Fuzzy Set Approach to the Assessment of Student-Centered Learning

Authors: Jian Ma, Duanning Zhou(HK)From: IEEE Transactions on Education Vol.43,No.2,May 2000,p237-241Presented:廖佳慧 (9254608)

outline

• Introduction• Generate the assessment criteria• Fuzzy grading system• Application• Summary• comment

Introduction Assessment is an important but difficult

task in whole teaching and learning process.

Student-centered learning often takes place in the form of problem-based learning,project-based learning and lab-based learning.

The nature of student-centered learning, criterion-referenced assessment methods are commonly used for evaluating students’ outcomes

Introduction (cont.)The lecturers in charge are solely

responsible for determining the assessment criteria and their corresponding weights.

This paper uses the brainstorming technique to allow lecturers and students to generate the basic set of assessment criteria with reference to the course objectives and the industry standards for software quality management.

Introduction (cont.)It uses the fuzzy set method for students

and lecturers to vote for their preferred assessment criteria.

The criterion-referenced assessment method– The generation of the basic set of assessment

criteria.– The selection of the assessment criteria from the

basic set of assessment criteria.– The determination of the corresponding

assessment criteria weights.– The evaluation of the students’ outcomes using

the agreed criteria.

Generate the assessment criteria

A fuzzy set is a class of objects with a continuum of membership grades.

A membership function, which assigns to each object a grade of membership, is associated with the fuzzy set.

A fuzzy grading method that utilizes students’ and instructor’s performance measure to produce a ’fair’ mark distribution.

Generate the assessment criteria(cont.)

Where U: a classical set of objects A: a fuzzy set of characterized x: generic elements

μA(x) : membership function,[0,1]

)(...A , }{ 11 UAAAU nn iAAA i Au,(u)}(u)...μ{μ(u)μ A

n1i into classified becan max satisfies When

Fuzzy relation X × Y

The composition result P(X,Y),Q(X,Y) fuzzy relation R(X,Y) R=P 。 Q

Generate the assessment criteria(cont.)

They work collaboratively to propose a basic set of assessment criteria.C = {c1,..,cn}

Generate the assessment criteria(cont.)

• A brainstorming technique is used to generate the basic set of assessment criteria.

• The lecturer can lead the students to study the course objectives and relevant international standards for software quality management.

• A fuzzy value between [0,1] is assigned by the participant to represent his/her preference over the criteria.

Generate the assessment criteria(cont.)

• The ranking preference by the DM Vi=(vi1,…vij)

where

(i=1,…k;j=1,…m) k: DM’s m: assessment criteria

• According to Miller’s theory, Vi=

]1,0[ijv

m

j ijv1

9

Generate the assessment criteria(cont.)

• Lecturers generally have clear expectations on the course requirements and experience, they should have the priority in expressing their opinions on the assessment criteria.

• This can be realized by assigning different rates Q={q1,…qk} ;

• The final assessment criteria preference

k

iq

11

Generate the assessment criteria(cont.)

• Different weights should be assigned to the assessment criteria with reference to their importance.

• The quantified judgments on pairs of criteria ci,cj, are represented by an n-by-n matrix A= (aij)(i,j = 1,…n).

• The ratio aij represents the relative importance of ci over cj .

Generate the assessment criteria(cont.)

• The comparison scale ranges from 1 to 91 equally important.3 weakly more important5 strongly more important7 demonstratively more important9 absolutely more important2,4,6,8 intermediate values between adjacent judgment.

Fuzzy grading system• Different rates are assigned to the

participants, R={r1,..,rt} ,

• In this paper, students are asked to express the evaluation results using a 100-point scale.

Mi={mi1,..,min}, 0≦mij≧100,(i=1,..t,j=1..n),t: participants, n: criteria

• The evaluation results

t

i ir11

)',..,','(

,...,,

......

,...,,

,...,,

),...,,(' 21

21

22221

11211

21 n

tntt

n

n

t mmm

mmm

mmm

mmm

rrrMRM

Fuzzy grading system (cont.)• A membership function needs to be defined

which transforms a mark grade into a letter grade G={g1,..gd}

• To given a 100-point scale mark m’,represents the degree that the mark belongs to the letter grade gi.

• A fuzzy mapping can be defined which combines the membership functions together. )(: GCf

))'(),...,'(),'(( 21 igdigigi mmmc

)'(mgd

• Use eid to represent μgd(mi’),

• The final letter grade of the students’ learning outcomes can be determined by

• Thus, the corresponding letter grade gi is the students’ final grade.

Fuzzy grading system (cont.)

Application• A group decision support system (GDSS)

has been developed to facilitate the assessment process and to automate the computation of fuzzy matrix operations.

• Students and lecturers then sat down together and used the GDSS system to brainstorm the possible assessment criteria set.

Application (cont.)• The basic set of assessment criteria

C={functionality, reliability, usability, efficiency, maintainability, portability, reusability}

• A sample ranking vector from a student (1,1,0.8,1,0.6,0.6,0)

• V=(0.97,0.972,0.98,0.81,0.832,0.32,0.182)

• Top 5 assessment criteria C={functionality, reliability, usability, efficiency, Maintainability}

Application (cont.)• A paired comparison matrix from a student

• The criteria’s weights Computed by the GDSSW=(0.205502,0.214881,0.475251,0.042013,0.062352)

Fun.

Rel.

Usa.

Eff. Mai.

Fun.

1 1 1/3 4 5

Rel.

1 1 1/3 5 5

Usa.

3 3 1 7 7

Eff. 1/4 1/5 1/7 1 1/3

Mai.

1/5 1/5 1/7 3 1

Application (cont.)• The 4 Scale letter grades

g1=Eg2=Gg3=Sg4=P

Application (cont.)• Example

w=(0.205502,0.214881,0.475251,0.042013,0.062352)

The final grade of the student was g2=G(Good).

Summary • The commonly agreed criteria are then used to

evaluate the students’ learning outcomes.• The proposed assessment method and GDSS

system encourages the students to participate in the evaluation of their learning.

comment

• 因有效資料不足，且發現有公式內變數代碼有誤，花了一些時間去理解。

• 來自同儕的評比部份，雖比率上佔不多，但仍給這樣的評量方式多了一個很難控制的變數，在學生與教師的比率上，如定一固定比率，自然就有所謂的測驗公平性了。