The Bridge of Theory and Practice: The Knowledge Web of Mathematics Teachers
Yuan-Shun Lee
Dept. of Mathematics and Computer Science Edu. Taipei Municipal Teachers College
leeys@tmue.edu.tw
Abstract
The researchers found that theory and practice were two separate topics in mathematics
teachers’ education in the past. Therefore, I have set up the Knowledge Web of Mathematics
Teachers (KWMT) on Internet as the learning sources of linking theory with practice. Then I
investigate if the learning sources can be the bridge of theory with practice for mathematics
teachers’ education. From the results of this action research, I find that the website has been able to
be the bridge of theory and practice while student teachers are learning about mathematics teaching.
I find that the student teachers can comment on the teaching cases from theories that they have
learned at school. Also, student teachers’ knowledge/capability is growing.
Keywords：the bridge of theory and practice, learning about mathematics teaching, teacher
education
Introduction
Owing to the hardware and software of Internet are developing well, the learning ways of the
people are in changing gradually. Hence The Science Education Department of National Science
Council (NSC) pays close attention to the e-learning on Internet as the key research plan in 2003.
In mathematics teachers’ education, Lin (1997), Chin (1995), Dolk and den Hertog (2001), Lee
and Lin (1998 and 2000), and Tan and Hsiung (1999) found that student teachers, while they were
learning about mathematics teaching theory, had a gap between theory and practice.
The purposes of this paper report the established process of the Knowledge Web of
Mathematics Teachers (http://www.MTedu.tmtc.edu.tw Chinese version, http://www.MTedu.tmtc.
edu.tw/wwwroot_en/index_en.asp English version) and the case that student teachers used this
website to learn about mathematics teaching.
Discussions on studies
The aim of this section is to discuss both foreign and domestic theories about e-learning by
using Internet as resources for teachers’ learning.
Lee, Y.S. 2003
The bridge of theory and practice
Theory of e-learning by using Internet
Following the development of new technology, every country in the word pushes positively the
idea of e-learning. According to evaluation by IDC (Liu (2002)), the market of e-learning on-line in
the whole world will achieve 63 hundred millions U.S. dollars in 2001 and 230 hundred millions
U.S. dollars in 2004. Moreover, the idea of e-learning will establish an e-society that includes
e-entertainment, e-commerce, e-communication, e-medical-care, and e-culture.
It must be supported by some theories that expenses of e-learning in the whole world are
increasing and people pay much more attention to e-learning year by year. Both the theory of
situated learning and social constructivism are the learning theories of e-learning. Lave and Wenger
(1993) and Young (1999) emphasized that happening of learning often depends on that learner
interacts with situations and that members of learning group participate in social interaction. Chang
(1998) indicated that the e-learning was to arrange a great quantity of learning ways for learner to
explore and learn on Internet and that all knowledge derived from abundant resources of Internet,
the real life of learner, and sharing in knowledge with each other. Moreover, Chen (2001) indicated
that learner not only needed to construct his own knowledge actively but also needed to interact
with the others, in order to establish a common consensus within group that was reciprocally
principal part when he learned by using Internet. So, Young (1999), Chang (1998), and Chen (2001)
thought that the theory of e-learning was also based on the theory of social constructivism.
The problem of theory and practice
From recent studies, I found that there was a gap between theory and practice in teachers’
education. Lin (1997), Chin (1995), Dolk and den Hertog (2001), and Tan and Hsiung (1999) found
that, when student teachers learned about mathematics teaching theory, they could not learn
teaching theory from the viewpoint of teaching practice because of no actual teaching practice, but
could learn it only by their own learning experiences that they were educated at school. Besides,
from interviewing with elementary school teachers about their practice experiences, I found when
student teachers commented on teaching practice that they inspected and learned from other
teachers’ teaching, they usually paid close attention to classroom management, such as “Why should
we arrange the seats of students like this? What advantage shall we have if we do so? ” Furthermore, Chin (1995)
and Lee (1999) also found that in-service teachers had more plentiful experiences of teaching
practice but, under the press of limiting teaching hours, they could not apply the theory that they
learned into their teaching practices. For example, they would think: “The idea of diagnostic teaching is
very good. But instruction is of regular rate of progress. Teachers should teach content of courses to students with
fluency. About the misconception of students, the experienced teachers know it, but it is not necessary to point out in
instruction process, because they will understand naturally while they are at higher grade”.
