CK-12 Engineering: An Introduction for High School
Page 15
Science connection. A knowledge of the science underlying the various existing techniques is necessary so that the widest range of approaches to providing water is explored.
Math connection. Mathematical models may be used here to examine water costs for different systems so that a reasonable set of requirements and constraints are used in generating the problem statement. There are mathematical models that describe costs for existing techniques, but new models would need to be created if a new technology was devised.
Brainstorm Alternative Solutions. At this stage of the process the widest variety of ideas and/or possible solutions needs to be explored for the design problem. These ideas can come from many different sources: existing products, brainstormed ideas, ideas from scientific principles, and any other approaches possible. The body of these possibilities, or design concepts, needs to then be shaped into a component, system or process that could fulfill the set of requirements and constraints as possible problem solutions. Some approaches may be thrown out early if they have little potential (e.g., supplying pure water from icebergs to a village near the equator is probably not feasible).
Science connection. A variety of solutions could be generated based on scientific principles as shown with the following examples. Sea water can be purified by freezing, but this is not a good approach for a village near the equator. Purifying sea water by distillation (evaporation and condensation) could be used in a solar still or in a flash evaporation plant. Purifying seawater by removing salt with a membrane could be done with a reverse osmosis plant. Moving pure water to the town by new wells, by truck or by pipeline are other possible solutions without much science.
Math connection. Mathematical models to roughly estimate costs for the various approaches could be generated in the first portion of this step of the design process. They are also used to predict a cost for various alternative solutions that arise during idea generation phase and can help analyze the linkage between the science behind a technique and the cost of implementing it with materials, fabrication or manufacturing, operation, and maintenance. These costs then need to be normalized for the sake of comparison with other options to cost per thousand gallons of water.
Evaluate Solutions. Potential designs are evaluated relative to the constraints and criteria, and one or more are selected to be designed in detail and prototyped. The selection is made using a structured process that requires the requirements be met and chooses the best design according to the requirements and constraints. To continue to show math and science connections it will be assumed that the best design was a solar still for desalination (Figure 7). Using that choice other design steps will now be considered.
Design and Build Prototype. The selected design is developed in full detail and components' specific shapes and dimensions determined. Materials are selected and components are fabricated and prototype assembled. Prototype operation and performance may be modeled on a computer. For the hypothetical design a prototype solar still is built.
Science connection. A more detailed knowledge of the science can be created with more accurate values of physical parameters which will also provide information that may affect various costs for the components of the prototype. The nature of the physical phenomena that are occurring within various components should be modeled from the viewpoint of the science-based ideal so that performance can be evaluated when the prototype is tested.
Math connection. Mathematical models of performance based on science phenomena will be generated to evaluate the prototype.
Test and Evaluate prototype. Prototypes are tested to see if the design meets all requirements and performs acceptably. The performance should be compared to the ideal performance determined from mathematical modeling of the prototype. Differences between the ideal and real performance should be analyzed and understood. The design process may be iterated and refined to improve performance until it is acceptable. Sometimes, testing and evaluation show that a design will not work, so that a different design concept must be selected by returning to evaluate alternative solutions. If the hypothetical solar still meets performance specifications and fulfills constraints then solution can be communicated
Science connection. The scientific model of operation should approximate the actual prototype performance; if not, then there may be science phenomena not correctly implemented in the model or there may be other issues in construction or operation that needs to be diagnosed to have a model that is a good predictor of performance.
Math connection. The mathematical model of operation should be tested to make certain that the model has been constructed properly using the appropriate science and mathematics.
Communicate results. The activities and results of the design process should be documented and communicated to the appropriate client or customer.
Science connection. All steps of the design process should be documented and justification for decisions should be made clear. The science behind the choice of the solution to the design problem should be made clear, including factors and weights of requirements and constraints used to select the solution.
Math connection. The mathematical model of operation should be well documented so that a basis for performance and effectiveness of the design is demonstrated. The model should also be documented so that the effectiveness of the design in fulfilling the client's needs is demonstrated.
