Consider the following two statements:
Although at first glance these two statements seem to contradict each other, I feel that they are both correct.
Seymour Papert's seminal 1980 book is titled Mindstorms: Children, Computers, and Powerful Ideas. In this Logo-oriented book, Papert discusses empowering children&endash;making use of computers to facilitate children doing exploratory projects and developing mental models that will help their learning throughout their lifetimes. He talks about computer-based constructivism, in which students build on their previous knowledge and learn by doing. These are examples of powerful ideas that have continued to be at the forefront of information technology in education over the past two decades. Powerful ideas tend to provide an enduring framework for educational renewal and improvement.
Today's microcomputers have thousands of times the compute power (speed, memory) and vastly improved software compared to the microcomputers of 1980. The pace of technological change during the past 20 years has been overwhelming. But, Papert's Powerful Ideas&endash;as well as Logo&endash;have endured and are still quite relevant to our educational system.
Ten Powerful Ideas
The remainder of this editorial is a list of Powerful Ideas of IT in education that I feel will have enduring value. These ideas can help guide educators in their work with students. For each Powerful Idea, I include a very brief discussion. I will discuss some of these Powerful Ideas in more detail in future issues of Learning and Leading With Technology.
As you work with your students, you will want to help them gain a functional understanding of the Powerful Ideas outlined in this current article. A good way to do this is to weave these ideas into whatever aspects of IT you and your students happen to be using. Also, you may want to develop lessons that specifically focus on some Powerful Ideas. These Powerful Ideas will serve your students far into the future.
Quite likely you have your own ideas of possible additions to the list of Powerful Ideas given in this article. I hope that you will share your Powerful Ideas with others and me.
Logan, Robert K. (1995). The fifth language: Learning a living in the computer age. Toronto, Canada: Stoddart Publishing Company.
Moursund, D. (1999). Project-based learning using information technology. Eugene, OR: ISTE.
Norman, Donald A. (1998). The invisible computer: Why good products can fail, the personal computer is so complex, and information appliances are the solution. Cambridge, MA: The MIT Press.
Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York: Basic Books, Inc.
In the September 1999 issue of L&L, I listed 10 powerful ideas that are helping shape the present and future of information technology (IT) in education. Each of these powerful ideas cuts across many disciplines, makes effective use of IT, and has enduring value.
Lesson plans can be designed to help students simultaneously learn powerful ideas in IT and in other fields. I call these interdisciplinary IT (IIT) lesson plans. This months editorial discusses desirable features of IIT lesson plans.
The Principle of And
A good lesson plan has multiple, mutually supportive goals, all targeted toward supporting student learning. A good IIT-oriented teacher might make the following type of statement about a lesson plan she or he is developing: In this constructivist-based lesson I will help students learn one of the really important ideas in math and learn one of the really important ideas in IT and practice cooperative learning and work on their higher-order problem-solving skills and reinforce their basic skills. Note the ands in this sentence. As a teacher gains knowledge, skills, and experience, the teachers lessons tend to include more and more ands.
Features of a Powerful IIT Lesson Plan
This section lists and briefly discusses six features of a powerful IIT lesson plan. This list may help you as you develop powerful lesson plans for your own use and to share with others.
This section illustrates some of the thinking that might underlie the development of a powerful IIT lesson.
Graphing is a powerful idea from mathematics. Students learn to graph functions, relations, and all kinds of data. Such visual representations are useful for a wide range of problems and are fundamental to knowing and doing mathematics.
IT brings us computer graphicsthe ability to use a computer to graph functions, relations, and all kinds of data. The use of computer-based graphing brings new power to people working to solve math problems. Even such a modest tool as a graphing calculator is having a significant effect on the math curriculum.
Next, think about transfer of learning. Developing and using visual models is a powerful idea in many disciplines besides mathematics. For example, architects and engineers develop visual models of the structures they are designing. With the aid of computer graphics, they can allow such models to be viewed from different directions (including from the inside) and under different weather and lighting conditions.
Visual models are a key component of virtual realities. Virtual realities are a type of simulation, and computer simulation is a powerful idea from IT. With the aid of powerful computers, virtual realities (more generally, computer simulations) can be constructed that aid learning and problem solving in any discipline.
Notice how the discussion has moved from the relatively concrete (graphing in math, use of computers to do math graphing), to visual representations as an aid to representing and solving problems in many disciplines, to use of computer graphics in virtual realities. Virtual realities are an overarching IIT idea that will eventually have a profound effect on teaching, learning, and problem solving.
