Written by
Mahdalena
Graduate School of Mathematics,
University of Sumatera Utara
Abstract
Finding
the optimal teaching for an individual stuadent is difficult even for an
experienced teacher. Identifying and incorporating multiple optimal teaching
strategies for different students in a class is even harder.On the one hand, students ability, availability of resources, and
lecturers' preparation time are uncertainties. On the other hand, decision is
influenced by individual preference for tutorial formats such as
student-centred, chalk-and-talk, or computer-based tutoring. This paper
presents homogeneous Markov chain, Markov chain clustering to
education.
1. INTRODUCTION
In the first application is to discuss teaching effect assessment methodof basic
In the second application is to discuss adaptive teaching strategies for online learning
For example, the probability a student answered a level 3 question correctly (3C), and then answers a level 5 question wrong (5W) is 0.1.
3.Conclusions
Homogeneous Markov chain approach can be sensitive to reflect the true effect of
4. References
1. A. Bergeron and G. Paquette, Discovery enviroments and intelligent learning tools, in C.
A LEARNER is a cognitive system that develops by his own information and knowledge-processing activities. To maximise the learner's cognitive development, knowledge-intensive environments are essential to help him explore a situation, construct his own concepts, and discover general laws by his own problem-solving activity [1]. The lecturer, as knowledge facilitator, has an extremely complex problem on his hands. Before deciding exactly what course of action to take, he needs to consider many issues, including suitable environments
and the uncertainties involving students'
abilities and school resources.
In the
future, the challenges of the times are so complex, the progress are so fast,
and the educational situation is not easy, it is clear that needed more
professional and qualified teachers. But in the field, the complaint against
the quality of the teacher is often being the subject of public talks, such as
lack of teacher’s knowledge and lack of professional disciplines when teaching
in the classroom. While the professional teacher will be very selective in
choosing the appropriate strategies, approaches, models and techniques to thelearning
topic and student characteristics.
Analysis of
the learning process and mathematics learning output is always interesting
to be discussed and reviewed. From the problems as the
low of student math scores, the use of appropriate methods and media, to the
existence of facilities and infrastructure. The serious attention through
constructive innovations that are expected to give a brighter hope on the
development of mathematics education and mathematics learning in particular.
Factors that determine the progress of a nation, namely innovation (60%) networking (25%) technology (10%) and resources (5%). Realistic mathematics education movement (PMRI) could produce young people who are able to create innovation and technology, so they can encourage the Indonesian nation’s development [2 ].
Factors that determine the progress of a nation, namely innovation (60%) networking (25%) technology (10%) and resources (5%). Realistic mathematics education movement (PMRI) could produce young people who are able to create innovation and technology, so they can encourage the Indonesian nation’s development [2 ].
Competency-based
learning and assessment has become a necessity to do so
considering the advantages possessed, far beyond the
traditional learning that is more teacher-centered [ 3]. For that, a
willingness to try while making some innovations at learning practices should
be cultivated. Therefore it is required self-evaluation, and starts by trying
to evaluate instructional practices that is used, looking at the advantages and
disadvantages; and making some improvement from both of them.
2.
Application Examples
In the first application is to discuss teaching effect assessment methodof basic
courses based
in engineering institutions based on homogeneous Markov chain [4].Real,
comprehensive, accurate assessment of the project based on teaching effectiveness
of institutions can promote theimprovement of teaching quality and has
important role in high-quality talent. Teaching quality assessment is a
complexdynamic system engineering, and teaching method of assessment should be
determined by the nature and characteristicsof teaching. A suitable teaching
assessment method and model suit for all schools does not exist; Teacher’s
participationis the basic condition for implementing any method of teaching
assessment, and also is the security for achieving goal ofteaching evaluation ;
The goal of any teaching assessment method or model use is only one, i.e.
improve the teaching,improve large-area fully quality of teaching and train
talents.
