Abstract

For this project, I was interested in implementing strategies that could help my grade 3 French Immersion students improve their communications skills in math. This is an area of weakness for my students because the math program is delivered in French, which is their second language. The previous year's class had performed poorly on standardized tests and I wanted to prepare my students and help increase their results on the test they would be writing. I used a variety of strategies throughout the year including implementation of math journals and a math wordwall, using open-ended investigations, assigning homework based on language taken from previous year's tests and having students perform activities from previous years tests. I also allowed and encouraged my students to discuss their thinking and provided opportunities for group work. Throughout this study, I also questioned the validity of continuing the use of French within the math program and provincial testing and have included some of my thinking and findings on this topic.

Background/Context

I currently teach in an Early French Immersion program which "offers students the opportunity to learn French through other subject areas and to enhance their skills in an intensive program. Children receive all or most of their instruction in French from a teacher who speaks the language fluently." (GEDSB website, April 15, 2003) Note that this is a program that is designed for English-speaking children. When I began teaching grade 3, the class I taught received 80% of their instruction in French, including all curriculum subject areas except for 1 hour per day of formal English Language Arts instruction. In January of the school year, I began to instruct the mathematics portion of the curriculum in English in preparation for the Education Equality and Accountability Office (EQAO) Provincial testing that would take place in May, as the students would be writing the mathematical component of the test in English. The decision to do this was made because in previous years, grade 3 students from our school had performed poorly on these province-wide standardized tests when they were done in French.

In the Spring of 2001, I was a member of an Immersion Committee that reviewed the conducting of grade 3 provincial tests within the Grand Erie District School

Board (GEDSB). The Ministry of Education offered 3 options for grade 3 French Immersion students and it was our mandate to discuss the strengths and weaknesses of each option. We would then report back to the board that would decide on the option all GEDSB French Immersion students. The available options were (and are still currently):

Option A: Students complete all components of the assessment in English.

Option B: Students complete the reading and writing components in English and a French translation of the mathematics component of the English-language assessment.

Option C: Students complete only a French translation of the mathematics component of the English-language assessment. (These students do not complete the reading and writing components and will only receive results for mathematics.)

From 1998-2001, our students had participated in Option A. This allowed some noted improvement in results. By 2000-2001, 58% of grade 3 students at our school achieved level 3 or 4 on the assessment (met and exceeded the standards set in the Ontario Curriculum documents respectively), which was up from only 7% in 1997-1998. In 2001-2002, the GEDSB had decided to participate in Option C. When I returned to teaching grade 3 at Dufferin French Immersion School in 2002-2003, after taking a year maternity leave, I learned that my students would be completing Option C of the test as well, which meant only writing a French translation of the English Mathematics test. I also learned that the results from 2002 had only 16% of students achieving in levels 3 and 4. I was concerned and I wanted to help the students I was teaching do better on the test in 2003 and to improve their overall results in a math program that was being conducted in their second language, French.

Finding a Question

When I began this project, I thought I was focussing on using a math journal as a regular part of my math program. As the project unfolded, my question developed into more of what I could do to help my students prepare for the standardized tests they would be taking in May of the school year and the math journal became only one vehicle to facilitate this improvement. My question became; How can I help my students improve their math communication skills in a second language and thus increase their achievement on provincial standardized tests?

Gathering and Analysing Data

During the early months of the school year, I began using a math notebook with my students on a regular basis (once or twice a week). We used this book more as a dictionary or reference book, writing terms and definitions relative to our topics of study. After some discussion, I would write an agreed upon definition on the blackboard and ask the students to copy the information into their notebooks. After 1 month, I asked the students to study the information and gave them a quiz on October 4. Although this seemed like a good starting point, I quickly realized that the students were studying the terms and language for the test but they needed some practical applications to consolidate their understanding of the information. Results were good; 69% of students achieved at levels 3 and 4, but what about the other 41%? Some students seemed confused by the format, which included matching up definitions and terms, while others lacked experience reading and comprehending instructional vocabulary in their second language, which negatively affected some of their results. Therefore, the quiz did not seem to serve as accurate data to show whether the students' communication skills were improving but it did give me a baseline to understand how my students learned best, their ability to work and comprehend independently and their test-taking skills. This coupled with new information I learned through attending in-service on math literacy and math journals helped create a gap analysis, which led to the next phase of my research.

