Infusing Technology into a Mathematics Methods Course:

Any Impact?

Dr. Qing Li

Abstract

In this article, I examine some issues within the new frontier of integrating technology into teacher

education and professional development. I present an approach to teach a secondary mathematics methods

course integrating technology, specifically, multimedia and online discussion. Specifically, this study

focuses on how the integration of multimedia and online discussion into a mathematics methods course

affect student teachers’ beliefs about geometry and their attitudes toward educational technology. Empirical

data collected from students enrolled in a methods course include students’ written assignment, transcription

of online discussion, multimedia projects, and instructor’s journal. The qualitative analysis of data revealed

that two themes are particularly salient: 1) the student teachers’ attitudes about using technology in

classrooms had changed; and 2) for at least some of the student teachers, the fact that multimedia project

focused on geometry positively affected their attitudes toward geometry and teaching geometry. Three

cases are described of the impact that the use of technology had on student teachers’ learning experience.

Reflection on the experience and recommendations for design principles for teacher educators are presented.

Key Words: educational technology, teacher education, mathematics education, secondary mathematics,

attitudes, pre-service teachers

1

Introduction

“Technology is essential in teaching and learning mathematics; it influences the mathematics that is

taught and enhances students’ learning” (National Council of Teachers of Mathematics [NCTM], 2000).

This call for the integration of technology with mathematics education challenges not only school

mathematics, but also pre-service and in-service mathematics education in North American. In its report,

the National Council for Accreditation of Teacher Education (National Council for Accreditation of Teacher

Education [NCATE], 2001) highlights the challenges

To what degree are higher education institutions meeting their responsibility for preparing tomorrow’s classroom teachers? Bluntly, a majority of teacher preparation programs are falling far short of what needs to be done…. colleges and universities are making the same mistake that was made by K-12 [kindergarten to grade 12] schools; they treat “technology” as a special addition to the teacher education curriculum – requiring specially prepared faculty and specially equipped classrooms – but not a topic that needs to be incorporated across the entire teacher education program…. [Teachers] rarely are required to apply technology in their courses and are denied role models of faculty employing technology in their own work.

Research studies demonstrated that new roles, responsibilities and technologies are developing and

need to be mastered by teachers. Hence, one of the most important tasks for our teacher educators is to

prepare teachers “who can utilize technology as an essential tool to developing a deep understanding”

(Drier, 2001) of the subject matters and the pedagogy. This underscores the new trend in education that

emphasizes the importance of learning with technology instead of learning from technology (Jonassen,

Howland, Moore, & Marra, 2003). Consequently, we need to help pre-service and in-service teachers

develop the ability to make use of technology by effectively integrating it into teacher education.

Inherent in this is the need to infuse technology into all aspects of teacher education (Li, 2003a; Willis,

2001). The infusion of technology into each part of teacher training should not be viewed as discrete

components, rather, pedagogy, field experience and technology training needs to be considered as an

integrated whole.

2

In this article, therefore, I examine some issues of integrating technology into teacher education and

professional development. I present an approach to a secondary mathematics methods course integrating

technology. In here, mathematics methods courses refer to pedagogical courses focusing on mathematics

teaching. The intent of this study is to provide information that can be useful in implementing rational

changes to mathematics teacher education.

I started this project with the idea that I wanted to find out how infusing technology into a

mathematics methods course would affect pre-service teachers’ views of the educational value of specific

technologies and whether technology is useful in mathematics teacher education. In addition, I wanted to

provide teachers with hands-on experiences of incorporating technology into their learning of the pedagogy.

As the initial data and the early experience of the semester began to influence my thoughts about what I was

learning, I focused more narrowly on how pre-service teachers’ experiences of using instructional

technology impacted their beliefs about mathematics and the educational values of the specific technologies.

In particular, the following question guided this research: how does the integration of multimedia and online

discussion into a mathematics methods course affect student teachers’ beliefs about geometry and their

attitudes toward educational technology? The specific multimedia used was PowerPoint or Hyperstudio

presentation, and WebCT® was used for online threaded discussions (i.e. students and the instructor using

computers to post threaded messages in any time).

Goals and Theoretical Background of the Course

The course, Mathematics for Secondary Schools, was a required undergraduate methods course for

student teachers. The main objectives of the courses for students were

Formulate a personal sense of what is mathematics and what it means to teach mathematics;

Become more prepared to teach mathematics using technology as a tool;

Learn different techniques of teaching mathematics;

Develop resources of good mathematical problems and ways to assess them;

3

Enhance teachers’ understanding of mathematics teaching, learning, and assessment based on

the National Council of Teachers of Mathematics’ Principles and Standards (NCTM, 2000).

