Mohi-Al-Deen Technologies

Evaluating Controversial Topics

 

Abstract: We consider built in teacher bias when evolving topics are taught by teachers belonging to different schools of thought. We have evolved a grading strategy that seems to eliminate teacher bias.

 

 

 

Introduction: Cutting edge education cannot stop with text book materials alone. We need to teach evolving topics where different schools might strongly disagree with each other. One such topic is whether ‘Evolution’ or ‘Intelligent Design’ produced life on earth. Another topic could be comparative study of two or more religions, for example Christianity and Islam.

 

 

 

Reposing faith in a single teacher to honestly convey the concepts from opposing viewpoints of a topic might result in the teacher’s own bias getting conveyed as truth. To avoid this it is recommended that the class be taught by more than one teacher. For example, in a class for ‘Comparative Study of Christianity and Islam,’ it would be appropriate to have a Christian teach about Christianity and a Muslim about Islam.

 

 

 

How do we evaluate the student performance in such a controversial course? For the purposes of discussion let us agree that we assign equal weight to the two opposing or competing approaches. Relative grading is resorted to eliminate teacher bias. Of course relative grading taken to the extreme rewards a group of extreme (excellent or mediocre) students as though they are average students. For example, let us say a class of students all score from 80% to 100% of marks. The same examinations are given to another group of students taught by another instructor. This group of students scores from 40% to 60%. Since the students belong to different classes, the student scoring 80% in the first group is awarded an ‘F’ while the student getting 60% from the second group walks away with an ‘A’. The correction of such normalization induced disparity is outside the scope of this discussion.

 

 

 

Problem: The problem of our concern is the unavoidable bias between the students and teachers of the same class. For illustration we use the teaching of Christianity and Islam. The results apply to other competing concepts as well.

 

 

 

While teaching Christianity the Christian teacher is justified in expecting the student to respond as a believing Christian. Similarly, the Muslim teacher expects the students to behave as though they believe in Islam. Unfortunately no rational thinking student would behave simultaneously as a believer in Christianity and Islam. In particular the concept regarding the nature of God is irreconcilable: Islam claims all actions – good and evil committed by human are sanctioned by God, whereas Christians insist that their God sanctions good actions alone. Because of the unbridgeable divide, some students believing in Christianity would offer unsatisfactory answers on questions related to Islam and vice versa with respect to Christianity. How do we overcome these built in biases?

 

 

 

Basic Mathematics: Let us consider some mathematics before attempting a solution. The following URL discusses the normal distribution that is accepted by virtually all academics.

 

 

 

http://mathworld.wolfram.com/NormalDistribution.html

 

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A normal distribution in a variate with mean and variance is a statistic distribution with probability function.

 

 

…de Moivre developed the normal distribution as an approximation to the binomial distribution, and it was subsequently used by Laplace in 1783 to study measurement errors and by Gauss  in 1809 in the analysis of astronomical data.

 

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Now-a-days the normal distribution is the standard. For ease of analysis and discussion, we approximate the normal distribution by the binomial distribution.

 

 

 

Grading philosophies: Small classes are about 30 and big classes are about 60 students. We consider the distributions for 32 students only. The binomial distribution is:

 

 

I	nCI (n = 5)
0	1
1	5
2	10
3	10
4	5
5	1
Total	32

 

 

 

What grades do we give for the above class of 32 students? Should there be mandatory failure? Should there be mandatory ‘A’ signifying excellence? It might be in order to be flexible with the following extremes for the five grades A, B, C, D, and F.

 

 

 

Skewed towards high grades: 6 As, 10 Bs, 10 Cs, 6 Ds and 0 F.

 

 

 

Skewed towards low grades;    0 A, 6 Bs, 10 Cs, 10 Ds, and 6 Fs.

 

 

 

Assumptions: For simplicity let us assume that the class of 32 has 16 Christians and 16 Muslims. The students are given labels C1 to C16 and M1 to M16. A student with index i is better than a student with index j while i<j.

 

 

 

Let us assume that the marks for A lie in the range 91% to 100%; B in 75% to 90%; C in 55% to 74%; D in 35% to 54% and F in 0% to 34%. When many students fall in the same grade the best student gets the highest mark and the worst student gets the lowest mark in the range. The other students get marks in linear proportion to their relative position rounded off to a full integer. The following table gives the marks scored by the students on Christianity and Islam respectively.