Moreover, the
probationary teachers I interviewed also said that theory and practice were two things entirely not
related in his instruction at school. So, theory and practice have been two separate topics in
mathematics teachers’ education for a long time.
Lee, Y.S. 2003
2
The bridge of theory and practice
Use e-learning to construct the bridge of theory and practice
The idea of e-learning is effecting upon learning ways of people in the whole world and
changing learning environment of school. I think that people can use the characters of Internet,
which includes high-speed propagation, being able to be structuralized, and being easy to search in
it, to establish a knowledge web. This web contains both theory and practice which is of digitized
teaching narrative, which can be the resources for teachers’ learning about mathematics teaching
and promoting their own professional development. Therefore, I investigate into the related studies
about learning mathematics teaching by using Internet, which are used to be the foundation of this
study.
We found, Liu (2001) and Chang (1998) found that the learning environment of Internet could
promote teachers’ professional development. Tan and Hsiung (1999) indicated that probationary
teachers often addressed their opinions of classroom management and teaching strategies by their
own subjective experiences. From domestic literatures, we did not find such a learning resource that
was constructed as the bridge of connecting theory with practice by using Internet for mathematics
teachers’ education. There is a research overseas that is more related with this study that MILE, a
special project in the Netherlands (Goffree and Oonk, 1999).
The MILE project (Goffree and Oonk, 1999) was to digitize the teaching in school to be
teaching narratives for student teachers to link teaching theory and practice. The MILE system
includes a video database of teaching narratives, communication tools for learners, a search engine,
a scrapbook, and a journal for the learners.
Though the teaching narratives in MILE have been digitized, they are only set in mathematics
teachers’ education institutions rather than in Internet to be the teaching resources. Form my
conversation with Dolk and den Hertog, whom were the planners of MILE, we could know that the
initial establishment of digitized teaching narrations in MILE was restricted by Internet bandwidth
and AV (audio and video) compressed technology at that time so that audio and video could not be
transmitted clear through Internet. Therefore, the database of teaching narratives was set in
computer but Internet had not been used as a database to transmit digitized video and did not have a
discussion area for teachers to discuss the teaching cases.
So far we have not find the related research about using Internet as the bridge of theory and
practice for mathematics teacher education. Nevertheless, from the way of MILE to digitize
teaching narratives and bandwidth and compressed technology nowadays, it seems to tell us that we
may establish a learning resource on Internet as the bridge of theory and practice for mathematics
teacher education. Lee (2002) indicated that the video that needed 250Kbps while being transmitted
had not only been able to be transmitted by the bandwidth in campus but also by ADSL and Cable
modem at home. Furthermore, now MPEG4, a new compressed technology, has been able to
compress audio and video effectively and makes the bandwidth with 250Kbps to be able to transmit
320×240 frame clear. Also, the full frame that needs the bandwidth with 1500Kbps has been
transmitted successfully in the same school. So, I can use Internet to transmit dynamic teaching
narratives clear that can be the resources for the far teachers to learn about mathematics teaching.
Lee, Y.S. 2003
3
The bridge of theory and practice
Summaries
The purposes of this study are to establish an Internet learning environment that can linking
theory with practice for mathematics teacher education and use it to investigate how student
teachers to learn about mathematics teaching.
The research method I used is the action research. Atweh (2000) indicated that, in the process
of action research, what it emphasized was the recurring processes of plan, act, observe, and reflect.
The data of our study are collected from November 2001 to May 2003. The main participation
student teachers are the juniors and the seniors in teachers college and probationary teachers. The
main data I collected are the writings that are posted by teachers. Some of these writings are written
down by student teachers after they have viewed teaching cases and some others are discussed by
student teachers after they are clinical observation and microteaching at elementary school. Because
the data I collect are open on Internet, those persons who have viewed the discussed writings
on-line can test the reliability and the validity of this study.
The processes of action research
This section presents the problems that I observed in this process of action research and the
spiral recurring processes of reflect and drafting the plans of solving problems.
The construction of the knowledge web – plans and acts
I plan to establish a bridge between teaching practice and educational theory for teachers. Thus,
I begin to find the ascribed needs and the felt needs of teachers whom are learning about
mathematics teaching in elementary school or junior high school. I study these two needs from
some websites that are established by Internet experts, research centers, mathematics teacher
education institutions of, elementary schools, and junior high schools. From these observations, I
want to establish a bridge between practice and theory by using Internet and a knowledge web for
mathematics teachers’ education. According to my research results, I begin establishing this
knowledge web. This website includes mainly area of dynamic teaching cases, Area of education
data, a search engine, and discussion area (Lee, 2002).