Moreover, virtual realities are a topic that many students find inherently interesting. Many of the computer games that girls and boys enjoy playing make extensive use of graphics to depict simulated worlds. These simulation games can be thought of as examples of virtual realities.
It is not easy to develop a powerful IIT lesson plan. It can be very helpful to have input from practitioners, discipline-oriented specialists, IT specialists, and educational researchers. That is the approach that ISTE has been using in the second phase of its NETS project. In this phase, sample IIT lesson plans have been developed. These lesson plans are available online at http://cnets.iste.org.
This fall, I have been discussing 10 powerful ideas that help shape the present and future of IT in education. Each of these powerful ideas cuts across many disciplines, makes effective use of IT, and has enduring value. This editorial is about lifelong learning #10 on the powerful ideas list. For the whole list, visit www.iste.org/L&L.
Historically, education has been viewed as a time-limited endeavor. We go to school, we get educated, and then we continue on with our lives. This model worked fine in a time of very slow technological and societal change, but it does not work well now. Lifelong learning is needed because ones limited number of years of formal schooling soon become seriously out of date.
Learning to learn and working toward being an independent, self-sufficient, lifelong learner are now important educational goals. IT is both one of the reasons for this and an aid to accomplishing it.
The Inquisitive, Playful, Fearless Learner
Consider the following scenario. You receive a package containing a new piece of hardware (such as a scanner, digital camera, or modem) or software. Which of the following best describes your approach?
Most adults take a cautious approachcloser to 1 than to 4to learning new hardware and software. This is in marked contrast to the way many children see such a learning task. Many children approach new hardware and software in an inquisitive, playful, fearless manner. They explorethey learn by doing. If they are with a group of their peers, they share their learning. Most IT educational leaders feel this is a very good approach.
Wouldnt it be great if all children had this set of learning characteristics, applied them both to IT and to everything else they wanted to learn, and maintained this approach throughout their lives?
This fearless approach suggests two educational goals. First, teachers should provide opportunities for students to develop and maintain their naturally inquisitive and exploratory approach to learning new hardware and software. Second, teachers should foster transferring this approach to learning from IT to other fields.
Some Implementation Ideas
1. Time is a precious commodity. Students have only a limited amount of time to learn what they need to know. Thus, educational content needs to be balanced among a variety of learning tasks, such as rote memory of important facts, developing higher-order cognitive and problem-solving skills, and learning to learn. Every lesson teachers prepare and every topic students study should be viewed as an opportunity for students to make progress toward these learning goals. Examine several of the lesson plans you have recently used. For each, estimate the percentage of student effort you feel was directed toward:
2. Routinely bring new pieces of software into your classroom. (This activity assumes that you have one or more computers for student use in your classroom. It can be modified to work in a computer lab.) As time and computer access allow, a student takes a new piece of software, installs it on the computer, and learns to use the software. The student then deinstalls the software and writes a brief report on the learning experience. This report focuses on the learning approach used, successes and failures, and insights gainedespecially insights about learning. This same activity can be used with hardware.
3. Take a look at the menu options in any relatively sophisticated software application such as a word-processing or graphics program. There may be dozens of options, and many of these may have suboptions. In total, there may be hundreds of different settings, choices, and optionsenough so that a person seldom masters all of them. A student can be directed to explore one of the options, learn some uses, help a fellow student learn it, and write about the overall learning experience.
4. Every few weeks, have every student do a Learn on Your Own assignment. A student selects a topic and develops an initial level of knowledge, skill, and expertise on that topic. Students set their own learning goals and self-assess. They write a report on each of their learning projects, with major focus on what they are learning about themselves as learners and the overall learning and self-assessment process. Some variations:
5. Browse the Web (or have your students do so) to find tutorials suitable for use by your students. Periodically (every few weeks), each student uses a tutorial to accomplish a learning task. The students are to self-assess the nature and extent of their learning and report on what they have learned about their own learning. This same activity can be used with computer-assisted learning tutorials available on disks and CD-ROMs.
Lifelong Learning in Your Classroom
What do you do to help your students learn to be independent, self-sufficient, lifelong learners? Please e-mail me some of your most successful practices.
Moursund, D.G. (December/January, 1999/2000). A typical student in 2016. Learning and Leading with Technology. Eugene, OR: ISTE.
