Educational flexibility to promote the success of allophone students in mathematics

In this text, we will draw a portrait of allophone students in mathematics in order to fully understand the difficulties they may encounter and we will suggest means of flexibility to be implemented in the classroom according to the needs observed.

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By Marie-France Dubé and Matthieu Martin, educational advisers

Portrait of allophonia in Quebec

Almost everywhere in Quebec, allophonie is more and more present in schools. Indeed, according to the Office québécois de la langue française quoted in the Canadian Press (2017), the rate of elementary and secondary students who do not have French or English as their mother tongue and who attend schools Francophones in Quebec went from 15% to 89% in Quebec schools between 1971 and 2015. The adoption of Bill 101 was certainly an important factor in this meteoric increase in allophone students in French-language schools. This movement has forced certain school boards in the province of Quebec to open reception classes and it would not be surprising to see other school boards follow suit in the years to come. To give you an idea, at the time of writing this article, the Commission scolaire de Montréal has about 320 reception classes, primary and secondary combined. The vast majority of students in the reception class will eventually make the jump to regular class, if they are not directly integrated into these classes, as is the case elsewhere in certain school boards in Quebec.

The reality of the very diverse composition of the classes has led us to question the teaching provided to these students and more specifically the teaching of mathematics, both in the reception class and in the regular class. In this text, we will first draw up a portrait of these students in order to fully understand the difficulties they may encounter. Then, we will propose some means of flexibility that it would be possible to implement in mathematics class according to the observed needs.    

Portrait of allophone student in mathematics

The host class pupil who joins the regular class has generally been educated and followed mathematics courses in his country of origin. He has developed strategies, skills and acquired mathematical notions (Desrosiers, D. Gauthier, J. Martin, M, 2018). Regarding mathematics in the welcome class, the teacher offers different types of tasks during which the student certainly develops his mathematical skills, but the objective should first be in the acquisition of the mathematical vocabulary necessary for operate in regular class. It is therefore very likely that the pupil leaving the host class will join the regular class with conceptual deficiencies in mathematics, especially since, depending on his migratory path, he is likely to have had different mathematical school experiences. in terms of continuity over time and the acquisition of concepts. For example, he may have done more geometry and less algebra for a given level compared to Quebec study programs (Desrosiers, D. Gauthier, J. Martin, M, 2018). In addition, in their country of origin, the student has developed an understanding of their role as a student which may be different from the one we have here in Quebec. His experience as to what was expected of him, what was allowed or prohibited in a classroom, and the vision that was conveyed about learning and teaching mathematics in his home country may be at odds with what is conveyed in its new school environment. It is therefore essential that the teacher learns about the school experiences of all allophone students to facilitate their integration (Desrosiers, D. Gauthier, J. Martin, M, 2018).

In addition, you should know that all mathematics courses in secondary school are taught by mathematics specialists while in primary school, teachers of ordinary classes are generalists. Neither is usually trained to teach French as a second language. As a result, these teachers do not know the stages of acquiring a second language and do not have many tools adapted to the needs of allophone students. However, to continue to see to the development of the acquisition of the vocabulary of the pupil is part of the role of every teacher of ordinary class. Indeed, this is a task that must be shared between the teachers of the reception class and those of the ordinary class, because allophone students will take five to seven years to master the language of schooling (language of learning school). Taking into account the different portraits of the allophone student and the complexity that learning a second language can cause, we will propose in the following paragraphs some ways to adapt the teaching of mathematics in order to minimize the knowledge gaps between these students and others.

Diversification of tasks in mathematics

First of all, the animation of math discussions is a good time for students to practice using accurate and precise mathematical vocabulary and to listen to their peers speak. In addition, mathematical discussions are akin to debate, which prompts students to give their opinions, readjust their positions and take risks. Indeed, the students will speak, even if they do not always have the necessary vocabulary to do so. Allowing students to use their native language with class peers can be a tool that facilitates their participation. At the same time, we allow the transfer of knowledge from the pupil's mother tongue to French and he experiences less breakdown in understanding when faced with the task. According to Bruce (2007), the problems that would most elicit discussion among students are those that allow the use of more than one strategy or that give rise to more than one response. These tasks are more stimulating when they go beyond simple math and encourage students to think more abstractly. 

With this in mind, rather than having students work individually, it would be wise to find ways to put students in communication so that they reuse the vocabulary taught and acquire new ones. Different problem-solving practices allow students to verbalize. For example, in teams of three or four, students are asked to solve a problem involving various fields of mathematics. In addition, it is possible to take breaks during which the students can explain to the class the strategies they have used so far. Rather than bringing together all the presentations at the end of the activity, the alternation between the periods of pooling and work offers the possibility for more students to come and present their strategies without losing the attention of the rest of the class. These periods of discussion promote awareness of the existence of different ways of thinking about mathematics and of the multiple approaches that make it possible to solve the same problem.