After reevaluating the format of the journal, I decided that I needed to add more higher level thinking questions that involved problem solving and required students to communicate their thinking using pictures, numbers and words as this would be required on the EQAO test. I re-visited the resources available and began to use activities from: Intéractions, Ontario Maths - Cahier 3, Linking Assessment to Curriculum in Mathematics and Quest 2000 Problem of the Week (used as homework since it is in English). I also re-structured my program delivery. I began using a shared, modelled, guided and independent approach. We looked at 2 areas of the mathematics curriculum in November: identifying and explaining pattern rules and drawing and writing conclusions about bar graphs. We spent time developing answers together as a class, where I was able to model some appropriate language frameworks for the students to use when responding in their journals. I then created a wordwall to display vocabulary that students could use in their own math writing.

The wordwall was divided by strands (the five strands or areas of emphasis in our math curriculum, which are: Number Sense and Numeration, Data Management and Probability, Measurement, Geometry and Spatial Sense and Patterning and Algebra). When students did work in their journals, they would bring it to me and together we would discuss what was well done in the response and what needed to be changed or added to improve the clarity and precision of communication. In mid-November, quiz time came and the students had an opportunity to independently recognize and write some pattern rules and read a bar graph and draw written conclusions about it. As I observed students working, I noted that some students who had shut down over written mathematical explanations in the past, were able to use the wordwall to find vocabulary to communicate information independently about the required task. The results of the quiz showed that 72% of the students achieved at the expected level or above in writing pattern rules and 88% of the students were able to develop some written conclusions about a bar graph independently. We were making progress and I planned to continue to use a shared, modelled, guided, independent framework as well as using the wordwall on a regular basis.

By November 27, I was feeling more comfortable using more open ended activities with my students and was seeing the value in using more group work in math. This approach was allowing me to see what my students were capable of from a new angle:

...I find myself trying all kinds of different activities to facilitate communication in math... I am allowing more time for discussion and analysis of completed responses. We are taking the time to discuss what a level 4 answer looks like and why. I am moving away from strictly pencil and paper tasks that demonstrate primarily understanding of concepts and I am including more problem solving and open ended activities, just the types of activities I shied away from in the past. I am taking more risks in my math program and with each new risk, the kids never cease to amaze me with how well they adapt and demonstrate learning.

We had been working on counting in a variety of ways. There were several events that opened my eyes to just how much "math knowledge" my students possessed. For example, Eric surprised me on two different occassions:

#1: When writing in his math journal about where it might be useful to count by 100's, he discussed with me how when we did our unit on measurement and measured the classroom in metres, we could have counted by 100's to determine the number of centimetres in that length.

#2 While working beside my desk, Eric overheard a conversation with another student and offered his "expertise". John was stuck on a counting pattern that counted by 25's that he was supposed to continue:

John: I don't know what to do.

Me: What do you do to 25 to make 50?

Eric: John, it's 25. You add 25. You take 20+20 and that =40. Take 5+5 and that =10. 40+10=50

John: Wow. He's smart.

Although John didn't understand what Eric was talking about, I learned a great deal about Eric's thinking. This was a turning point for me. I changed the way I looked at my math program and I decided to give students the opportunity to work together in groups to come up with a complete written response. Each group was given a basket of manipulatives and told to count how many were there by amounts other than 1. They were given an index card to record their answers on. The students worked fairly well together and were able to come up with consice answers that communicated the information mostly clearly in French. One group, who counted playing cards wrote: "141 cart. On a fet des grip de dix et on a conter par dix et il y a 141 cartes" (Translation: 141 cards. We made groups of 10 and we counted by 10 and there are 141 cards).

