ELECTRONIC JOURNAL PARTNERSHIPS:
AN ACTION RESEARCH PROJECT INVOLVING PRE-SERVICE TEACHERS AND ELEMENTARY MATH STUDENTS
Sharon Murray,
Assistant Professor, Department of Education
St Thomas University, Fredericton, NB
Research Orientation
As a university educator of pre-service teachers I continually investigate and reflect on ways to promote dialogue around mathematics teaching. What I try to do is encourage pre-service teachers to create effective bridges between their public dialogue and private meaning making. One way, I believe this can be done, is by providing pre-service teachers with learning experiences that involve the students they will teach. Through these authentic learning experiences, I hope, these soon to be teachers will integrate their understanding of both theoretical and practical issues of mathematics teaching. Involving them this way is a form of classroom action research. The term action research was coined in the 1940s by Kurt Lewin who applied it to self-reflective cycles of planning, acting, observing and reflecting in social settings. The later applications of action research particularly in educational research in the 1980s, maintained the spiral nature of Lewin but placed more emphasis on the idea of strategic action. Carr and Kemmis (1983) who represent one strand of action research, see the two main aims of action research as improvement and involvement (p 154).
This project’s action research involves particular pre-service teachers and students in particular classrooms. Through this involvement in classrooms, I hope pre-service teachers will improve their understandings of mathematics teaching, particularly the importance of communications through journal writing. The pre-service teacher’s interactions with school age students while studying mathematics theory is also a means for them to research and think about how young children come to understand mathematical concepts. The project, therefore, provides pre-service teachers opportunities to construct knowledge through a process of reflection in action and later reflection on action. This form of action research which focuses on the process of individual reflection and a bottom-up practical approach to educational change is supported by Donald Schön (1983) in the United States and John Elliott (1991) with whom I studied at the Centre for Applied Research in Education in England. Action research is an ideal research design to meet my need for pre-service teachers to investigate ways to make meaningful connections and improve their teaching through active student/teacher interactions.
Project Description
Thirty university education students enrolled in an elementary mathematics course were paired with an elementary student at the grade three and grade six level in two local elementary schools. The students communicated with each other through electronic mail. The schools are part of the New Brunswick provincial government's U.N.I.T.E. (Using Networks to Integrate Technology with Education) project which by 1996 placed local area computer networks (LANs) in all elementary and middle schools. The U.N.I.T.E. project goals are to support writing across the curriculum and to support research and telecommunications. This particular project was able to promote two of the three goals of the U.N.I.T.E. project (writing and telecommunications). The focus of this project, however, is the engagement of pre-service teachers and elementary students in a shared dialogue about mathematics.
Background Theory
Communication is the basis for the shared ideas of mathematicians. It is the way mathematicians learn and build on ideas and theories. They use symbols and words as a way of communicating their findings and of dialoguing with others. The National Council of Teachers of Mathematics (NCTM) recognizes the important role communication plays in demonstrating an understanding of mathematics and it is included in their standards. Most North American educational jurisdictions have followed their lead. In Atlantic Canada the mathematics foundation document lists communication in mathematics as one of the curriculum outcomes from entry through grade twelve. This document urges teachers to have students discuss and write about mathematical ideas by involving students in descriptions of a problem solving process, explanations of procedures, explanations of concepts, evaluations of responses to problems and descriptions of how two concepts, graphs, procedures, shapes, etc. are similar or different.
Communication is also an important part of mathematics education for students (pre-service teachers) in university education mathematics courses. In fact for the university students it is even more critical because their facility with communication involves several layers - the ability to communicate their personal understanding of mathematics, the ability to communicate their understanding to future students, and thirdly the ability to assist students in developing an external discourse in and about mathematics. The university students involved in this study were experienced in portfolio writing, collaborative writing, and ink shedding (free writing) as some forms of communication. For future teachers to implement and assess these communication strategies, they need to experience the practice of communication not just in their university classrooms but also in public school classes. The value of writing in mathematics classrooms is indicated through a growing body of evidence that claims that writing and in particular journal writing clarifies thinking and promotes student learning, helps teachers pinpoint where the student is having problems and why the problems occurred, encourages a growth of a community of learners, and helps teachers recognize misconceptions as well as enabling students to become aware of what concepts they do and don't understand and thus take some responsibility for their own learning ( Gordon and MacInnis 1993; Drake 1994; MacIntosh 1991; Miller, 1991; Scott 1992).