Many colleges have carried teaching
assessment. Practices
have proved that
classroom
teaching assessment is an importantmean for feedback the teaching information,
which can help teachers and students to effectively monitor the
classroominstruction and classroom learning process, improve the quality of
teaching and promote self-improvement of teachers. However, for some reasons,
in practice the current traditional method based solely on student’s average
performance,variance and teacher evaluating students’s learning attitude to
assess the quality of teaching is one-sided and inaccurate.Because the test
scores of students depend on many factors, where the basis difference of
students is a very importantfactor. Many colleges exist many problems of
teaching assessment, which have a certain negative effect on teaching
andlearning activities.
Homogeneous
Markov chain analysis is a statistical method based on probability and
using
mathematical models toanalyze the number development and changes in the process
of object relations. Homogeneous Markov chain is widelyused in the forecast
stock prices, business unit forecast of human resource flows, the RMB exchange
rate forecast, as wellas a variety of market forecast. Zhenhua Ma, in
literature, researched Markov chain theory andApplications [5]. Xiangyang
Cheng, in literature, using the
properties of homogeneous Markovchain, analysis the models of structure of
school talents to carry out modeling analysis [6].
In a random process, if the probability
of a state transition from one state to another only has anything to do with
the current state, but has nothing with the state before this moment, which is
known as Markov process. Markov chain is aMarkov process for discrete state and
time , referred to Markov chain. According to the composition of Markov
chain,the process has the following three characteristics:(1) Discreteness of
process. (2) Stochastic process. (3) Process without aftereffect. The
transition probability of system only is with the current state, and has
nothing to dowith the previous state.
Select two ”Advanced Mathematics”
courses of seven classes to assess the results. The examination transition
vectors ofall students computed by contrasting two scores are as follows:
Then
the transition matrix is as follows:
The limit vector of this transition matrix is
b. Adaptive Teaching Strategies for
Online Learning
In the second application is to discuss adaptive teaching strategies for online learning
[7]. AtoL (Adaptive Tutor Strategy
for Online Learning), for computer science laboratories that identifies and appliesthe appropriate teaching
strategies for students on an individual basis. The optimal strategy for a student
is identified in two steps. First, a basic strategy for a student is identified
using rules learned from a supervised learning system. Then, the basic strategy
is refined to better fit the studentusing models learned using an unsupervised learning system that takes
into account the temporal nature of the
problem solving process.
AtoL is a web-based tutoring system that contains a question tutor, the program tutor, and a course management component, the two tutors in AtoL present a sequence of questions to be solved and programs to be completed with different levels of difficulties based on each student's understanding of the concept. The system automatically gradesstudentresponses and records them for the coursemanagement andpersonalized tutoring sessions. make certain teaching sessions.
AtoL is a web-based tutoring system that contains a question tutor, the program tutor, and a course management component, the two tutors in AtoL present a sequence of questions to be solved and programs to be completed with different levels of difficulties based on each student's understanding of the concept. The system automatically gradesstudentresponses and records them for the coursemanagement andpersonalized tutoring sessions. make certain teaching sessions.
It has been
observed that students that share the the same basic learning model
(reinforcement type, regular type,
and challenge type) can behave quite differently from lab to lab. Therefore, to fine tune the teaching
strategy supplied by the student model identifier, the strategy adjustment
module use a Markov chain (MC) model
based unsupervised learning system to cluster students within each basic group in to subgroups that share
similar behavior patterns. The new models are then used to adjust the basic
teaching strategy.
A MC model is characterized by the set of states in the model and the conditional probability transition martix that governs the transitions between states. Currently, AtoL usesthree difficulty levels (1, 3, and 5) for questions and programs. Considering that a student response is either correct or wrong, there are sixpossible discrete states in a MC model: level 1 correct (1C), level 1 wrong (1W), level 3 correct (3C), level 3 wrong (3W), level 5 correct (5C), and level 5 wrong (5W).
A MC model is characterized by the set of states in the model and the conditional probability transition martix that governs the transitions between states. Currently, AtoL usesthree difficulty levels (1, 3, and 5) for questions and programs. Considering that a student response is either correct or wrong, there are sixpossible discrete states in a MC model: level 1 correct (1C), level 1 wrong (1W), level 3 correct (3C), level 3 wrong (3W), level 5 correct (5C), and level 5 wrong (5W).
