One of the most common problem types encountered in schools is the algorithm. Most common in mathematics courses, students are taught to solve problems such as long division or equation factoring using a finite and rigid set of procedures with limited, predictive decisions.

One of the most common problem types encountered in schools is the algorithm. Most common in mathematics courses, students are taught to solve problems such as long division or equation factoring using a finite and rigid set of procedures with limited, predictive decisions.

Decision-making problems typically involve selecting a single option from a set of alternatives based on a set of criteria.

Decision-making problems usually require that problem solvers select a solution from a set of alternative solutions. Traditional conceptions of decision making posit a set of alternative criteria that decision makers work through in order to identify the optimal solution. Those criteria may be provided to the problem solver(s), or the solver(s) may have to identify the most relevant criteria.

Decision-making problems are usually constrained to decisions with a limited number of solutions.

Diagnosis-solution problems are similar to troubleshooting. Most diagnosis-solution problems require identifying a fault state, just like troubleshooting. However, in troubleshooting, the goal is to repair the fault and get the system back online as soon as possible, so the solution strategies are more restrictive. Diagnosis-solution problems usually begin with a fault state similar to troubleshooting (e.g. symptoms of a sick person). The physician examines the patient and considers patient history before making an initial diagnosis. In a spiral of data collection, hypothesis generation, and testing, the physician focuses in a specific etiology and differential diagnosis of the patient’s problem. At that point, the physician must suggest a solution. Frequently, there are multiple solutions and solution paths, so the physician must justify a particular solution. It is this ambiguity in solution paths that distinguishes diagnosis-solution problems from trouble shooting.

Diagnosis-solution problems are similar to troubleshooting. Most diagnosis-solution problems require identifying a fault state, just like troubleshooting. However, in troubleshooting, the goal is to repair the fault and get the system back online as soon as possible, so the solution strategies are more restrictive. Diagnosis-solution problems usually begin with a fault state similar to troubleshooting (e.g. symptoms of a sick person). The physician examines the patient and considers patient history before making an initial diagnosis. In a spiral of data collection, hypothesis generation, and testing, the physician focuses in a specific etiology and differential diagnosis of the patient’s problem. At that point, the physician must suggest a solution. Frequently, there are multiple solutions and solution paths, so the physician must justify a particular solution. It is this ambiguity in solution paths that distinguishes diagnosis-solution problems from trouble shooting.

Electronic mail (e-mail) allows the sender to transmit a message, almost instantly, to an individual or a group of individuals. With most e-mail programs. the transmitted message can include attachments that might contain complex documents, Images, sounds, or even brief Videos. The receiver of a piece of electronic mail can easily respond, forward the message to other users, and efficiently save the message in an electronic form.

Another method for representing story problems is provided by HERON (Reusser, 1993), a computer-based tool that used solution trees to conceptualize the structure of mathematical problem solving. Like these other tools, the tree model in HERON is designed to directly mediate the translation of the problem text into an equation without the use of a structural or situational model of the problem. HERON uses a graphical solution (conceptual planning) tree to represent the operation required to solve the problem.

Another method for representing story problems is provided by HERON (Reusser, 1993), a computer-based tool that used solution trees to conceptualize the structure of mathematical problem solving. Like these other tools, the tree model in HERON is designed to directly mediate the translation of the problem text into an equation without the use of a structural or situational model of the problem. HERONuses a graphical solution (conceptual planning) tree to represent the operation required to solve the problem.

The Internet is a worldwide network ofnetworks composed of thousands of smaller regional networks connecting millions of users in more than 90 nations around the globe. These regional networks are composed of still smaller networks that serve institutions, businesses, and individuals who connect their computers to the regional networks via modems and telephone lines. To gain access to the Internet, you need to connect your computer to a network that is part of the Internet, or contact an access provider that will allow you to connect to ist network for a fee.

Logical problems tend to be abstract tests of reasoning that puzzle the learner. They are used to assess mental acuity, clarity, and logical reasoning.

