Pagemaker - Pdf file creation. Shockwave - For ... Toolbook II - For authoring less complex modules (contains built-in templates and has interactive capability).
The UNLOCK System: Enhancing Problem Solving Skills for Students T. Beaubouef
R. Lucas
J. Howatt
Department of Computer Science Southeastern Louisiana University Hammond, LA 70402 USA {tbeaubouef,rlucas,jhowatt}@selu.edu
Introduction Over the past several years we have been struggling to reduce the 50% attrition rate in our CS-1 and CS-2 classes. We tried changing our teaching approach, programming languages, textbooks, and assignments, to no avail. Then we realized the obvious—the majority of our students were lacking fundamental problem solving skills. It wasn't that they could not solve computing problems; it was that they could not solve problems in general!
The ability to solve problems is at the heart of computer science. Without this ability, students are setting themselves up for failure in their studies and in their careers. Therefore, it is essential that computer science majors develop good problem solving skills early in their academic programs. They must learn to apply various analysis techniques, choose from alternative design methods based on the development and production hardware and software, formulate solutions mathematically or symbolically, translate the formulation into a programming language, and finally, verify and validate their results. In addition to the technical tasks, they must accurately estimate the time and resources needed to get their jobs done, all the while communicating effectively and interacting ethically with their peers and end-users. Thus, the ability to analyze and solve problems, both technical and non-technical, is crucial for success as a computer scientist.
Some people have a talent for solving problems--it comes easy for them; their problem solving ability is innate. Others, including most of our entry-level majors, must develop these skills. They must learn how to be effective problem solvers. A review of the literature reveals many approaches to learning these skills. Some view problem solving as an art [Ack78, NH99, NH98, F93], where creativity is one of the
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most important traits. Others argue that there are certain logic and thinking skills that must be learned and applied to problem solving [WL99]. Still others focus on developing cognitive skills, self-awareness, and motivation [Lev94]. We hope to combine all of these ideas in teaching our students.
We believe that most students can succeed in CS-1/CS-2, after being taught the fundamental problem solving skills that they lack. Thus, we are developing lessons to teach those skills. The lessons begin gently. We initially refrain from presenting mathematics and computing problems, so as to not scare away the math-phobics. Then, we ease in math concepts so the students will begin to “do math” without realizing it. Later, we segue into computing problems and begin teaching elementary analysis and design. The tool for doing all this is our UNLOCK System. We believe that use of this system will result in students who are better prepared to think critically, solve problems, and write programs.
In the following paragraphs, we describe our approach to designing UNLOCK, give examples of lessons that present different problem-solving approaches, discuss issues related to the actual presentation of the lessons to the students, and conclude by discussing the logistics of developing and implementing the system.
Preliminary Design The major purpose of the UNLOCK system is to serve as user-friendly educational software. It is therefore designed with students in mind. The students should not be overwhelmed, should not be required to learn a lot about the system itself in order to use it. They should be able to learn the system quickly, and enjoy it as much as possible. The graphical user interface must be easy to use and the progression through the modules easy to follow. We developed the system as a collection of game-like modules, and tied them all together with the idea of obtaining “keys” to knowledge. The goal is to master all of the problem-solving concepts, thereby collecting all the necessary keys and winning the game.
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UNLOCK contains various learning modules grouped by categories into units. Each unit is related to mastering a particular skill or concept. When the student has mastered the unit, he will be given a “key” for that unit. The student then “has the key” to solving problems where that skill is required. This key can be used in later modules to provide hints in solving other types of problems, if that skill is required for the particular problem.
When the student has earned all of the different types of keys, he will be exposed to problems that are more complex. These problems will involve a combination of several of the skills learned from the individual modules. Upon successful completion of these problems and a “final exam” covering concepts learned, the individual will earn a “master key”. He is now properly equipped to unlock the secrets of problems in the real world.
In the next section we present a few sample modules that can be found in UNLOCK. We discuss the key concept for each and explain how the solution to the problem relates to this problem-solving concept. An entire module must be mastered before the key for that module is awarded. Modules include several problems each, although only one or two are included for illustration purposes in the sample modules discussed below.
Sample Modules Key 010: Do not add additional constraints to the problem. PROBLEM: Connect the dots below by using 4 straight lines.
