Fields | Projects and contracts | Collaborations | |
Automatization of counting procedures in children with dyscalculia
2017 - 2020
Applicant : Catherine Thevenot
Other partners : Jeanne Bagnoud
Researchers in numerical cognition usually think that the greatest and most common difficulty in children suffering from dyscalculia is retrieval of arithmetic facts from long-term memory. However, we have recently shown that retrieval might not be the optimum strategy in mental arithmetic. In fact, expert adults would rather solve simple problems such as 3 + 2 by automated and unconscious procedures. Therefore, we hypothesize that children with dyscalculia might not present deficit in retrieval but, instead, in counting procedure automatization. The aim of the current project is to test this challenging position. Through a longitudinal approach, we plan to precisely examine the behavior of children suffering from dyscalculia over a 3-year period. Children will be aged between 8 to 9 years at the beginning of the study and we will precisely observe the evolution of their solution times when they solve simple addition problems involving one-digit numbers. If children with dyscalculia still struggle with simple additions at the age of 10 to 11, their solution times plotted on the sum of the problems should still follow an exponential function. Indeed, if counting is not automated, difficulties necessarily increase with the progression on the number line or the verbal sequence, hence the exponential function. On the contrary, if counting procedures tend towards automatization, moves along a number line will progressively become as easy at the beginning of the line as at the end, hence the linear function. Importantly, a retrieval model would predict exactly the inverse pattern because, according to this model, the linear function, which is unanimously considered as the hallmark of counting procedures, should progressively be replaced by a non-linear function through practice.
The winning finger counting developmental trajectory
2022 - 2026 (48 mois)
Applicant : Catherine Thevenot
Children who use their fingers to solve arithmetic problems in kindergarten outperform children who do not. However, this pattern of result is reversed at the end of Grade 2. Thus, the winning developmental trajectory seems to consist in using fingers to perform calculations in Grade 1 and abandoning this strategy during Grade 2. It is therefore possible that to develop their numerical skills, finger counting should be promoted and even explicitly taught to young children. However, this conclusion may be premature and the present project aims at examining it. First, we will determine whether efficient children who use their fingers to count in kindergarten are the same as efficient children who do not use their fingers in Grade 2. Another possibility is that Grade-2 children who do not use their fingers and outperform finger users have never used their fingers during development. Therefore, it could be that the disadvantage of not using fingers to calculate at a young age becomes an advantage at a later developmental stage. To examine this, a longitudinal study is necessary. This is what we plan to do in a first part of the project in which finger counting behaviors of about 100 children will be examined over 3 years from the age of 5 to 8 years. We will also observe which specific finger counting strategies are used by children and for which problems. These observations will be matched with their performance. To directly tackle the general question of our project, the second part of our project will consist in an intervention study. More precisely, through explicit teaching, we will help children to adopt the most successful developmental trajectory determined from the first part of our project. All in all, this project will have theoretical and more applied implications to education. More precisely, the results of this project would allow researchers and educators to determine whether finger counting should be promoted in schools and whether explicit teaching of this strategy should be implemented in school.
NEAR - NEuro-cognitive development of Arithmetic fluency: Reconstructive or Reproductive mechanisms ?
2019 - 2021 (24 mois)
Applicant : Catherine THEVENOT, Jérôme PRADO (CNRS, Institut des Sciences Cognitives, Lyon, France)
Arithmetic fluency, or the ability to quickly and effortlessly solve simple arithmetic problems (e.g., 2 + 3), is foundational to math learning in children. Yet, the type of mechanism that supports its development remains debated. On the one hand, it has long been assumed that the development of arithmetic fluency involves a shift from reconstructive strategies (e.g., procedures such as counting) to reproductive strategies (e.g., retrieval of answers from long-term memory) over the course of learning. On the other hand, recent evidence indicates that expert adults may still rely on fast reconstructive processes when solving simple arithmetic problems.
The goal of the present proposal is to shed light on this debate by identifying the neuro-cognitive mechanisms supporting the development of arithmetic fluency in children. Notably, we will measure the behavioral and neural correlates of the problem-size effect for very small addition problems in children as they gain fluency with addition problem-solving.
To test between these hypotheses, we will measure the neural correlates of the problem-size effect in 3 groups of children (8-year-olds, 11-year-olds, and 14-year-olds) groups of children and one group of adults. We will also use independent localizer tasks to precisely identify (i) the superior parietal region involved in attentional shifts along the mental number line and (ii) the left temporo-parietal regions involved in verbal-phonological retrieval, on a participant-by-participant basis. We will then evaluate whether there is a developmental increase in the neural correlates of the problem-size effect in the superior parietal or left temporo-parietal regions as age and fluency increases.