In another vein, the various mathematical tasks currently presented to students are complex due to their language requirements and their context sometimes far removed from their reality. Moreover, it is beneficial for the student to be led to demonstrate his mathematical skills without being hampered by the difficulties that mathematical discourse can cause. Indeed, the short texts and the lack of redundancies amplify the difficulty that the pupils have to enter a task, since the words, the sentences and the ideas do not repeat themselves, which increases the importance of understanding them well. You have to remember that you cannot expect a student who learns French to manage like a native speaker. Therefore, it may be possible for the teacher to offer his students different versions of the same task, but presented in different degrees of language complexity: the full text, a lighter and better organized version of text containing the essential of the mathematical situation, another containing text with pictograms or drawings and a last almost entirely pictorial. 

Ex. Problem of Christian Ainsley, Mannix Coursol, Diane Laplante and Rosa-Maria Sandoval adapted by Marie-France Dubé:

Another way to make tasks more accessible to students is to use linguistic simplification (Tardif-Couture, R. 2016). This does not mean rewriting all the problems in order to remove all the difficulties, but having in mind that certain aspects of the language may complicate or prevent comprehension. The use of referent such as the word in makes reading more difficult for the pupil, since it is more difficult to know which word he is referring to. For example, it would be desirable to modify this sentence: "John has 7 pencils, Matthew has 5 more" by the following sentence: "John has 7 pencils, Matthew has 5 more pencils than John". With regard to relationship markers such as if, and, but, it is important that students understand the logical relationships they make between words or sentences. It is therefore advisable to take the time to discuss with the students the links that these words generate in the problem. Finally, the understanding of the tasks will be facilitated if the context is close to the students' experience and the words used are frequent. 

Through the writing of this article, we have tried to highlight the importance of working on mathematics and vocabulary simultaneously. To do this, it is not necessary to completely modify the tasks offered to the students, but to think about the different ways in which we can make them interact with each other and in a large group during the lessons. This new vision of mathematics teaching allows students from host class to continue working on their language of schooling in mathematics, especially since the time spent in host class mainly allows them to develop the language of socialization. (usual French) which is relatively independent of learning mathematical vocabulary (Millon-Fauré, 2017). In this regard, it is common for students from the host class to have difficulty keeping up with the rhythm of the regular class.

Indeed, it is not because a student understands when spoken to in usual French that he will automatically understand the explanations provided during the teaching of mathematics (Millon-Fauré, 2017). Thus, by having a concern for the teaching of vocabulary, mathematics is valued in the eyes of the pupil, because it is then possible for him to participate in discussions, to reflect with his peers on tasks more suited to his language level. and we offer him the necessary tools to be able to manage when he is faced with a breakdown in oral or written comprehension. This is very important, because students will not always have the reflex to come and ask a question when they do not understand for fear of disturbing or being judged by others (Millon-Fauré, 2017). 

To go further, you can visit the website of Marie-France Dubé and Matthieu Martin Mathematics in the welcome class.

About the authors

Marie-France Dubé (CSDM) and Matthew Martin (CSDL) are educational advisers in mathematics for the reception classes of primary and secondary schools and form a team that works on the development of a vision of teaching and valuing mathematics to allophone students. They are particularly interested in the impact of vocabulary learning on the acquisition of mathematical concepts and the development of tasks more suited to students learning French. You can visit this website to go further.

Bibliography

  • Bruce, C. (2007). Interaction between students in a math class: Competition or exchange of ideas? Ontario, Literacy and Numeracy Secretariat and the Ontario Association of Deans of Education. 
  • Desrosiers, D. Gauthier, J. Martin, M (2018). Mathematical reference system for teaching staff in classes of students in linguistic, academic and social integration. Laval, Laval School Board.
  • Canadian Press. (2017). Allophones on the rise in French-language schools in Quebec. Retrieved on June 3, 2019, from https://ici.radio-canada.ca/nouvelle/1025626/allophones-hausse-ecoles-francophones-quebec-oqlf.
  • Millon-Fauré, K. (2017). Teaching Mathematics to Allophone Students: Studies of the Impact of Language Difficulties on Teaching and Learning. France: Knowledge & Knowledge.
  • Tardif-Couture, R. (2016). Mathematics problem solving for allophone elementary school students. Quebec, Theses and dissertations.

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