This course also had a 30-hour field experience component. This course was grounded in theories

and research from cognitive research (Bruer, 1993) and constructivist learning theory (Vygotsky, 1978;

Young, 1997). Although cognitive theories emphasize individual learning process and heterogeneity in the

community while socio-cultural theorists focus on the social and cultural processes in relation to the

individual’s knowledge generation (Cobb, 1994), it was argued that “each of the two perspectives…tells

half of a good story, and each can be used to complement the other” (p. 17). A shared view amongst many

theorists and researchers is that neither of the perspectives is better than the other, rather we should feel free

to choose or “mix-and-match” the views in the most appropriate ways (Bereiter, 1995; Cognition and

Technology Group Vanderbilt, 1996). “The important point is that … the educational goal for social

constructivists is to create social environments that encourage students to construct their own

understanding” (Lin, Hmelo, Kinzer, & Secules, 1999).

In this study, it is believed that “the learning that occurs in context is considered more useful or

valuable to the learner than the learning that occurs in isolated situations” (Guy, Li, & Simanton, 2002) and

knowledge is constructed and advanced through social interactions (Kanuka & Anderson, 1998). Methods

courses provide more authentic contexts for the learning of technology than stand-alone technology courses.

Further, various technologies such as computer-mediated communication (CMC) and multimedia provide

“an effective means for implementing constructivist strategies that would be difficult to accomplish in other

media” (Driscoll, 1994). Based on these beliefs, the course was designed integrating technology with

sustained educational experiences to help the student teachers develop skills and advance knowledge in

mathematics education.

4

Methods

Data

Subjects were selected from students enrolled in a course in a university located in a rural area of the

Northern part of US. The course was a mandatory secondary mathematics methods course. Students

enrolled in this course, typically in their twenties, were pre-service teachers (student teachers thereafter)

preparing for teaching mathematics at middle school or secondary level. This was their first and only

required mathematics methods course. Those student teachers often majored in mathematics at secondary

level or double majored at middle school level. Students majored in mathematics are required to take 125

credits mathematics, 36 of which must be year 3 or above courses. Students with double majors are required

to take 45 credits from each major. Typically, a three-credit course involves roughly 45 hours of instruction.

Therefore, they usually have a solid background in mathematics. For the past decade or so in North

America, there has been a considerable shift of focus of mathematics teaching to real world connection and

a wide range of resources (Baratta-Lorton, 1995; Burns, 2000; Driscoll, 1999) were developed over the

years to encourage students to engage in mathematical activities in relation to the world around them. Most

of these student teachers, however, had their school education in typical traditional settings.

The course described in this paper was taken by a group of eight student teachers. Three of these

student teachers, Tina, David and Kyle (all pseudonyms), were selected to provide a focus for the study.

These three offered a balance of gender and academic background. Tina was in her fourth year at the

university with a double major (social studies in secondary school and mathematics in middle school). Both

David and Kyle were in their final year of the program majoring in secondary mathematics. David,

however, was in his seventh year at the university. He was in various university athletic teams in which he

was an active member. Because of his busy schedule, it took him much longer to complete his program than

others.

Data Collection

5

In this study, several data collection techniques were used to ensure triangulation of the data. The

primary data sources of this study included my own journal and the artifacts of the course. Following, each

data source is described along with the means by which data were collected and the information each source

was expected to provide.

Instructor’s journal: Throughout the semester, I kept a journal to record my action and reflections

on activities, administration issues, and the structure in general. This journal also included lesson plans and

summaries of a wide range of issues that arose from week to week. As well, an informal interview

conducted with two students was documented in this journal. This journal provided insights into the

teaching methods I used and my interpretation of the activities.

Threaded discussion: Each week, student teachers were asked to respond to course readings and

discuss related issues in online discussions. They needed to reflect, critique, and evaluate their personal

experiences and positions against others’ thoughts based on the readings. The purpose of the threaded

discussion was to promote higher-order thinking and ultimately knowledge construction. The entire corpus

of the threaded discussion was printed from the computer.

Multimedia Project: The final project involved the use of digital cameras to capture geometry in real

life and then the creation of presentation slideshows (PowerPoint or HyperStudieo). This project was

derived from a paper-pencil activity: “scavenger mathematics hunting”, which is described below. The

purpose of this activity was to bring the outside world into mathematics classrooms. This activity was

designed to help student teachers to further recognize the relationships between abstract mathematics and

the real world to enhance their understanding. It also modeled technology supported teaching and learning.

The students’ final slideshows were collected and printed from the computer.

Written Assignments: Student teachers’ written work was collected, including their mathematics

auto-biographies submitted early in the term. Another important written work was their field journals. This

course had a field component, and the student teachers were required to have field experience directly

6

related to this course. Specifically, each student was assigned to a practicing teacher and went to the

assigned schools every week. Written reflective field journals were required every week to document

observations, questions, and thoughts. This data provided information on the type of growth and the reasons

causing this growth that students had during the course.

Data Analysis

First, I created electronic and printing files for all the data sources. Then I aggregated, summarized,

and coded the data relating to each source. Emergent themes were identified and a coding scheme was

developed. A three stage data coding was used in the analysis of the case studies. First, I identified themes

by open coding of the informal interview, my journal, and student artifacts. To ensure the reliability, the

emergent themes were triangulated across datasets. Data clips that addressed each theme were grouped.

Finally, concept maps were constructed to organize the broad theme categories and their constituents and to

make interconnections explicit.

