Distance Learning Complements a Pre-Service Mathematics Education Model
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During the spring 1995 semester, students enrolled in the Mathematics for Childhood Education course within the Department of Early Childhood and Elementary Education at East Stroudsburg University participated in a distance learning project with a school in the Pleasant Valley School District located about 20 miles from the university. Two-way full-motion, interactive video enabled pre-service teachers to observe and, ultimately, to better understand the role of an elementary mathematics teacher. As recommended by the National Council of Teachers of Mathematics (NCTM) in their Curriculum and Evaluation Standards[1] and Professional Standards,[2] future teachers need to become familiar with a variety of teaching techniques and assessment methods. In particular, they must become familiar with the potential uses of technology to enhance the effectiveness of an elementary mathematics program. The distance learning project with a local school district enabled our pre-service teachers to see how manipulatives and real-life problem situations supplied worthwhile mathematics tasks for real elementary students. Pre-service teachers could discuss with these elementary teachers the effectiveness of implemented tasks. And, although not the project's primary focus, it also enabled pre-service teachers to become aware of distance learning's potential in an elementary classroom, as well as in a methods course.
Two Strategies Tested
The first strategy for using distance learning to enhance this mathematics methods course was to allow pre-service teachers to actually see, in real time, what takes place in a classroom before, during and after a well-planned mathematics task is implemented. Our second strategy was for pre-service teachers, in a team-teaching format, to plan and implement a mathematics task under the guidance of the methods course instructor and the K-12 classroom teacher. In order for pre-service teachers to better understand what they observed, a reflection session with the methods course instructor and the classroom teacher followed each distance learning strategy. Once a local cable TV company installed the hardware and the university's telecommunications technicians prepared it for use, the distance learning project was underway. Coordinating schedules between the two locations (the elementary school classroom and the university) was the most challenging aspect of the project. Since the pre-service teachers' schedules were predetermined by their overall course schedules, the classroom teacher at the elementary school was very accommodating in maneuvering her students' classes and lunch periods to create time slots in common with the two sections of the methods course at the university.
Strategy One: Classroom Teacher
On the day of the scheduled live observation, the pre-service teachers met in the television production studio where they were able to see and hear the fifth-grade students as they were getting ready for math class. With two-way audio and video capabilities, the youngsters were able to hear and see the pre-service teachers as well (who did not appear as animated while on camera as the youngsters!). Then the actual math lesson began.
The fifth-grade teacher presented a mathematics task that challenged the youngsters to prepare for a party at an apartment that desperately needed new carpeting installed beforehand. Numerous mathematical concepts and problem-solving strategies were integrated throughout the activity, reflective of the NCTM standards. The task provided an opportunity for the fifth-graders to make decisions based on the concept of area. Since the carpeting was available for purchase at $4.50 per square foot, students were reminded of a previous lesson on population density that dealt with square miles. This connection with another form of square units set the stage for a demonstration of measuring the area of the blackboard using a square foot model. Students understood the essence of the square foot after actually measuring each side of the model, thus discovering why it is called a "square foot." Before the model was used to measure the area of the blackboard, students offered their own estimates of the area. This problem prefaced the solving of "living room" problems. Several scaled rooms were drawn on the blackboard and students used their square foot models on the classroom floor to find the amount of carpet needed for each room. With guiding questions from the classroom teacher, students began to see a pattern between the dimensions of the room and the area in square units.
Taking the students from the concrete stage to the abstract stage, the classroom teacher presented similar problems with larger dimensions. Rather than using the square foot model, the students, who had access to calculators, determined the area of each of the hypothetical living rooms. One should note that the activities for this mathematics task did not include coverage of the formula to find the area of a rectangle. Although more time consuming than just focusing on the formula, the activities were very effective in getting students to calculate the cost of the carpet needed for the party apartment. What will students wear to the party? What food will be served? How will the apartment be decorated for the party? These are questions the classroom teacher could use to set the stage for future mathematics tasks, depending on the intended objectives.
Via the two-way audio and video distance learning capabilities, pre-service teachers participated in a Q&A session a couple of days after the actual mathematics task was implemented with the fifth graders. During this session the fifth-grade teacher responded to various questions with explanations that clarified the reasons why things were done the way they were done. Based on actually observing the mathematics task, and on the reflection and discussion with the fifth-grade teacher, pre-service teachers were better able to understand the effectiveness of integrating the NCTM Standards.