 

 

 

Tables:

 

 

 

Table 1: Both teachers grade High.

 

 

 

Table 2: Christian teacher grades High while Muslim teacher grades Low.

 

 

 

Table 3: Christian teacher grades Low while Muslim teacher grades High.

 

 

 

Table 4: Both teachers grade Low.

 

 

 

Final grading policy: Let us agree that both teachers agree to convert the total marks to grades following a moderate distribution as given below:

 

 

 

3 As, 8 Bs, 10 Cs, 8 Ds, and 3 Fs. The grades awarded to the students under the different philosophies are given in the table below.

 

 

 

Table 5: Grades under different styles of teachers.

Sl.No.	(High, High)		(High, Low)		(Low, High)		(Low, Low)
1	C1, 174	A	M1,164	A	C1,164	A	C1,144	A
2	M1,174	A	M2,159	A	C2,159	A	M1,144	A
3	C2,170	A	M3,154	A	C3,154	A	C2,139	A
4	M2,170	B	C1,154	B	M1,154	B	M2,139	B
5	C3,166	B	C2,150	B	M2,150	B	C3,134	B
6	M3,166	B	M4,149	B	C4,149	B	M3,134	B
7	C4,163	B	C3,146	B	M3,146	B	C4,129	B
8	M4,163	B	M5,144	B	C5,144	B	M4,129	B
9	C5,159	B	C4,143	B	M4,143	B	C5,124	B
10	M5,159	B	C5,139	B	M5,139	B	M5,124	B
11	C6,154	B	M6,138	B	C6,138	B	C6,118	B
12	M6,154	C	M7,135	C	C7,135	C	M6,118	C
13	C7,151	C	C6,134	C	M6,134	C	C7,115	C
14	M7,151	C	C7,131	C	M7,131	C	M7,115	C
15	C8,147	C	M8,131	C	C8,131	C	C8,111	C
16	M8,147	C	C8,127	C	M8,127	C	M8,111	C
17	C9,144	C	M9,127	C	C9,127	C	C9,107	C
18	M9,144	C	C9,124	C	M9,124	C	M9,107	C
19	C10,140	C	M10,123	C	C10,123	C	C10,103	C
20	M10,140	C	M11,120	C	C11,120	C	M10,103	C
21	C11,137	C	C10,120	C	M10,120	C	C11,100	C
22	M11,137	D	C11,117	D	M11,117	D	M11,100	D
23	C12,132	D	M12,113	D	C12,113	D	C12,90	D
24	M12,132	D	C12,109	D	M12,109	D	M12,90	D
25	C13,126	D	M13,107	D	C13,107	D	C13,81	D
26	M13,126	D	M14,102	D	C14,102	D	M13,81	D
27	C14,121	D	C13,100	D	M13,100	D	C14,73	D
28	M14,121	D	M15,96	D	C15,96	D	M14,73	D
29	C15,116	D	C14,92	D	M14,92	D	C15,64	D
30	M15,116	F	M16,90	F	C16,90	F	M15,64	F
31	C16,110	F	C15,84	F	M15,84	F	C16,55	F
32	M16,110	F	C16,75	F	M16,75	F	M16,55	F

 

 

 

Moderation: In the above table we notice that at the boundaries of the grades, one student gets a higher grade while the next gets the lower grade. We need to moderate such anomalies. We could moderate high giving the higher grade or moderate low giving the lower grade. We moderate high for the (High, High) and (Low, High) and moderate low for the (High, Low) and (Low, Low) columns in Table 6.

 

 

 

Table 6: Moderated grades.

