ACTION RESEARCH - TEACHING MATHEMATICS WITH PROJECTS

Paula Rasokas

The autumn of 1997 brought new experiences to the elementary teachers of Ontario. In 1995, the newly-elected conservative provincial government repudiated the Common Curriculum for Grades 1-9, introduced between 1993 and 1995 by its social democratic predecessor, and began to develop its own Ontario Curriculum with grade-by-grade learning expectations in each subject area. The Ontario Curriculum: Grades 1-8, Mathematics was released in 1997. Along with a new Ontario Report Card, it required teachers to evaluate their current practices and make changes.

My colleagues and I found the Mathematics curriculum to be daunting. Not only did all of the strands of Mathematics have to be taught each term, each strand had to have its own mark on the report card. (The strands identified by the Ontario Curriculum for Mathematics are: number sense and numeration; measurement; geometry and spatial sense; patterning and algebra; and data management and probability.) We spent time, early in the first term, discussing how best to teach and assess each strand effectively within the time constraints of a single term.

Initially, my personal approach was to keep doing what I had always done. I had taught Mathematics for years and not only enjoyed it but felt quite competent in the subject area. I had always taught all of the strands in a single term, allowing time to re-visit concepts throughout the year. I had not been using a textbook for a long time but instead focused on a thematic approach to Mathematics, relying on my school board’s curriculum for Mathematics, as well as children’s literature and my students’ real life experiences.

I had planned the Mathematics program by identifying a theme that was consistent with the subject matter in other subjects, generally Social Studies or Science. By studying the Ontario Curriculum I identified expectations to be addressed in an orderly fashion. My time lines allowed about one week to introduce, apply, and assess a specific expectation, or at most two expectations. Thus, each week there was a particular focus in Mathematics that related to content in other areas. For example, when students first arrived in September the classroom theme was "Getting to Know You." Therefore, the activities in Mathematics focused on measurement in meters and centimeters of hallways and classrooms as students "got to know" the school.

Identifying My Research Questions

The problem I was encountering by the end of September was that I was not addressing enough expectations in a timely fashion. I knew that I would run out of time in the year before we had addressed all of the required expectations for Grade 5. As well, it was clear there was not going to be enough time to allow us to revisit particular expectations to enable the students to reinforce their learning over time.

I no longer felt confident about what I was doing. I began to feel that I was rushing the students through the activities and concepts just so that I could check them off in the curriculum. I was feeling pushed to get enough done in a single class and felt that at the end of every week I had definitely not accomplished as much as I should have. This may have been due to my own heightened awareness of the need to be able to explain every student’s performance in every strand, or it may have been the result of general anxiety around this issue in the school as a whole. Regardless, if I was feeling this way, I reasoned, the students could be sensing my anxiety and feeling stressed too. It became clear that I needed to be doing something differently.

Hence, the idea of using projects was born. In fact, this was not a new idea. I had taught using Mathematics projects before, but I had thought of them as a way to connect learning in Mathematics to learning in other subjects. Now I wanted to connect learning in different areas of Mathematics to real life experiences the students were having outside school. I also wanted to teach in a meaningful way that would allow me to work with individuals who needed special attention and also provide opportunities for students to work at their own pace. More importantly though, I wanted to be able to relax and enjoy teaching again. If I could have enthusiasm for the work, I felt the students would as well.

My research questions became:

• will teaching Mathematics using a project approach enable me to develop and evaluate students’ skills, in all the strands of The Ontario Curriculum, efficiently each term?
   
• will this approach lead to a more relaxed pace in the classroom for me and the students?

Beginning to Work with Projects

In beginning my work with projects I set a few goals for myself. A project had to:
 

1. address every strand, and include problem solving
    
2. meet provincial learning expectations for Grade 5
    
3. provide the students with enough experience in a strand that I could use the project as an evaluation tool of a student’s abilities in that strand.

As it was October when I began planning my first project, Halloween seemed to be a likely motivator for students. I developed a series of seven activities connected to different aspects of Halloween. The activities were as follows:

1. estimate, then calculate the cost of all the Halloween candy they would be giving out at their own homes
    
2. plan and draw a route of a specified distance, on a map of their town, for trick or treating, using the scale on the map
    
3. determine the probability of receiving different ghoulish items described in a Halloween poem
    
4. given a variety of candy boxes, determine area, perimeter, and volume of rectangular prisms
    
5. look for, and write equations for, mathematical patterns related to the numbers 31 and unlucky 13 ( two activities)
    
6. estimate, then measure, the mass of popped and un-popped popcorn.

The students were pleased with the idea of the projects when they were introduced on the first day. They liked the Halloween connection and they liked being able to work on any activity they chose, at their own pace. The time-line for completing the activities was two weeks of class time.

Unfortunately, a political protest by teachers against changes to the Ontario education system being made by the provincial government began soon after I introduced the project. Therefore everything was delayed by two weeks. When the protest was over so, unfortunately, was Halloween. Nevertheless, we persevered to complete what we had started. It soon became clear that we would need more than two weeks of class time to complete the activities as many of the students found them more challenging than I had thought they would.

