Decision Matrices
A Problem Solving Aid Webquest for Middle/High School Students
Designed by Richard G. Kaiura
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Introduction Task Process Resources Evaluation Conclusion Credits Homepage Multimedia Presentation Multimedia Lesson Plan
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Problem solving skills are key enablers and by-products of critical thinking. Teachers seek to develop and hone these skills in students to prepare them for their future in a world full of uncertainty, where difficult choices must often be made. This webquest helps students through the process of deciding which course of action is most desirable once they have developed or been provided two or more courses of action from which to choose.
The student will use the Internet to conduct research to decide on a car purchase. The student will develop three courses of action (choices), identify and define evaluation criteria, rate each course of action using these criteria, and display their results using one of two decision matrix formats.
Situation: Student! It is your lucky day! Dad says he will buy you a car for your high school graduation present IF (and only if) you do, in fact, graduate. The question he asks you is what you are interested in. He has told you that it can be whatever you want, with the following limitations.
1 - Cost must be under $20,000.
2 - It should get at least 20 mpg overall.
3 - It should have enough space in it to haul your things to college (hint, hint).
Step 1 - Use the web-sites listed under Resources to find and select three different selections for cars you want to compare before deciding on which one to purchase. As you go through this process, think about what factors you will likely base your choice on, such as: cost, gas mileage, comfort, style, etc. Record these factors for later consideration. You may change your mind several times as to which cars you want to consider and which factors are most important; this is okay.
Step 2 - Once you have 3 courses of action (choices) for consideration, the next step is to review each course of action to ensure it is feasible, acceptable, and suitable. This is sometimes referred to as the FAS test. The definition of each FAS element is provided below.
Feasible – The capability to accomplish the course of action in terms of available time, space, and resources exists. This means, in essence, can the car dealer provide you with what you want. A quick check with a local dealer will confirm or deny any problems with supply or long wait times. You don't want to wait a year to get your car. In most cases, this should be no problem.
Acceptable – The advantage gained by accomplishing the COA must justify the cost in resources (e.g., time, equipment, funds, material, etc.) as well as risk (e.g., potential risk to injury for people or property, potential risk for loss of life.) This means, in essence, are you satisfied that you will be able to get the most out of the car you select. There are always trade-offs. Convertibles are neat for cruising, but do not have a lot of cargo space. Two-seaters won't let you drive the gang to a movie. Some cars are safer than others. You will probably spend your most time thinking about trade-offs.
Suitable – The course of action must comply with any specified conditions that have already been established. (Note: If a factor has not been limited, it may be considered for use as a criteria to be evaluated further.) This asks, in essence, "Have you done what dad said to do as far as his limitations are concerned?"
A course of action worksheet like the one shown below is used in recording the problem, a proposed course of action and any restrictions or constraints already imposed on that course of action.
Note: To download a Powerpoint file containing the forms used in this webquest, use the below hyperlink.
Step 3 – Assuming you now have three courses of action, the next step is to identify evaluation criteria to use in assessing each course of action.
Evaluation criteria are those factors used to measure or quantify the effectiveness and efficiency of each course of action on its own merit. Simply put, these are the factors you were asked to think about in Step 1 as you went through the process of selecting cars from which to make your choice. Now, you must determine which four factors you feel are most important to you.
Normally, at least 3-5 factors should be identified. You may have many more depending on the complexity of the problem under consideration. An evaluation criteria worksheet like the one shown below may be used to record identified evaluation criteria, how each is measured and what constitutes an average, above average, or below average rating.
Step 4 - Once evaluation criteria have been identified, you now conduct an assessment of each course of action using these criteria. As each course of action is assessed, note whether or not it possesses some advantage or disadvantage with respect to each criterion. For example, low cost might be an advantage. Expenditure of large amounts of material may be a disadvantage. Record your assessments on a course of action assessment worksheet like the one shown below. If a course of action offers neither an advantage nor disadvantage, no comments are noted.
Step 5 – Once each course of action has been assessed, the next step is to select a matrix format to use in recording assessment results. There are many ways to present assessment results. Two common formats are provided below: plus-null-minus (PNM) format and numerical format.
PNM Format. This format simply lists each evaluation criteria down the left side of the matrix and the courses of action along the top of the matrix. (See table below). Start by assessing each course of action against each factor using a “+” if the course of action possesses some advantage with regard to the factor; a “o” if the course of action possesses neither and advantage nor disadvantage with regard to the factor; or a “-” if the course of action possesses some disadvantage with regard to the factor. At this point, you should also be comparing courses of action. Where two courses of action possess an advantage, but one is more significant than then other, you may elect to give the course of action with the more marked advantage a "+", and the other an "o". This decision is subjective.
