Brief Introduction to Roles of Computers in Problem Solving

Dave Moursund
Updated 12/07/06

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This short book provides an introductory overview of the field of problem solving as well as an introduction to roles of computers in problem solving. The book is intended for preservice and inservice educators. It is designed for use in workshops, short courses, integration into non-computer courses, and for self-study.  

PDF Version of the booklet. Last updated 12/13/04.

Microsoft Word Version of the booklet. Last updated 12/13/04.

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** These materials are Copyright (c) 2004 by David Moursund. Permission is granted to make use of these materials for noncommercial, non-profit educational purposes by schools, school districts, colleges, universities, and other non-profit and for-profit preservice and inservice teacher education organizations and activities.

Other free educational materials developed by Dave Moursund are listed at http://darkwing.uoregon.edu/~moursund/dave/Free.html.

Possible references for use in next revision:

http://questioning.org/Q6/question.html. Question asking.

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Notes for 1-hour Presentation 12/04/02

The 50-page booklet Brief Introduction to Roles of Computers in Problem Solving is suitable for use in a 10 class-hour unit of study. When faced with only one hour in which to hit some of the highlights, I focused mainly on the first 11 pages. Here are my notes for working with a group of about 40 inservice teachers.

A Few Key Ideas on ICT in Problem Solving

Dave Moursund 12/4/02

We will work in groups of about 3-4 people. Within each group, each person should designate themselves as a different one of the following:

  • A Language Arts person
  • A Math person
  • A Science person
  • A Social Science person
  • An "Other Discipline" (name the Specific Discipline) person

In the small group discussions that we will be employing throughout this hour, each person should try to reflect their "Discipline" orientation and point of view.

While We Wait for Late Arrivals

Take a look at the Google Search provisions provided on the OTEC Website. One can search the OTEC site, the Darkwing Domain, or the WWW. Just for the fun of it, search for Virtual Manipulatives on the OTEC site. And, think about the idea that a hardcopy book is organized in a linear fashion, with a Table of Contents and an Index to aid the reader in finding specific content. That is quite a bit different from the aids to information retrieval available for electronic documents.

Part 1: Introduction

1A. The term "problem solving" includes:

  • posing, clarifying, and answering questions
  • posing, clarifying, and solving problems
  • posing, clarifying, and accomplishing tasks
  • posing, clarifying, and making decisions
  • using higher-order, critical, and wise thinking to do all of the above

1B. Activity. Each person in a discussion group is to give some examples of the general types of problems from the Discipline that they represent. We are looking for examples of problems that require higher-order thinking skills, rather than lower-order thinking skills.

2A. Each academic discipline can be defined by the general nature of the problems it addresses, the methodologies that it uses, and its accumulated results. It is not enough to say that math addresses math problems while history addresses history problems. More detail is need on the nature of the problems that are addressed, the methodologies used, and the results that have been achieved.

2B. Activity. Each person in a discussion group is to give some examples of some of the Big Ideas in the accumulated results of the Discipline they represent.

3A. An Educational Goal: We want to help students to gain increased expertise in problem solving.

3B. Activity. Each person in a discussion group is to explain how both a teacher and a student can gain increasing expertise within the Discipline they represent.

Part 2: A Few Golden Nuggets

4A. There is no fine dividing line between lower-order skills and higher-order skills. Typically, "real-world" problem solving requires the use of a combination of lower-order and higher-order skills drawn from a wide range of disciplines. The two theories Constructivism and Situated Learning tell us that teaching & learning environments us that teaching environments and content should be an appropriate blend of:

  • Lower-order and higher-order
  • Specific discipline and multidiscipline

4B. Activity. Each person in a discussion group is to give some examples of teaching/learning environments within their Discipline that focus mainly on lower-order skills, and some examples that focus mainly on higher-order skills.

 

5A. One of the most important goals in education is to facilitate students learning in a manner that transfers over time, distance, and problem domains.

5B. Activity. Each person in a discussion group is to give some examples on how they teach for transfer of learning as they teach their Discipline.

 

6A. Typically, real-world problem solving makes use of a wide range of resources, and one way to view some of these resources is via the diagram given below. Information and Communication Technology (ICT) includes a large and steadily growing collection of powerful resources

6B. Activity (Whole group). Brainstorm and discuss how Information and Communication Technology fits into items 1-5 given above.