When we finally finished the project, I was as tired of it as the students were. In their Mathematics Journals, the students expressed their initial pleasure at working with projects because they liked the sense of freedom allowed by being able to choose the pace and the order in which the activities were completed. They also liked being able to choose whether to work as part of a small group of two or three or work individually. Further, they expressed the sentiment that they were tired of the topic and felt the project had been too long. From my point of view, however, I was pleased that we had addressed 19 different expectations in 3½ weeks of class time. While this project had not been perfect, it had enabled me to teach a greater quantity of material in a relatively short period of time.

Experiencing Increased Success

Believing the project concept to be a good one I tried it again, making some changes for improvement. My second project connected to the theme of "Christmas Around the World". Again, the students were pleased to begin work on the project. In their Mathematics journals, they cited the same reasons as before for enjoying the project but this time there was the added bonus that the Mathematics project involved a mapping component which helped them complete a project they needed to do for the Environmental Studies teacher.

This time I only included five activities, allotting the same two-week period for completion. Further though, I gave the students a good idea of the length of time I thought they should spend on each activity to allow them to be finished within the two- week time frame. The students commented that they appreciated this guidance. The activities again incorporated all of the five strands of Mathematics and were broad enough to allow me to use the project as an evaluative tool for each student’s skill level within each strand. We were much more successful in the completion of this project in that the students were able to complete the work on time and were still enjoying the work even when they got to their final activity.

I was much more pleased with this project as well. Entries in my own learning journal reflected the growth I felt we were experiencing as a class. Throughout the two- week period I felt I had time to circulate and work with individuals as they needed help and to observe all of the students as they did their work. This gave me valuable insights into the needs of each student. I also felt more relaxed each day as the students worked, knowing that appropriate concepts were being developed and at a reasonable pace. The Christmas project addressed 12 expectations in the two week period. Again, this was a significantly greater number of expectation than would have been addressed if I had maintained my earlier pattern of 1 - 2 expectations per week.

The third and most recent project I completed with the class was about the Olympics. This seems to me to be my most successful project to date. The students were motivated to complete the activities because they were all following the progress of the Olympic athletes, especially the Canadians. As well, the results of the timed events provided many real life examples of the uses of decimals, which was the main focus of the project.

Perhaps the biggest difference between this project and the others was that there was a greater mix among individual, small group, and large group activities. While the students liked working at their own pace, they also appreciated working with the whole class on some of the more challenging activities. I also included some experiments related to mathematical concepts connected to the Olympic games. The students enjoyed performing these. Finally, the activities required the students to find their own data in the newspapers. This proved to be very motivating in that, by choosing their own data, students could choose how challenging to make their number work. This project included five activities and all of the strands, some of which were included in more than one activity. Some activities required skills in more than one strand. We completed the project quite comfortably in two weeks of class time.

Data Collection and Analysis

In consideration of my work over several months I have revisited my learning journal, the journals of the students, and notes I kept as a record of ongoing conversations with a colleague who was also teaching grade 5. I reviewed my evaluation of students’ projects and class tests. I also analyzed the checklist of expectations I kept throughout the year. Each expectation was checked off and dated when it had been addressed in the classroom. The checklist clearly showed the time lines needed to meet the requirements of the curriculum.

Findings and Conclusions

When the students were working on projects, we were much more efficient in the time it took to work through the expectations than we had been before the projects were introduced.

The Ontario Curriculum describes four levels of achievement for students. Level 3 is considered the standard for each grade. In terms of student learning, the majority of my students demonstrated consistent achievement at Level 3, with a few students achieving at Level 4 and a few at Level 2. While these assessment results were what I would have expected in a more traditional approach to teaching, it was clear that using projects was not negatively influencing student achievement. Therefore, it seems reasonable to continue to use projects in the Mathematics program along with whole class instruction. I will continue to base homework assignments, Family Mathematics activities, and practice/drill activities on project work.

In conclusion, I have learned that the following factors seem important in the development and implementation of Mathematics projects:

1. the theme of the project needs to be interesting to the students and this is most easily accomplished by focusing on a topic that involves the students’ out of school experiences.
    
2. five activities in one project seem to be optimum. This permits all of the strands to be covered, at least once, but does not take so long to complete that the students get tired of the project.
    
3. a combination of whole group, small group and individual activities seems to address students’ needs to work at their own pace but also interact with others in the development of new skills.

My goal for future work with Mathematics projects will be to involve the students more in the planning and implementation of each.

References

Burns, Marilyn. (1992). About Teaching Mathematics: A K-8 Resource. Sausalito, California: Math Solutions Publications.

McNiff, J. (1993). Teaching As Learning: An Action Research Approach. London: Routledge.

McNiff, J., Lomax, P., & Whitehead, J. (1996). You and Your Action Research Project. London: Routledge.

Ontario Ministry of Education and Training. (1997). The Ontario Curriculum: Grades 1-8, Mathematics. Toronto: Ontario Ministry of Education and Training.