Action research –recurring processes of observe, reflect, plan, and act
After the website has been established, I ask for student teachers to see and discuss the
dynamic teaching cases. Also, I do my possible to see their discussions everyday. If there is an
urgent question, I will reply it immediately; otherwise, I will leave it with others to present their
opinions or request the teacher filmed for this teaching case to read the messages left by others and
to try his best to reply.
Lee, Y.S. 2003
4
The bridge of theory and practice
i. The discussions of teachers need guidance – observe and reflect
At the initial stage of the knowledge web, because “Teaching Information” had not been
established yet, I found, from observing teachers’ discussing process after they viewed teaching
cases, that the quality of teachers’ discussion was not very good. For instance, there is a video that
is concerned with the area unit for the 2nd semester of Grade 5 (May 30, 2001). Its title is “Is this a
square or a rhombus?” . Some student teacher left his message: “We wonder at the length of this video that
it is only 38 seconds. … so that we could not judge whether the teacher in the video taught well or not.” (Nov. 1, 2001)
I found that only well connecting of education data with dynamic teaching cases could not
make this knowledge web to become the bridge of learning theory and practice immediately. Also,
it could not help teachers to understand from it. Carelessly, student teachers may even make a
personal attack. Student teachers left messages about the fraction unit, which they paid close
attention to its drafted affection. That is a fraction unit for the 2nd semester of Grade 5 (May 30,
2001). The question is: “Mother bought many pieces of pizza. Ying-Ren ate three-fourths of one
pizza. What possible ways can we take to divide pizzas into some parts?” Some student teacher left
his message: “About this question, basically, it is somewhat impossible. …According to this logic and if mother buys
more than one pizza, the pizza eaten by Ying-Ren must be bigger than the size of six pieces. It is very terrible.” (March
18, 2002). “Actually, he did not share pizzas with others. He was unable to eat any more after he had eaten
three-fourths.” (March 18, 2002). “In fact, Ying-Ren has only one sister but no brother. I am Ying-Ren’s
sister—Ying-Chi. I can prove that my brother is a person who has a big stomach.” (March 18, 2002). “I am the mother
of Ying-Ren and Ying-Chi.” (March 19, 2002)
Now, the teacher who was filmed in this teaching case felt very angry about an injustice done
to her student. She reply: “Ying-Ren is a very gentle boy in my class. The way of a quiz is due to the teacher. Your
discussions make me feel sorry for my students, no matter what you discussed about Ying-Ren, Ying-Chi, or their mother.
If you were Ying-Ren, how would you feel about?” (March 27, 2002)
This reply reminds me of the seriousness of inspecting to nose out a problem. I not only make
some necessary replies but also reflect how to lead everyone to connect theory with practice lest
someone would make a personal attack carelessly on the website. I find that I need to give some
guidance and examples to teach student teachers to comment on teaching cases from the viewpoint
of theory and to be away from making a personal attack to others.
ii. Constructing an example of discussion –plans and acts
In addition to reply to the matter caused by student teachers immediately, I begin to establish
the teaching problem of “Teaching Information” and try to lead their discussions to focus on the
teaching problems. Also, I write an article “An example of discussion – wish to have a discussion of
high quality” to expect that student teachers can discuss problems from the viewpoint of theory.
This way may avoid making carelessly a personal attack.
iii. Discussing teaching practice from theory – observing again
After having established the teaching problems of “Teaching Information” and “An Example
Lee, Y.S. 2003
5
The bridge of theory and practice
of Discussion”, I find that student teachers have been able to discuss teaching problems from the
viewpoint of theory while discussing a teaching case. For instance, student teachers have viewed the
teaching cases on Nov. 22, 2001 and Dec. 13, 2001. They reply: “... Though, in the theory of Piaget, the
elementary school students of grade 2 have not been able to understand that a plane has two dimensions, but we find
that some of them have noticed this character.” (April 8, 2002). “About teacher Young’s instruction, I have some
following opinions. … 2. Make a cognition conflict and use the learning way of cooperating with classmates, in order to
promote children to solve their own problems actively.” (April 14, 2002)
After student teachers had clinical observation teaching, they can also remember the teaching
case as a narrative. They reply: “In order to help students to apply their concept of area to real life and to connect
it with life, I want to give some suggestions… can also use something connecting with life like windows, blackboards,
textbooks, desks, handkerchiefs, etc. (All these things are mentioned in the teaching contents on Nov., 22, 2001 and Dec.,
13, 2001.)” (observe teaching, April, 16, 2002)
About the other articles discussed by student teachers in the discussion area, the readers can
refer to the next section.
