Learning Scenario - Community College (Vensim)

Basic Model:

Description

College graduation largely depends on how much time, effort, and class work one puts in. This model attempts to analyze the college experience to find the best plan to balance all factors that contribute to a student's graduation. Users of this model may move the sliders for several factors and see how they affect the enrollment levels at a community college. Students at this community college have a two-year track to graduation, and each year those who do not satisfactorily complete the requirements are cut. The goal of this model is to understand how all variables and commitments one has to their college affects whether or not they will graduate.

Background Information

Many students don't realize-or ignore the fact-that a certain amount of time must be devoted to classes in order to graduate from college. This includes factors such as lab time, time devoted to classes, etc. The more a student spends on the subject, the better chance he or she will have of passing. On the other hand, there are factors that are out of the student's control. Classrooms, summer vacation time, and the content per day are often decided by the school and teachers, yet they still have an effect on the number of graduating students. In this model, students will be able to find and understand the best plan to graduate the most number of people while still keeping a high mastery level.

Science/Math

The fundamental principle behind this model is HAVE = HAD + CHANGE. For each run of the simulation, the following things are calculated and displayed:

1. The number of freshmen who passed their classes are promoted to sophomores
2. The number of sophomores who passed their classes are graduated
3. Class density is plotted on the graph over time
4. The minimal and mastery level are plotted on the same graph as class density

As collegians enrolled in the community college progress from freshmen to sophomores and from sophomores to graduation, each level goes through a number of CHANGES that affect their progress. Students who use this model may manipulate the change in order to produce and learn from a different result.

Teaching Strategies

Many of these factors might be intuitive for students. Therefore, where the teacher might benefit in introducing this model is treating the model as a social study. Ask the students to come up with hypotheses for each of the following questions and compare them to the results obtained through experimentation:

1. How would the length of class and number of classes affect the amount of time a student must study to pass?
2. Which is better to master the material: several classes with a moderate amount of time studying or a few classes with lots of studying? Explain.
3. What are some factors that go into someone's schooling success that are out of his or her control?
4. What are the potential dangers and benefits from moving the minimal and mastery levels higher and lower? Explain.

Again, these may be compared to the results that students obtain by playing with the model.

Implementation:

How to use the model

This is a very in-depth model that calculates many variables. Each of the following has an effect on the output graph and the function as a whole:

1. Content mastered, lab time, length of class, and summer vacation time all affect the matriculation of students into the college
2. Content per day affects the content mastered, and classes per day affect the content mastered as well as the length of class.
3. The learning rate dictates how many freshmen will be promoted to sophomores
4. The time devoted to class and success rate both determine how many sophomores graduate
5. The number of sophomores per classroom (class density) is calculated and plotted on the graph
6. The minimal and mastery levels are plotted on the graph

Many of these variables may be changed by dragging the appropriate slider when the simulation is run. The others may not be changed, but they are calculated in as constants in real time. To run the simulation, click the SyntheSim button on the top of Vensim. This could be pictorially represented by a running man or green triangle with sliders behind it. A graph will instantly appear and change as the variables are manipulated. For more information on Vensim, reference the Vensim tutorial at: http://shodor.org/tutorials/VensimIntroduction/Preliminaries

Learning Objectives

1. Understand the effect of personal variables versus college imposed variables on the graduation rate
2. Understand the effect of variables on the proportion of students who master the material

Objective 1

The amount of students who graduate from the college is largely dependent on how much time each spends on school and the class load that he or she has. To accomplish this objective, students should change the variables that are directly under the control of the student. These variables include lab time, content mastered, content per day, and time devoted to classes. The other variables are generally controlled by the college. Have students manipulate these variables in order to see which has a greater impact on the graduation of the students and answer the following questions:

1. Set the mastery level to 15 and the minimal level to 5. What effect does the time devoted to classes have on the graduation rate? How is this represented in the graph? With the other variables as they are, how many months would it take to master the material in about 48 months?
2. If the time devoted to classes remains the same, what effect does the classes per day have on the number of students moving to the next level? Does this make sense in terms of the real world? What would be required with an increasing number of classes?
3. How does the learning rate of the students affect the graduation numbers? If the learning rate is very high, what might be said about the minimal and mastery levels of the school? Would they be changed?
4. Some factors are not controlled by the students, such as the number of classrooms and the summer vacation time. If the college was relatively small (~30 classrooms), how would this affect graduation rates? Mastery rates? Explain your findings.
5. Does the length of summer vacation have any effect on the graduation rate or those who master the material? Why or why not? What does it affect?