Activity - Connecting Math and Science to the Engineering Design Process in Addressing a Global Societal Issue or Problem
Select one issue of your choice from the list of global issues in Table 1 of the What Is the Role of Science and Mathematics in Engineering? section. Specify and write down the problem scenario that describes the people and their situation who are the clients who will benefit from your design problem solution for the chosen Societal Issue. Now explain and write down what types of engineers are needed for the project team that will be working on the Societal Issue. Now, as was demonstrated for the Case Study previously, describe and write down for each step in the Simplified Design Process what is happening for the chosen Societal Issue along with what math and science is being used and how it is being used.
Review Questions
Multiple Choice
The following question will help you assess your understanding of the Connecting Mathematics and Science to the Engineering Design Process section. There may be one, two, three, or even four correct answers to each question. To demonstrate your understanding, you should find all of the correct answers.
An important use of mathematics in engineering is to determine how much engineers should be paid for a design
the price of software needed to create a design
the cost of different designs of the same product
how much to charge a customer who wants a design
Free Response Questions
What role do math and science play in the creative process of engineering design?
What impact do science and math play in designing and developing a better artifact from the engineering design process?
How do math and science connect with engineering in the engineering design process compared to what happens in other types of design processes (architectural, fashion, etc.)?
How can you tell if an artifact created from a design process has considered enough ideas from engineering, science, and math connections, and the associated variety of possible problem solutions to ensure that a high-quality artifact has been created from an effective design process?
What is the role of math and science in connecting to engineering in developing characteristics of a good problem definition statement?
How are math and science connections to engineering used in the steps of the engineering design process? Why the steps are not always completed in order?
How does the connection of math and science to engineering affect the team decision making processes in the engineering design process?
What role does the connection of math and science to engineerin
g play in creating a detailed design from implementing the major concept of the chosen solution to the design problem?
Review Answers
Connecting Mathematics and Science to the Engineering Design Process
c
Vocabulary
Accredited
To have been endorsed or approved officially. Undergraduate engineering programs are accredited when they meet the standards of a national board, Accreditation Board for Engineering and Technology (ABET).
Artifact
Something created or modified by humans usually for a practical purpose.
Component
A distinct part or element of a larger system.
Constraint
A constraint is a limitation or condition that must be satisfied by a design.
Criterion
A criterion is a measurable standard or attribute of a design; for example, weight and size are both criteria. Criteria are used to compare different possible designs and determine which better solve the design problem.
Engineer
someone who uses scientific and mathematical knowledge to solve practical problems and produce goods and processes for the benefit of society.
Engineering design process
“the process of devising a system, component, or process to meet desired needs. It is a decision-making process (often iterative), in which the basic sciences, mathematics, and the engineering sciences are applied to convert resources optimally to meet these stated needs.” (ABET)
Implement
To successfully put into action or carry out to completion.
Innovation
The process of incrementally or radically modifying an existing product, system, or process to improve it.
Integrated circuit
An electronic circuit of transistors etched onto a small piece of silicon which is sometimes referred to as a microchip.
Invent
To come up with a new, useful, and nonobvious idea, plan, explanation, theory, principle, novel device, material, or technique which is a creation of the mind.
Invention
A new and useful device, method, or process developed from study and experimentation.
Iterative
Repetitive or cyclical. The engineering design process involves the completion of project tasks or phases in repetitive cycles until a desired result is achieved.
Mathematical model
The quantitative general characterization of a process, object, or concept, in terms of mathematics, which enables relatively simple manipulation of variables in order to determine how a process, object, or concept would behave in different situations.
Prerequisite
Something required beforehand.
Phenomenon
An observable fact or event; an outward sign of working of a law of nature.
Prototype
A trial working model of a design that is built to test design decisions and identify potential problems.
Prosthesis
An artificial replacement for a missing body part.
Science
The observation, identification, description, experimental investigation, and theoretical explanation of natural or human-made phenomena.
Semiconductor
A substance that conducts electricity better than an insulator but not as well as a conductor. Silicon is a semiconductor used to make microchips.
System
A group of interacting, interrelated, or interdependent elements forming a complex whole.
References
ABET, Inc. “Criteria for Accrediting Engineering Programs 2007–08”. March 17, 2002. Available on the web at
http://www.abet.org/Linked%20Documents-UPDATE/Criteria%20and%20PP/E001%2007-08%20EAC%20Criteria%2011-15-06.pdf
American Association for the Advancement of Science (AAAS). Project 2061: Science for All Americans. American Association for the Advancement of Science, Inc., Washington, D.C., 1989.
