AN ACTION RESEARCH PROJECT ON IMPROVING STUDENTS’ WRITTEN COMMUNICATION IN MATHEMATICS
George Neeb, Grand Erie District School Board, May 2000
My research question was, "What can I do to improve students’ written communication in Mathematics?"
Introduction
I was concerned when the students at my school obtained the lowest results in the Mathematics section on 1998-99's Grade 6 Provincial Assessment. Upon analysis of the sub tasks, I found that one of the poorest results was the students’ ability to communicate understanding in Mathematics.
1998-99 Mathematics Results
Percentage of Students Achieving a Level 3 or 4
Problem Solving |
13% |
Understanding Concepts |
13% |
Appplication of Mathematical Procedures |
26% |
Communication of Required Knowledge |
13% |
Although problem-solving and understanding of concepts were also weak, I concentrated on communication because it is embedded in all the scores. I was also concerned that, because the provincial assessment is written, students who have trouble with writing are not being assessed accurately on their mathematical ability. Most of my students are stronger orally and the test demands high levels of writing to explain reasoning.
"It is easier to say it verbally. In math I can never think of what to write." Student
In the past, I had never thought of written math responses as needing the time and dedication of language skills. I felt students should just write a response and move on, without really thinking of ways to teach them to do so. I do believe that students need to improve their understanding of math concepts, but I also believe students have much knowledge that is already there but not showing up in the test results. Students need practice and encouragement in sharing in the written form. I decided I would try to teach students to write math responses the way I teach them in Language using a writing process. In essence I borrowed a "Language" technique to apply to mathematics. This strategy is a form of integration on my part.
Methodology
Under the guidance of Diane Morgan, Educational Consultant and James Ellsworth, Curriculum Coordinator, and as part of an action research group, I studied my classroom practice during 1999-2000. Data collection included student work samples, EQAO test scores and sub tasks, regular journal keeping, and videotaping class lessons. We were trained by Educational Consultant Ruth Sutton to use corrective feedback. With the support of Diane, James and critical friends in the group, I analyzed and shared my learning.
Procedure
I planned to develop ways to improve writing by coaching students to build on knowledge that was already there and use their oral ability as a starting point to written responses. I planned to motivate students and encourage them to help each other to feel more confident about writing the provincial assessment. This would be accomplished through the following strategies:
- use a process writing approach to solving math problems
- use corrective feedback (Sutton, 1997) with students
- explicitly teach problem-solving steps and strategies
- clearly outline evaluation expectations
- teach the required math terminology
- replicate testing circumstances in the classroom
Process Writing To Solve Math Problems
Commonly in my practice, I encourage them to talk over ideas with others (like prewriting), then write a response using a problem-solving model (drafting), then re-read their response (proofing), share their response with others (conferencing and corrective feedback), and finally, make any changes in ideas and edit for clarity (final draft). I encourage students to do more than one draft of their responses, just like authors do several drafts of stories.
"Conferencing with others about my math answers helped me to notice my mistakes and help others." Student
Corrective Feedback
Although students were using corrective feedback (Sutton, 1997) in their conferences, I think it is still important to discuss it directly here. Students need to be taught how to help others improve their work and teachers need to understand the importance of this skill and how to use it effectively. I taught students to focus on making two statements to the writer: "You did well...." and "You could improve your answer by...." I reinforced repeatedly that telling someone their work was "good" or "excellent" really does not help them. Everyone can improve in some way. I would always have my students use a conferencing sheet to evaluate how well the stories they were sharing met certain requirements. Students had to staple this formative evaluation onto their stories when they handed in drafts for me to read and I encouraged them to use this feedback to revise their stories before handing them in. I thought this sheet would work for math responses so I had the class help me decide what we should look for in a question. They came up with suggestions and, over time, we realized that there was a standard practice to writing a complete math response.
Problem-Solving
Then I found an actual "Steps for Math Problem Solving", GEDSB document which we used as a basis for our model, conferencing and feedback form. These were the steps:
Explicit Evaluation and Practice Tests
Students need to know how their responses are being evaluated. In class, I always have rubrics ready before the students start on an assignment so they know what I am looking for in a Level 3 or 4 answer. Using the overhead, I showed students the actual rubrics for the provincial tests. Although the rubrics are very general, we had a lengthy discussion on what each section meant. When we took up the practice tests together, I modelled responses based on the rubrics sent by EQAO and clearly identified why I was doing what I was doing in the response.
