# Ongoing research projects:

## Evaluation of a digital tool to identify and intervene on learning difficulties or disorders in mathematics in the school context

### Research funded by the HEP Vaud

This project is part of the “*mission mathématique*” of the Canton of Vaud, initiated in 2018-2019 in order to improve the knowledge and skills in mathematics of primary school students. One of the recommendations of this mission is to propose a computer-based learning programme to improve the performance of primary school pupils in calculus. In order to select this computer-based programme, a study was conducted to specifically compare two programmes: Calcularis and Matheros. One difference between these two programmes is that Calcularis was designed for pupils with learning difficulties in mathematics. The aim of this project is to investigate the potential of this application, on the one hand, to identify learning difficulties and disorders in mathematics and, on the other hand, to intervene on these difficulties and disorders. The first research question concerns the intervention dimension: to what extent does Calcularis allow intervention with children with learning difficulties and disorders? In particular, to what extent does it enable them to progress? The second research question relates to identification: to what extent can Calcularis enable the identification of learning difficulties and disorders in mathematics of pupils within the class?

## Exploring MLD in mathematics education: literature review

### Riteam research project

In this research, we are investigating how MLD (= Mathematics Learning Disability) is studied in the field of mathematics education on the basis of a systematic review of the literature. The specificities of this field of research led us to define three categories representative of what we call “MLD in Mathematics Education” (students with a specific learning disability in mathematics but without a primary diagnosis, students assessed with a specific mathematics test and students diagnosed with a specific criterion).

A first literature review was carried out over a period from 2007 to 2016 (Deruaz & al., 2020). We identified 17 articles and 2 meta-analyses. The analysis of these articles shows that research on MLD in mathematics education literature has developed since 2013, particularly in the United States. Most studies address arithmetic content at the primary schools level and the focus is on educational interventions. A scientific watch is underway to update this review regularly.

Deruaz, M., Dias, T., Gardes, M.-L., Gregorio, F., Ouvrier-Buffet, C., Peteers, F., & Robotti, E. (2020). Exploring MLD in mathematics education: Ten years of research. The Journal of Mathematical Behavior, 60, 1-17. doi:https://doi.org/10.1016/j.jmathb.2020.100807

## Students with MLD in early algebra

### Thesis project

### Gregorio, F.

Neuroscience and mathematics education research on MLD has focused almost entirely on basic arithmetic. With the aim of broadening the mathematical domains studied, in this thesis, under the supervision of Cécile Ouvrier-Buffet and Thierry Dias, we focus on students with MLD in early algebra. We ask the following questions: How can we describe the algebraic thinking of students with MLD? What is the role of generalisation in the algebraic thinking of students with MLD? What is the role of examples in proof for students with MLD?

Initial results indicate that students with MLD show traces of algebraic thinking, despite their severe difficulties in mathematics.

Gregorio, F. (2019). Mathematical learning disabilities in early algebra. In M. Graven, H. Venkat, A. Essien & P. Vale (Eds.). *Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education* (Vol. 4, p. 138). Pretoria, South Africa: PME.

## The difficulties of students with MLD in learning fractions

### Riteam research project

In this ongoing research, we aim to identify the characteristic difficulties of students with MLD in learning fractions. To do this, we plan to create a test to identify persistent difficulties from the year after the introduction of fractions to the end of lower secondary education. The study will be carried out in different countries (France, Italy and Switzerland) and on a large sample of students in order to ensure the absence of teaching and curricular bias.

# Completed research projects:

## Impact of a video game about learning fractions on children with and without learning disabilities: neuro-cognitive and didactic aspects (DysCog)

### Research financed by Région Auvergne-Rhône-Alpes

### Gardes, M.-L.

This research, which is financed by the Région Auvergne-Rhône-Alpes and which is called *Impact d’un jeu vidéo sur l’apprentissage des fractions chez l’enfant avec et sans trouble de l’apprentissage : aspects neuro-cognitifs et didactiques* (*Impact of a videogame about learning fractions on children with and without learning disability: neuro-cognitive and didactic aspects*), takes place at the Cognitive Science Institute Marc Jeannerod in Lyon. The goal of this research is to assess the impact of the use of a didactic videogame about learning fractions in primary school. It is part of a new area of research integrating cognitive science (psychology and neuroscience) and didactic knowledge with the aim of understanding and improving school learning. The research is broken down into three specific objectives. The first one is the evaluation of the impact of the videogame on learning fractions and on the brain functions of typically developing children from all social backgrounds, playing the game in their families. The second specific objective is the evaluation of the impact of the videogame on learning fractions in children with deep learning difficulties in mathematics (dyscalculia, for example). The children are from all social backgrounds and play the game in their families. The third specific objective is the evaluation of the impact of the videogame on learning fractions in children who play the game in class, within a learning sequence constructed by the teacher.

The research started in September 2017 with the production of a diagnostic test to evaluate the knowledge and the skills of the students on fractions (later years of primary school) and with the first class’ experimentations in the last year of primary school and the first year of middle school.