To check reliability of coding, I first coded all the messages using the coding scheme. These

messages were grouped into each category. Then I chose 60 messages that were representative of all

messages from each category and asked a graduate student to code them. There was almost complete

agreement (only one exception) between the two. We discussed the discrepancy until an agreement was

reached.

Course Design

The course was structured by combining regular classroom instruction with participation in an

asynchronous computer conference. The course started with reflective inquiry by the student teachers on

their experiences with mathematics teaching and learning. Then, the student teachers examined theoretical

and practical issues in mathematics education. They wrote in their reflective field journal every week to

document their observations, questions, and thoughts. They were required to develop a technology

7

integrated mathematics lesson and were encouraged to teach it in their field classes. In the final project, they

developed ways to apply course content to improve their own teaching and learning of mathematics.

The final project involved the use of digital cameras to capture geometry in real life and then the

creation of presentation slideshows (PowerPoint or HyperStudio). Previously, when the course was

delivered completely through face-to-face meetings, one activity was the mathematics field trip: “scavenger

mathematics hunting”. This activity was designed to help student teachers to further recognize the

relationships between abstract mathematics and the real world in order to enhance their understanding of

real world application of mathematics. It also served as an innovative teaching model. In this activity,

student teachers would go out and search for real world mathematics, such as different geometric shapes

used in architecture and various patterns discovered in plants. They would then record their findings on the

‘scavenger hunting’ sheets and later share them with the whole class. Although this activity enabled student

teachers to bring the outside world into mathematics classrooms, the static nature of the tools (i.e. paper and

pencil) limited student teachers’ creativity, allowing student teachers neither to capture images nor to

present them interactively.

Thinking that dynamic features of technology could provide new tools to approach this, this activity

was transformed to an electronic version. In particular, because of the belief that multimedia provides

excellent tools for creating visually attractive and interactive products, the final project was designed to

involve the development of multimedia slideshows of real world mathematics that could be used in real

classrooms.

Results

The analysis of data revealed that the following two themes are particularly salient: 1) the student

teachers’ attitudes to using technology in classrooms had changed; and 2) for at least some of the student

teachers, the fact that the multimedia project focused on geometry positively affected their attitudes toward

geometry and teaching geometry. Following, I described Tina, David, and Kyle’s cases to demonstrate

8

these themes. These cases were explored from different analytical standpoints. In Tina’s case, I depicted

how her strong reaction to geometry led to my intentional creation of student mental dissonance by the

modification of a pedagogical approach which, in turn, sparked a rich discussion and led to their further

exploit. In David’s case, I explored how the creation of a multimedia project inspired him to examine the

newly acquired knowledge in field classrooms, which allowed to him observe its impact on students and the

cooperating teacher. Witnessing such impact, consequently, affected his beliefs and attitudes. For Kyle, I

focused on how he spontaneously started a debate in online discussion which resulted in his reexamination

and reshaping of his beliefs about technology. Because the cases were intertwined, descriptions of the three

cases were not mutually exclusive. Student teachers’ messages, assignments, actual excerpts of their

comments, and my perceptions were provided to explain and rationalize the findings.

Tina

On the first day of the course, the student teachers were asked to construct autobiographies that

focused on reflections on their history of mathematics learning. This assignment was intentionally given

early to eliminate any influence of this course on the autobiographies. As part of the assignment

explanation, question prompts were provided to help students to focus: what do you like/dislike about

learning mathematics? What is the first memory you have learning math? How did your experience affect

your learning/teaching of mathematics?

In her autobiography, Tina described herself as a quick learner, excelling in mathematics. At the end,

she concluded: “I still enjoy doing math (except the proofs), and working with the numbers in my head.”

Throughout her four-page autobiography, this was the only place – that is, three words in a parenthesis --

that she ever indicated her dislike about an area of math. For this reason, I overlooked this incidence.

During the course interaction, I noticed that Tina was a very smart student, confident in her mathematics

ability, and loved the challenges brought by mathematics problems. However, something surfaced when we

were discussing their preferred classrooms for field experience. Tina stated that she “hated” geometry and

9

would not want to be assigned to a geometry class for field experience. This strong statement really struck

me and I probed further: “what if you are hired and required to teach geometry?” She answered: “I would

still teach it, but I am going to suffer and my students are going to suffer.” Later that week, in the online

discussions, Tina posted a message in the Geometry forum: “I HATE GEOMETRY”.

Well I guess hate is a pretty strong word. Ninth grade at my high school was geometry. What I remember from that class is probably why I cannot stand it. Geometry was all proofs, this was my first proof class, or even the first proofs I ever did. I hated doing them, to me yes this picture in front of me was clearly a right triangle, now why did I have to write an 8-step proof [proofing of certain hypothesis involving 8 separate steps] as to why. …I can not recall doing anything else in that class….How do I feel about teaching geometry? Let’s just say that I would not like it for any student I am teaching to have to go through what I went through in the class…(and no [the instructor], I do not want to be placed in a geometry class for field experience). If when I do get hired, I will have to teach geometry, my enthusiasm will not be in it, but I will teach it and suck it up.