Findings and Conclusions
Students need to buy into the importance of written communication in the test setting (and the importance of the skill in everyday life). One way was to leave Mathematics and discuss the Reading section of the provincial test. I asked students to explain how they thought they would receive a reading score. Most assumed they would be reading to someone. I explained that their reading score was based on the writing they did about the story they read, the reasons why we have been doing response journals all year! This helped them see that writing was clearly important.
Students need to be prepared to answer questions independently. It is important for them to realize that they will not have the corrective feedback they had in the classroom on the provincial test. In the third term, I gradually removed the conferencing option so students would solve the problems more independently.
Students greeted the writing process approach to math with enthusiasm. The class was unanimous in agreeing this not only made math journalling more fun, but it actually did help their mathematical understanding. A few said it helped them to clarify their ideas and make their responses better.
"I liked conferencing with others about my math answers because I got to see what other people thought of my work before I handed it in." Student
Summative Evaluation
Even if the conferencing and sharing only made math more enjoyable, it was still a help because I believe the more enjoyable the experience, the more effort will be put into it. My own practice of corrective feedback to students has improved this year. I feel more confident giving students strengths, weaknesses, and next steps comments with marks being optional. This formative approach helps students see how they can improve as opposed to just receiving a mark and ignoring the comments. I still use summative evaluation but with corrective feedback in mind, and I give students opportunities to improve their work after they have received the feedback.
In working independently in third term, I found many students still did as well in their responses because they could conference alone, using the corrective feedback ideas discussed in class. Students were re-reading their responses, going through the "Steps for Math Problem-solving" independently and also revising and editing. Some were even doing second drafts.
I videotaped students hard at work and conferencing, using the camera as my eyes. Usually I was quiet, just observing, sometimes asking questions. This gave me a wealth of information about my students. When I viewed the tapes later, I found I was seeing things I had not noticed (who was working with whom, who was more on task, who was giving helpful advice). I could also listen to my own questioning and see how students were responding to me. I then showed the video to them. This offered us a process for formative student self-evaluation, teacher-student evaluation, and teacher self-evaluation.
I have seen incredible growth in my students’ mathematical communication. We still have a way to go, but I believe I have implemented some techniques to help students that will become part of our everyday classroom programming
I had students give feedback on math this year. They made some powerful statements about their own learning:
"Problem-solving is my favourite part of math because it is both fun and challenging."
"I find it easier if I have discussed the problem rather than having to do everything in my head."
"I have improved in problem-solving. When I first started I was bad at it. Now it’s my favourite part of math. I don’t know how I improved, I just did."
Our school results are in from last year’s Provincial Assessment. I have only analyzed the data from the Grade 6 students that I taught last year. I have compared the data to the previous year’s scores (mentioned above - none of these students I taught). I am happy to report an increase in communication (and all mathematical scores).
Comparison of Mathematics Results
Percentage of Students Achieving a Level 3 or 4
1998-1999 |
1999-2000 |
|
Problem Solving |
13% |
34% |
Understanding Concepts |
13% |
26% |
Application of Mathematical Procedures |
26% |
46% |
Communication of Required Knowledge |
13% |
25% |
Concluding Comments
Again, with the support of James Ellsworth, I am continuing my research during 2000 - 2001 to see if I can sustain my learning and continue to improve student learning and achievement. I am presenting my research at the Ontario Educational Research Conference in December 2001.
I continue to work towards improving student communication in mathematics, and strive to include corrective feedback strategies in all areas of my program.
Reference
Sutton, R. (1997). The Learning School. Salford: RS Publications.
Bibiographical Note:
Name: George Neeb
Current Position: teaches Grade 6 at North Ward Public School, Paris, ON.
Academic Background: BA Psychology McMaster, Hamilton, ON, BEd, Western, London, ON, Masters of Arts in Teaching, McMaster
Areas of Interest: member of ETFO, member of Community Builders focusing on building an inclusive community in schools, enjoys Visual and Dramatic Arts
Mailing Address: 33 Lincoln Ave, Brantford, Ontario N3T 4S6