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Many of us have seen this problem in puzzle books. The people who fail to solve the problem often make the false assumption that the lines must each begin and end on a point. This restriction was not stated in the problem. It simply formed in the reader’s brain, probably based on experience from other problems with dots and line segments encountered in the past. A solution appears below:
If the student fails to solve the problem, he can request a hint. In this example, the first hint might be “Lines are not required to start and end on points.” If the user still requires help, he can request further hints, one at a time, until he either solves the problem or depletes all the hints and requests the solution to the problem.
When the student solves the problem, additional information will appear on the screen related to the concept being learned. The student must carefully read the information. He will be tested on the information at the end of the module.
When the student working on this module solves the problem correctly and has studied any material supplied with the problem’s solution, he will be given other problems in this category. After correctly solving all the problems in the module and correctly answering the “test what you have learned” type questions, the student is given a “key” to add to his key chain. This key will enable the student to gain hints in later problems related to the skills learned for this key.
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A related problem in this category may be stated as follows: A girl is walking through the forest when she reaches a river that is thirty meters wide. She looks as far as she can in either direction and notices that the best place to cross is directly in front of her. She must cross the river (for some reason), but she cannot swim at all. On the bank beside her are several small branches of wood. The only thing in her backpack is a coil of rope 10 meters long. How does she cross the river?
The student may use the same concept, don’t add additional constraints, to help unlock the solution to this problem. A hint for this problem may state: Don’t assume that the river is deep. Obviously then, the girl can simply wade across the river to her destination.
Here is still another problem: A man is at the edge of a huge gorge. He is given the challenge of crossing the gorge on a swinging rope bridge. If he crosses the gorge in less than a minute, he will win $10,000. There is one catch. A small bowl of water filled to the brim is placed beside the man. He is told that he must carry the water with him across the bridge without spilling any of it on the bridge or in the gorge. Is it possible for him to win the money? The winds are getting stronger and he will have to hold on tightly.
Let’s now remember the topic of this unit: Do not add additional constraints to the problem. If the student needs a hint at this point, then the following hint might be provided: The bowl is not required to cross the gorge, only the water. The solution, then, is for the man to drink the bowl of water, and then to cross the gorge, both hands free to hold the ropes.
Key 047: Identify those facts that are useful information and disregard the useless facts. PROBLEM: Little Red Riding Hood wants to take some flowers to her grandmother who is ill. It is now 3:00 p.m., but it does not get dark until 7:00 p.m. She must make it to her grandmother’s house and back before dark. So Red quickly grabs her red cloak and heads outside to pick some pink monarda, her
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grandmother’s favorite flower, which is also a favorite flower for bees. She then begins her trek to Grandmother’s.
As Red begins walking, she notices that there is a little bee on her bouquet. It flies back to her home garden, and then flies back to Red. It continues to fly back and forth from Red to her home for the entire journey. This bee is very fast—it flies at a constant speed of 30 mph. Red is amused that the bee keeps coming back to her, but soon begins to get bored with her walk. She decides to count the number of paces it takes to get to grandmothers, and to use this to figure out the distance to Grandmother’s. She knows that she is exactly 5’4” and that her step is 2 ½ feet long. This makes every two steps, or one pace, equal to 5 feet. Soon Red gets to the steep hill that is about halfway between her house and her Grandmother’s. By this time she has seen her little bee friend at least 10 times, flying back and forth between her and home. Red struggles up the hill, noting that her steps are probably not 2 ½ feet long anymore, but shorter. When she gets about 60% up the hill, Red slips, and tumbles back down to the bottom of the hill. She is disheartened until her little bee friend appears again momentarily and leaves. With renewed energy she again tackles the tall hill, and soon finds herself descending the other side. In all the confusion, she gave up on counting her paces, estimating that it must be about 3000, and hurried on to her grandmother’s house. She arrived at the grandmother’s house at 4:30 p.m., just as the little bee landed on her bouquet for the last time, exhausted, and her favorite game show was coming on TV. How many miles did the bee travel since Red left her house?
Obviously, facts such as the grandmother’s favorite flower and the time of Red’s favorite game show are of no consequence in this problem. However, neither are the facts related to Red’s paces, the terrain, or the time it gets dark. In order to answer the question, we need only to know the speed of the bee (30 mph) and the time that elapses for Red’s trip (1 ½ hours). From these we can calculate that the bee traveled 45 miles.
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Some students have trouble in ignoring facts that look important, but really are not. They may have struggled with word problems in the past, but learned somewhere along the way that all the numbers in the problem are used in some equation. This is probably true for many problems that students have been presented with in grade school and high school. It is possible that the students did not really understand such problems completely, but memorized formulas and could figure out which of the values to plug in for each of the variables.