Objective 2

When running a college, it is important to have a system that allows the most number of students to succeed. If the minimal level is barely passing (i.e. a D) and the mastery level is developing a full understanding of the subject (i.e. an A), a college wants to have as many people in the mastery level as possible. Students should manipulate the variables to see the affect that they have on the mastery level of students. Have them analyze the extent to which the optimal parameters are both beneficial and realistic. Ask the following questions:

1. What do the minimal and mastery levels represent? How would you infer how many students have mastered the subject versus those who have not?
2. Move the "Time Devoted to Classes" slider until all the students are above the mastery level. Is this time realistic? Why or why not?
3. Which variables would allow the most students to master the material while spending the least amount of time on the subject?
4. Is there a set mastery and minimal level in the real world? What would the implications be of lowering the mastery and minimal levels?

Extensions:

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1. Analyze other factors that could affect graduation rates in a real-world community college
2. Understand mathematical modeling in its application to sociology
3. Use the same modeling method to find factors that control the advancement of students in high school

Extension 1

There were several variables discussed in this model that affect the graduation rate of students, but many more exist. Tell students to research the number one reason that people do not graduate college and how the cost of college has increased significantly in the past several years. Ask the following questions:

1. How big a factor does money have on the amount of students who drop out of college? Explain.
2. What has the trend been in college tuition over the past couple decades? What influenced this trend?
3. In what way could you incorporate finances into the Community College Model? How would the graph change as cost increased or decreased?

Extension 2

Mathematical modeling is often used by sociologists, who try to determine and understand social patterns and interactions. The Community College model is an example of one such simulation. Have students find other sociological models online and research the way that scientists use these models. Ask the following questions to guide students in their study:

1. Why do sociologists use mathematical models for in their field? What do they use it to study?
2. How does the Community College model act as a type of mathematical model? Explain.

Extension 3

This model simulated a two-year community college, but the same modeling method can be used to study other progressive systems. Students may be more familiar with the progressive steps and requirements for high school. Have students come up with a system that models the four years of high school and the factors that influence the graduation rate. Ask the following questions:

1. What factors would influence someone moving from one grade to the next? Which are more of a factor in high school, personal commitments or school regulations? Explain.
2. In what ways would a high school model differ from a community college model? Are there more personal or school-related factors in high school?
3. 3. What limitations do you see from modeling education in this way? How good of a model is this for predicting actual graduation rates?

Related Models

Reversible Consecutive First-Order Reactions (Vensim)

http://www.shodor.org/talks/ncsi/vensim/index.html The Reversible Consecutive First-Order Reactions model has similar functionality to the Community College model. Students are able to manipulate certain variables-the rates of reactions-to see the effect that each constant has on the shape of the resulting graph. The model simulates two reversible reactions that will eventually reach equilibrium. When the reaction reaches equilibrium is dependent upon the four rates of reaction set before running the simulation. In the Community College model, many different factors went into the graduation rate and class density; in this model, the same is true, but the equilibrium point is influenced by the rates of reaction.

Dosing Model

http://www.shodor.org/talks/ncsi/vensim/index.html The minimal and mastery levels in the Community College model provided a boundary to aim for and keep the class density within. These boundaries, while able to be changed in the model, are often very similar to real-world limitations. For example, the toxic and medicinal levels of certain drugs are factors that a pharmacist has to take into account when working with medicine. In the Dosing Model, students take control of the dosage level, time, and absorption rate of a drug in order to understand this concept. Through experimentation, the students may expand upon the idea of real-world boundaries introduced in the Community College model and the potentially deadly consequences of surpassing them.