Initializing Student Models in Web-based ITSs: a Generic Approach

Victoria Tsiriga & Maria VirvouDepartment of Informatics

University of Piraeus

Adaptivity in Web-based Tutoring Systems

Adaptivity is crucial in Web-based tutoring systems.

To be adaptive, a Web-based educational system should be able to draw inferences about individual students.

Therefore, the student modelling component is crucial for the purpose of adaptation.

Student Modeler

The student modeling component performs two main functions:

creates the model of a new student, and

updates the student model based on the student’s interaction with the system.

Initializing Student Models

It seems unreasonable to assume that every student starts up with the same knowledge and misconceptions about the domain being taught.

An ITS may be considered as worthless, if it fails to make plausible hypotheses about a student, before the student loses her/his patience with the system.

Initializing Student Models-Approaches

The ITS may assume that a student knows nothing or has some standard prior knowledge.

The student’s prior knowledge may be evaluated by using a pre-test.

Exhaustive pre-tests.

Adaptive pre-tests.

The system may use patterns among students in order to group similar students to categories (e.g. stereotypes).

Initializing Student Models (ISM) Framework

It makes initial estimations concerning the knowledge level and the error proneness of a new student in each domain concept.

It uses an innovative combination of stereotypes and the distance weighted k-nearest neighbor algorithm.

It has been applied in two different Web-based ITSs.

The ISM Framework - Architecture

Interview

Preliminary Test

Generation of the second student

model vector using the distance

weighted k-NN algorithm

Students of the Same Knowledge Level Stereotype

CategoryStudent Models

Knowledge Base

Generation of the first

student model vector

Stereotypes Knowledge

Base

Personal Characteristics

PriorKnowledge

First student model vector

Second student

model vector

Representation of the Student Model in ISM

The student model is represented as a pair of feature vectors. The first student model vector is constructed based on an interview and a preliminary test:

<Student_Code, Name, Stereotype, Characteristic1, Characteristic2, …, Characteristicn>

The second student model vector is constructed taking into account other similar students:

<Student_Code, Knowledge_Level(Concept1), Errors(Concept1), Knowledge_Level(Concept2), Errors(Concept2), …, Knowledge_Level(Conceptn), Errors(Conceptn)>

Distance Weighted k-NN – Main Decisions

The features that would be used to formulate the input space of the distance function have to be selected. A distance function must be identified to estimate the similarity between two instances.The number of neighbors (k) that would participate in the classification task should be defined. A function has to be designed in order to classify new instances.

Distance/Similarity Attributes

They should influence the student’s process of learning.

Different for different tutoring domains.

They can be selected: by human teachers,

by empirical studies that involve human teachers and students.

Calculating Distance between StudentsDistance between two values x and y of a given attribute a:

where:

The overall difference measure of two students sx and sy is calculated as:

where n is the number of attributes used to measure the similarity between students.

otherwise 1,

y = x if 0,)y,x(overlap

n

1aaaayx )y ,x(d)s,s(

valuesreal arey x,if ,)yx(

valuesnominal arey x,if ),y ,x(overlap

else unknown, isy or x if 1,

)y,x(d

2

a

Defining k in the k-NN Algorithm

In ISM the number of k is defined to be the number of students that belong to the same stereotype category with the new student.

Students that belong to different stereotypes are not expected to have similar knowledge of the domain, irrespective of their other personal characteristics.

Classification Function

k

1ii

k

1=iixi

qx

w

)s ,eptLevel(ConcKnowledge_ w

)s ,eptLevel(ConcKnowledge_

2iq

i)s ,Δ(s

1w

Case Study I

Application of ISM to Web-Passive Voice Tutor (Web-PVT).

ISM is instantiated by assuming that students of similar knowledge level of English, who have the same mother tongue and know the same foreign languages have similar strengths and weaknesses when they learn the passive voice.

Representation of the Student Model in Web-PVT

The student model is represented as a set of feature vectors.

<Student_Code, Name, Stereotype, Carefulness, Mother_Tongue, Language1, Language2, …>

<Student_Code, Know_Concept1, Errors_Concept1, Know_Concept2, Errors_Concept2, …>

Evaluation of the Initialization Module (1)

Participants: 3 teachers of English and their students.

The teachers were asked to evaluate 5 randomly chosen initial student models from each supported stereotype (novice, beginner, intermediate and advanced) at two phases:

before any student of this particular stereotype had been registered to the system.

after Web-PVT had constructed individualized models of 15 students of each stereotype.

Evaluation of the Initialization Module (2)

The experimental hypothesis was that the initial student models of the second phase would be superior to the initial student models of the first phase.

The hypothesis was evaluated using a one-tailed paired t-test.

The results showed that the student modeler in all the cases performed better at initializing the model of a new student when it took into account other students of the same knowledge level stereotype.

Case Study II

Application of ISM to Web-EasyMath.

ISM is instantiated by assuming that students of similar knowledge level, who attend the same class (and instructors) and have similar skills in simple arithmetic operations have similar strengths and weaknesses when learning the new topic of algebraic powers.

Similarities and Differences with Web-PVT

Difference: the student attributes of the first student model vector.

<Student_Code, Name, Class_Code, Knowledge_Level_Stereotype, Carefulness, Addition,

Subtraction, Multiplication, Division>

Similarities: The second student model vector. The way the second student model vector is produced.

Main Points

Generation of a framework for the initialization of student models in Web-based ITSs - ISM.

ISM uses of a novel combination of stereotypes and the distance weighted k-Nearest Neighbor algorithm.

ISM has been applied to two totally different tutoring domains:

language learning (Web-PVT) and

mathematics (Web-EasyMath).

The evaluation of the student modeler of Web-PVT, showed that ISM produced more individualized initial student models than stereotypes alone.