Logic problems tend to be abstract tests of logic that puzzle the learner. They are used to assess mental acuity, clarity, and logical reasoning. Classic games such as missionaries and cannibals or tower of Hanoi challenge learners to find the most efficient (least number of moves) sequence of action. Rubik’s Cube was a popular game in the 1970s requiring the user to rotate the rows and columns of a threedimensional cube to form patterns. In each of these “problems,” there is a specific method of reasoning that will yield the most efficient solution. It is up to the learner to discover that method. Research has shown that the ability to solve these problems does not transfer to other kinds of problems (Hayes & Simon, 1977; Reed, Ernst, & Banerji, 1974).

Logical problems tend to be abstract tests of reasoning that puzzle the learner. They are used to assess mental acuity, clarity, and logical reasoning.

Listservs are a Variation of e-mail. When users interested in a particular topic subscribe to a listserv on some topic, they begin to receive messages from the other members of the list. To get a message to all of the list's subscribers, a user sends a single copy of the note to the list, and the Computer that hosts the list sends a copy to all subscribers. The sender generally does not even know how many nsers there are, let alone who they are.

MUDs (multiuser domains) and MOOs (object-oriented MUDs) are virtual environments that you enter and participate in. Originally derived from online "Dungeons and Dragons" environments, some MUDs have an educational focus, such as MIT's MicroMUSE. Users can enter the virtual environment and travel between locations - for example, homes, museums, coffee shops, or science labs. Visitors not only interact, but, depending on their level of experience, can participate in the design and construction of the environment itself.

Just what is a problem? There are only two critical attributes of a problem. First, a problem is an unknown. If we have a goal and do not know how to reach that goal, there is an unknown, so we have a problem. Second, finding the unknown must have some social, cultural, or intellectual value to someone. If no one believes that it is worth finding the unknown, there is no perceived problem. Finding the unknown is the process of problem solving.

Just what is a problem? There are at least two critical attributes in my definition of a problem. First, a problem is an unknown entity in some context (the difference between a goal state and a current state). Second, finding or solving for the unknown must have some social, cultural, or intellectual value. That is, someone believes that it is worth finding the unknown. If no one perceives an unknown or a need to determine an unknown, there is no perceived problem.

Just what is problem? There are only two critical attributes of a problem. First, a problem is an unknown entity in some situation (the difference between a goal state and a current state). Those situations vary from algorithmic math problems to vexing and complex social problems, such as violence in the schools. Second, finding or solving for the unknown must have some social, cultural, or intellectual value. That is, someone believes that it is worth finding the unknown.

Many problems require that learners induce rules in order to solve problems. When encountering a new machine or system, it is necessary to figure out how the system works, that is, to induce the rules that describe how the system functions. Learning how to use transportation systems in foreign countries poses myriad rule-induction problems. Qualitative-analysis labs in chemistry provide students unknown compounds on which they conduct numerous tests in order to discover the identity of the compound. Those tests represent rules that are defined by the causal relationships among the chemical elements. Doing so requires that they induce rules that describe the behavior of various reagents. These are generally perceived as more difficult problems than applying rules, although the level of experienced difficulty depends on individual differences in cognition.

In an attempt to situate algorithms in some kind of context, many textbook authors and teachers employ story problems. This usually takes the form of embedding the values needed to solve an algorithm into a brief narrative or Situation.

In an attempt to make problem solving more meaningful, textbook authors, teachers, and professors assign story problems to students. These can be found at the backs of textbook chapters in virtually every science, mathematics, and engineering textbook in existence. Traditional methods for solving story problems require learners to

1. represent the unknowns by letters;
2. translate relationships about unknowns into equations;
3. solve the equations to find the value of the unknowns; and
4. verify values found to see if they fit the original problem (Rich, 1960).

A Swiki is an open-source, collaborative Web site (CoWeb) space developed by Mark Guzdial and others at Georgia Tech's Graphics, Visualization, and Usability Center. Anyone given a password as part of a Swiki group can create a new page and/or edit an existing page. Users of a particular Swiki can use the Edit tool to make changes to the Web page. Files may be attached to the page and a History button displays dated edits with links to all versions. This archiving feature allows a Swiki to serve as a group memory with a collective repository of dialogue and knowledge. Swikis can be a useful tool for collaborative writing.

A WebQuest is an inquiry-oriented activity in which teachers choose Web resources for students to use as information sources in activities designed to support analysis, evaluation, and synthesis of information.