iv. Modifying the discussed articles – observe, reflect, plan, and act again
From my observation, I find that the articles, which are posted by student teachers in the
discussion area of dynamic teaching cases, are growing in number. Student teachers have opened up
877 subjects on the website (149 dynamic teaching cases) till Dec. 11, 2002. Because there are too
many subject areas, some student teachers will open up another new one under the circumstances
that they have no time to search for the articles of teaching case that they want to read. So, student
teachers are unable to read the articles of some other persons and respond to them appropriately,
which can not only result in some opinions repeating or no common thought on this teaching case
but can also not well absorb the experiences of some other persons. Hence I reflect that it is
necessary to gather stray articles under the same topic and to give an only one topic for users to link
conveniently and search easily.
Thus I begin to write computer programs, to collect the dispersing everywhere articles
discussing the same teaching case in the area of the same topic, and to rename it as the date to film
and content of this teaching case. Furthermore, I establish the buttons of quick link both in the
player of teaching cases and in the tableau of the Teaching Information, which can help users to link
this topic immediately to read the articles posted by some other persons and to express their own
opinions for social interaction.
Moreover, I find that student teachers have posted 2134 articles on the website until Dec. 11,
2002. Some articles there are responded more than one hundred times. I reflect and find that
teachers might have no time or not be patient of reading all the articles. Therefore, I begin to write
computer programs that can help the administrator of this website to hide easily some articles of
similar contents or no worth to read, which can reduce the number of articles that teachers want to
read to be less than twenty or thirty pieces. Certainly, I reserve the right of users to appreciate all the
articles. Users can read all the articles posted on the website, if necessary.
Lee, Y.S. 2003
6
The bridge of theory and practice
Learning about Mathematics Teaching
The purpose of this section is to analysis the website I established from the articles posted by
student teachers whether it can be the bridge of connecting theory with practice while student
teachers are learning about teaching Mathematics. Because there are too many articles posted by
student teachers, it will be a great workload to analyze all the articles overall. Consequently, I
select two teaching cases from all articles (amounted to 223 pieces) to be the main contents of my
analyses. One of these two teaching cases is concerned with the unit of area of grade 5 filmed on
May 30, 2001 that “06. Is this a square or a rhombus?” and another is concerned with the unit of
proportion of grade 6 filmed on April 2, 2002 that “09-1. What is the relation between a square and
a rhombus?”
The learning of connecting practice with theory
One of the main purposes of establishing the Knowledge Web of Mathematics Teachers is to
help teachers to discuss teaching practice from the viewpoint of theory and then to recognize the
meaning of theory. In the discussions of these teaching cases, student teachers can not only respond
the discussions of teaching problems that I established but can also realize the age of thinking over
geometry, which is presented by Van Hiele. They reply: “Though van Hiele did not say clearly which age
should be at which stage, it seemed to be of the differentiation of age. …In the instruction guidebook, it points out …that
the geometric development stage of the children of grade 4 is still at the stage of Analysis but is not fit to be at the stage
of Informal Deduction.’ (20010530-06, April 12, 2002) “ The geometric development of children has been to the stage
of Informal Deduction presented by Van Hiele. They can analyze a figure according to its composing elements and the
relation among these elements, establish actively the characteristics of some figures, and make use of these
characteristics to solve problems.” (20020402-09-1, Oct., 20, 2002)
The learning about knowledge and capability of instruction
We also found that student teachers would make clear of these capabilities and knowledge of
teaching, which will make their opinions on teaching become more confirmative in their future
instructions.
i.
Knowledge of mathematics
Most people think that the mathematics in elementary school is the easiest; nevertheless, some
student teachers have never found students’ confused conception. From the processes of viewing
and discussing a teaching case, student teachers have found that they have some difficulties in
their knowledge of mathematics. At the same time, they also make clear about relevant knowledge
of mathematics. They reply: “…My concept of geometry is always paradoxical. After more discussions about it, I
got more the outlines of it. …However, I think there should be some children who have the same confusion as I do that
I will confuse about a parallelogram, a square, a rhombus, a shape like a kite, and a rectangular. What on earth are
the inclusion relations between these shapes?” (20010530-06, Oct. 19, 2002) “It turns out that my concept to the
rhombus is wrong. I remember that my teacher has ever told us that the only distinction between the square and the
rhombus is dependent on whether it is of right angles or not.” (20020402-09-1, Jan. 10, 2003)
Lee, Y.S. 2003
7
The bridge of theory and practice
ii.
