Collaborative Manipulative Mathematics Research: Teacher Role

Lillian Forsythe and Vi Maeers

In implementing Saskatchewan's new mathematics curriculum for kindergarten to grade five, Forsythe, an experienced primary mathematics teacher, recognized that much was left up to the teacher in actually enacting the curriculum in the classroom. She saw a need to define or articulate her role and to determine how she could maximize student learning using a manipulative mathematics approach. She found collaborative support in Maeers, a member of the Faculty of Education at the University of Regina, who agreed to act as an outside observer documenting Forsythe's role in classroom mathematics instruction. Together they began a two-year ethnographic study to identify what Forsythe does as a teacher as she implements a mathematics program in her grade one classroom.

Forty-seven grade one students were involved in the project over two years. They came from a variety of backgrounds and socio-economic situations and were a multi-cultural group. Their school was located in a middle-class area of an urban centre and provided educational opportunities to students from single-parent and two-parent families, upper middle class and economically disadvantaged households. The range of student abilities covered about a three-year span, although all the students were in grade one. There was a slightly higher than average mix of males to females in this grade grouping.

Forsythe began the research project by defining her personal beliefs about children's learning, mathematics and teaching, and then reading and reflecting on the research literature in these areas. Having established a theoretical base for the project, she used videotape, collaboration with the local university, parent interviews and feedback, journal writing and reflection to gain insight into the role of the primary mathematics teacher. Students were actively involved in the project, not only in doing mathematics, but also in self-evaluation, math journaling and math IMPACT homework. Excerpts from student work were used to validate Forsythe's observations, anecdotal notes and journaling and the research field notes of her collaborative partner. The question of teacher role was researched through the eyes of parents, students, the teacher and a university mathematics educator.

From the data collected, Forsythe and Maeers drew common phrases and ideas. They then identified and organized common themes around four main areas: the student, the teacher, the curriculum and the milieu. The themes in these areas were described and explained in both a written report and a video entitled Thinking Mathematically.

Forsythe and Maeers acknowledge that their effort to identify critical factors in the teacher's role only "highlighted how many factors impinge on each classroom and teacher," making it "unlikely that this study is generalizable to other clasrooms." Nevertheless, they believe a similar analysis could be used by other teachers, with results emerging in a variety of ways dependent on individual classroom dynamics. They note that similar studies would be useful in examining consistency of certain factors in the classrooms of teachers of mathematics whose programs appear to be successful.

Above: Math is fun!

Above: A student and a parent comment on math experiences.

Lillian's Story: The Journey of a Primary Mathematics Teacher

A journey may be described as travel from one place to another, usually taking a rather long time, or passage or progress from one stage to another. Either definition applies to my personal journey in the primary mathematics field.

I began teaching primary mathematics over twenty years ago much like any other teacher, using the prescribed workbook and my newly acquired knowledge of teaching theory. Working within time constraints as a new teacher, seldom was the curriculum consulted, since it was assumed the approved program for that school system covered the required material. That lasted for a number of years, but gradually I added to the workbook mathematics: I set up learning centers; I made up mathematical games; I tried using "found" materials to vary my teaching approach and make mathematics more fun. I was on a quest or journey that I did not totally understand but which kept niggling away at my thoughts about mathematics and student learning. During this time I had the uncomfortable feeling that I was doing a disservice to children and the mathematics subject by simply working rather blindly through a series of pages until (whether independently or with one-on-one help) each page was completed and clipped. I knew intuitively that there was more I should be doing to help children really understand mathematics and be able to apply that knowledge to new situations.

Some ten years ago, with administrative support, I stopped ordering workbooks and began the use of a truly manipulative approach to teaching primary mathematics. I had my curriculum, access to a number of mathematics programs, but most important, the desire to build children's mathematical understanding by having children work first with concrete materials and then record what they had learned.

It is important to underline the role of administration in my journey through the change process and my growth as a teacher. My principal served as mentor, encouraging the change process, supporting my attempts to mesh my beliefs with practice, and discussing with me the successes and pitfalls of that practice as I implemented my "workbookless" mathematics. At the system level I worked with superintendents who were willing to listen, to support my efforts and foster change by providing assistance and approval. A new journey was underway! I enriched that journey through graduate classes to affirm my understandings of how I thought children learned, and to build a stronger theoretical basis for the judgments I was making. I continued to read professional literature to inform my practice and gradually modified and extended my instructional strategies through daily reflection on classroom happenings, documentation of occurrences and refinement of management and teaching techniques.

As my confidence grew and I found that mathematics really was fun for the children, I built in children's self-evaluation and more co-operative work. Over the last five years I have added a parental component so that parent and child working together could keep abreast of what we were learning in mathematics and apply that knowledge beyond the classroom walls. Not yet totally satisfied I now undertake further research...

This research affirmed many of my beliefs about children's learning while enhancing my perception of myself as a constructivist teacher - one believing that chldren construct their own knowledge through multiple experiences, that children need both autonomy and direction, that children's interests, curiosity and abilities should be considered in planning, and that children should be equal partners in the teaching-learning process. My appreciation of the role of parents in education was again affirmed, as was the importance of having students play a role in planning for instruction and assessment. Integration and extension of mathematics activities in and beyond the school shone brightly as I analyzed data from all sources.

Conclusion

The study highlighted some of the factors which are important to the teacher's role in the mathematics classroom. As documented by Forsythe and Maeers, the following factors were critical:

• Students were engaged in building mathematical understanding through hands-on, experiential learning. Curriculum was seen as an active, lived experience rather than a document.
• All players were involved - students, parents and teacher. Collaborative, interactive learning promoted a positive view of mathematics and helped students make the connections and apply their knowledge beyond the classroom. An effort was made to meet individual student needs through activities, interactions, extensions and reinforcement.
• Parents were involved through parent evenings, communications and Math IMPACT so that they communicated with their children about mathematics learning and had an appreciation of the approach to mathematics in Forsythe's classroom.
• Students became a Community of Learners working together in a classroom environment that supported risk-taking.
• Mathematics was made "fun" and interesting so that students developed a positive attitude towards it.
• Students had opportunities to extend their learning beyond curricular expectations through mental math, estimation, problem-solving, and the setting of high expectations for student learning and classroom work.

Above: Lillian Forsythe works on math with her students.