What will the new millennium bring? Change! And, one of the major areas of change is apt to be education. The following scenario depicts some ideas about what I believe is likely to occur by 2016.
A Day in the Life of a 21st Century Student
It is still raining and cloudy early in the morning when Saundri finishes her breakfast and opens her personal education assistant (PEA). Clouds and rain mean the household solar energy system is not producing much power. Today is Saundris 15th birthday, and she is looking forward to a busy and fun-filled day. She hopes the weather will improve so that a lack of electrical power will not interfere with her evening party plans.
Glancing at her PEA, Saundri notices that the wireless connectivity to the Internet is solid at 2 MB per second. The battery level indicator is at the one-third level, indicating that she has about five hours of power. She will have to charge the batteries later in the day.
She also notes that her PEAs free memory is down to 25 GBsoon she will have to do some cleaning.
With a few voice commands, Saundri sends her previous evenings homework to her various teachers. While doing so, she thinks briefly about her math teacher located in
London; her science teacher in Washington, D.C.; her global studies teacher in Mexico City; her health teacher in San Diego; and her ancient history teacher in Athens. It would be neat to someday meet them face -to-face. Being in secondary school is fun, but she misses the face-to-face contacts of elementary school, when the teachers and students came together each school day.
Next, Saundri checks her inbox. She sees that she has quite a few e-mail, voice mail, and videophone messages.
A lot of her friends and fellow students from around the world have messaged her for her birthday. Also, all of her course instructors have provided feedback on the schoolwork she turned in yesterday, and her teammates have sent messages about several group projects.
Saundri opens the birthday greetings and talks to a couple of her friends. Because of time zone differences, many are not available, so she leaves messages. Several of her friends speak and write in languages Saundri does not know, but her PEA provides reasonable translations in real time. One message contains a gift for a free video (two viewings). She asks her PEA to download Gone with the Wind, her current all-time favorite. She will share it with a few friends and her family this weekend.
In her courses, Saundri is working on several large projects. In math and science, for example, her project is to explore situations in which research in mathematics has led to new discoveries in science and vice versa. She is one member of a four-person team collaborating on this project. Her specific task is to understand what led to the development of the math topics she is currently studying. One of the team members is working on developing animations based on drawings, paintings, and photographs of some of the research scientists and mathematicians. The intended audience for this team term project is students located throughout the world who are interested in both math and science. The team will publish its report as an interactive Web site designed to help the user learn about how math and science have benefited each other.
Saundri is working on another project individually. It combines global studies with health education. She is particularly interested in how the various levels of education in different countries around the world may be affecting levels of healthand vice versa. This is a project near and dear to her heart, because one of her brothers died from an infectious disease when he was only six years old. So, Saundri decides to work on this project for awhile.
She sets herself the task of looking at death rates from infectious disease
Meanwhile, her PEA has searched its own databases and begun a Web search. It reports that its own databases contain baseline data on education in the 273 countries, but that the desired health data is scattered over many thousands of databases available on the Web. Saundri picks two countries for her pilot study and tells her PEA how to set up the database. Her PEA indicates this will take at least an hour to explore the 72 Web sites that seem relevant. A number of commercial databases that contain this type of data are also available, and the PEA will check out the costs.
Rather than sit and twiddle her thumbs, Saundri asks to speak to her Personal Tutor. Her Personal Tutor is another computer-based agent that works with her as she uses the intelligent computer-assisted learning (ICAL) materials in her PEA. It immediately appears on screen and praises her for beginning her schoolwork so early in the morningand, on her birthday! Her Personal Tutor has complete records on what Saundri has studied, her interests, her preferred learning styles, and her areas of greatest intelligence from Howard Gardners most recent list of 10 intelligences. Saundris Personal Tutor and the ICAL system make it possible for her to study anything that she happens to want to study, at any time she wants to study it. The nature and level of instruction is always appropriate to her current knowledge and skills and incorporates the best current theories of teaching and learning.
Later in the morning Saundri takes a virtual reality (VR) field trip to a small village on Crete2,200 years ago. She wanders around the Greek village, stopping from time to time to observe in detail what the people are doing. This type of VR is a routine tool in the ancient history course she is taking.
