical. The simple conclusion to be drawn is that the Design Cycle is more pertinent to solving "everyday" problems. Let's compare the two to gain a better understanding of how both problem solving methods work.
Step I: Investigate vs. Read. Obviously, Investigate is the broader term. Read is a good term to use when solving mathematical problems, but problem solving does not stop there. Every “challenge” in life can be defined as a problem. With time, some challenges simply become routine habits—like feeding yourself in the morning. One of the better definitions for Investigate comes from Wikipedia. In this definition they are using the term "exploratory search"—after all, that is what you are doing when you are first confronted with a problem and realize that something needs to be done. I give you, Wikipedia: “Exploratory search is a specialization of information exploration — a broader class of activities where new information is sought in a defined conceptual area; exploratory data analysis is another example of an information exploration activity. In exploratory search, users generally combine querying and browsing strategies to foster learning and investigation.”
In essence, this is where you define your problem and acquire an understanding for it. In terms of an algorithm this is where we define our
Initial
State. ”Understanding is a psychological process related to an abstract or physical object, such as, person, situation and message whereby one is able to think about it and use concepts to deal adequately with that object.” (ibid.)
Step II: Plan vs. Plan. These two steps use the same word which only reinforces our hypothesis that both methods are primarily the same. During the plan you are defining the process that will enable to generate a solution or your Goal State. This is where you need to be creative. Learn to think outside of the box. Remember: with creative thinking nothing is taboo or wrong—it just might not work. The Wikipedia definition of plan is: “The term planning implies the working out of sub-components in some degree of detail. Broader-brush enunciations of objectives may qualify as metaphorical roadmaps.
Planning literally just means the creation of a plan; it can be as simple as making a list. It has acquired a technical meaning, however, to cover the area of government legislation and regulations related to the use of resources.
Planning can refer to the planned use of any and all resources, as in the succession of Five-Year Plans through which the government of the Soviet Union sought to develop the country. However, the term is most frequently used in relation to planning for the use of land and related resources, for example in urban planning, transportation planning, and so forth.
Plans are nothing; planning is everything.-- Dwight D. Eisenhower
Step III: Create vs. Solve. This is where you actually generate a solution to your problem. In terms of an algorithm, these are the steps that take you to get from your
Initial
State to your
Goal
State. During this phase you are actually taking each of the steps that you created above and “running” them. Mathematics is a great field to use as an example for this step—this is the step where you “crunch” the numbers, or “plug-and-play.” Again, this is the step that will take us to our
Goal
State, but we do not know if it is correct or not, or if we have attained the desired result which lead us to our final step.
Step IV: Evaluate vs. Check. This is where you determine if the desired result has been attained or not. This is where we actually ascertain whether or not the
Goal
State has been reached. If the
Goal
State has been reached, then we can pat ourselves on the back and proceed with the next task at hand. If not, then we need to go back to our Planning stage and redesign the solution. This process is also called “feedback,” or in cybernetics lingo we refer to it as the “feedback loop.” The Wikipedia definition of feedback is: “Feedback is (generally) information about actions.
In cybernetics and control theory, feedback is a process whereby some proportion or in general, function, of the output signal of a system is passed (fed back) to the input. Often this is done intentionally, in order to control the dynamic behavior of the system. Feedback is observed or used in various areas dealing with complex systems, such as engineering, architecture, economics, and biology. Continuous feedback in a system is a feedback loop.”
A feedback loop is a system where outputs are fed back into the system as inputs, increasing or decreasing effects.
Often feedback and self-correction leads to adjustments varying with differences between actual output and desired output.
