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- 1. Chapter 6: Modeling Problems by Alex Calloway , Ray Bandas & Sabina Maza
- 2. Chapter Summary <ul><li>Personal, or internal, representations of problems guide the interpretation of information about a problem, simulate the behavior of the system based on what we know about it, and can help to develop a solution. Quantitative models differ from qualitative ones in that they are strictly numerical, like a formula. This might include a spreadsheet of some kind with test results from many people revealing which of them had cancer and various biological risk factors, or one related to blood analysis such as the example in the book. In contrast, qualitative models involve a value judgement that affects our understanding of a particular problem. An example of a qualitative model would be a graph which asked and posed the difference in these factors based on age or socio-economic status. </li></ul>
- 3. <ul><li> Databases can also be used to model problems, such as Jonassen's example in the book of a table combining data about drugs, their replacements, and side effects for nutritionists looking for alternatives to conventional drug therapies. </li></ul><ul><li>Another example might be a table about food and its ingredients for the purpose of making a healthier menu. Concept maps are models that can be used to solve problems in chemistry, or even word problems involving people and their belongings . Spreadsheets can also be used in modeling problems, such as the blood analysis spreadsheet mentioned previously. Another example of this would be the use of a spreadsheet to model the effects of careful diet management upon a patient's diabetes. An expert system based on causal reasoning might inform the public about the likelihood of different weather events, or it might help people pick good diet plans based on the information provided by doctors. </li></ul>
- 4. Modeling Tools can be used to model population growth, such as colonies after a hurricane, or citizens in a new country. Visualization tools can be used to graph things such as the descent of a shuttle, or the setting of the sun. Systems modeling tools are especially effective for modeling problems because learners can test their models for accuracy. Jonassen again uses the example of a molar conversion problem in chemistry in the text. An additional example of a systems modeling tool could track the new citizens in a country. Finally, visualization tools are helpful for modeling abstract concepts like mathematic problems. Visualization can be used to plot the descent of a shuttle or the setting of the sun.
- 5. <ul><li>The ability to model problems qualitatively as well as quantitatively is crucial to our understanding of concepts as we encounter them in the real world. </li></ul><ul><li>Databases, concept maps, spreadsheets, expert systems, systems modeling tools, and visualization tools are all excellent ways that can be used together or apart to achieve maximum learning potential. </li></ul><ul><li>1) Are there any other examples of different modeling types that you can think of? </li></ul><ul><li>2) Can you think of any other examples of issues that can be analyzed both quantitatively and qualitatively? </li></ul><ul><li>3) Does the presentation of qualitative data allow for more than one interpretation of a modeling problem? </li></ul>

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Quantitative representation of models is just a direct translation of a problem using a formula to solve it (numerically). Qualitative representation requires understanding of what the problem was about. They: 1) explain the meaning of irelevant nformation stated only implicitly in a problem, and; 2) provide preconditions and constraints that determine the guideliness for the quantitative representations.

For example an elementary school student can be asked to compute the pressure of a gas. If the student has all the information and is provided with the formula to solve it, the student may accurately calculate the pressure (quantitative representation), but he may not know how to explain why the pressure got reduced as a result of the decrease in temperature (qualitative representation).

Tools for Modeling Problems

Databases. Way to organize the data and make it accessible. An example is a data table with the nitrutional facts of the food and the actual amount ingested to calculate the daily nutritional intake of a hospital patient.

Concept maps. Organizes ideas in sequences. It can be used to follow a laboratory protocol in a science laboratory.

Spreadsheets. Help to represent and solve a problem quantitatively. Can be used to compare student academic performanced based on different paramenters such as gender, demographics, etc.

Expert systems. They represent the deeper reflection in historical events than memorization of data. Expert system can be used to analyze the different factors that led to the civil right's movement.

Modeling Tools. System modeling tools are used to model dynamic, feedback-driven systems. It can be used to track the effect of climatic changes in the population dynamic of fish species along the Gulf Coast.

Vasualization tools. Helps to represent abstract concepts and models that are difficult to visualize otherwise. In the General Chemistry class that I teach, students have a difficult time visualizing the effect that different types of bounds will have on the three-dimentional structure of a complex organic compound. Tools that can help illustrate or virtually rotate these models give a better understanding of the actual configuration to the students.

Also, early on, the chapter mentions the design of word problems in textbooks. The problems are often found to be shallow and predictable. I find this to be true in literary selections where questions are at the end of each story. There are predictable, formatted questions, but they do have some usefulness in determining if students have a basic understanding of the text. For this reason, I create my own questions using the text as well as more higher-order thinking questions. In this way, students get a layered level of questions - some with which they will surely be successful and others which require the students to think about the principles that are presented in the literary work.