Notes for 2-hour Presentation 4/16/03

 

 

 

A Few Key Ideas on ICT in Problem Solving: 2-Hour Session

Dave Moursund

University of Oregon

The 50-page booklet Brief Introduction to Roles of Computers in Problem Solving is suitable for use in a 10 class-hour unit of study. When faced with only two hour in which to hit some of the highlights, I focused mainly on the first 11 pages and then a few additional highlights. Here are my notes for working with a mixed audience of teachers, school administrators, and other educators. The book is available at: http://darkwing.uoregon.edu/~moursund/SPSB/.

 

Getting Started

Organize Yourselves into Small Groups

Problem solving is part of each discipline or field of study. We will work in groups of about 3-4 people. Some people in a group will need to "pretend" that they are filling a particular role. Within each group, each person should designate themselves as a different one of the following:

  • A Language Arts person
  • A Math person
  • A Science person
  • A Social Science person
  • An "Other Discipline" (name the Specific Discipline) person

In the small group discussions that we will be employing throughout this presentation, each person should try to reflect their "Discipline" orientation and point of view. Begin by introducing yourself within your areas of actual expertise, and saying what teaching area you will represent in small group discussions.

 

 

The following diagram represents the reason why we are doing an entire two-hour session on ICT and problem solving.

 

Three Key Ideas in this 2-Hour Session

  1. Problem Solving, Critical Thinking, and Higher-Order Knowledge and Skills are part of every subject taught in school, and at every grade level. When we say Problem Solving during this presentation, we mean the full range of solving problems, accomplishing tasks, critical thinking, higher-order thinking, posing and solving hard problems, and so on.
  2. Information and Communication Technology (ICT) is now a useful aid to problem solving in every subject area. Our education system needs to help students gain knowledge and skill in making effective use of ICT both as an aid to problem solving and as a source of new problems within the various non-ICT disciplines. ICT is an aid to the key idea of "revise, revise, revise) that is useful if writing, composing music, working in the graphic arts, and in doing almost any other project that takes place over a period of time.
  3. We want to help our students increase their level of expertise in many different disciplines.

 

 

 

 

Examples of Problems in the Various Disciplines

Ask for volunteers to briefly state the kinds of problems and/or the kinds of tasks that a student learns to deal with in each of the following areas:

  • Language Arts
  • Math
  • Science
  • Social Science
  • An "Other Discipline"

The goal is to help make it more clear that each discipline includes a focus on Critical Thinking and Problem Solving--on higher-order knowledge and skills. Each discipline has a "higher-order" component and study of the discipline is oriented toward students moving into this higher-order realm.

Research in problem solving tells us:

  • There are some aspects of problem solving that cut across many different disciplines.
  • There are other aspects of problem solving that are highly discipline specific.
  • Each discipline has lower-order and higher knowledge and skills. While rote memorization of facts and information is one aspect of getting better at problem solving, no amount of such memorization can make you good at problem solving within a discipline.

Activity

In your small group, think about the emphasis on lower-order knowledge and skills versus the emphasis on higher-order knowledge and skills in the curriculum and assessment. Discuss:

  • Roughly what percentage of student learning time and effort focused on lower-order knowledge and skills at the elementary school level (grades K-5) and at the secondary school level (grades 6-12)?
  • Are there significant differences among the different disciplines, in terms of the teaching emphasis on lower-order versus higher-order knowledge and skills?

At the current time, the following beam balance scale represents our educational system's treatment of lower-order and higher-order knowledge and skills.

 

Beam balance of lower-order versus higher-order knowledge and skills. Lower-order is the more heavily emphasized side.

 

 

Information Retrieval Using the Web

This section requires good Web access. If that is not available, skip this section.

The Web can be thought of as being a Global Library. Problem: How do you find what you want to find when faced by such a huge library?

Example: Suppose that you wanted to know more about me (Dave Moursund).

Answer: Use a search engine such as Google. Lets try the search word Moursund. Then try David Moursund. then try "David Moursund"

Example: Now, suppose that you want to know where I went to college as an undergraduate. How do you find information? How about using Google and the search phrase

  • Where did David Moursund do his undergraduate college work?

This doesn't work very well. But it would work really well if you were talking to a person who knew the answer. There is a difference between retrieving information from a book, from a computer, and from a person.