This aspect of the program facilitated oral communication and allowed students to combine ideas to prepare a complete written answer. This activity was highly successful:

"With the current unit we are studying, I have noticed that the children are referring to the definitions we created when completing assignments so they are using the information from their math journals to complete assignments. I also noticed that students are using words from the wordwall to complete tasks. They are communicating independently, even though it is still sometimes difficult for them to communicate exactly what they want to say in French. With the words we added to the wordwall this unit, students are writing about 3-D shapes using appropriate vocabulary. They are now comfortable with using the wordwall and are beginning to make connections between the definitions they are studying and the concepts they are studying. I continued to prepare similar activities for my students to work on."

I continued incorporating the wordwall, the math journals, group work and discussion as regular activities in the math program.

In mid-March, I began to introduce activities intended to specifically prepare students for the EQAO testing. I started by assigning homework that would help them become familiar with the glossary (or French-English dictionary). In order to facilitate the students learning the meaning of a variety of instructional terms, I developed an additional glossary that included instructional terms from the previous year's test (see Appendix A). Students were assigned 3 French terms each night and were asked to fill out the following chart with parental assistance (which is why the work was done in English. All but 1 student in my class come from English first language homes and would therefore need to complete tasks in English to receive parental support).

Word: Explanations using pictures, numbers and words:

Strand:

Translation:

This portion of the program started slowly, but as the students became more familiar with how to use a glossary, they were able to complete this easily.

I then began to use samples from previous year's tests to familiarize the students with the format of the test. When doing these activities, the classroom environment was set up as it would be for the actual testing. Students followed the same rules as for the actual testing: each task was time-limited and the only permitted teacher assistance was to ask to have any words on the page read to them (but not explained or translated into English by the teacher).Once again, progress seemed to be slow. Only 28% of the students performed at levels 3 and 4 and 50% of students left at least one question blank because they did not understand.

"April 9- After doing the first strands activity from last year's test, I see my students are still in need. Results were poor and several students left questions blank. When I asked the students what they found to be the most difficult, the general consensus was understanding some of the French words."

The tasks from last year's test were more difficult and labour intensive than those we had worked on previously in class. Once we went over examples of level 3 and 4 answers and students became more familiar with the style of questions, many of them were able to communicate more clearly. In fact, 39% of students were able to independently achieve at level 3 or 4 on the second task completed. Even though the achievement wasn't as good as I had hoped for, I was thrilled that there had been some improvement and that my students had independently used the wordwall and/or glossary to assist with vocabulary.

After several weeks of this, I sent home a questionnaire for the parents. One of the questions asked was "Do you have any comments or suggestions about the mathematics work your child has been doing at school and as homework to prepare for the EQAO Grade 3 Test?" 50% of parents responded, most with positive comments including:"I think you're doing a great job preparing the students...I commend you for your methods and your empathy for the students. I think it will ease the pressure somewhat on the students." "Excellent preparation." "The concept to practical format of the yellow books(glossary exercises) was well laid out. Mock tests, also are a great way for preparing the children for what to expect." I felt successful in achieving my goal.

Findings

During the EQAO testing, I was genuinely impressed with the quality of work students were producing. Although I did not mark the work, I was able to observe a great deal of what the students were writing. I noticed students demonstrating sustained task commitment, referring to the wordwall for appropriate vocabulary and using pictures, numbers and words to fully explain their work. I fully anticipate that the results will have improved from last year and am anxious to see the results when they arrive late this fall.