Knowledge of students’ cognitions
In the following discussion about teaching cases, a student teacher finds that her knowledge of
students’ cognitions is not enough. She says: “… Children ask me a question that “Is a square the same as a
rhombus?” All of a sudden I cannot know how to answer this question at that time, so I only reply that they are not the
same but have no further interpretation why they are different. After reviewing this unit, I finally know the differences
between them and how to compare with them. (20010530-06, March 20, 2003) Now
she understands the problem
of students. Another student teacher finds that: “From the films, we can find that even the children of grade 6
still use the stage of Visualization to think over the geometric questions in the beginning.” (20020402-09-1, Nov. 2,
2002)
iii.
Knowledge of teaching methods
From discussing, student teachers talk about their difficulties in application of teaching
methods. They also think about how to teach well. He says: “Some students will think that a square rotated
with some angle can form the rhombus. It is thus evident that the misconception of students exists originally…. teachers
have the chance to find out the misconception of students at each stage of instruction. So, I think it is necessary to
diagnose concepts of students all the time.” (20020402-09-1, Jan. 6, 2003)
From refection and learning from many other teachers’ instructions, student teachers can find
their own defects in teaching. Then they will feel apologetic to her students for not teaching well
before and begin to notice the matters that need to be watched out in future instruction. They say:
“After having observed many instructions of other teachers, I feel sorry for my students all the time…It is harmful to
students’ learning that I don’t translate the abstract definitions of these two figures into colloquial words.”
(20020402-09-1, May 10, 2003) “… However, it is very difficult to teach children and to help them to follow my
instruction. I have ever tried to teach my niece. Her logic in mathematics is better than mine but, unexpectedly, she can
not understand on one occasion what I teach her. Therefore, the situation that children can not understand what their
teachers teach them is not children’s faults but is teachers’ responsibilities.” (20020402-09-1, Oct. 23, 2002)
Reflections of different viewpoints
In the social interaction of discussing teaching case, that appearing different opinions on the
same thing is able to excite student teachers to think over the following things. What are the merits
and the defects of their teaching? What kind of the teaching method will be suitable for them to use?
In the discussion of teaching case, some teachers think the film boring because it does not
communicate some meaningful information. However, some others think it of great teaching effect.
They say: “This teacher is very funny… This film shows us no other meanings but that it is the square. I think it very
boring.” (20010530-06, April 1, 2003) “To my surprise, it had a great effect that the teacher simply rotated the figure
by 45 degrees.” (20010530-06, May 25, 2003)
In the discussion, student teachers have different opinions on the question about whether the
elementary school students should be taught by the mathematicians or not. They say: “Sometimes I
think it will be better, even though the mathematics curriculum of the element school, that the elementary school
students are taught by mathematicians. … it should be easier to point out the questions in mathematics if the elementary
school students are taught by mathematicians. … They will teach well, no matter their students are college students or
elementary school students.” (20020402-09-1, Oct. 23, 2002) “I don’t think a mathematician is suitable to teach
Lee, Y.S. 2003
8
The bridge of theory and practice
elementary school students. … I think it possible for a mathematician to make a mistake like my sister did if he teaches
at the elementary school. Their specialized knowledge is too deep so that they may think too much but to deal with a
simple question. I think the main question to us is how to promote our professional and instructional capabilities.”
(20020402-09-1, Oct. 24, 2002)
Conclusions
From the results of this action research, I find that the website I established has been able to be
the bridge of theory and practice while student teachers are learning about mathematics teaching.
After having written some examples of discussion, I observe that the student teachers can comment
on the teaching cases of this website from theories that they have learned at school. Also, I find that
the contents in the website I established have been able to be the teaching narratives of discussing
teaching problems while student teachers are learning about mathematics teaching. Student teachers
can also know clear the related knowledge/capability about mathematics teaching from them and
bring up different ideas to others for reflection.
Implications
Brown and Borko (1992), Cooney and Shealy (1994) indicated that it was a slow process for
teachers to develop their professional teaching knowledge. Moreover, Chin (1995) and Lee (1999)
found that the knowledge/capability of in-service teachers for preparing their instruction in advance
were not the same as that of student teachers. As for in-service teachers, they have plentiful
experiences of teaching practices but can not teach by applying the theories learned from
mathematics teachers’ education institutions. Hence, for in-service teachers, teaching theory and
teaching practice are two isolated topics. So I use the knowledge web of mathematics teachers to
investigate the professional development of in-service teachers and the relevant problems about
connecting theory with practice.