Our findings will have theoretical implications for theories of arithmetic learning and may critically inform educational practices in the classroom
Development of finger use and finger counting habits in young children
2015 - 2018
Applicant : Catherine Thevenot, Pierre Barrouillet (UNIGE)
This project aims at investigating the development of finger use and finger habits in the numerical domain in young children. We will not only describe children behaviours but also evaluate the potential impact of their finger use and habits on their numerical abilities and mental number representations. We will explain below why such influences can be expected and why these questions are important for our understanding of children's numerical cognition. Kindergarten children aged between 5 and 6 years will be involved in our study and their behaviours will be examined longitudinally over 3 years. This doctoral project will be organized around two interrelated parts. For the first part of the project, children will be assessed on their finger use and on their abilities in a verbal counting task, an enumeration task and in an arithmetic task. For the second part of the project, children will be additionally tested on their spatial representations of numbers.
Mental addition in children: A longitudinal study
2014 - 2017
Applicant : Catherine Thevenot, Pierre Barrouillet (UNIGE)
Strategies in mental arithmetic have been studied by cognitive psychologists for many years and this has led to an impressive amount of studies. Yet and quite surprisingly, the conclusions reached in the literature are not always coherent and it is difficult to draw a clear picture of what happens exactly when adults and children solve simple problems. For addition, it was commonly assumed that the transition from counting procedures to retrieval took place around the age of 10. At this age, children were indeed considered as able to solve most simple addition problems without counting. Addition facts were supposed to have already been constructed in long-term memory and easily activated in arithmetic problem solving task (Ashcraft & Fierman, 1982).However, we have recently challenged the strong consensus that very simple additions (involving operands from 1 to 4) are solved by adults through retrieval from memory (Barrouillet & Thevenot, 2013; Fayol & Thevenot, 2012). If adults still use procedural strategies to solve such simple problems, the view that children use retrieval for those problems needs to be reconsidered. This is the aim of the present project. In a longitudinal approach, we would like to test children aged from 8 to 9 (before the transition from counting to retrieval is supposed to occur) to 11-12 (when the transition is supposed to have occurred) on their ability to solve one-digit additions. As in our previous research with adults (Barrouillet & Thevenot, 2013), children will simply be asked to solve the additions and to give their answers out loud as quickly as possible. Children's answers as well as solution times will be recorded by the computer. Five classrooms of third graders (around 125 children) will be tested. The same children will be retested one year and two years later. Moreover and in order to further investigate individual differences, children's working memory capacities and arithmetic skills will be measured and examined in relation to their arithmetic strategies.
Numerical abilities in 5- to 14-year-old children with cerebral palsy
2013 - 2018
Applicant : Catherine Thevenot, Pierre Barrouillet (UNIGE)
A relationship between finger gnosia and numerical abilities has been well documented in the literature. It has been shown for example that five- to six-year-old children arithmetic capacities are better predicted by their results to finger discrimination tests than by more classic intelligence tests. One possible explanation to account for this relationship is that early finger counting constitutes the foundation of more developed mathematical abilities. The object of the current project is to go further in the examination of the relationship between numbers and fingers. To do so, basic and more complex numerical abilities will be examined in children with cerebral palsy of normal intelligence. Those children, who present motor deficits, have the characteristic to have more or less difficulties in using their fingers. Through a transversal and longitudinal approach, 5- to 14-year-old diplegic, hemiplegic and quadriplegic children will be assessed on their general cognitive abilities and their numerical abilities. If numerical abilities are indeed partly rooted in early finger use, they should be impaired in children with cerebral palsy. Moreover, the severity of the impairment should increase as a function of the difficulties children encounter in finger use. Children will be tested five times over 3 years and their performance will be compared to those of normal developing children. This will allow us to determine whether or not potential numerical lags in children with cerebral palsy increase or decrease across development. Both possibilities can be envisioned: It could be that early numerical impairments result in further and further difficulties in more complex numerical abilities that are built on basic skills. In contrast, formal teaching or the implementation of derived strategies could compensate early difficulties. Moreover and importantly, our longitudinal approach will permit the determination of precise predictors of future numerical achievement.
Is simple addition solving based on direct retrieval from long-term memory? A training study.