US Department of Labor. “Occupational Outlook Handbook.” July 2008. Available on the web at
http://www.bls.gov/oco/
Instructor Supplemental Resources
Standards
ASEE Draft Engineering Standards This chapter is focused on “Dimension 2: Connecting Science and Mathematics to Engineering” of the ASEE Corporate Members Council Draft Engineering Standards; these draft standards will serve as input to the National Academy of Engineering process of considering engineering standards for K-12 education. This dimension includes the following outcomes:
Students will develop an understanding of the essential concepts and application of science and mathematics as they pertain to engineering design.
Students will be able to apply concepts of science and mathematics in an engineering design process.
Student Preconceptions about Engineering and the Math and Science Connections
Students hold many preconceptions about who engineers are, what they do, and how science and math connect to their activities. These preconceptions may negatively affect precollege students’ decisions about considering engineering as a career, especially so for females and minorities. Some preconceptions are discipline specific and some are for engineering in general.
What do engineers do? Some precollege students believe that engineers work mainly on technical hands-on activities such as repairing cars, installing wiring, driving machines, and constructing buildings but do not work on activities such as designing things, designing for clean water, and supervising construction.
Who can be an engineer? Precollege students and their teachers often believe that females and minorities less likely to succeed when they intend to go into the engineering profession.
Chemical engineering preconceptions. Precollege students believe that chemical engineers principally work in their own labs; work in dirty and unsafe places; and do not care about the environment.
Math and science ability. Many middle and high school students believe that, in order to succeed in studying the subjects of engineering, mathematics, or science in college, a person must have to be very smart and/or have a talent for those subjects.
The nerd factor. Students’ images of professionals are strongly influenced by media stereotypes, so they think of scientists and engineers as brainy, absentminded, unkempt, and wild-haired eccentrics. Many do not know any real scientists or engineers.
Financial aid. Many middle school and high school students do not think there are resources to help support their higher education. Their lack of awareness of financial assistance may prevent them from enrolling in engineering where there are multiple resources such as scholarships, company internships, and undergraduate research.
Career opportunities. In one middle school students had unrealistic career expectations. A survey revealed that three-quarters of them thought they could become scientists or engineers, but the same number also thought they could become professional athletes. With 4 million people in US STEM careers and 3,500 in professional athletics, the odds are about 1,000 to 1 in favor of a student having a STEM career compared to becoming a professional athlete. This seems like a good reason to consider enrolling in math and science classes in precollege education.
Chapter 6: A Brief History of Engineering
About This Chapter
Today, much of the world’s population lives in engineered environments. Most of us are surrounded by technological devices that dramatically affect how we live our lives. We live in houses whose structural, electrical, plumbing, and communications systems have been designed by engineers. We travel in cars, trucks, trains, and airplanes; we communicate with each other using televisions, computers, telephones, and cell phones. Engineers have played a key role in the development of all these devices.
It is not difficult to imagine life without many of these advances; in fact, some of the world’s poorest people live today without the benefits that we take for granted, such as clean water and working sanitation systems, plentifu
l food, and electronic conveniences. Much of the history of engineering has been directed at such problems, and we are the beneficiaries of their solutions as well as the inheritors of unforeseen new problems that engineering solutions have created.
The work of engineers has dramatically affected the nature of our society today as well as the course of civilization throughout the centuries. Engineers are often seen as purely technical individuals whose only concern is the development of new devices or structures. However, this is far from the truth. Throughout history, engineers have worked within their societies and have been constrained by their societies; the success or failure of engineering endeavors often has less to do with technical issues than with nontechnical issues including economics, social conventions, and luck.
Most modern definitions of engineering emphasize the application of knowledge of science and math to develop useful objects, products, structures, and so forth. While this is certainly true of modern engineers, engineering practice has historically extended beyond the use of science and math to include the ingenuity required to make things work. Many engineering feats of the past are even more impressive because they were achieved without a complete understanding of important scientific principles. Thus, for example, medieval cathedral builders can be considered as engineers even though their scientific understanding of forces and loads in structures was limited. Even with today's rapid advances in knowledge, much modern engineering practice involves solving problems that are not necessarily rooted in math or science.