Several other student teachers shared similar feelings in online discussions indicating that they

“dislike” geometry too. They felt that geometry is a very different field from other mathematics areas, and

that the abstractness and the lack of connection made geometry a very difficult topic to learn and to

appreciate. The fact that several student teachers in this class showed this negative attitude toward

geometry convinced me to focus the field trip activity on geometry. I thought this design could create some

dissonance and uncertainty in them which would encourage and even force them to evaluate the potential

solutions to the problem in light of their existing knowledge.

The final project was then changed from a field trip to the development of multimedia presentations

of real world geometry. Rather than a day trip activity, the student teachers had three weeks to work on the

project. The student teachers discovered real world geometry and captured these images using digital

cameras. Then they designed and developed electronic presentations of “Real World Geometry” using

either PowerPoint or HyperStudio. Finally, their slideshows were presented to the whole class toward the

end of the course.

Tina’s slideshow contained various pictures she took from the campus and information on how

geometry was used in this real world. It ranged from trees and buildings to manholes. In the narrative part

10

of the slide show, she provided not only her discoveries of geometry in the pictures, but also why the

specific geometric shapes are used in real life. For instance, the following narration explains why a

manhole is in a circular shape:

A manhole is a circle, because if it were a square the top will fall through to the bottom (or the men with the belly’s [sic] can fit easier into the sewer).

In addition, she included examples of how student teachers could use these pictures to teach

mathematics. Her slide show clearly demonstrated that she had gone beyond thinking that geometry only

involved proofs; rather, she was able to relate geometry to her daily life, apply her knowledge to the real

world and provide professional suggestions for the educational use of her work.

Because of Tina’s particularly ‘anti-geometry’ attitudes at the beginning, a short interview was

conducted at the end of the semester. When asked whether she still hated geometry, she replied assertively:

“No! I don’t hate geometry anymore.” Further probing her idea of technology, she explained that “I really

like David’s slideshow for its fun and down-to-earth demonstration of the topics. What’s really nice about

his [slide] show is that it not only shows real-life application of geometry, but also enables students to

manipulate the ‘real life’ stuff in relation to geometrical principals. These experiences opened my eyes and

forced me to rethink about geometry – it’s not all about proofing. It showed just how much we can do to

teach geometry, particularly with the use of technology.” She indicated that after she had done her own

multimedia project, watched her classmates’ multimedia presentations, and been introduced to various

manipulatives, she was convinced that geometry can be enjoyable and wanted to use technology in her

future classroom.

Tina, who had negative attitudes toward geometry, had changed. It is very probable that this change

was brought by the synergetic effects of several factors which were impossible to attribute to any single one.

First, her earlier experience of geometry was negative, as she found the subject irrelevant and meaningless.

The real-life pedagogical approach used in this course might result in her recognition of the relevance of

geometry in real life objects such as “trees, buildings and manholes”. Secondly, the online discussion

11

provided her a space to reflect on her experience and to share her opinions. This reflection and her

interaction with others might reshape her beliefs. Further, it resulted in the modification of my teaching plan

to focus on geometry, which in turn, enabled her to explore multiple approaches to teaching and learning

geometry. Thirdly, the experience of creating/presenting the major project and observing others’ slideshows

broadened her views about geometry and teaching geometry. Fully recognizing the synergetic effects,

however, I argue that the meaningful use of technology in this course contributed greatly to the change of

her attitudes. Her statement in the informal interview was a testimony of such impact. For example,

watching David’s project enabled her to further recognize the value of technology because it could give

students a mechanism to manipulate ‘real life’ objects that would be difficult to achieve without the

technology.

David

At the end of the final project presentation, the best slide show was elected. This slideshow --- “Real

life geometry that you and I see every day!!!” was created by David. At the end of the course, he shared in

the online discussions that he did not care about geometry at all when the course started (I had not known

this previously). By coincidence, he was assigned to a geometry class for field experience. Although he did

not like geometry at the outset, in just several weeks studying pedagogy from this course and observing a

geometry class, David showed more interest in the subject and was motivated to apply his knowledge in a

real classroom. In responding to the online discussion about the “like/dislike of geometry”, he posted a

message that indicated his growing interest in learning the pedagogical techniques of teaching geometry.

I have found myself in an interesting position in my observation classroom. The 2 periods that I watch at S School are Geometry, Wow what a coincidence, I am taking Geometry [4th year university math course] right now also. I am very intrigued by the difficulty that the students are having right now. I am wondering how I can incorporate what I am learning into what they are learning with out blowing their minds away... I am very interested to see what I am come up with, I would like to use my geometry class some how in my lesson that I teach to my class.

David was also a player on the university American football team. The American football team won

the national championship towards the end of that semester. That was a huge event not only for the

12

university, but also for the entire town (45,000 residents). David played exceptionally well in one of the

playoff games. He was the hero of that game and the local newspaper used a whole page reporting his

performance. That day David brought a digital camera to the field and took some snapshots of the game.

Using those images and others he took from daily life, he created a fascinating PowerPoint presentation. His

slideshow clearly demonstrated geometric ideas in applied settings. It also showed that geometry is a way

for us to understand the world we live in. For instance, based on one picture of the football game, he

generated a word problem, namely “Pythagorean theorem at work”, connecting geometry to the game.