While completing this study, I found myself questioning and weighing two conflicting values: the integrity of second language learning in the Immersion program versus allowing students to learn mathematics in their first language to facilitate their understanding. I was able to have my students participate in some English mathematics activities during the year by working with GEDSB consultants, as their services are only available in English. I noted the change in attitude (more positive) and achievement (communication is more clear and precise) when students worked in English. I also noted that even when my students were working on French activities, their discussions amongst each other were always in English. In the Winter 2003 Curriculum Update presented by the Curriculum Implementation Partnership in cooperation with the Ontario Ministry of Education, there is an article summarizing the Expert Panel on Early Math report. This article lists several aspects to building and effective learning environment including "learning mathematics through talking, (and ...that) children should feel comfortable to take risks when trying to solve problems." From my observations in the classroom, I see that my students participate in and learn best form talking in English. They also appear to be more comfortable taking risks in mathematics activities when the language of discussion and response is English.

The EQAO wrote to the Modern Languages Council (dated February 24, 2000) and included a summary of French immersion students performance on grade 3 and 6 tests. This executive summary noted some interesting facts about Grade 3 performance on Provincial Testing across Ontario. The summary noted that:

"...the research literature suggests that knowledge acquired in French (in math, in this case) transfers and can be tested in English...." (Hart, Lapkin & Turnbull,, 2000, pg. iii)

It is also noted that:

"The results offer virtually no support to the argument that testing in English (in mathematics) disadvantages immersion students, at least in comparison to testing in French translation, even though instruction in mathematics up to Grade 3 has been in French." (Hart, Lapkin & Turnbull,, 2000, pg.vi)

If this is the case, I feel that whether the delivery model of the program is in English or in French, the students will be able to succeed when writing the test in English. Why not give them this opportunity since the have a much greater vocabulary base and ability to communicate in English?

I believe that in order to keep up with increasing demands of the Ontario Curriculum, students need to be exposed to mathematical language in English. As the new curriculum and the test unit both focus on higher level thinking and communication of strategies, it is my belief that performing mathematics in the first language can only provide an advantage to grade 3 students who have a very limited exposure to French vocabulary by Grade 3. It may, in fact, be the case that the ability of the students to master certain concepts and communicate their thinking clearly may be genuinely inhibited by the language barrier created when performing tasks in their second language. Do the math test scores (when the test is performed in French) truly reflect mathematical knowledge or French language ability? In terms of remediation, does the child need support with French language acquisition or mathematical ability and understanding? It becomes difficult to differentiate.

During the assessment task, no teacher assistance is to be provided comprehending any words on the page. Students may look up any of the mathematical terminology provided in the glossary or may ask the teacher to read verbatim any words on the test. Although this is of some assistance, if a student does not know the meaning of one of the words in the question, his/her ability to respond is inhibited, even if he/she has mastery of the mathematical concepts required. This creates yet another linguistic hurdle for students to overcome when attempting to answer mathematical problems on the test. One may also argue that the fact that the Ministry recognizes the need to provide English translation of terms for the mathematics portion of the French test for Immersion students may be an indication that students better understand these terms in their first language.

When using a French translation of an age and grade appropriate English text (be it the EQAO test or a regular curriculum program such as Intéractions), the level of French language is often beyond the level of independent language comprehension of the French Immersion students, even though the mathematical concepts are grade appropriate. The level of difficulty of the "French Language" in these texts is often more suitable to French first language learners. Resources that match grade levels in French language comprehension at an Immersion level are often well below the level of mathematical concepts required by the curriculum for that grade level. For example, a grade 1 French first language math activity will be appropriate mathematically for our grade 1 students but the independent reading level (vocabulary and instructions) of that activity may be better suited to late grade 2 or grade 3. Once again, a language barrier is created for Immersion students and it brings back the question of whether we are testing language capabilities or mathematical capabilities.

When I read policies about English As A Second Language (ESL) learners, I wonder how the same principles apply to my students who are French As A Second Language (FSL) learners. The provincial test allows accommodations for ESL students because "It is assumed that these students require accommodations for classroom assessment tasks throughout the school year." (Education Quality and Accountability Office, 2003, pg.5) This is also true of my students, yet they received no accommodations during the testing. At the very least, I feel that the FSL students should be allowed more time since some of their time is used looking up terms in the glossary provided with the test.