You might try: using a phrase in the search.

  • "David Moursund" resume
  • "David Moursund" vita

Conclusion: Even in this simple task we see that there is quite a bit to learn in dealing with the problem of finding information. It takes a lot of education and practice to be good at solving information retrieval problems.

Activity

Information retrieval is a very important problem area--part of education in every discipline at every grade level. How do we educate students in this discipline? In discussing the topic of information retrieval, include a focus on:

  • To what extent is information retrieval domain specific, and to what extent can we help students gain information retrieval knowledge and skills that cut across most disciplines?
  • How do computers and other ICT affect the information retrieval? (For example, can students gain a higher level of knowledge and skill at a lower grade level, as compared with "traditional" methods of retrieving information such as from hard copy books?)

The Overall Problem of Information Storage and Retrieval

Information storage and retrieval--along with information overload and rapid growth in the totality of human knowledge--is a major problem. This section helps to emphasize that "problem" is not just a math problem.

  • What are the various "media" used to store information? Examples include materials, people, photographs, audio tape, video tape, electronic media, hand tools, power tools, machines, paintings, statues, and other artifacts. In addition, there is much information stored in our environment, in "nature."
  • For each storage medium, what are aids to retrieving information that is in that storage medium?
  • For each storage medium, what do we want students to learn about storing information? For example, we want student to learn to write. Do we want them to learn to do still and video photography? Do we want them to learn to make tools? Do we want them to learn to develop hypermedia documents such a Web pages?
  • It is clear that the computer has added new storage media and new aids to retrieving information. Does this allow us to drop anything from the information retrieval curriculum?

Activity

Carry on a discussion on the idea of helping students learn how to:

  1. Retrieve information from a variety of storage sources, deciding which sources and which information is valid and useful in a particular problem-solving situation. Note that each teacher is responsible for this within the disciplines they teach.
  2. "Write" (that is, develop) hypermedia documents. If you support this idea, who should teach it, and when? What should be dropped from the curriculum to make room for this new Language Arts topic?

Problems and Problem Solving

 

What is a problem?

 

The term "problem solving" includes:

  • posing, clarifying, and answering questions
  • posing, clarifying, and solving problems
  • posing, clarifying, and accomplishing tasks
  • posing, clarifying, and making decisions
  • using higher-order, critical, and wise thinking to do all of the above

   

You (personally) have a problem if the following four conditions are satisfied:

  1. You have a clearly defined given initial situation.
  2. You have a clearly defined goal (a desired end situation). (Some writers talk about having multiple goals in a problem. However, such a multiple goal situation can be broken down into a number of single goal problems.)
  3. You have a clearly defined set of resources that may be applicable in helping you move from the given initial situation to the desired goal situation. There may be specified limitations on resources, such as rules, regulations, and guidelines for what you are allowed to do in attempting to solve a particular problem.
  4. You have some ownership--you are committed to using some of your own resources, such as your knowledge, skills, and energies, to achieve the desired final goal.

Important point: Most of the things that we call problems actually do not satisfy the definition given above. If one or ore of the components are not satisfied, we call this a "problem situation." An important aspect of attempting to resolve a problem situation is to first get the problem situation clearly stated (clearly defined) as a problem.

Activity

Within your groups, discuss what new types of problems or areas of study are added by computer technology, and what aids to problem solving are provided by computer technology. Each person is to discuss this from the point of view of the discipline they are representing in their group. Example: in Language Arts, we now have the problem of helping students learn to read and write interactive hypermedia that includes text, color, sound, still and motion graphics, and pictures, and video.

Expertise in a Discipline

What do we mean when we say that a person has a high level of expertise--a high level of knowledge and skills--within a particular area?

If the person is a young student, we might compare the student to other young students. If the person is older, we might compare the person to other equally old people.

In any case, we can look at an Expertise Scale, where the comparison is made within a specified group.

 

 

Moving up the Expertise Scale involves :

  • Gaining increasing knowledge and skills in the lower-order aspects of the discipline.
  • Gaining increasing knowledge and skills in the higher-order aspects of the discipline.
  • Gaining in fluency, experience, quality of performance, etc.
  • Gaining increased knowledge and skills in using the tools of the discipline.
  • Gaining increased understanding of the goals of the discipline, what has been accomplished, what constitutes high standards, and so on.