Then the transition matrix is as
follows;
|
State
|
1C
|
1W
|
3C
|
3W
|
5C
|
5W
|
|
1C
|
0.45
|
0.1
|
0.35
|
0.1
|
0
|
0
|
|
1W
|
0.8
|
0.2
|
0
|
0
|
0
|
0
|
|
3C
|
0
|
0
|
0.65
|
0.1
|
0.5
|
0.1
|
|
3W
|
0.2
|
0.05
|
0.7
|
0.05
|
0
|
0
|
|
5C
|
0
|
0
|
0
|
0
|
0.8
|
0.2
|
|
5W
|
0
|
0
|
0.6
|
0.1
|
0.1
|
0.2
|
For example, the probability a student answered a level 3 question correctly (3C), and then answers a level 5 question wrong (5W) is 0.1.
The key here
is to find the MC model representing a students most similar peer group
based on their performance on a few
questions. This is achieved by computing the likelihood of the student’s
initial performance data to the set of MC models. The model that gives the
highest probability is the most fit model.
3.Conclusions
Homogeneous Markov chain approach can be sensitive to reflect the true effect of
teaching.
Traditional teaching approachis based on student’s scores of a particular
distortion, only taking into account achievements of students, which resultsthe
assessment. The analysis result of homogeneous Markov chain is only concerned
with the transition matrix, andhas nothing to do with one examination result of
students, which is assessed according to the transition state of
twoexaminations. The good or bad effect of teaching is reflected by the rise or
decline of students scores, which reflectssuperiority and objectivity of Markov
chain theory. Researching the teaching method is the basic subject, and also
isthe eternal subject. Only pursuing high-quality effect and high standard
teaching effect for teachers can truly embodythe diathesis education and the
forever value of quality education, find out assessment method suit for basis
courses incolleges, and train high-quality talents.
Furthermore, AtoL employs a two-step
semi-supervised learning system for strategy adaption. First, a classification
algorithmdetermineds the basic learning type of a student. Then models learned
from a MCC algorithm are used to predict the most closely fitting behavior
model and to refine the teaching strategy.
4. References
1. A. Bergeron and G. Paquette, Discovery enviroments and intelligent learning tools, in C.
Frasson and
G. Gauthier (eds), Intelligent Tutoring System: At the Crossroads of Artificial
Intelligence and Education, Ablex Publishing Corporation, Norwood, NJ (1990).
1.
Samani,
Muchlas, Progress is determined by the Innovation Nation, PMRI Magazine,
ISSN 1907-8358, vol 6, No. 2, April 2008, (London: Institute of
Development
Realistic Mathematics Education Indonesia (IP-PMRI) Faculty of Mathematics ITB (2008)
Realistic Mathematics Education Indonesia (IP-PMRI) Faculty of Mathematics ITB (2008)
2.
Marhaeni,
A.A.I.N. Innovative Learning and Authentic Assessment in the FrameworkCreating
Effective and Productive Learning. Paper presented at the Workshop Innovative
Curriculum and Learning in the Faculty of Agricultural Technology, the
University of Udayana Denpasar 8-9 December 2007.
3.
Dong, Y.,
Li, W., and Shi, H. Teaching Effect Assessment Method of Basis Courses in
Engineering Institutions Based on Homogeneous Markov Chain. Journal of
Mathematics Research, 2010, 2: 89-92.
4.
Ma,
Zhenhua. Modern Applied Mathematics Handbook - the rate and random process.
Beijing: Tsinghu University Press, 2002, 521-527.
5.
Cheng,
Xiangyang. Application of Markov Chain in the Educational Assessment. University
of Mathematics, 2007, 23(2), 38-41.
6.
Li, C., Yoo,
J., and Pettey, C. Adaptive Teaching Strategy for Online Learning. Computer
Science Department Middle Tennessee State University, USA (2004).
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