Strategy Two: Pre-service Teachers
For the second strategy, the pre-service teachers met again in the television production room to observe another presentation to fifth graders. This time, however, four of their peers were present in the fifth-grade classroom, ready to implement their respective mathematics tasks. These written mathematics tasks, which were submitted by the pre-service teachers for review by the methods course instructor and the classroom teacher prior to the day of implementation, reflected the integration of NCTM Standards, and in particular, integration of children's literature.
The focus of the first mathematics task was linear measurement as it related to the length of the students' sh'es and their sh'e sizes. The task was initiated with a reading of the story, "Who Lost a Sh'e?" A connection was made to the classroom teacher's lesson on carpeting an apartment for an upcoming party. Students were asked which type of sh'e they would like to wear to the party in order to create categories for a graphing activity. This prepared students for a second graphing activity that resulted in two bar graphs reflecting data collected by the students as they measured the length of their sh'es and recorded their actual sh'e size. Students were asked to think if they noticed any relationship between the two graphs and to pursue a research project to determine how sh'e sizes were actually developed.
The focus of the second mathematics task was also on linear measurement, but in contrast, it related to the length of the students' arm span, height, forearm and right foot. This second task was initiated by reading the p'em, "Backward Bill." A connection between the p'em's content and calculator riddles provided a warm-up calculator activity for students, who were eventually asked to find the average length of the arm span, height, forearm and right foot of the members of each group in the class. Using the groups' data sheets of individual and group measurements, students completed a class chart of the data. This was used to help students see the patterns and relationships between the resulting dimensions.
Reflection sessions took place a couple of days after the implementation of the two mathematics tasks to give all the pre-service teachers, the methods course instructor and the classroom teacher an opportunity to discuss those aspects of the mathematics tasks that were perceived to be effective and those that could have been enhanced with techniques suggested by participants in the reflection sessions.
Conclusions
Upon completion of the two strategies within the context of the elementary mathematics methods course, several conclusions were drawn. Since the course began with numerous in-class discussions regarding NCTM Standards, the project enabled the pre- service teachers to see -- in the real world -- how the Standards can be effectively integrated in a fifth-grade classroom, and to understand the role of the teacher in a Standards-integrated classroom. Pre-service teachers saw how a problem-solving situation with which students could relate provided an opportunity for students to use a manipulative model (a paper square foot), prior knowledge (population density and square miles), a facilitating teacher (demonstrating procedures and asking guiding questions), and technology (calculators) to determine a solution (cost of the needed amount of carpet for the party apartment) to a problem. The implemented mathematics task provided an explicit model for the pre-service teachers as they compiled their mathematics tasks that needed to reflect NCTM Standards. Only four pre-service teachers served in the role of the classroom math teacher during the project; the others participated as observers during team-taught presentations. These presentations of mathematics tasks by the two teams of pre-service teachers provided an opportunity for all present to see and reflect upon the effectiveness of the tasks when implemented with actual youngsters -- a significant difference from the remaining pre-service teachers who implemented their tasks with their peers in the mathematics methods classroom.
Future Distance Learning Strategies
The ultimate goal of this distance learning project was to enhance pre-service teachers' understanding of the role of the elementary mathematics teacher. Included in our future plans is a third distance learning strategy. NCTM Standards-integrated mathematics tasks will be implemented by pre-service teachers in the university television production studio while elementary students participate in the activities in their classroom. It will be of interest to determine if pre-service teachers will be able to effectively facilitate the activities via the two-way audio and video capabilities, rather than from a physically approachable distance. As this distance learning project (hopefully) evolves at East Stroudsburg University, participants will continue to monitor its value within mathematics education.
Denise LePage, an assistant professor in the School of Professional Studies at East Stroudsburg University, teaches mathematics methods courses to pre-service and inservice teachers, and a research course to graduate students. She holds a doctorate in educational technology from Lehigh University. E-mail: [email protected]
References:
- National Council of Teachers of Mathematics, (1989), Curriculum and Evaluation Standards for School Mathematics, Reston, VA: NCTM.
National Council of Teachers of Mathematics, (1991), Professional Standards for Teaching Mathematics, Reston, VA: NCTM.