 

Problem: What are Efficient and Effective Ways to Increase in Expertise?

Think of the problem or task of gaining increased expertise in a discipline. For each discipline where we are thinking about an Expertise Scale, we can ask several key questions:

  1. To what extent are computers and other aspects of ICT now an actual part of the discipline?
  2. To what extent can computers and other ICT help in the process of gaining increased expertise in the discipline?
  3. To what extent have computers and other ICT helped make some of the discipline content that we used to call "higher-order" into less high-order, or even lower-order?
  4. How is the teaching of the discipline affected by an increasing ability of computers (perhaps artificially intelligent computers) to solve many of the problems and accomplish many of the tasks in the discipline? 

Small Group Discussion

Each discipline has its "traditional" tools that its practitioners use. In each discipline, Information and Communication Technology provides a new set of tools. Share your thoughts on the extent to which we should be teaching students to make effective use of the new tools, even if this means that students will gain less skill in using the older, "traditional" tools.

Strategies Useful in Problem Solving

A strategy is a plan of action, a general approach to attempting to solve a problem or accomplish a task. Research tells us:

  • Many strategies are domain specific.
  • There are relatively few strategies that cut across most domains.
  • Students do not know very many domain-specific strategies.
  • Students do not know many strategies that cut across a number of domains.
  • Education is improved by helping students learn more strategies and gain skill in their use.

Whole Group Discussion

Name some domain-specific and some general-purpose strategies for problem solving.

Strategy: Break A Big Hard Problem into a Collection of Smaller, More Manageable Problems

The goal is to arrive at a collection of smaller, easier problems that you can solve. Using this strategy we can help a student get better at problem solving by:

  • Helping students to gain a useful-sized repertoire of smaller problems that they are skilled at solving.
  • Helping students learn how to break big problems into smaller problems, solve the smaller problems, and then assemble the pieces.
  • Helping students learn to make use of the huge number of smaller problems that a computer can solve quickly and accurately.

Strategy: Don't Reinvent the Wheel (Make Use of Information Retrieval)

  • For a large and steadily increasing number of problems, one can "look up" information about how to solve the problem.

Strategy: Avoid Doing Highly Repetitive Tasks By Hand

  • For quite a few problems, a computer can store both information about how to solve the problem and can actually solve the problem.
  • Computers tend to be much faster, more accurate, and more precise than humans at doing repetitive tasks.

 

Whole Group Discussion

If a computer can solve (or, substantially help in solving) a type of problem that we currently teach students to solve without the use of a computer, how should this affect the curriculum and assessment on this topic?

Closure: Any Final Questions

 

Added References

In my writings about problem solving, I repeatedly indicate that one of the most importatn ideas in problem solving is building on the previous work of oneself and others. A human brain (unless significantly damages) is naturally curious, has a considerable ability to learn, is creative, and is a problem solver. A baby, as it grows to adulthood and beyond, gets petter at problem solving through:

  1. Learning in its environment. I need to say this more carefully. A person's environment can be divided into significant pieces. For a very yung child, the environment is the home or equivalent. This has certain people, culture, artifacts, types of food, and so on. The home environment is eventually supplemented by the environment of the neighborhood, community, religious institutions, and so on. Later it may be supplemented by nursery school and other preschool settings, then the K-12 setting, and so on.
  2. The artifacts in one's environment serve a variety of purposes. Think about them in terms of being aids to solving various categories of problems. Needs for safety, food, clothing, and shelter can be thought of as problems; people have developed many different tools (in a broad sense) to help in dealing with these problems.
  3. The human mind and body have limitations. We have developed physical and mental tools to help overcome some of these limitations and to extend physical and mental capabilities. These vary tremendously in how much time and effort is required to learn to make effective use of the tools, how useful they are, what they cost, their needed care and upkeep, and so on. For example, consider a pair of shoes with shoestrings. In most parts of the world ishoes (footware) are a useful aid to human feet. It is somewhat of a challenge for a young child to learn to deal with shoes—walking in shoes, keeping them on, taking them off, finding them, learning to tie shoes, caring for shoes, selecting the "right" shoes to wear with the rest of one's clothing or for a particular purpose, and so on.
  4. A "milestone" in the tool business was the development of written notation for verbal language. The time and effort to learn to make effective use of reading, writing, and arithmetic is large. Also, this tends to be a delayed gratification situation. I suppose that I can make up examples of informal and apprenticeship types of education prior to that time where it took many years of learing effort to achieve a useful level of knowledge and skills. However, in some sense the reading, writing, and arithmetic were different. Also, in thinking about this, keep in mind the Thomas Jefferson idea of wanting to provide free educaiotn, up through the third grade, for children. I believe he had in mind that three years of grammar school could teach the necessary rudiments of reading, writing, and arithmetic to meet the neads of a typical youngster who would eventually be an adult citizen.
  5. Note our increasing understanding of the plasticity of the human brain and how this is involved in the learning process. See "Why Practice Makes Perfect (2000) by Anne Pycha. Retrieved 12/17/06: http://www.brainconnection.com/topics/?main=fa/practice. Quoting from the article:

Not long ago, many neuroscientists believed that the connections among neurons firmly established themselves within the first few weeks of life, and that cortical maps were fixed and unchangeable. Cervella sighs when she hears this: "Well, not long ago, even the best mapmakers never dreamed they'd have to draw a unified Berlin." But times have changed. Thanks to twenty years of research, we now know that the brain is plastic: it can and does remodel itself, sometimes within a remarkably short period of time.

Adult rats and monkeys have provided some of the most concrete evidence of brain plasticity. Rats, for example, are heavily reliant on their whiskers to send sensory information to the brain. When a rat learns to use his whiskers to discriminate the roughness of different surfaces (is it a sewer grate? is it a banana peel?), the cortical map of the whiskers can change within a matter of hours. Similarly, the cortical maps in a monkey's brain can expand within a matter of days as the monkey learns a new task, such as picking up a tiny ball, discriminating between sounds of different frequencies, or tracking a moving object with her eyes.

What is the Big6? Accessed 11/08/05: http://www.big6.com/showarticle.php?id=415

"Data collected from thousands of students showed that students who were taught informative nonfiction using the Big6 approach with a combination of analytical, creative, and practical activities, outperformed students who were taught two alternative apporaches (see materials at: www.yale.edu/pace)." -- Linda Jarvin, Ph.D., Associate Director, PACE Center, Yale University

The Big6™ is an information literacy model. Some people call it a metacognitive scaffold, or an information problem solving strategy. When you apply these stages, you have an essential framework to approach any information-based question. Here are the six stages we call the BIG6. Two sub-stages are part of each main category in the Big6 model:
1. Task Definition
1.1 Define the information problem
1.2 Identify information needed
2. Information Seeking Strategies
2.1 Determine all possible sources
2.2 Select the best sources
3. Location and Access
3.1 Locate sources (intellectually and physically)
3.2 Find information within sources
4. Use of Information
4.1 Engage (e.g., read, hear, view, touch)
4.2 Extract relevant information
5. Synthesis
5.1 Organize from multiple sources
5.2 Present the information
6. Evaluation
6.1 Judge the product (effectiveness)
6.2 Judge the process (efficiency)
People go through these Big6 stages—consciously or not—when they seek or apply information to solve a problem or make a decision. It’s not necessary to complete these stages in a linear order, and a given stage doesn’t have to take a lot of time. We have found that in almost all successful problem-solving situations, all stages are addressed.

TRIZ (n.d.). The TRIZ Juornal. Retrieved 10/10/06: http://www.triz-journal.com/. Quoting from the Website:

"TIPS" is the acronym for "Theory of Inventive Problem Solving," and "TRIZ" is the acronym for the same phrase in Russian. TRIZ was developed by Genrich Altshuller and his colleagues in the former USSR starting in 1946, and is now being developed and practiced throughout the world.

TRIZ research began with the hypothesis that there are universal principles of invention that are the basis for creative innovations that advance technology, and that if these principles could be identified and codified, they could be taught to people to make the process of invention more predictable. The research has proceeded in several stages over the last 50 years. Over 2 million patents have been examined, classified by level of inventiveness, and analyzed to look for principles of innovation. The three primary findings of this research are as follows:

  1. Problems and solutions were repeated across industries and sciences
  2. Patterns of technical evolution were repeated across industries and sciences
  3. Innovations used scientific effects outside the field where they were developed