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

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.

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;
  • 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.

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

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 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 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 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?