Rationale
As a new teacher, and very unfamiliar to the concept of action research, formulating a question was most challenging. My question has changed many times since I initially decided to conduct this research. I think it is important to understand my thought process prior to my actually introducing you to my research question.
Becoming a seasoned combined grade teacher was not my life goal as a teacher. I envisioned myself bouncing from one side of the classroom to the other, trying to ensure that all students were working on their assigned tasks. All the while, I kept trying to keep firmly implanted in my mind, the intended expectations that each of the grade levels was to be achieving. THIS DROVE ME CRAZY! I decided that there must be a more effective way to teach a combined grade. More important, there must be a more student-oriented program that could address the individual needs of each set of learners. I needed to look at the overall picture, keeping in mind a couple of goals:
- I wanted to maintain consistent assessment tools among both grades.
- I wanted to use one theme to accomplish many expectations through integration across the curriculum.
- I wanted to provide my student with the necessary strategies essential for becoming good problem solvers.
My initiation into combined grade teaching was during my first year at Port Rowan. I quickly realized that this experience was going to be very different from my experiences teaching in a solid grade during my practice teaching. The diversity of learners and the time of year made it virtually impossible to make any drastic changes. It did, however, present me with a very clear question, that being; "What could I do to address the learning needs for students in both grades?" As I pondered this question, it became very clear that I needed to find some commonalities between the two grades that I was teaching. For the purpose of this research, I focused my attention to the area of mathematics.
During the summer of 2002, I was determined to plan and implement a math program that would address the individual needs of my grade two and three students. Rather than looking at the unending number of expectations that were to be addressed from the Ontario Curriculum, I decided to pinpoint the components of a good math program.
I initially sectioned my planning into the four areas of learning. These areas were clearly outlined in the Ontario Curriculum. I rearranged the components in an order that best fit my teaching style. These components were:
- Understanding key concepts
- Application of mathematical procedures
- Problem Solving
- Communication of required knowledge.
Once I had a clear framework, I needed to look at the curriculum to see if there were any connections between the two sets of expectations. I knew that there was no possible way that I could cover the number of expectations that were outlined in the current documents. As I filtered through the five strands of math, I was very relieved, and pleased, to find that many connections existed between the grade two and the grade three curriculum. This knowledge just reinforced my belief that a unified program could be implemented and would produce success for both sets of learners if culminating tasks targeted each specific grade.
So, the next step for me was to devise and adopt effective pedagogy that would cover the necessary math expectations for this specific group of students. Once again, I reverted back to those learning needs mentioned before.
During my second year of teaching, I used my knowledge of the essential components outlined in the Ministry Document and the specific strands of math to design very task-specific, theme-related jobs. As an organizational tool, I designed a thematic template to keep track of the levels of achievement and the strands that I was targeting. For each thematic unit, I planned specific jobs that were oriented to not only these achievement levels, but their corresponding math strand. Although my planning was clear to me, implementation of the theme jobs , with these kinds of goals, was confusing at best (not just for me but for the students to.)
I wanted to know why this wasn't working. I thought that if I gave the students concrete materials to use for specific tasks, and very specific targets; they should gain the conceptual knowledge necessary for achievement. However, it didn't work out that way. According to my teaching journal, I noted that students often were found wandering from task to task without finalizing anything. Other notes indicated that children were constantly stating, "I don't know what to do." I had followed the common schema for gradual release (Model-Share-Guide-Independent). Once again, I needed to rethink my practices.
In the fall of 2002, I decided to turn to current research and practices for teaching math. I wanted to know how other teachers were teaching math and what was important to teach them. I came across a book titled, Helping Children Learn Math. It was through this material that I was finally able to formulate my question. "Can children of combined classes become good problem solvers if they are given a fixed framework with which to practice problem solving skills?"
This reading material confirmed that my goals were realistic. However, the authors offered teachers a more constructive achievement paradigm. Kilpatrick and Swafford, 2002 guidelines were as follows;
- Understanding: Comprehending mathematical concepts, operations, and relationships -- knowing what mathematical symbols, diagrams, and procedures mean.
- Computing: Carrying out mathematical procedures, such as adding, subtracting, multiplying, and dividing numbers flexibly, accurately, efficiently and appropriately.
- Applying: being able to formulate problems mathematically and to devise strategies for solving them using concepts and procedure appropriately.
- Reasoning: Using logic to explain and justify a solution to a problem or to extend from something known to something not yet known.
- Engaging: Seeing mathematics as sensible, useful, and doable-- if you work at it -- and being able to do the work.
I quickly realized that this was exactly how I wanted to teach my students math. After a careful comparison, I realized that these goals were very similar to the criteria that I had been using the previous year. However, there were clearer guidelines for student learning and teacher planning. I set out to design a math program that would embrace these five areas.
I began to work with another teacher on staff to provide a mentoring type program that would allow students opportunity to experience hands on learning. I knew, through my past experiences with "Reading Buddies", that this type of tutoring gave children the necessary confidence to succeed. I believed that similar results would occur in a "Math Buddy" situation.
Children would learn concepts through the Model stage of gradual release. They would then have opportunity to be guided by their mentors through these same concepts. During specific timetable slots, children would be given occasions to share their learning prior to performing their independent tasks.
The road to math mentoring was a rough one. The older students often viewed it as one more additional responsibility. One of their first responses was, "Why do we have to teach these kids. That's your job!" It took many weeks to help the older students to realize that they were affecting how their younger counterparts viewed themselves as math learners.
At this point I needed to back track a little. I set up a time slot to go into the Grade 8 classroom to address some concerns that were present:
- What skills had their buddies developed?
- What was expected of them as a mentor? and
- What were they going to gain from this experience?
During each session, I planned activities that incorporated Kilpatrick and Swafford's learning needs. At the end of each session, both groups of students were expected to record a journal entry that reflected on their individual ability to understand, apply, compute, reason and engage in the given task. Each guided task was assessed in the following areas:
- Neatness
- Meeting the established expectations
- Use of mathematics and mathematical terms.
Did Students Meet Intended Objectives of this research project?
The onset of this research project was very difficult. There were many challenges to our getting started. Cooperation between the two groups seemed to be the first obstacle.
It was now time for them to attempt their second task.
I found the best way to depict what was occurring during a mentoring session was to keep a photo journal. What follows is an excerpt from my journal.
The second task consisted of both students working cooperatively to design a game board for the theme Endangered Species.
Students were given a very clear outline of mathematical expectations for this project. I was able to observe that students were working more cooperatively through this task.
Students discussed many options for accomplishing the task. They were discussing who would do what part of the project. I observed students discussing the size of the board that criteria had outlined.