The reader may also have made some false assumption while reading the problem. For this example, they may have incorrectly assumed that the question would be related to computing the distance between Red and her grandmother’s houses. This type of incorrect assumption can get the reader thinking along those lines, and by the time he reads the actual question, his judgment is clouded into thinking in terms of using distances and paces. The following example illustrates this concept further.
Key 029: Don’t limit your thinking to what is typical. Consider all possibilities. PROBLEM: An alien spaceship hovered over a fairly flat area on the earth. Alien1 spoke to Alien2 in their alien language about exploring this strange planet. They decided to land the ship and go for a little excursion, since no Earthlings could be seen. They put on their hiking boots, packed some water, appropriate clothing, and their compasses, and stepped outside. Since they were facing south, they decided to head first in that direction. They had walked for two kilometers, when Alien2 had had enough of Alien1’s ceaseless chatter. He suggested that they might cover more terrain if they split up. Alien1 would go due east for two kilometers, then due north for two kilometers, then due west for two kilometers, ending up back at the ship. Alien2 would go due west by the same amount, then head due north for two kilometers, then due east until he arrived at the ship. Since it had only taken about 15 earth minutes to get this far, Alien2 figured that he would have about 45 minutes of peace and quiet away from Alien1. He was not so fortunate, however. In thirty minutes the aliens were both back at the ship. How did this happen?
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When most of us think about the cardinal directions, we think of the compass rose. North is 180 degrees opposite of South. East and West are perpendicular to North and South, with East being 180 degrees opposite of West. There are then 90 degrees separating each of the directions from the next. If we travel south, then east, then north, then west, we will traverse a square. However, the curvature of the earth renders this type of reasoning invalid, especially as the size of the “square” gets large. The error is most pronounced near the poles.
If the student could not figure out the alien problem, he could be presented with some hints derived from the discussion above. (We would not use hints unrelated to learning the concept, so there would be no hints about Santa or polar bears unless the student has exhausted all of the hints and is ready for the solution.) Finally the student will arrive at the solution: the aliens landed their craft on the North Pole.
The following is an example [Dav00] of one of the many types of logic problems that can be found in puzzle books and on standardized tests. Albert Einstein, the author of this particular problem, believed that less than two percent of the people in the world could solve it. Most people do not know how to begin to work these types of problems, but with some instruction in how to keep track of the ‘knowns’ and ‘unknowns’ with systematic record-keeping, many more people can learn to solve these types of problems.
Key 031: Use the known facts and logic in a systematic fashion to derive additional unknown facts. PROBLEM: Use the FACTS and HINTS below to determine which of the five men has the fish as his pet.
FACTS: 1. There are 5 houses (along the street) in 5 different colors: blue, green, red, white and yellow. 2. In each house lives a person of a different nationality: Brit, Dane, German, Norwegian and Swede. 3. These 5 owners drink a certain beverage: beer, coffee, milk, tea and water, smoke a certain brand of cigar: Blue Master, Dunhill, Pall Mall, Prince and blend, and keep a certain pet: cat, bird, dog, fish, and horse. 4. No owners have the same pet, smoke the same brand of cigar, or drink the same beverage.
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HINTS: 1. The Brit lives in a red house. 2. The Swede keeps dogs as pets. 3. The Dane drinks tea. 4. The green house is on the left of the white house (next to it). 5. The green house owner drinks coffee. 6. The person who smokes Pall Mall rears birds. 7. The owner of the yellow house smokes Dunhill. 8. The man living in the house right in the center drinks milk. 9. The Norwegian lives in the first house. 10. The man who smokes Blend lives next to the one who keeps cats. 11. The man who keeps horses lives next to the man who smokes Dunhill. 12. The owner who smokes Blue Master drinks beer. 13. The German smokes Prince. 14. The Norwegian lives next to the blue house. 15. The man who smokes Blend has a neighbor who drinks water. Normally, a large grid is used to keep track of the interrelationships of the various combinations of possibilities. For this example, there are five different categories of five possibilities each, so we may choose to create a 25 x 25 grid as a starting point, and then begin to eliminate those grid locations that represent combinations that are not possible. Sometimes several passes through the hints are necessary to eliminate a sufficient number of the combinations. Next, a table such as the one below is constructed to hold the developing solution. Using the table, the grid, and some logical thinking, a solution can eventually be reached: it is the German who has the pet fish. Number Color Nationality Beverage Cigar Pet
1 Yellow Norwegian Water Dunhill Cat
2 Blue Dane Tea Blend Horse
3 Red Brit Milk Pall Mall Bird
4 Green German Coffee Prince Fish
5 White Swede Beer Blue Master Dog
Development Tools We developed lesson modules using Toolbook, Photoshop, ImageReady, and Flash. For future modules, we plan to use Authorware, Director and other support software (see the list, below) so we can create more exciting, and entertaining, modules by including additional graphics, video, and audio. This will
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make the modules more “game like” and should create more interest in pursuing them. A complete list of the hardware and software1 used in developing UNLOCK lesson modules can be found in the appendix.