Sl.No.	(High, High)   Moderate High		(High, Low)   Moderate Low		(Low, High)   Moderate High		(Low, Low)   Moderate Low
1	C1, 174	A	M1,164	A	C1,164	A	C1,144	A
2	M1,174	A	M2,159	A	C2,159	A	M1,144	A
3	C2,170	A	M3,154	B	C3,154	A	C2,139	B
4	M2,170	A	C1,154	B	M1,154	A	M2,139	B
5	C3,166	B	C2,150	B	M2,150	B	C3,134	B
6	M3,166	B	M4,149	B	C4,149	B	M3,134	B
7	C4,163	B	C3,146	B	M3,146	B	C4,129	B
8	M4,163	B	M5,144	B	C5,144	B	M4,129	B
9	C5,159	B	C4,143	B	M4,143	B	C5,124	B
10	M5,159	B	C5,139	B	M5,139	B	M5,124	B
11	C6,154	B	M6,138	B	C6,138	B	C6,118	C
12	M6,154	B	M7,135	C	C7,135	B	M6,118	C
13	C7,151	C	C6,134	C	M6,134	C	C7,115	C
14	M7,151	C	C7,131	C	M7,131	C	M7,115	C
15	C8,147	C	M8,131	C	C8,131	C	C8,111	C
16	M8,147	C	C8,127	C	M8,127	C	M8,111	C
17	C9,144	C	M9,127	C	C9,127	C	C9,107	C
18	M9,144	C	C9,124	C	M9,124	C	M9,107	C
19	C10,140	C	M10,123	C	C10,123	C	C10,103	C
20	M10,140	C	M11,120	C	C11,120	C	M10,103	C
21	C11,137	C	C10,120	C	M10,120	C	C11,100	D
22	M11,137	C	C11,117	D	M11,117	D	M11,100	D
23	C12,132	D	M12,113	D	C12,113	D	C12,90	D
24	M12,132	D	C12,109	D	M12,109	D	M12,90	D
25	C13,126	D	M13,107	D	C13,107	D	C13,81	D
26	M13,126	D	M14,102	D	C14,102	D	M13,81	D
27	C14,121	D	C13,100	D	M13,100	D	C14,73	D
28	M14,121	D	M15,96	D	C15,96	D	M14,73	D
29	C15,116	D	C14,92	D	M14,92	D	C15,64	F
30	M15,116	D	M16,90	F	C16,90	F	M15,64	F
31	C16,110	F	C15,84	F	M15,84	F	C16,55	F
32	M16,110	F	C16,75	F	M16,75	F	M16,55	F

 

 

 

 

 

Analysis: When both teachers give high grades or give low grades, the grade distribution between the Christian students and the Muslim students is the same as below:

 

 

 

Christians: 2 As; 4 Bs; 5 Cs; 4 Ds; and 1 F.

 

Muslims:   2 As; 4 Bs; 5 Cs; 4 Ds; and 1 F.

 

The above distribution is for (High, High) moderated High corresponding to the first column.

 

 

 

We have:

 

Christians: 1 A; 4 Bs; 5 Cs; 4 Ds; and 2 Fs.

 

Muslims:   1 A; 4 Bs; 5 Cs; 4 Ds; and 2 Fs,

 

corresponding to column 4 with (Low, Low) moderated Low.

 

 

 

When we consider column 2, we get:

 

Christians: No A; 5 Bs; 5 Cs; 4 Ds; and 2 Fs, whereas

 

Muslims:    2 As; 4 Bs; 5 Cs; 4 Ds; and 1 F.

 

 

 

The above distribution is when the Christian teacher grades High and the Muslim teacher grades Low with Low moderation. This result is unexpected. When a Christian teacher gives more marks, it is expected that the Christian students get better grades. However due the nature of the marks distribution between the different grades, the Muslim students end up with better grades.

 

 

 

We find a similar effect in column 3 as well. Here the Muslim teacher gives better grades and the Muslim students get lower final grades.

 

Christians: 3 As; 4 Bs; 4 Cs; 4 Ds; and 1 F.

 

Muslims:   1 A;   4 Bs; 5 Cs; 4 Ds; and 2 Fs.

 

The above corresponds to (Low, High) with High moderation.

 

 

 

Conclusion: Based on the above distributions, we formulate the following hypothesis:

1. Take the marks awarded by the contesting teachers individually and award grades following a single distribution.
2. Convert the grades to marks based on the relative position of the students based on marks given by the teacher following the strategy described above.
3. Add the marks from both teachers and get final marks for the students.
4. Grade the final marks as per agreed upon grade distribution and moderate when students with same final marks get different grades.

 

 

 

We expect the final grade to be free of teacher bias even though the teachers believe in different and contesting concepts.