Electronic journal writing through e-mail allows for rapid exchange to anywhere in the world, is convenient, and has no cost. Using technology as a delivery vehicle also has the added benefit of encouraging familiarity with this medium of communication by both the pre-service teacher and elementary student. Electronic mail is asynchronous - does not occur simultaneously like a telephone conversation. The students have time to read messages and time to think about their responses and to write drafts (as the pre-service teachers did) of their next communication. This period of reflectivity would not be possible in a face-to-face communication. E-mail communication occupies a place between face-to-face communication and a written journal entry. Multiple correspondences can occur back and forth in the time span of an hour and because you are not writing and posting a piece of paper but receiving (becoming part of the electromagnetic spectrum) it's as if the person is present (in fact they are 'telepresent'). It's this form of communication in the classroom that needs to be encouraged - a two-way dialogue as opposed to one-way transmission approach.
...it is hardly surprising that schools should mirror the larger society in their fright over "two-way" or interactive communications technologies, giving preference to "one-way" such as broadcasting or closed-circuit radio and television and film, and more recently, computers, whose interactivity --far from being harnessed to encourage inter-cultural learning --has too often been restricted to that of a "surrogate teachers" which dispense prepackaged lessons (Sayers 1995, p16).
Project Dialogue
The pre-service teachers wrote introductory letters to their buddies as a way of setting a comfort zone with the students. They spent time in class writing introductions and sharing ideas about what might be a good way to introduce themselves to the students. The class agreed that they should share some of their feelings about math and include them in their introduction. One student wrote "When I was in grade three, I sometimes would not understand something but I was too shy to ask. If this happens to you, send me a message and I'll get right back to you about it."
A sample of a full introductory message is below:
Hi Stacey,
How are you? My name is Sally Kelly and I am a student at St Thomas University. I am going to be an Elementary school teacher. I think that it is really neat that we get to send letters to one another as a part of Math class! Do you like Math? Are you having any problems in Math that I could help you with?
Right now in Math class we are doing place-value. I found it a bit confusing at first but I think I am getting the hang of it now. It has been a LONG time since I have taken Elementary math so it is a bit fuzzy in my brain right now!
....
I hope we will have fun writing to each other.
Talk to you soon.
Your Math Buddy,
Sally
Once contact was established, the pre-service teachers used a combination of prompted and unprompted journal entries. Prompted entries need to be clear and specific and this proved to be a challenge particularly without face-to-face communication. A sample prompted entry:
Hi Jason,
How is math class going? I hope you liked the last questions I sent you. I am writing to send you more questions to try. In math class we are doing place value and the meaning of numbers. My teacher wants us to send our buddies some questions like we have been doing in class.
My first question is about the number 458. I want you to try and explain what each digit in the number stands for or means. For example, what does the 4 stand for? What does the 5 stand for and what does the 8 stand for?
Here are a couple of other questions for you to try:
1. Write two ways to state the number of paper clips in a package that contain 550 paper clips. But do not write 550.
2. Explain what 4 963 means. Include an explanation of the 4, 9, 6, and 3.
Another student framed this question using a more creative and perhaps motivational way to encourage the student to respond to questions about place value.
3. Write up what you would say to a creature from Mars if it said to you, "Tell me what you mean by place value?
I hope you like these questions and I hope to hear from you soon.
By the way, how were the rounding off questions? Were they too easy?
Jennifer Jones
Project Outcomes
Communicating in a mathematical language via electronic means in many ways forced the university students to become clearer in their language usage. In the example above both the student and teacher needed to share an understanding of what stands for means. The electronic journal entry can't provide additional verbal clues; so the pre-service teacher has to attend to communication in a language that is common if she wants her expectations met. The context of language use often provides a clue to meaning but not always. Attending to the language of mathematical communication is crucial for both the student and the pre-service teacher. The pre-service teachers quickly realized the difficulty of different interpretations and as a result they made attempts to compensate for it in their correspondence. Several suggested the use of a manipulative as a necessary aid in doing problems within a particular context and others became aware of the difficulty of not being present so passed on the responsibility. "It is going to be difficult for me to check your answers. You might ask your teacher when she isn't too busy. Let me know if this question was too hard or easy for you."
