October 2007 Volume 10 Number 4 - Educational Technology ...

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A Review of Biswas’ Methods for Students’ Answerscripts Evaluation Biswas (1995) used the matching function S to measure the degree of similarity between two fuzzy sets (Zadeh, 1965). Let A and B be the vector representation of the fuzzy sets A and B, respectively. Then, the degree of similarity S( A , B ) between the fuzzy sets A and B can be calculated as follows (Chen, 1988): S( A , B ) = A ⋅ B , (8) Max( A ⋅ A, B ⋅ B) where S( A , B )∈[0, 1]. The larger the value of S( A , B ), the higher the similarity between the fuzzy sets A and B. Biswas (1995) presented a “fuzzy evaluation method” (fem) for evaluating students’ answerscripts, based on the matching function S. He used five fuzzy linguistic hedges, called Standard Fuzzy Sets (SFS), for students’ answerscripts evaluation, i.e., E (excellent), V (very good), G (good), S (satisfactory) and U (unsatisfactory), where X = {0%, 20%, 40%, 60%, 80%, 100%}, E = {(0%, 0), (20%, 0), (40%, 0.8), (60%, 0.9), (80%, 1), (100%, 1)}, V = {(0%, 0), (20%, 0), (40%, 0.8), (60%, 0.9), (80%, 0.9), (100%, 0.8)}, G = {(0%, 0), (20%, 0.1), (40%, 0.8), (60%, 0.9), (80%, 0.4), (100%, 0.2)}, S = {(0%, 0.4), (20%, 0.4), (40%, 0.9), (60%, 0.6), (80%, 0.2), (100%, 0)}, U = {(0%, 1), (20%, 1), (40%, 0.4), (60%, 0.2), (80%, 0), (100%, 0)}. He used the vector representation method to represent the fuzzy sets E, V, G, S and U by the vectors E , V ,G , S and U , respectively, where E = , V = , G = , S = , U = . Biswas pointed out that “A”, “B”, “C”, “D” and “E” are letter grades, where 0 ≤ E < 30, 30 ≤ D < 50, 50 ≤ C < 70, 70 ≤ B < 90 and 90 ≤ A ≤ 100. Furthermore, he presented the concept of “mid-grade-points”, where the mid-gradepoints of the letter grades A, B, C, D and E are P(A), P(B), P(C), P(D) and P(E), respectively, P(A) = 95, P(B) = 80, P(C) = 60, P(D) = 40 and P(E) = 15. Assume that an evaluator evaluates the first question (i.e., Q.1) of the answerscript of a student using a fuzzy grade sheet as shown in Table 2. Table 2. A fuzzy grade sheet (Biswas, 1995) Question No. Fuzzy mark Grade Q.1 0.1 0.2 0.3 0.6 0.8 0.9 Q.2 Q.3 … … … … … … … Total mark = In the second row of Table 2, the fuzzy marks 0.1, 0.2, 0.3, 0.6, 0.8 and 0.9, awarded to the answer of question Q.1, indicate that the degrees of the evaluator’s satisfaction for that answer are 0%, 20%, 40%, 60%, 80% and 100%, respectively. In the following, we briefly review Biswas’ method (1995) for students’ answerscript evaluation as follows: Step 1: For each question in the answerscript repeatedly perform the following tasks: (1) The evaluator awards a fuzzy mark Fi to each question Q.i and fills up each cell of the ith row for the first seven … 231
columns shown in Table 2, where 1 ≤ i ≤ n. Let F be the vector representation of Fi, where 1 ≤ i ≤ n. i (2) Based on Eq. (8), calculate the degrees of similarity S( E , F ), S(V , F ), S(G , F ), S( S , F ) and S(U , F ), respectively, where E , V , G , S and U are the vector representations of the standard fuzzy sets i E (excellent), V (very good), G (good), S (satisfactory) and U (unsatisfactory), respectively, and 1 ≤ i ≤ n. (3) Find the maximum value among the values of S( E , F ), S(V , F ), S(G , F ), S( S , F ) and S(U , F ). Assume that S(V , F ) is the maximum value among the values of S( E , F ), S(V , F ), S(G , F ), S( S , F ) i i i i i and S(U , F ), then award the letter grade “B” to the question Q.i due to the fact that the letter grade “B” i corresponds to the standard fuzzy set V (very good). If S( E , F ) = S(V , F ) is the maximum value among the values of S( E , F ), S(V , F ), S(G , F ), S( S , F ) and S(U , F ), then award the letter grade “A” to the i i i i i question Q.i due to the fact that the letter grade “A” corresponds to the standard fuzzy set E (excellent). Step 2: Calculate the total mark of the student as follows: n 1 × ∑ = Total Mark = [ T ( Q. i) × P( g i )], (9) 100 i 1 where T(Q.i) denotes the mark allotted to Q.i in the question paper, gi denotes the grade awarded to Q.i by Step 1 of the algorithm, P(gi) denotes the mid-grade-point of gi, and 1 ≤ i ≤ n. Put this total score in the appropriate box at the bottom of the fuzzy grade sheet. Biswas (1995) also presented a generalized fuzzy evaluation method (gfem) for students’ answerscripts evaluation, where a generalized fuzzy grade sheet shown in Table 3 is used to evaluate the students’ answerscripts. Table 3. A generalized fuzzy grade sheet (Biswas, 1995) Derived letter Question No. Fuzzy mark grade Mark Q.1 Q.2 … … … F11 F12 F13 F14 F21 F22 F23 F24 … … … i i g11 g12 g13 g14 g21 g22 g23 g24 … … … Total mark = In the generalized fuzzy grade sheet shown in Table 3, for all j = 1, 2, 3, 4 and for all i, gij denotes the derived letter grade by the fuzzy evaluation method fem for the awarded fuzzy mark Fij and mi denotes the derived mark awarded to the question Q.i, where 4 1 mi = × T (Q.i) × ∑ P ( g ij ) , (10) 400 j= 1 n ∑ i= 1 and the Total Mark = m . i i i i i m1 m2 i … … … i i i i 232
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October 2007 Volume 10 Number 4
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Abstracting and Indexing Educationa
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The Relationship of Kolb Learning S
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a question about learning together
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affordances of networked learning s
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included a unit on collaborative le
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on at different times and work indi
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• the numerous evaluation studies
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wanted to work. The same inquiry pr
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usability studies have a place in t
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Milrad, M., & Jackskon, M. (2007).