The bus into Nairobi will be coming through her village in a few minutes, and Saundri is looking forward to this afternoons workout with the soccer team. Because this is Wednesday, she will have to be on time getting back to her village, because she has an important meeting with the village planners late in the afternoon. Saundri is developing a computer model of the environmental and infrastructure resources in and around her village. She is using geographic information systems (GIS) and decision support software to help village planners address problems the village faces. Part of the plan is to improve the water system to help prevent disease.
On the other four days of the week Saundri has choir practice and band practice early in the evening. She enjoys participating in the village's choir and band.
Moursund, D.G. February, 2000). IT as language and content: Powerful ideas shaping our educational system. Learning and Leading with Technology. Eugene, OR: ISTE.
In my September 1999 editorial, I listed 10 powerful ideas of information technology (IT) in education. (Read them online at www.iste.org/L&L.) Each of these powerful ideas cuts across many disciplines, makes effective use of IT, and has enduring value. Powerful Idea 5 is addressed here.
Logan (1995) argues that IT is a language-the fifth in the series that begins with natural language, reading/ writing, mathematics, and formal science. What is particularly interesting about the third and fourth languages- mathematics and formal science-is that each is both a "language" and a content area. For example, the language and tools of mathematics are inextricably intertwined with its content.
IT as language and the discipline of computer and information science are, of course, inextricably intertwined. But, IT has emerged as an aid to representing and solving problems in academic areas outside computer science. Thus, we have an entirely new phenomenon.
IT is becoming an integral component of both the language and the content of every academic discipline. This is gradually changing what it means to know and work in the various academic disciplines.
The spreadsheet was originally developed for use in business, and it certainly has changed the content of business courses. However, the spreadsheet is useful in representing and helping solve problems in a wide variety of disciplines. For example, a spreadsheet can be used to represent population data, do computations on the data, and draw graphs using the results of the computations. Because of its capability, the spreadsheet has affected the content of math, science, social science, and other subjects.
Geographic information systems (GIS) are a powerful aid to problem solving in geography, cartography, environmental engineering, and related fields. (GIS are spreadsheet-like, specifically designed for creating graphical representations of data stored on or with maps.) GIS contribute to major changes in die ways of representing and solving a wide variety of social science, science, engineering, and environmental problems.
In math, we have long had powerful math problem-solving and manipulation systems such as Mathematica and Maple. Many secondary school mathematics courses now make routine use of handheld calculators that can automatically graph functions or solve equations. These and similar powerful tools are now routine parts of the ways of understanding and using math throughout all areas of science and engineering.
Graphic design software has completely changed mechanical drawing and graphic artist coursework. Musical Instrument Digital Interface (MIDI) software and related hardware have changed the music industry. Desktop publishing software has changed the publishing industry. Computer-based animation and computer-based editing have strongly affected the movie industry. In each of these examples, the content of the discipline and how one solves problems in the discipline are becoming inextricably intertwined with IT.
Some Implementation Ideas
These teaching ideas focus on IT as interdisciplinary language and content.
IT is of growing importance within the content of each academic discipline. Therefore, each teacher needs to help his or her students learn how IT is affecting the disciplines he or she teaches. Schoolwide and districtwide planning and coordination are needed in this endeavor, with a special emphasis on articulation across different courses and grade levels.
Maple is available from Waterloo Maple, Inc. Find out more by visiting www.waterloomaple. com or calling 800.267.6583 or 519.747.2373.
Find out more about Mathematica by calling 800.441.MATH or 217.398.5151 or by visiting Wolfram Researchs Web site at www.wolfram.com.
Word is available as a stand-alone product or as part of Microsofts Office suite from your local software reseller or at www.microsoft.com.
For more on geographic information systems, visit www.geoinfosystems.com, and for more on the Global Positioning System, visit www.gpsworld.com.
Logan, R. K. (1995). The fifth language: Learning a living in the computer age. Toronto, ON: Stoddart Publishing Company.
In the September issue of L&L (vol. 27 no. 1), I briefly discussed 10 powerful ideas that are helping shape the present and future of information technology (IT) in education. Each of these powerful ideas cuts across many disciplines, makes effective use of IT, and has enduring value. Communication is an underlying theme in many of these powerful ideas and is especially emphasized in #1 and #8. For the whole list, visit www.iste.org/L&L.
Humans are social creatures. They have developed many different aids to communication, such as written language and the telephone. These aids to communication have helped change the world. Now many of us make routine use of cyberspace aids to communication such as e-mail, the Web, and interactive hypermedia.
