Answered by Marie-Pier Forest, Doctoral Candidate in Didactics of Mathematics at the University of Quebec at Rimouski, Lévis Campus, firstname.lastname@example.org and Dominic Voyer, Professor in Didactics of Mathematics at the University of Quebec at Rimouski, Lévis Campus, email@example.com
It is now well-known that students’ reading skills have an important role in mathematics, in particular for solving word problems. Many studies have been conducted on this subject, including some indicating that students who have combined difficulties in mathematics and reading are considerably less successful than their peers in solving word problems (Jordan et al., 2003). Other research studies have attempted to identify the specific reading skills that are involved in understanding word problems. One of these skills is the ability to make inferences, which is connected to performance in solving written mathematical problems (Goulet and Voyer, 2014; Luquette, 2018; Voyer et al., 2012). Word problems require students to make inferences, connecting the explicit information in a text and their own knowledge, in order to deduce implicit information (Giasson, 2011; Kispal, 2008).
But how can we put this knowledge, derived from research, to use in the classroom? In other words, how can we develop a student’s ability to make inferences, both for reading and for solving word problems? It seems that teaching strategies related to inferences could have beneficial effects for students through bridging the disciplines of language and mathematics (Voyer et Forest, 2021). We hypothesize that it can be useful, particularly for those with LDs, to connect what students already know about the production of inferences, in the context of text comprehension, to solving word problems. Since we know that students with learning disabilities (LDs) generate fewer inferences than their peers during reading (Barth et al., 2015), one might think that it would be an additional challenge to transfer knowledge constructed during reading instruction and apply it to their benefit in math. However, reading is always an “interactive process of solving problems [that] aims to construct the meaning of a text” (Ontario Ministry of Education, 2006b, p. 8). Similarly, reading is what makes it possible to construct the meaning of a word problem in order to succeed in solving it.
In the context of reading, teachers frequently lead their students to ask questions about the texts, either before or after reading them. Giasson (2011) recommends teachers encourage students to form an image in their minds of the characters, to visualize the sequence of events and to clarify what the text does not explicitly say, producing inferences. Thus, the students are led to make inferences based on the titles, subtitles, images, etc.
While lessons like this are common during reading instruction, they seem to be less frequent in mathematics. But that does not mean that students do not require these same skills in the math class. Here is an example of a word problem:
“Danielle goes to feed the chickens and cows on her farm. She counts 20 legs. How many chickens and how many cows does Danielle need to feed? Explain how you found the answer.” (Ontario Ministry of Education, 2006a, p. 62)
When reading this problem, the teacher could similarly encourage the students to form an image in their minds of the context and to clearly state information that is implicit, similarly to what is done during reading instruction. Indeed, in order to solve this problem, students must necessarily generate an inference based on their previous knowledge, that is, knowing the number of legs on chickens and cows. It should be pointed out that the Ontario Ministry of Education (2006a) encourages transferring strategies in this way.
During reading instruction, pupils are also encouraged to formulate their own questions about the text. Research suggests that writing questions about the texts they read helps students generate inferences (Giasson, 2011). This avenue is also worth pursuing in math. Starting from a word problem without any questions, students can write their own questions and then ask their peers these questions. Consider the following problem:
"Today is a perfect day for doing outdoor activities! Mahika and her mother take advantage of this to go to the ski centre, which is a 30-km drive away. Once they have arrived, they wait in line for 20 minutes to rent equipment. Thankfully, they have their annual pass. Finally, they are ready to ski, and they do 6 downhill ski runs on the “Family” course, 2 downhill runs on the “Fun” course, and then 4 downhill runs on the “Optimist” course. They stop for 50 minutes to have lunch. In the afternoon, they do 3 more downhill runs than they did in the morning. At the end of the day, Mahika and her mother return home.”
Based on a word problem like the one above, guide the students to formulate questions leading to different types of problems: problems requiring research to find information, problems containing superfluous or implicit information, problems that have several solutions, etc. Students can be encouraged to write questions requiring an inference: for example, “What distance did Mahika and her mother travel by car in order to spend their day at the ski centre?” In order to answer this question, it is necessary to make an inference, that is, about the trip to and from the ski centre, given that this information cannot be found directly in the stated problem.