The process of designing and creating the multimedia presentation really made David rethink his

attitude to geometry and the teaching of geometry. His following message revealed the impact of this

project on his attitude toward geometry:

I had the same sentiment as Tina did at the beginning of the semester. I don’t really care for geometry, but after observing all semester in a geometry class and doing the PowerPoint thing, I think there are a lot of things that can be done to make geometry fun.

This activity changed David not only in terms of his attitude toward geometry but also his view about

teaching geometry. He took one step further: he brought it to his field experience classroom and showed it

to the students. Because of the creative expression and the concrete representation of abstract ideas, both the

teacher and the students in that classroom were captivated by the slideshow. The cooperating teacher, after

watching the presentation and observing the changes of student behavior brought by the presentation, was

convinced that this was a meaningful use of technologies, and that it offered an alternative way of teaching.

David, noticing the big impact on both the students and their teacher brought by the experience, was

intrigued. His deepened understanding of how pedagogical and didactical characteristics of education and

technology can influence students was amplified in his log:

“While showing my PowerPoint presentation to my 3rd period class, the one that is usually not very attentive and some disruptive, I found that they were very interested in the pictures I took, the problems I gave, and the presentation in general. I was very intrigued at the interest the [students] showed in my presentation. I think it is just a testament to what different types of teaching strategies and different uses of technology can do for students in the classroom. Mrs. S [cooperating teacher] even mentioned how she was impressed with the class’ attentiveness. She even save[d] a copy of the presentation on her hard

13

drive so she could show it to her 7th period geometry class. I really think the PowerPoint program will play a big role in my teaching on[c]e I get out and get a job.”

David has changed his view of learning and teaching geometry. He will take this new view into

future learning and teaching practices and will possibly experience greater success both as a learner and a

teacher, in either traditional or technology-enriched settings, because of his increased confidence and

empowerment.

This final multimedia project turned out to be a huge success. It seems that this project influenced

not only the student teachers’ attitudes toward teaching and learning geometry, but also the attitudes of

some practicing teachers who were in contact with the trainees during their field work. The transformation

of this field trip activity from a paper-pencil version to a multimedia version had apparently brought in some

unexpected positive outcomes in ways beyond what the author could bring about in paper-pencil format.

The student teachers were actively engaged in creating representations of their own understanding of the

pedagogy and the content. The multimedia allowed them to transform abstract mathematics ideas into

concrete representations. The dynamic and visual aspects of the technology enabled the student teachers to

achieve and even exceed the course goals.

Kyle

Kyle is another male teacher who majored in secondary mathematics and intended to continue his

graduate study in mathematics after graduation. He was hardworking and very intelligent. He often held

completely different views from others. His classmates described him as obstinate. However, his openness

toward technology at the end of the semester and his dramatic change about technology over the course of

the semester made Kyle a particularly interesting case in this study.

It was apparent at the beginning that Kyle was not impressed with instructional uses of technology.

In one class, he stated that he hated technology and wished he could have destroyed all computers. Although

he acknowledged that he uses technology as well, he really believed that technology has more detriments

14

than benefits. Particularly, he could not see any value in the instructional use of technology. Later, he

elaborated his comments in the online discussions:

The other day in class I mentioned that I would like to get rid of computers and hate technology, but was unable to explain what I meant by this…. The kicker is computers save us so much time. I don't necessarily agree… but no one really mentions how much time is wasted waiting for computers to work, when the crash, rebooting, trying to find something.

A couple of weeks later, in responding to other messages in the online discussions regarding whether

schools should allow students to use another type of technology --- calculators, Kyle wrote:

You know what I am going to do when I have my own classroom? The first day, when going over rules, handing out textbooks, etc. I am going to take a calculator, sledgehammer and bust the calculator to pieces. That should get my point across to the students on whether they can use calculators or not. I might have to wait til I have a long term contract.

He further elaborated that he did not believe that technology was useful, particularly in classrooms.

He believed that everything we do with technology could be done without technology. All the instructional

goals we strive to achieve in mathematics classrooms could be better achieved without technology than with

technology. In other words, educational technology was useless, and often the use of technology even

hindered the effectiveness of instruction. Not surprisingly, he had no desire or motivation to learn about

educational technology.

Kyle’s comments really sparked everyone’s interest and in the following weeks messages flew back

and forth discussing the pros and cons of technology integration in classrooms. A debate was naturally

evolved in the online forum. Student teachers searched for learning theories, identified significant research

results, consulted their partner teachers, interviewed their professors, and reflected on their own experiences

to explore this issue. The debate really enabled them to engage in reflective and critical thinking processes.

Kyle, who was trying to defend his opinions in the first place, inevitably became deeply involved in this

ongoing and evolving learning process. The arguments and concrete examples provided in the rich online

discussion opened his eyes and he started to reexamine and question his existing information and beliefs.

15

This process, coupled with the introduction to various educational technologies throughout the whole

semester, especially the multimedia project, reshaped his beliefs and changed his views.