Most of the correspondence between email buddies was in the form of prompted cognitive questions and the students were engaged in this type of exchange. Journal entries from individual elementary students tended to corroborate the feelings of engagement experienced by the university class.
Dear Shelly,
Could you give me another math problem? I figured out the answer to the one you gave me. The answer is 45, if you don't count the owners you get 90, then I misused 45 and got 45.
Your math buddy,
Heidi
As well as the involvement of the respective students, the third positive outcome of the project was the healthy exchange of dialogue of an affective nature about the study of mathematics. Students responded very openly to questions such as "How did taking the math test make you feel?". The elementary students reacted to this sharing of feelings about mathematics and discussed their feelings with their buddies at the university. They assessed their own strengths and weaknesses and expressed this to an electronic pal.
Jane;
My favourite kind of math is rounding off and my hardest is subtraction. This is because I have a hard time subtracting. Are you good at subtracting Jane?
I do like math. It is my second favourite subject in school. What is your favourite subject?
I don't like problem solving so for a math question could you please give me a rounding off question?
Here is a math question for you.
1000 X 2050 =?
Your math pal,
Jerry Geoff
The pre-service teachers at the university also experienced this:
In writing my third and sixth grade "math buddies" (math e-mail pal), I was encouraged to express my like or dislike of mathematics and to ask what my "buddy" thought of math as well. At the time, I didn't realize what good this would do beyond making conversation and finding out whether or not the child liked math. Norwood and Carter's observation on the importance of beginning with the affective makes this strategy clear to me and my past experience in turn supports their suggestion.
Impact of the Partnerships
The project’s intent to explore the possibilities for involvement through interactive dialogue of an electronic nature as a means of improving learning and understanding for both elementary students and university pre-service teachers was successful. The electronic journals provided insight for the pre-service teachers into the importance of a shared and contextual language in mathematics and also the importance of the affective domain in mathematics education. The pre-service teachers were able to apply theory to authentic practice when they began a dialogue with students during the first month of their education program. Students at the elementary school level had the opportunity to share concerns with university students and to receive remediation from a person other than their classroom teacher. Their use of electronic communication was purposeful and two-way; they got to practice their problem solving skills and their communication abilities.
This is a continuing project with a focus this year on improving organizational structure, using letter writing as well as email, and interacting with the students more frequently on a face-to-face basis. The grade three teacher reported that her students often had difficulty reading the entries from the university students. This was attributed to the reading levels of the elementary students and the difficulty the pre-service teachers had with expressing their problem so that it would be clear and understandable. The teacher often had to read and explain the problem to the students. She usually typed their responses because of their lack of keyboarding speed which was compounded by and the availability of only one computer in the classroom. This was time consuming for the teacher and this intervention between teacher and grade three student removed the personal connection that might have more easily occurred between the buddies. Limited access to computers was also a problem for the grade six students and message response time was very slow.
A solution to these organizational problems might be to create a liaison team not only to maintain contact but also to be more aware of what areas of the mathematics curriculum the classes are studying. Pre-service teachers would then be able to develop prompts that would be appropriate and relevant to the students. The buddies might also decide on a reasonable response time or a particular response day on which teachers give students time to put their thoughts on paper before coming to the computer which would reduce keyboarding time and increase reflection on the electronic entry.
The electronic journal writing at the beginning of the university education programme was successful since it reinforced the importance of all forms of mathematical communication. We had a successful project. The pre-service teachers and elementary students engaged in a shared dialogue about mathematics. The electronic journal correspondence helped elementary students clarify their thinking about mathematics and helped pre-service teachers better understand how communication plays an important role in the study of mathematics.
References
Carr, Wilfred and Stephen Kemmis. (1983) Becoming critical: knowing through action
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