a model for tutoring the guided study program in system dynamics

8/9/2019 A Model for Tutoring the Guided Study Program in System Dynamics

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A Model for Tutoring the Guided Study Program in System Dynamics

By Michael McCurley

AbstractIt is possible to design a simple model that illustrates how a tutoring program

could work for the Guided Study Program in System Dynamics. This model shows how

entrance rates could affect student levels, and includes attrition and completion rates

for the program. Thus it would indicate how the workload that a tutor might expect to

have, as well as how attrition or continuance, might affect program completion.

The following model does this fairly well, in spite of the fact that it simplifies

average real conditions that would be more irregular. Results also seem to show that

better tutoring could improve program completion without actually increasing the

workload of a tutor significantly, and that actual observations of program results

combined with modeling could help a tutor to manage the tutoring workload moreeffectively.

Introduction

A tutor for a distance learning guided study program, which is fairly long,

challenging and complex, will probably notice an incidence of entry rates and attritionthat affect the levels of students who are studying and the number of students who

complete the program. If that tutor were to offer a 9-month program once a year, with an

attrition rate of 50 percent, half of the students would be gone by the end of the program.One way to maintain higher active levels of students would be to offer registration for the

program several times a year. Because the guided study program could be individuallytracked, a good tutor can help different groups of students at the same time and offerentrance into the program once a quarter for a small number of students, rather than

handling a larger number of students all at once that would decrease due to attrition over

a longer time period.

Creating a model would help a tutor to plan for student management of lesson

assignments and could project how program performance would determine the number of

students completing the guided study program over a period of years. While it might bepossible to mentally simulate these projections with the help of a calculator or spread

sheet, a simulation model can provide a better visualization of several simultaneous

variables that would help make planning easier, and provide a clearer idea of outcomes.

Keeping assumptions for the model as simple as possible is of key importance for

creating a basic model. While these may not exactly represent all specifics, what isimportant is an overview that would be of greatest service for conceptualization and still

be accurate. Changing parameter values and comparing different simulation runs would

give the tutor a good idea of possible performance outcomes under a variety of

conditions.


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Defining Parameters for the Model

For the purposes of this model, assumptions for basic parameters could be as

follows: 6 students would enter each quarter period (of 3 months). The term for theprogram period would be 10 months (actually adjusted from an official 9 months for

students who may delay completion of the program).

This model tracks the students who enter and are in the guided study program,

students who proceed throughout the program and complete it, and students who

eventually drop out of the program and leave it over a 5-year time period.

Attrition of students from a large program of this type might be as high as 60

percent due to a variety of factors, some of which will not be discussed in this paper. This

implies that 40 percent of the people who start guided study for this informal openeducation program would finish it. On the other hand, examination of an inverse situation

is also noteworthy (and included in a later simulation run).

Model Diagram for Tutoring the Guided Study Program

Students

Finish Pr

Students Who

Have Left

Students Who Are

in Programstudents finishingstudents entering

students leaving

Candidates who enter per quarter

length of quarter attrition

ATTRITION RATE

completion

COMPLETION RA

length of pro

attrition period

Details of the Model

Assume an entry rate of 6 students per quarter, 4 times a year, for fall, winter,

spring and summer sessions. Not all students will finish for various reasons. Some willleave because they find lessons difficult or only wish to complete a few lessons. Others

will have time difficulties and find they cant make the time commitment to complete

lessons that make monthly payments worthwhile. Assume an attrition rate of 30 percentfor the first part of a 9-month period, and another 30 percent attrition for the second part

of the same 9-month period. 40 percent of those who enter may complete the program

normally in 9 months, or slightly more than that for an average completion period ofabout 10 months.


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Running the model and graphing three of the levels shows an S-shaped type curve

for a consistent number of students who enter the program, the accumulating level ofstudents who finish the programand an accumulating level for students who would

leave the program. A real graph for students entering the program would actually vary, as

would the rate of increase for accumulating levels of students who finish or leave theprogram, but variable input can be averaged over a period of time. A somewhat more

complex model with a pulse train could also represent this.