The exposure to different technologies and various ways of using technologies made him realize that

appropriate incorporation of technology in education can enhance teaching and learning. His pride and

enjoyment of feeling of empowerment brought by his successful completion of the multimedia project were

evident in his message:

I liked the hyperstudio. Before I was forced to work on that project I had done nothing with that program. Doing that project forced me to work with a program that was foreign to me and showed me that it wasn’t too hard to do. Now I know something I didn’t before I took [the course]!

Kyle’s increased competency in using technology resulted in his higher level interest in using

technology. Being engaged in purposeful reflective thinking processes and exposed to different approaches

to using technology in meaningful ways, as well as having the opportunity to design and create a multimedia

project, Kyle started to realize and appreciate the educational values of technology. For Kyle, this was a

drastic change of attitude toward the educational use of technology. His attitudes certainly did not take a

180-degree turn, but he is, at the very least, now willing to explore possible applications of educational

technology. The degree of change that Kyle had over such a short period of time was clearly dramatic and

interesting. One implication of this case might be that this kind of incorporation of technology into a

method course is particularly useful for student teachers like Kyle.

Conclusions and Instructor’s Reflection on the Experience

The experiences with teaching mathematics methods courses has convinced me that the appropriate

integration of technology into teacher education has the potential to achieve, and even exceed, the goals of

mathematics education. I felt inspired to incorporate technology into the course as the process made me

rethink my assumptions about the pedagogy, the course content and goals, and the technology.

Although I originally speculated that the integration of technology would enhance the student

teachers’ knowledge of mathematics education, I was not sure what kind of specific impact it would bring.

16

The actual outcome of the course surpassed my expectation. At the end of the semester, I found that the

student teachers had a broader understanding of both “why” and “how” they might choose to use technology

in mathematics classrooms; their attitudes about instructional uses of technology had changed; and for at

least some of the student teachers, the fact that the multimedia project focused on geometry positively

affected their attitudes toward geometry and teaching geometry.

The integration of technology in this course impacted on different groups of people in various ways.

It affected the pre-service teachers, myself, and, in at least the case of David, his field experience

cooperating teacher and students. Although it was expected at the beginning that the student teachers would

become more competent and more versatile in their ability to incorporate technology into their teaching,

what surprised me was the degree to which their attitudes about the technology and toward geometry had

changed. This further supports the idea that attitude is a factor that is open to influence (Volman & van Eck,

2001) and that pedagogically and didactically appropriate use of technology can promote positive attitudes.

It is very probable that the change of attitudes toward geometry were synergetic effects brought by

several factors which were impossible to attribute to any single one. One such factor might be the

pedagogical approach in the course, in which the more self-directed and open-ended nature of the task

which made it more meaningful and genuine. The results concur with the idea that mental dissonance often

causes a great deal of reflection and ultimately brings about changes in teachers’ attitudes (Shaw &

Jakubowski, 1991). In this case, while the student teachers were not convinced of their abilities to teach

geometry in ways that would link up with daily life, the task set for them was precisely to look for instances

where geometry could be observed in real life contexts. This in itself perhaps already created dissonance in

them. This dissonance was evoked in a supportive way which resulted in the active, intentional and

purposeful process of exploration and discovery. This process forced the student teachers to think

reflectively and critically about what they had learned and how their knowledge could be applied in the real

world. This, in turn, led to a renewed ways of thinking (Collins, 1991).

17

Fully recognizing the possible impact of such pedagogical change, however, it is also critical to

realize the important role technology played in this study. First, the threaded discussion enabled student

teachers to share their opinions and ideas which furthered their understanding of the content. In Kyle’s case,

his spontaneous sharing of his thoughts on technology sparked a lively debate which led him to question his

beliefs. The threaded discussion also allowed me to better understand my students, giving me instant and

ongoing feedback, which in turn enabled me to adopt more appropriate pedagogical approaches. For

instance, Tina’s initial strong reaction to geometry led to the shift of project focus to geometry. Secondly,

the integration of multimedia slideshows offered student teachers first hand experience of the design and

development of technology-supported learning experience, broadened their view about technology

integration into classrooms, and allowed them to witness the possible empowerment of students by the

meaningful use of technology. In David’s case, he was inspired to test his work in field classes. This

experience allowed him to observe the actual impact of the meaningful use of technology on both school

students and their teachers. This observation, in turn, promoted his reflection which enabled him to see and

better appreciate the educational value of technology. One important implication is that, when integrating

technology into education, technology components should be designed to be authentic tasks. And most

importantly, learners need to be encouraged to apply their knowledge and work in real world situations.

Throughout the course, the student teachers investigated relationships concerning curriculum,

teaching, learning, and assessment via computer text messaging. When there were questions, they searched

for theories, examined their own experiences, consulted with in-service teachers, and acquired knowledge of

the relationship between theory and experience. The course web sites not only maintained the overall flow

of the course but also enhanced the course content via related links, and particularly their asynchronous

online discussions. The online discussions also provided an assessment tool, which gave me instant and

ongoing feedback. I gained a broader awareness of the student teachers’ thoughts and beliefs through the

18

asynchronous online discussion. In short, the online discussion offered feedback and direction that gave me

useful information for changing, refining, and enhancing instructional choices.