Once the table is filled out, note the number of “+”, “o”, and “-” for each course of action and assigns a score to each course of action receiving 3 points for every “+”, 2 points for each “o”, and 1 point for each “-”. The course of action having the highest number of points is the most desirable course of action.
Numerical Format. This format also lists evaluation criteria down the left side of the matrix and the courses of action along the top of the matrix. (See table below). A weight is also assigned to each evaluation criterion. Weight is simply the level of importance associated with each criterion. In the PNM format, all criteria are valued equally. In the numerical format, you can assign more weight to one or more criteria.
Each column space under each course of action is split into two parts. In the left part, the student assigns a plus, null or minus assessment just as in the PNM format. You may find two or more criteria receive the same assessment. This is okay. At this point, you should also be comparing courses of action. Where two courses of action possess an advantage, but one is much more advantageous than the other, you may elect to give the course of action with the more marked advantage a "+", and the other an "o". This decision is subjective. The same logic applies where two course of action possess a disadvantage, but one is more disadvantageous than the other.
In the right part of the matrix, assign a numerical score. The score is based on the number of courses of action being considered. Without considering the weight of the criterion, the total amount of points that can be awarded for each criterion among all courses of action is equal to the sum of the total number of places all courses of action can be ranked. For example, for three courses of action, the total number of points that can be awarded is 6 (1+2+3=6). For four courses of action, the total number of points that can be awarded is 10 (1+2+3+4). You then multiply the total number of points that can be awarded by the weight assigned to the criterion.
In meting out the points awarded for each criterion, you must consider how many courses of action received a “+”, a “o”, and a “-”. For the simplest case where three courses of action receive a “+”, a “o”, and a “-”, the student assigns points with the “+” receiving 3 points, the “o” receiving 2 points, and the “-” receiving 1 point. Where two courses of action receive the same assessment, you combine the points they would have received had they been rated one different than the other, divide these points in half, and assign the same amount to each. For example, where one course of action receives a “+”, and two receive “o”s, you would assign 3 points to the course of action receiving the “+”, and 1.5 points to the courses of action receiving the “o”s. (See table below)
Step 6. Once you have completed the decision matrix using either PNM or numerical format, present your results using materials provided in class.
The following web-sites are available to support student inquiry concerning the purchase of a car.
http://www.fordvehicles.com/index.asp?bhcp=1 Note: The bottom left corner of the page contains a tool called "Compare Vehicles". Clicking on this tool takes you to a site where you can select from many different makes and models of vehicles and see side by side comparisons of features, specifications, and cost.
http://autos.msn.com/research/compare/default.aspx?src=category Note: This MSN.com site allows you to view and select several different makes and models of vehicles and conduct a side-by-side comparison of features, specifications and costs.
Students are evaluated on each part of the Decision Matrix Process. A total of points may be awarded for application of this webquest to assess and present a course of action recommendation as follows:
Course of Action Identification Worksheet: [Total of 12 points]
1 - Student identifies three courses of action for situation provided. [1 point]
2 - Student fills out a worksheet for each course of action [3 points each sheet]
Evaluation Criteria Worksheet: [Total of 8 points]
1 - Student identifies appropriate (up to four) selection criteria [two points each criterion]
Course of Action Assessment Worksheet: [Total of 12 points]
1 - Student fills out a worksheet for each course of action [4 points each]
Decision Matrix: [Total of 30 points]
1 - Student fills out a matrix, applies criteria, scores each course of action. [2 points for each scoring area.]
Decision matrices are useful tools for assisting in assessing courses of action and presenting the results of course of action assessments. The procedures for preparing decision matrices in this webquest may be applied to any problem solving situation where more than one course of action is under consideration and there is enough time to apply these procedures.
Grabe, Mark, and Cindy Grabe. Integrating Technology for Meaningful Learning. 4th Ed., Houghlin Mifflin Company. Massachusetts: Boston, 2004.
Kerr, Marena. Instruction received during TED 312, Technology Applications for the Classroom; especially discussion on the structure and content of webquests and the use of Frontpage.
US Army Field Manual 101-5, Staff Organizations and Operations, Headquarters, Department of the Army, Washington, D.C. 31 May 1997.
