20IO 2nd International Conference on Computer Technology and Development (ICCTD 2010)

Technology in Education: A Model for Evaluating Academic Tenure

Ved Madan, Ph.D. Professor of Mathematics, St. Mary's University College

Calgary, Alberta, T2X lZ4 Canada ved.madan@stmu.ab.ca

Abstract-A mathematical model related with Bayes' theorem

is used to determine the tenure status of faculty members using criteria such as teaching, research, professional development, committee assignments and community service. The tenure status is determined by scale factors assigned to different

activities and accepted levels of cumulative achievements.

Keywords - Bayes' Theorem, Tenure

I. INTRODUCTION

Bayes' Theorem [1] is a theorem of probability originally stated by Reverend Thomas Bayes. It has been used to clarifY the relationship between theory and evidence. Unwin [3] has applied Bayes' theorem in a paperback "The probability of God: A Simple Calculation That Proves the Ultimate Truth". Starting with the maximum ignorance on the question of God i.e. 50-50 chance that God exists he calculates the probability of God's existence. Several assumptions are made in calculations but nevertheless the work is a good illustration of Bayes' theorem. Later Madan [2] presented a mathematical model to determine the probability of salvation based on the theory of Karma. In this paper we apply Bayes' theorem to determine the tenure status of university and college professors, which is deemed a more practical application of technology in education. Tenure is granted to faculty members based on their annual progress in areas of teaching, research, professional development, committee assignments and community service. Other criteria may be added by the institutions as necessary. Various academic activities such as teaching, research, professional development etc. are assigned a scale factor based on their merits. The probability of tenure is determined simply by averaging all cumulative achievements of the faculty members. Tenure is granted based on a point system instead of subjective information of colleagues who may be members of the tenure committee.

II. MATHEMATICAL MODEL FOR EVALUATING TENURE

Bayes' Theorem may be modeled for tenure as follows

Model T:

Pbefore*k Pafter = , k = scale factor

Pbefore * k + (1- Pbefore)

Where Pbefore is probability of tenure at time of hiring, Pafter is probability of tenure at the end of one year, and k is a scale factor allotted to the specific activity. We attach the following scale factors to job activities as shown in Table 1, although one can be flexible in assigning different numerical values to scale factors.

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TABLE I ASSIGNING SCALE FACTORS K

k Teaching Research Professional Committee Comm. Development Assignments Service

I Needing No Acquiring None None Improvement Publications Skills

2 Good 1-2 Papers Attending Member of Volunteer Per Year Conferences Committee

3 Excellent 3+ Papers Speaker Chair Serving Per Year Comm.

Example: We attach the following scale factors to various activities for member XYZ. See Table 2

TABLE II SCALE FACTORS EXAMPLES

Activity Teaching Research Professional Committee Comm. Development Assignments Service

Scale 3.0 3.0 1.5 14 1.1 Factor

In Table 2 teaching and research accomplishments are given equal values for scale factors followed by other activities. Assuming that the faculty member has 50% chance of tenure at time of hiring i.e. Pbefore = 0.5, we generate the following values for Pafter first year of service. Scale factor of 1.0 involves no change in tenure status, while higher values of scale factors mean

positive impacts on tenure decisions. We consider values of k that are more than or equal to one.

TABLE III. SCALE FACTORS: PBEFORE AND P AFTER VALUES

Activity Scale Pbefore Pafter

Factor Using Model T k

Teaching 3.0 0.5 0.75 Research 3.0 0.5 0.75 Professional 1.5 0.5 0.6 Development Committee 1.4 0.5 0.5833 Assignments Community 1.1 0.5 0.5238 Service Average 2.0 0.5 0.6414

We see from Table 3 that the cumulative average probability of tenure has increased from its initial value 0.5 to 0.6414 in one year. Furthermore, if the same trend continues then the probability of tenure in successive years may be found by repeated applications of model T. The results are displayed in Table 4 below.

2010 2nd International Conference on Computer Technology and Development (ICCTD 2010)

TABLE IV. TENURE STATUS IN SUCCESSIVE YEARS

The faculty member can thus receive tenure in his/her fifth year for assumed scaling factors with probability of 86.71 %, providing a Pafter value of 85% is considered as an

acceptable level for granting tenure. The tenure time would of course be dependent on the initial value of probability. Furthermore each institution can set scaling factors for various types of activities in accordance with its goals. New activities may as well be added to the above list as determined by the tenure committee.

College institutions may revise the scale factors to give more emphasis to teaching excellence and professional development so that the revised scale factor K is equal to original scale factor k times an adjusting percentage factor bi assigned to an activity. The revised factor K = k*bi would increase or decrease the original scale by factor bi. This is shown in Table 5.

TABLE V. TENURE STATUS USING REVISED SCALE FACTORS

Activity Original Revised Pbefore Pafter Scale Scale

Factor k Factor K Teaching 3.0 4.5 0.5 0.8182

Research 3.0 1.5 0.5 0.6000

Professional 1.5 2.0 0.5 0.6667 Development Committee 14 2.0 0.5 0.6667 Assignments Public Service 1.1 1.0 0.5 0.5000

Average 2.0 2.2 0.5 0.6503

In Table 5 above more weight is granted to teaching, professional development, and committee assignments while less weight is applied to research and public services. We see that the probability of tenure has increased from its initial value of 0.5 to 0.6503 at the end of one year. Furthermore, if the same trend continues then the probability of tenure in successive years may be found by repeated applications of the same procedure. The results are displayed in Table 6 below.

TABLE V!. TENURE STATUSES WITH REVISED SCALE FACTORS

Table 6 shows that the faculty member can thus receive tenure in hislher fourth year with the assumed scaling factors with probability of 86.45%, providing a Pafter value

of 85% is considered as acceptable level for granting tenure as before.

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The following worksheet may be used to evaluate tenure status of faculty members by adjusting parameters such as scale factors and Pbefore.

TABLE VII. WORKSHEET CALCULATIONS

Professor's Name Institution (---------) Pafter=

(-----------) (Pbefore*k)/(Pbefore*k+(l-

Excel Worksheet For Pbefore)) Modell

P after one year P after

Activity Scale factor P before two years Teaching 3 0.5 0.75 0.9000 Research 3 0.5 0.75 0.9000 Prof Dev 1.5 0.5 0.6 0.6923 Committee Assignments 1.4 0.5 0.5833 0.6621 Community Service 1.1 0.5 0.5238 0.5475

Average 2 0.5 0.6414 0.7403

Note: The application of Bayes' theorem using Model T for evaluating tenure status of faculty members is just an example. Students may also employ this model for different types of

activities such as education, sports, special projects, and volunteer work etc by assigning suitable scale factors in the

formatted Table activities to evaluate success in meeting with

respective goals.

ACKNOWLEDGEMENT

The author would like to acknowledge the help of Dr. Gary Grothman in reviewing the paper.

REFERENCES

[I] Bayes' Theorem

http://www.trinity.edu/cbrown/bayesWeblindex.html

[2] V Madan, "Mathematical Model for Probability of Salvation: Theory of Karma", Proc. Of Second International Conference on Computer Research and Development, May 7-10, 2010, Kuala Lumpur, Malaysia, pp. 459-460.

[3] The Probability of God: A Simple Calculation That Proves the Ultimate Truth, Stephen Unwin, Three Rivers Press, 2004, ISBN 978-1400054787