As a specific example, in creating the module for the nine-dot problem, we used Toolbook to provide a multiple-page, interactive lesson to present the problem and prompt for a solution. The first page displays a menu to provide navigation to any other page within the module. Page two states the problem and displays the nine dots. Page three, the most complex (see the next paragraph), not only displays the nine dots, but also allows the problem solver to draw lines to connect them. In this page, when the student draws a line, he will not be able to erase it. This forces a decision about a possible solution before starting. Entering a different solution, requires starting anew (going back to the menu to return to page 3). If the student fails to find a solution, he may advance a page to receive a hint and then return to the problem. Additional hints are provided on succeeding pages. The final page of the module provides one or more solutions. It, more importantly, describes the appropriate problem-solving approach and any “rules” or heuristics that the student should remember.
Page 3, which contained the interactivity, was created using Photoshop's graphic capabilities. Then, it was imported into Flash to provide the interactivity for line drawing. In the final page, Photoshop and ImageReady were used to animate the solution. Thus, through the combination of tools, which allow easy integration of components, we were able to quickly implement what we hope will be effective lessons.
Conclusion Many students enter college these days lacking basic problem solving skills. We have designed UNLOCK as an interactive, educational tool to instill and enhance problem solving skills in those students. In this paper we have discussed the motivation behind and basic design of the system, and presented a small sampling of the various problem-solving modules. The modules of UNLOCK present a suite of problem
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We have no financial or other interest in the software and hardware listed and described.
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solving techniques that can be used as a basis for learning software analysis and design. As students master the various modules, they become “armed” with the knowledge and skills of the modules and ready to apply these same techniques to related problems in real life.
UNLOCK is currently being implemented at Southeastern Louisiana University. In the next academic year, we plan to test this system on introductory computer science students and to make it available as well to students in other disciplines. Our goal in developing UNLOCK is to provide students with needed, fundamental problem-solving skills. By satisfying this goal, we hope also to achieve our larger goals of retaining more computer science majors and better preparing them for advanced studies in computer science and for successful software development careers.
Acknowledgement This research was supported in part by Louisiana Board of Regents grant LEQSF(2000-02)-ENH-UG-49.
References [Ack78] Ackoff, Russell, The Art of Problem Solving, John Wiley & Sons, New York, 1978. [Fob93] Fobes, R., The Creative Problem Solver’s Toolbox, Solutions Through Innovation, Portland, 1993. [Lev94] Levine, M., Effective Problem Solving, 2nd ed., Prentiss Hall, New Jersey, 1994. [NH99] Nadler, G., S. Hibino with J. Farrell, Creative Solution Finding, Prima Publishing, Rocklin, California, 1999. [NH98] Nadler, G. and S. Hibino, Breakthrough Thinking, Prima Publishing, Roseville, California, 1998. [WL99] Whimbey, A. and J. Lochhead, Problem Solving & Comprehension, 6th ed., Lawrence Erlbaum Associates, Publishers, New Jersey, 1999. [Dav00] “Einstein’s Problem,” from http://www.davar.net/math/problems/einstein.htm, December, 2000.
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Appendix – Hardware and Software Used Software The following list of software is being used in developing the Problem Solving modules. The resulting modules will be available in CD or WWW format. Sonic Foundry Sound Forge - Audio editing. Illustrator - Vector Graphic Creation. Flash - Graphic Animation. Pagemaker - Pdf file creation. Shockwave - For putting Director movies on the Web. Photoshop - Graphic editing. Premier - Digital video editing. Toolbook II - For authoring less complex modules (contains built-in templates and has interactive capability). Authorware - Multimedia authoring (Computer Based Training - CBT). Director - Interactive movie creation (Has excellent animation capabilities). Equipment Multimedia Workstations - Dell Precision 420 with Dual 933 Mhz processors, 256 MB memory, 18 GB hard drive, and multimedia equipment Color Scanners - HP ScanJet 6350 Cse Digital Camcorder - Canon ZR10
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