Five important factors underscore the value of the integration of technology into mathematics

methods courses. First, meaningful technology integration fosters higher order thinking skills. In this case,

the process of developing a multimedia project and engaging in intensive and elaborated online discussions

required student teachers to reflect and critically evaluate, which in turn resulted in their making sense of

and extracting meaning from their experience (Osterman, 1990). This “ability to reflect and evaluate…

encourages student [teachers] to be better learners as they become aware of their own thinking and monitor

their own learning process” (Liu, 2003). For instance, immediately after Kyle commented on his anti-techno

incentive statement in class, many of his peers debated this issue during which time he was not able to

enunciate his reasons. He felt unsatisfied and after taking time to contemplate, he was able to provide more

articulated justifications in the forum which resulted in an evolving online debate on the issue. This

intensive discussion motivated and fostered student teachers’ learning—in this process, they critically

examined different positions, reflected on their experiences, compared and contrasted their knowledge and

newly acquired information. Without the online forum, I could hardly see how such an intensive debate

could be conducted and sustained because of the time constraints. Even if we had enough time, he probably

would forget his arguments by the time we revisited this issue (which was at least a week later). “The

online forum thus enabled the discussions to develop at a much deeper level and with a broader scope than

merely face-to-face interactions” (Li, 2003b).

Second, my observation of student interactions suggests that face-to-face interaction and the online

forum complement each other. Interactions in face-to-face settings throughout the course enabled student

teachers to build trusting and friendly relationships, which in turn resulted in the establishment of a safe and

non-threatening online environment. In this environment, they could share their thoughts freely and not

worry about offending others. When they found their ideas were misunderstood, they simply elaborated,

19

explained, and clarified their positions further. If the course had been completely online, some of Kyle’s

comments could easily have led to “flaming” events. Here, flaming refers to emotionally charged, hostile, or

insulting postings in online environments (Thompsen, 1994).

Third, this experience suggests that purposefully engaging student teachers in a multimedia design

process fosters the incorporation of a wide range of thinking skills. The comprehensive nature and the

extensiveness of the process, coupled with the dynamic feature of technology, created a unique learning

opportunity for the student teachers which led to the development of highly valued cognitive skills. Most of

the core cognitive skills identified in research studies (Vockell & van Deusen, 1989), including focusing,

information gathering, remembering, organizing, analyzing, generating, integrating, and evaluating skills,

were required by this design task and hence exercised in this process.

Fourth, this unique learning experience made a broader and more profound impact than a methods

course without technology could have had, and further highlighted the importance of the field component.

In David’s case, technology enabled him not only to capture the exciting moments in the games but also to

transform them easily into a well-thought-through and carefully designed authentic slideshow of geometry.

His innovative use of technology increased high school students’ and their teacher’s interest. Experiencing

and observing this impact, David derived a reconstructed knowledge of geometry and a renewed state of

understanding about the teaching of geometry.

Fifth, the online forum provided me with a valuable and convenient tool for ongoing formative and

summative assessment, which in turn enhanced student teachers’ learning. I used discussion postings to

analyze and evaluate their understandings and concerns. This allowed me to make informed decisions and

adjustment for the instruction based on my students’ unique characteristics. For example, in our class

discussion, Tina was the only one who stated that she hated geometry. The resonance of many of her

classmates was not evident until the online discussion revealed it, which inspired me to change the project to

a geometry field trip. This change made the task more meaningful and genuine for these student teachers.

20

The intentional creation of a conflict situation forced students to examine contradictory thoughts. Hence,

possible inconsistencies, gaps, and misconceptions were recognized, challenged, modified, corrected, and

reconstructed. The dissonance created by this task promoted a great deal of reflection and ultimately

resulted in their change of beliefs. In addition, the forum provided an easy way to collect data for research

as well as reflection for the improvement of instruction.

Implications

The analysis of this research underscores the importance of the infusion of technology into methods

courses and suggests the following guiding principles for the design of those courses:

1) Contextualized learning: Integrating technology into intact education courses offers a meaningful

experience for student teachers because the technology is used in a relevant context. We must

therefore address the student teacher preparation issue within their courses. They need to be exposed

to technology within the context of their regular coursework.

2) Field component: The inclusion of field experience into the methods course appeared to be more

beneficial than a stand-alone methods course (Gallego, 2001). Student teachers had opportunities to

practice their newly acquired knowledge. This positively impacted on not only their mentor teachers,

but also school students. Further, witnessing these impacts can positively affect their beliefs and

enhance their learning. Potentially, mentor teachers, particularly those who are less competent in

technology, can have more time and gain more expertise in order to thoroughly plan and implement

proper integration of technology.

3) Blended learning: Face-to-face instruction and online interaction that complement each other provide

student teachers with more valuable experiences of learning the pedagogy and the content than any

single form of learning (i.e. merely face-to-face or online). Student teachers can have ample hands-on

experiences and establish a trustworthy and friendly relationship through face-to-face interaction,

while having extended and sustained discussions.