Communication (reading, writing, speaking, listening, and viewing) is part of the basics of education. Logan (1995) argues that information technology is a language (a new form of communication). Our educational system is faced with the challenge of deciding what we want students to learn about the cyberspace communication aids.
Synchronous and Asynchronous Communication
A face-to-face conversation is a synchronous communication. The speaker and listener alternate rolesindeed, both may talk at the same time. The telephone and videophone facilitate a synchronous interactive communication between people who are separated by great distances. Such a two-way communication can be carried on through the Internet.
Sending and receiving letters provides an example of an asynchronous communication. The communication may be interactive or one-way, and typically there is a substantial time delay between the sending of the communication and the receiving of the communication. The telegraph and e-mail both facilitate asynchronous communications.
Publishing and Broadcasting
Book and magazine publications, as well as radio and television broadcasts, tend to be one-way communications. Of course, you can write a letter to the editor or call a talk show. Thus, these forms of communication have some of the same characteristics as synchronous or asynchronous interactive communication. However, the level of interactivity is generally quite low.
The Web and Hypermedia
At first glance, one might think of a Web site or a hypermedia document as just another form of publishing or broadcasting. But wait! A hypermedia document or a Web site can be designed so that it is interactive. In essence, the hypermedia or Web site creator can design various types of immediate response to help give the communication some synchronous interactive features. This is a new type of communication, a sort of blend between the interactive and the one-way types of communication. In the remainder of this article, I will call it interactive broadcasting.
One of the goals of research and development in artificial intelligence (AI) is to significantly improve interactive broadcasting. Gradual progress is occurring in developing AI software that can understand incoming communications and that can respond (for example, by providing various types of written or oral output) in an intelligent manner. Perhaps you use a primitive form of such software to filter your incoming e-mail, dividing it into various categories, and perhaps automatically responding to some of the messages.
Some Implementation Ideas
A key idea to keep in mind is that the older forms of communication are not going away. A student needs to develop facility in both the older and newer forms of communication and learn when each is most appropriately used.
1. Have your students work in teams to make a list of modes of communication and classify each communication as interactive, broadcast (low or no interactivity), and interactive broadcast. The teams are to give examples of common uses of each of the modes of communication. Additional activities:
2. Have your students do research on Alan Turing (Alan Turing, 1998). One of Turings contributions to the field of computer and information science is now called the Turing Test. Turing challenged computer scientists to develop hardware and software that could carry on a conversation (for example, using e-mail) with a person. The test is to develop a conversation program that is so good that people cannot readily tell if they are communicating with a person or with a computer. Some additional activities:
In my September 1999 editorial (L&L vol. 27 no. 1), I briefly discussed 10 powerful ideas that are helping shape the present and future of information technology (IT) in education. This editorial is about information appliancesnumber 2 on the list. It also touches on ideas from number 4 (user interface) and number 6 (problem solving). See the whole list at www.iste.org/L&L.
What Is an Information Appliance?
Many years ago, I memorized the statement, A computer is a machine for the input, storage, processing, and output of information. In those days, my model of a computer was a mainframe housed in an air-conditioned building and supported by a large staff of technicians and computer operators. Eventually minicomputers and then microcomputers were developed. The need for a special air-conditioned building and staff disappeared. The humanmachine interface improved to the level that ordinary people could use a computer to accomplish tasks such as writing and e-mail communication.
However, microcomputers are not very user friendly. The humanmachine interface favors the machine, not the human.
Contrast this situation with the smart card. A smart card looks like a credit card, but it has embedded electronic circuitry. It can be used for the input, storage, processing, and output of informationthat is, it satisfies the definition of being a computer. I recently saw a newspaper article indicating that 1.25 billion smart cards were produced this past year. That is approximately one smart card for every five people on earth. They cost about $4 each to manufacture.
A smart card is an example of an information appliance. It can be thought of as a special-purpose computer designed to accomplish a specific task. For example, the task for a smart card might be fiscal (a credit card and a device that actually stores money) or medical (storage of medical records). The humanmachine interface is quite easy to use, and the focus is on the task to be accomplished, not the technology.
How many handheld calculators do you own? My wife and I collectively have a dozen or more. They are scattered around our various work and home offices and at convenient locations around the house. The handheld calculator is an information appliance. A person tends to have more than one of an appliance, like a radio or television, that is particularly useful. Moreover, the brand name tends not to be important. All four-function calculators are pretty much alike. They all can accomplish the task they are intended for, and it is quite easy to transfer ones calculator knowledge and skills from one of these inexpensive information appliances to another.