Students who Complete or Leave Program with a 60/40 Attrition vs. Completion Ratio

(Assume an entry rate of 6 students per quarter)

80

60

40

20

0

0 9 18 27 36 45 54

Time (Month)

Students Who Are in Program : Current Students

Students Who Finish Program : Current Students

Students Who Have Left : Current Students

Analyzing the results

For an entry rate of just 6 students who are tutored each quarter, there wouldeventually be about 18-19 students studying at a time in 4 broadly different assignment

phases. Over a 5-year period, given an attrition rate of 60 percent and a completion rateof 40 percent, about 40 students would finish the program and 66 would drop out.

Proportions are slightly out of phase because the time periods mentioned are different.

While these estimations may seem rather pessimistic, they would probably represent a

fairly good success rate in real terms. 40 students completing the program would be asignificant number, considering that not more than 30 students completed the official

MIT program during a school year. But this is an institution with several people working

with the Guided Study Program, compared to a single tutor (who does admittedly take 5years to do the job).

Equation and information data for the basic model is as follows:

(01) attrition=(ATTRITION RATE*Students Who Are in Program)/attrition period

Units: Students/Month

Students who drop out of the program.

(02) attrition period=4.5

Units: Month


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This is half of the program period.

(03) ATTRITION RATE=0.3

Units: dmnl

This is the percentage of projected attrition for half of the program period.

(04) Candidates who enter per quarter=6Units: Students

This is the number of students who enter per term.

(05) completion=(COMPLETION RATE*Students Who Are in Program)/length of program


These are the students who are completing the program.

(06) COMPLETION RATE=0.4

Units: dmnl

This is the percentage of students who complete the program.

(07) FINAL TIME = 60Units: Month

The final time for the simulation.

(08) INITIAL TIME = 0Units: Month

The initial time for the simulation.

(09) length of program=10

Units: Month

This is the adjusted period of the program, which is slightly more than 9 months.

(10) length of quarter=3Units: Month

Number of months per quarter.

(11) SAVEPER = TIME STEP

Units: Month

The frequency with which output is stored.

(12) students entering=Candidates who enter per quarter/length of quarter


Average number of students who enter per month.

(13) students finishing=completion

Units: Students/MonthThese are the students who complete the entire program.

(14) students leaving=attrition


These are the students who leave.

(15) Students Who Are in Program= INTEG (students entering-students finishing-students

leaving, 5)


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motivation and help for assignment related problems might encourage students to

complete more assignments and finish the program, while not actually increasing the

general workload in any significant way for the tutor. IF this observation is correct, thenanything we might do to encourage students to continue with the program would have a

significant overall effect on the number of people who finish the guided study program

withoutcreating a much heavier work load.

Adjusting the simulationincreasing the entry rate

If a larger entry rate of students is permitted per quarter, it would change theoverall level of the number of students who are studying at a given time. If we change

that number to an average of 8 students who enter per quarter, without changing any

other parameters, the results would be as follows:

Students who Complete or Leave Program with a 60/40 Completion vs. Attrition Ratio

(Assume an entry rate of 8 students per quarter)

100

75

50

25

0

0 9 18 27 36 45 54

Time (Month)

Students Who Are in Program : Current Students

Students Who Finish Program : Current Students

Students Who Have Left : Current Students

Analyzing the results

The number of students who are studying at the same time, would increase to 25.

In a 5-year period, 80 students would complete the program (compared with 60 in the last

example), and 59-60 students would drop out because more students overall would beentering the program.

General Observations:

Completion versus attrition rates would have little effect on the level of students

who are studying, while the number of students who are allowed to enter the program

each quarter does have a more direct effect on the level of students who are studying atany given time.


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a model for tutoring the guided study program in system dynamics

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