Thanks: The results of this paper are parts of the projects, supported by the National Science Council,
which serial number are NSC 90-2521-S-133-011 and NSC 91-2521-S-133-001. Thanks all the participation
teachers mentioned in this paper for willing to share with us their viewpoints and thanks Pro. Lin for his
providing us with related equipment, which makes this paper be able to be completed successfully. The
arguments in this paper belong to the author and are not in the name of the National Science Council.
References
Atweh, B. (2000). Action research workshop. National Taiwan Normal University. Taipei, Taiwan.
Brown，C.A. & Borko，H.(1992). Becoming a mathematics teacher. In D.A. Grouws (ed.) (1992).
Handbook of research on mathematics teaching and learning(pp.209-242)，National Council
of Teachers of Mathematics，Macmillan Publishing Company，New York.
Chang, J.C. (1998)：Design of teacher professional development network social and its effect and
challenge. Education Technology and Media, 40, 31-42。(In Chinese)
Lee, Y.S. 2003
9
The bridge of theory and practice
Chang, C.C. (1998)：Growth strategy of reflection ability growth of probationary teachers in
network environment. National Taiwan Normal University, Dissertation of Master。(In
Chinese)
Chen, P.N. (2001). The influence of network learning social for education ecosystem. PingTung
Education, 6, 15-19. (In Chinese)
Chin ,C. (1995). Mathematics teachers' beliefs，their classroom practices and influences on student
learning：Four case studies. The University Cambridge PHD.
Cooney，T.J. & Shealy，B.E.(1994). Conceptualizing teacher as field of inquiry：Theoretical and
practical implications. PME XVIII. Vol. II, 225-232.
Dolk, M. & den Hertog, J. (2001). Educating the primary school mathematics teacher educator: A
case study in the Netherlands. 2001 The Netherlands and Taiwan Conference on Common
Sense in Mathematics. Department of Mathematics, National Taiwan Normal University.
Goffree, F. & Oonk, W. (1999). When real teaching practice can be (digitally) represented in
colleges of education: The MILE project. Proceedings of the 1999 International Conference of
Mathematics Teacher Education. Department of Mathematics National Taiwan Normal
University. Taipei, Taiwan. 34-75.
Lave & Wenger (1993). Situated learning: Legitimate peripheral participation. Cambridge
University Press.
Lee, Y.S. (1999). Case study of professional development of mathematics teachers within a school.
National Taiwan Normal University PHD. (In Chinese)
Lee, Y.S. (2002). Action research of construction of primary teachers learning mathematics teaching
knowledge web. 2002 Proceeding of Normal University Learned Essays. Ministry Education
& National Chiayi University, Oct. 25, 2002-Oct. 26, 2002, 1275-1303。 (In Chinese)
Lee, Y.S. & Lin, F.L. (1998). An interaction model of professional development of mathematics
teachers within a school. Journal of Taiwan Normal University, 43(2), 1-23. (In Chinese)
Lee, Y.S. & Lin, F.L. (2000). Mathematics Teachers’ Professional Development: Making Sense of
Multi-Strategy Teaching. Journal of Taiwan Normal University, 45(1), 1-25. (In Chinese)
Lin, F. L. (1997). Development of Pedagogical Power: An Approach of Integrating Mathematics
with Pedagogical Content Knowledge (1/3). Research Report of National Science Council,
Department of Mathematics, National Taiwan Normal University (In Chinese)
Liu, J.H. (2002). National Science and Technology Programs for E-Learning，National Science
Council. 2003.03.09. http://elnp.ncu.edu.tw/oldSite/3-1.htm。 (In Chinese)
Liu, G. C. (2001). The professional development of a novice mathematics junior high teacher at
internet growth social. National KaohSiung Normal University, Dissertation of Master. (In
Chinese)
Tan, N.C. & Hsiung, C.T. (1999)：Teaching guidance of novice mathematics teachers in internet.
Research and Development in Science Education Quarterly, 15, 49-58. (In Chinese)
Lee, Y.S. 2003
10
The bridge of theory and practice
Young, S.C. (1999)：A case study a web-related course training and its diffusion. Chinese Journal of
Science Education, 7(4), 299-314。(In Chinese)
Lee, Y.S. 2003
11