In conclusion, we believe that there should be a closer connection between the strategies of inference used in text comprehension and the strategies used to solve word problems. We have provided a few examples in this article, but there are clearly many others: for instance, getting students to discuss word problems, to recognize the most important inferences in a given context, to proceed by deducing inferences, etc. While building inference skills occurs primarily during reading instruction, we believe that these skills should be developed in parallel in mathematics. All students, in particular those with LDs, could benefit from educators leveraging this connection in the classroom.
Barth, A. E., Barnes, M., Francis, D., Vaughn, S. et York, M. (2015). Inferential processing among adequate and struggling adolescent comprehenders and relations to reading comprehension. Reading and Writing, 28(5), 587-609. https://doi.org/10.1007/s11145-014-9540-1
Giasson, J. (2011). La lecture : apprentissage et difficultés. Gaëtan Morin Éditeur.
Goulet, M.-P. et Voyer, D. (2014). La résolution de problèmes écrits d’arithmétique : le rôle déterminant des inférences. Éducation et francophonie, 42(2), 100-119. https://doi.org/10.7202/1027908ar
Jordan, N. C., Hanich, L. B. et Kaplan, D. (2003). A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with comorbid mathematics and reading difficulties. Child Development, 74(3), 834-850. https://doi.org/10.1111/1467-8624.00571
Kispal, A. (2008). Effective teaching of inference skills for reading. Literature review (Research Report DCSF-RR031). National Foundation for Educational Research, Department of Education (Division of Children, School and Families).
Luquette, M. (2018). Nature et rôle des inférences impliquées dans la résolution de problèmes mathématiques [thèse de doctorat, Université de Montréal]. Papyrus. https://papyrus.bib.umontreal.ca/xmlui/bitstream/handle/1866/20053/Luquette_Marie_2017_these.pdf?sequence=2
Ministère de l’Éducation de l’Ontario. (2006a). Guide d’enseignement efficace des mathématiques de la maternelle à la 6e année. Fascicule 2. Gouvernement de l’Ontario. http://atelier.on.ca/edu/resources/guides/GEE_math_M_6_fasc2.pdf
Ministère de l’Éducation de l’Ontario. (2006b). Le curriculum de l’Ontario de la 1re à la 8e année - Français. Gouvernement de l’Ontario. http://www.edu.gov.on.ca/fre/curriculum/elementary/language18currb.pdf
Voyer, D., Beaudoin, I. et Goulet, M.-P. (2012). De la lecture à la résolution de problèmes : des habiletés spécifiques à développer. Revue canadienne de l'éducation, 35(2), 401-421. https://www.jstor.org/stable/canajeducrevucan.35.2.401
Voyer, D. et Forest, M.-P. (2021). Apprendre à faire des inférences en classe : une façon de développer ses habiletés en lecture et en mathématiques [communication orale]. 8e colloque international en éducation du Centre de recherche interuniversitaire sur la formation et la profession enseignante (CRIFPE).
About the Authors:
Marie-Pier Forest is pursuing doctoral studies in Education at the University of Quebec at Rimouski, at the Lévis Campus. She is a Researcher Student at the Centre de recherche interuniversitaire sur la formation et la profession enseignante (CRIFPE) and a Research Assistant at the Réseau de recherche et de valorisation de la recherche sur le bien-être et la réussite (RÉVERBÈRE). Her research interests include the teaching of Mathematics through problem-solving and the development of conceptual understanding in primary grade students.
Dominic Voyer is a Professor in Didactics of Mathematics at the University of Quebec at Rimouski, at the Lévis Campus. He is a Regular Researcher at the Centre de recherche interuniversitaire sur la formation et la profession enseignante (CRIFPE). He is Co-Director of the Réseau de recherche et de valorisation de la recherche sur le bien-être et la réussite (RÉVERBÈRE) and a Researcher at the Laboratoire sur la recherche-développement au service de la diversité (Lab-RD2). His current research focuses on the teaching of Mathematics in primary grades. He is particularly interested in the connections between reading skills and solving written mathematical problems, as well as the development of numeracy skills in young students, and the process for research and development in school settings.