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information- and communication tech
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Interactive Examination, the studen
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Table 1. Criteria for grading OD st
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content. Differences in the attitud
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Even though further research on the
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Olofsson, A. D. (2007). Participati
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Etzioni (1993) points out that an i
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programme. They are rather construc
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to be that each individual trainee
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Bernmark-Ottosson, A. (2005). Demok
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The Knowledge Foundation (2005). IT
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Figure 1. Design Theories in contex
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attention as we frequently discuss
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Blog Reflection This design concept
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Narrative Structure (Form) Content
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Löwgren, J., & Stolterman, E. (200
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critique, neither do the single ind
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suggested by Ljungberg (1999b) we c
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the del.icio.us site (see figure 3)
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Device cultures It is not only the
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uilt using a camera-equipped PDA ru
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Jones, C., Dirckinck-Holmfeld, L.,
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Milrad, M., & Spikol, D. (2007). An
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components to be able to deal with
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compulsory throughout the project.
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only with their existing day-today
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As our work continues, we will try
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cognition as well as self-regulated
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Mobile mind map tool for stimulatin
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the pictorial knowledge representat
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Ericsson, K. A., & Simon, H. A. (19
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Al-A'ali, M. (2007). Implementation
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complex cognitive skills involve em
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Table 1. CAT and a linear mathemati
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It is agreed that the difficulty le
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Figure 7. Our newly added factors i
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question factors according to IRT;
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Instructure 1 Login User-ID Passwor
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Shute, V., & Towle, B. (2003). Adap
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distinguish between partial knowled
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esponse is identified, then the sco
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are stored in the answer record and
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2 (7) MNSQ = ∑WniZ ni ∑ Wni =
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in the course. A randomized block d
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To test whether ET can effectively
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course, more comparison tests could
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Fleischmann, K. R. (2007). Standard
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educational standards in practice t
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laboratory activities, which are bu
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process is currently a largely top-
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Hsu, Y.-S., Wu, H.-K., & Hwang, F.-
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evolution with computing technology
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Resources 0.55 0.72 e17 In my schoo
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teachers’ instructional evolution
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Regression models indicating relati
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of beliefs about integrating comput
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Sinko, M., & Lehtinen, E. (1999). T
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concept of social support. Lastly,
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Procedure Content analysis procedur
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and mice are out of order. I have t
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feature of supportive online groups
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Anderson, J., & Lee, A. (1995). Lit
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Schwab, R. L., Jackson, S. E., & Sc
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Investigating the problem An extens
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meets the anywhere, anytime require
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minimise housekeeping tasks and fre
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3. Join Group Discussion 4. Attend
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Figure 4. Learning Shell showing He
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engineering the Learning Shell so i
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Olfos, R., & Zulantay, H. (2007). R
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portion of CourseInfo requires that
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Table 2. Assignment evaluation resp
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E-3c. Likert scale on usability: Th
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organized in four groups, namely: T
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The correlations were not high enou
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Data illustrate some reliability an
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nature, some specific core objectiv
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Frederiksen, J.R., & Collins, A. (1
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Bottino, R. M., & Robotti, E. (2007
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The Text Editor allows the editing
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Mathematical content and structure
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Page 249 and 250: enabling learner (subject) to work
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Page 253 and 254: (iii) Regulates the communication:
Page 255 and 256: Figure 3. A screen shot of the SCAL
Page 257 and 258: 2 nd study: Thirty-five students pa
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Page 261 and 262: Soller, A. (2001). Supporting Socia
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Page 265 and 266: Solution 2.2: Deliberately select h
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Page 275 and 276: Concept Mapping Concept mapping by
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esources. The use of synchronous te
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The use of digital communication mo
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contributed more information and en
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3. Use the second screen for the le
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• Use drawing to develop writing
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student and teacher on the synchron
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Vogel, J. J., Vogel, D. S., Cannon-
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Cases The first set of ten case stu
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Kılıçkaya, F. (2007). Website re
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