In the EQAO report on testing results, it is noted that: "... there has been a continuing concern that students may not learn "as much" content when they are schooled in a second language." (Hart, Lapkin & Turnbull,, 2000, pg. iii) Indeed, when I sent out a questionnaire to the parents in my class (see appendix B) and asked them "What are your thoughts, feelings and/or ideas about the EQAO Grade 3 testing?", 78% of all parents who responded expressed concern about the validity of testing the mathematical ability of their children in a second language. Comments included:

"...the language seems a little advanced for 8 or 9 year old children",

"-level of math concepts are not consistent with level of french reading and comprehension, therefore it the outcome based on math or reading skills?",

"the math in French is very difficult for a parent to help their child with. I believe that the math should be in English...Math done in French is like the student learning a third language..." ,

"I also vehemently object to the math testing (teaching) to be done in French (at any grade level). If a child is to excel in math they must learn it in their first (ie best) language in order to properly understand it."

Throughout my experience teaching in French Immersion, I have found parents to be very supportive of what was going on at school. I found this to be especially true when the decision to begin instructing math in English in grade 3 was made in the academic years of 1999-2000 and 2000-2001. In fact, parents, via the school council, initiated the change at a school and board level. When the math was taught in English, the parents seemed relieved that they were be able to provide more assistance to the children at home (as was also indicated in the results from the survey I sent home this year). The students were encouraged, enthusiastic and positive about performing mathematics in English. Because of the wealth of resources available in English language, students were able enjoy a wider variety of mathematical experiences.

Next Steps

When the EQAO results arrive in the fall, they will be analysed and a plan for improvement in any areas of weakness will be developed. I will continue to use math journals as part of my math program, but will also use a math wordwall, provide more opportunities for discussion and group work in math investigations, prepare more open-ended activities and real-world contexts for concepts being studied. I will also continue the implementation of activities based around previous years tests including work with the glossary and completion of sample test units but I will begin using them earlier in the year and more frequently. I would also like to increase use and analysis of exemplars provided by the Ministry of Education. Through available in-service, I will continue to seek new ideas to implement that will assist improving communication in mathematics.

I plan to continue to seek research pertinent to the relationship between second language learning and it's relation to mathematical understanding to further develop a personal philosophy.

Math Resources Listed

Hope, Jack, Small, Marion, et al., (1996) Intéractions. Montreal: Les Editions de la Chenelière.

Séguin-Mondoux, Julie and Mallard, Pénélope. (2000) Ontario Maths - Cahier 3. Montreal: Les Editions de la Chenelière.

Coordinators/Consultants Association of Primary Educators (C.A.P.E.) et al., (1999) Linking Assessment to Curriculum in Mathematics - Primary Years. Rosseau: Ontario Association for Mathematics Educators (O.A.M.E.).

Wortzman, R. et al., (1998) Quest 2000 Problem of the Week. Don Mills: Addison-Wesley Longman Ltd.

Bibliography

Education Quality and Accountability Office. (2003) Administration Guide for Teachers and Principals: Grade 3 and 6 Assessment of Reading, Writing, And Mathematics 2002-2003. Toronto: Queen's Printer for Ontario.

GEDSB. (2003) French Immersion Information: Early French Immersion. www.gedsb.on.ca.

Hart, Doug, Lapkin Sharon & Turnbull, Miles. (2000) French immersion students' performance on Grades 3 and 6 provincial tests: Potential impacts on program design, Executive Summary. OISE-UT Modern Language Centre, October.

Lapkin Sharon & Turnbull, Miles. (2001) Grade 3 immersion students' performance in literacy and mathematics: Province-wide results from Ontario (1998/99). OMLTA Conference, March 30.

Marks Krpan, Cathy. (2001) The Write Math: Writing about Math in the Classroom. Persippany: Dale Seymour Publications.

Suurtaam, Dr. Christine. (2003) Math Report points the way. Curriculum Update. News and Information for Ontario's Educators, Winter 2003, pp. 3-5.

Appendix A - Mathematics Glossary

Appendix B - Questionnaire to Parents