21

4) Design and development: Engaging student teachers in multimedia design processes contributes to

enhanced learning. My experience indicates that the tasks should be authentic and genuine to student

teachers. Further, if the tasks can be designed to create dissonance in student teachers’ thinking/belief,

higher-order thinking skills are more likely to be promoted.

5) Holistic design: the design projects should weave into both student teachers’ on-campus and field

experience. My experience suggests that student teachers may benefit the most if they design

technology-enhanced learning experiences using their newly acquired knowledge and then apply them

into field experiences. This way, they can examine the effectiveness of their experience and observe

potential impacts.

The choices in using technologies such as computers are like those relating to other educational

resources and methods. Both the pros and the cons of the specific technology need to be considered.

Technologies can be used to deal with content knowledge and pedagogy. The experiences shared above

suggest that we may benefit the most if we consider how learning mathematics education in face-to-face and

online settings can complement each other. The student teachers’ final evaluation and the outcome of this

course also suggest that having a field experience component of a methods course would be more useful for

this kind of integration of technology than a stand-alone method course. If technology-enhanced authentic

experiences can be designed for student teachers and at the same time provide them with opportunities to

implement and test their technology projects in real classrooms, student teachers and their students will gain

the most from this kind of experience.

22

References

Baratta-Lorton, M. (1995). Mathematics their way. Rev. ed.: Addison-Wesley.Bereiter, C. (1995). Constructivism, socioculturalism, and Popper's world 3.

Educational Researcher, 23(7), 21-23.Bruer, J. T. (1993). Schools for Thought: A Science of Learning in the Classroom.: The

MIT Press.Burns, M. (2000). About Teaching Mathematics: A k-8 resource. Sausalito, California:

Math Solutions Publications.Cognition and Technology Group Vanderbilt. (1996). Looking at technology in context: A

framework for understanding technology and education research. In D. Berliner & R. Calfee (Eds.), Handbook of Educational Psychology (pp. 807-840). NY: Macmillan.

Collins, A. (1991). Cognitive apprenticeship and instructional technology. In L. Idol & B. Jones (Eds.), Educational values and cognitive instruction: Implications for reform (pp. 347-361). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.

Drier, H. (2001). Teaching and learning mathematics with interactive spreadsheets. School science and mathematics., 101( 4), 170-179.

Driscoll, M. (1994). Psychology of learning for instruction. Boston, MA: Allyn & Bacon.Driscoll, M. (1999). Fostering Algebraic Thinking: A Guide for Teachers: Heinemann.Gallego, M. (2001). Is experience the best teacher? The potential of coupling classroom

and community-based field experiences. Journal of teacher education, 52(4), 312-325.

Guy, M., Li, Q., & Simanton, E. (2002). Integrating technology into an elementary mathematics methods course: Assessing the impact on pre-service teachers' perceptions to use and teach with technology. Paper presented at the annual conference of the American Educational Research Association, New Orleans.

Jonassen, D. H., Howland, J., Moore, J., & Marra, R. (2003). Learning to solve problems with technology: A constructivist perspective (2 ed.). Upper Saddle, River, NJ: Prentice Hall.

Kanuka, H., & Anderson, T. (1998). Online social interchange, discord, and knowledge construction. Journal of distance education, 13(1), 57-74.

Li, Q. (2003a). Integrating Internet into Teacher Education: What Works? Paper presented at the annual conference of the American Educational Research Association (AERA). Chicago.

Li, Q. (2003b). Would we teach without technology? A professor’s experience of teaching mathematics education incorporating the Internet. Educational Research (NFER), 45(1), 61-77.

Lin, X., Hmelo, D., Kinzer, C., & Secules, T. (1999). Designing technology to support reflection. Educational Technology Research and Development., 47(3), 43-62.

Liu, M. (2003). Enhancing learners' cognitive skills through multimedia design. Interactive learning environments.

National Council for Accreditation of Teacher Education [NCATE]. (2001). Technology and the new professional teacher: Preparing for the 21st century classroom. Washington, DC: National Council for Accreditation of Teacher education.

National Council of Teachers of Mathematics [NCTM]. (2000). Principles and Standards for School Mathematics. Reston, VA.: Author.

Osterman, K. F. (1990). Reflective practice: A new agneda for education. Education and urban society, 22(2), 133-152.

Shaw, K., & Jakubowski, E. (1991). Teachers changin for changing times. Focus on Learning Problems in Mathematics, 13(4), 13-20.

Thompsen, P. (1994). An episode of flaming: A creative narrative. Etc., 51, 51-72.Vockell, E., & van Deusen, R. (1989). The computer and higher-order thinking skills.

Watsonville, CA: Mitchell Publishing, Inc.Volman, M., & van Eck, E. (2001). Gender equity and information technology in

education: The second decade. Review of educational research, 71(4), 613-634.

23

Vygotsky, L. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.

Willis, J. (2001). Foundational assumptions for information technology and teacher education. Contemporary Issues in Technology and Teacher Education, 1(3).

Young, G. (1997). Adult development, therapy, and culture: A postmodern synthesis. New York: Plenum Press.

24