Zarpas, P. & Gardes, M.-L. (2019). Une jeu vidéo didactique pour l’apprentissage des fractions. Revue de mathématiques pour l’école, 231, 20-29. https://www.revue-mathematiques.ch/files/1615/5385/2681/RMe-231-Zarpas.pdf

Bhatia, P., Delem, M., Léone, J., Boisin, E., Cheylus, A., Gardes, M.-L., & Prado, J. (2020). The ratio processing system and its role in fraction understanding: Evidence from a match-to-sample task in children and adults with and without dyscalculia. Quarterly Journal of Experimental Psychology, 73 (12), 2158-2176.

Bhatia, P., Leone, J., Gardes, M.-L., & Prado, J. (submitted). Fraction knowledge in adults with persistent mathematics difficulties.

Bhatia, P., Le Diagon, S., Langlois, E., William, M., Prado, J., & Gardes, M.-L. (submitted). Impact of a game-based intervention on fraction learning for fifth-grade students: A pre-registered randomized controlled study.

## A disorder between different disciplinary fields (disability, health and education): dyscalculia

### Thesis project

### Peteers, F.

Within the framework of the ongoing thesis (co-founded by the Université de Reims Champagne-Ardenne and the Communauté d’Agglomération de Châlons-en-Champagne), we ask the following questions: what is the status of mathematics education in the research on dyscalculia? How can we reconcile the different approaches (cognitive and didactic) for a better understanding of this disorder and to promote interaction between professionals? The aim is to create a detection tool for mathematical learning difficulties to help the dialogue between teachers and speech therapists, proposing a common inventory of children’s difficulties usable by both. For this, we rely on theoretical elements of mathematics education, of numerical cognition and on an analysis of the existing tests for the evaluation of basic school mathematical skills or in order to determine a medical diagnosis.

The analysis of the tests revealed certain biases in the tests based on numerical cognition, thus confirming the interest of mathematics didactics in research on dyscalculia, particularly with regard to diagnosis. An initial validation of the device was carried out, which revealed a series of tasks that were not very discriminating, as well as certain specificities of pupils reported as having difficulties by the teacher and of pupils being monitored for mathematical disorders.

Peteers, F. (2018). *Un trouble à l’interface entre différents champs disciplinaires (handicap, santé et formation) : la dyscalculie – Une approche didactique*. (Thèse de doctorat). Université de Reims Champagne-Ardenne. Repéré à https://hal.archives-ouvertes.fr/tel-01944017

Peteers, F. (2020). Apports croisés de la didactique et de la cognition numérique pour l’étude des troubles des apprentissages en mathématiques. *Recherches En Didactique Des Mathématiques, 40*(2), 225-268. hal-03318881

## Action research to foster inclusive teaching and learning processes in mathematics (EduMath)

### Research financed by the Dipartimento Sovraintendenza agli studi della Regione Autonoma Valle D’Aosta

### Robotti, E.

This research aims to investigate the teaching and learning processes in mathematics in the context of inclusive teaching, identifying MLD students.

For this reason, the research objective focuses on the analysis of the didactic conditions and choices (organisation of didactic activities, choice of the instruments to use, definition of tasks…) which can support learning in all students of the classroom.

We use at the same time the theoretical framework of cognitive psychology and neuroscience, and the one of mathematics education, to benefit from combined efficient information.

The research started in 2013 within a research-action group, called EduMath, composed of 30 primary and kindergarten teachers and a researcher (Elisabetta Robotti). It developed both case studies and experimentations on fractions and arithmetical facts, in particular in primary school, with approximately 400 students.

Robotti, E., (2018). Geometry in kindergarten: first stepstowards the definition of circumference. Proceedings of PME42, Umea, Svezia

Robotti, E., (2017). How the representations take on a keyrole in an inclusive educational sequence concerning fraction, Proceedings of CERME 10, Dublino,Irlanda.

*Proceedings of the 9th Congress of the European Society for Research in Mathematics Education*, 1975–1981.

## Learning and teaching difficulties in mathematics

### HEP Vaud Project , 2013/2017

### Dias, T. & Deruaz, M.

The research goal is to help answer current questions about MLD in the school setting. The study deals with the complexity of intellectual disability diagnosis. At the same time, it proposes food for thought about support for difficulties in the school context. We would like to explore the correlations between learning difficulties and teaching difficulties. In particular, we believe that the term “dyscalculia” is used in quite inappropriate ways and that the consequences of a too quick and systematic categorisation of these school phenomena often leave teachers in uncomfortable professional situations (Deruaz & Dias, 2016 ; Dias & Deruaz, 2012). In Deruaz & Dias (2016), for example, we conducted a case study in relation to an individualised support system for secondary school students with difficulties. We showed that the particular character of the supports which were used allows us to put in perspective the idea of MLD. Our study refers to students of different levels of education. This continuity was necessary for a deep exploration of the correlation links that we want to highlight.

Deruaz, M. & Dias, T. (2015). Dyscalculie : et si les enseignants reprenaient la main ? In Anne-Cécile Mathé, Eric Mounier, *Actes du séminaire national de didactique des mathématiques de l’ARDM (Jan 2014)*, Bordeaux, Paris, France (pp.296-298). IREM de Paris.

Deruaz, M. & Dias, T. (2016). Elèves en difficultés : dyscalculiques ? *Petit x, 101, *7-35.

Dias, T., & Deruaz, M. (2013). Dyscalculie : et si les enseignants reprenaient la main ? *Apprentissages Neuropsychologiques des Apprentissages chez l’Enfant (ANAE), 120-121*, 529-534.