Chances are you have used a digital camera or a scanner. Digital cameras are still relatively expensivethey can be thought of as an emerging information appliance. Scanners are now available for less than $100, and some are now quite specialized. For example, one can purchase a scanner for digitizing photographs. Both a digital camera and a scanner are quite easy to use, and each is oriented to accomplishing a specific task. From a user point of view, the focus is on learning to accomplish the task, not on learning to use the technology.
Donald Norman (1998) presents a comprehensive picture of the gradual but accelerating emergence of information appliances. He also analyzes how a new technology can disrupt an industry. You are probably familiar with how IBM failed to adjust to microcomputers (a disruptive technology) and was severely damaged by this failure. Similarly, Microsoft was slow to adjust to the Web (a disruptive technology) but then rapidly made the necessary changes.
From the point of view of our education system, distance learning (especially Web-based distance learning) is a disruptive technology. At the postsecondary education level, distance education has introduced new courses that compete with existing courses and will eventually supplant some of them. Clearly, higher education will be disrupted. Moreover, such distance education is already available to a number of secondary school students. Disruption at the secondary level will also occur.
Information appliances are disruptive technologies. They disrupt businesses, and some of them will disrupt education. We see signs of this with calculators, which have affected math curriculum content and assessment. We see signs of this with handheld messaging devices (which may also be calculators, dictionaries, or word processors) that students may use to exchange information when taking a test. And, of course, students carrying electronic pagers or cell phones can be quite disruptive in class.
A deeper issue is illustrated by the following questions: If an information appliance can accomplish a task that we currently teach students to do by hand or by other means, how should this affect education? Should curriculum content, instructional processes, and assessment change to reflect inexpensive, readily available information appliances?
To stretch your mind a little bit, think of the emerging electronic digital global library. Imagine each student having a library appliance. It contains a huge built-in library, and it automatically accesses the global library as necessary when wireless or wired connectivity is available. Moreover, the user can readily add to this library with a personal database of people and documents and an appointment calendar. This library appliance contains the books and other resource materials that the student is studying now and has studied in the past. How would this affect what we currently teach about library use or about any specific subject matter? Should students use such an information appliance while taking tests?
Information appliances such as the handheld calculator and electronic dictionary have been with us for a long time. The continued rapid progress in chip technology, flat panel display screens, batteries, and connectivity will bring us many more information appliances in the near future. Many of these will be disruptive to our education system.
Think about how you deal with such technologies. Are you taking a proactive approach to acquiring these information appliances and introducing them to your students? Do you work to make these information appliances a routine part of your curriculum, instruction, and assessment? As an IT-knowledgeable teacher, do you enjoy living at the cutting edge?
Though microcomputers will continue to be very important in education, information appliances are emerging as a new cutting edge of IT in education.
Norman, D. (1998). The invisible computer: Why good products can fail, the personal computer is so complex, and information appliances are the solution. Cambridge, MA: The MIT Press.
In L&L vol. 27 no. 1, I listed and briefly discussed 10 powerful ideas of information technology (IT) that are helping shape the present and future of IT in education. Each of these powerful ideas cuts across many disciplines, makes effective use of IT, and has enduring value. This editorial is about problem solvingnumber 6 on the powerful ideas list. It also focuses on number 3 (effective procedure) and number 7 (modeling and simulation). (Read the complete list online at www.iste.org/L&L.)
What Is a Problem?
Each academic discipline can be defined by the types of problems that it addresses, the methodologies it has developed, and its accomplishments. Clearly, when a math teacher talks about math problems, the story is quite a bit different than when a psychotherapist talks about a patients problems or an elementary teacher talks about a students learning problems. Thus, the meaning of problem differs significantly from discipline to discipline.
However, there is some commonality. You have a problem when you experience a situation in which there is a difference between the way things are and the way that you would like them to be. You can then decide whether to apply your personal resources (e.g., time, knowledge, skills, and money) to achieve the desired goal or accomplish the desired task.
When you work to solve a problem or accomplish a task, you are building on your own and others previous work. In doing so, you are following the most important idea in problem solving.
Previous work includes humans development of reading, writing, and arithmetic. It includes the teaching of your parents and others who helped you learn to speak and listen. It
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