2013 - 2014
Applicant : Pierre Barrouillet (UNIGE), Catherine Thevenot
It is widely assumed that adults solve simple addition problems by retrieval of the answer from memory. This widespread conviction is based on the frequent co-occurrence of fast responses assumed to reflect a one-step process of retrieval with corroborating verbal reports. However, recent results challenge this assumption, and suggest that adults solve simple addition problems by algorithms or automatic principled knowledge. These contradictory results call for a thorough reinvestigation of simple addition solving.To find evidence in favor of one or the other view on simple addition solving, the present project aims to contrast the effects in adults of two training methods. The first corresponds to the rote memorization used by children when learning multiplicative facts, by which operands-answer associations The hypothesis that adults solve additions through direct retrieval predicts that both methods would have the same effect on response times and on the size effect, rote memorization and repeated solving being assumed to target problem-answer associations. Retrieval being a one-step process, problem size-effect should be strongly reduced and even vanish. Moreover, no transfer is predicted from trained to untrained problems. By contrast, if adults solve additions through fast and automated algorithms as we assume, the two types of training would lead to different outcomes. Whereas rote learning would enhance retrieval use and lead to reduced problem-size effect, training by repeated solving should primarily enhance and strengthen the use of algorithms, leaving the problem-size effect largely unaffected. Moreover, training through solving should lead to some transfer from trained to untrained problems. These effects will be compared with those observed on multiplications, for which the hypothesis of solving through retrieval is uncontroversial.
Strategies in mental addition problem solving
2012 - 2013
Other partners : Pierre Barrouillet, Catherine Thevenot
The aim of the present project is to further explore the determinants of the size effect in mental arithmetic. For this purpose, a set of chronometric data with a maximized reliability is needed. Thus, we plan to present a large sample of adult participants with numerous trials for each of the possible additions with operands from 1 to 9. Moreover, such a large sample will allow for a differential approach and the comparison of response time patterns in individuals varying in their skills in arithmetic and their working memory capacities. Variations of response time patterns in different populations, if they exist, would provide further clues about the nature of the strategies used by adults to solve additions.
Strategies in mental arithmetic: The use of the operand-recognition paradigm.
2012 - 2013
Applicant : Catherine Thevenot
This project constitutes a second extension of a project granted by the FNS in 2008 (100014-122637) and in 2010 (100014-131911). The original project was aimed at broadening the application of a new paradigm that we conceived a few years ago in order to study adults and children's strategies in mental arithmetic (Thevenot, Fanget & Fayol, 2007). This paradigm takes advantage of the fact that algorithmic computation degrades the memory traces of the operands involved in the calculation. As a consequence, contrasting the relative difficulty that adults encounter in recognizing operands after either their addition or their simple comparison with a third number can allow us to determine if the addition has been solved by an algorithmic procedure or by retrieval of the result from memory. Indeed, if it is more difficult to recognize the operands after their addition than after their comparison, then the operation has been solved by an algorithmic procedure. On the contrary, if the difficulty is the same in the two conditions, then the addition has been solved by retrieval; a fast activity that does not imply the decomposition of the operands. The first extension that was granted by the FNS allowed us to carry out a series of experiments on subtractions that are now published in one of the most prestigious journals in our field: The Journal of Experimental Psychology: Learning, Memory and Cognition (Thevenot, Castel, Fanget, & Fayol, 2010). Quickly after the publication of our paper, Metcalfe & Campbell (2011) published a paper in the same journal in which they questioned the validity of the operand-recognition paradigm and suggested that it might reflect difficulty-related switch-costs rather than individuals' strategies. However, a series of concerns relative to the methodology used by Metcalfe & Campbell strongly lead us to express doubts about the authors' conclusions. Therefore, it is my priority now to design and run these new experiments and it is the object of the current project.
The causes of performance improvement in mental arithmetic: A shift from slow counting to compacted procedures?
2012 - 2013
Applicant : Catherine Thevenot
In order to solve arithmetic problems, individuals can use two different strategies, namely retrieval or procedure. It is generally thought that a gradual shift from procedures to retrieval is possible through repetitive practice of algorithms in childhood, which would lead to the memorization of associations between operands and answers. In this context, the shift from inefficient to more efficient solution strategies through development is explained by a shift from slow procedures to retrieval (Logan, 1988; Logan & Klapp, 1991; Siegler & Shrager, 1984). However, a different view, which is supported by some of our recent results, is that the improvement of arithmetic performance through practice is due to a shift from slow counting procedures to the use of compacted procedural knowledge (Anderson, 1982; 1983; 1987; Baroody, 1994). The current project aims at providing new evidence for one or the other point of view.
Strategies in mental arithmetic: The use of the operand-recognition paradigm.
2011 - 2012
Applicant : Catherine Thevenot
This project constitutes an extension of a project granted by the FNS in 2008 (100014-122637). The original project aimed at broadening the application of a new paradigm that we conceived a few years ago (Thevenot, Fanget & Fayol, 2007) to the study of subtraction, multiplication and division problems and to adopt a developmental perspective and use our paradigm in order to study the changes from procedural to retrieval strategies in third, fourth, and fifth graders. That paradigm takes advantage of the fact that algorithmic computation degrades the memory traces of the operands involved in the calculation. As a consequence, contrasting the relative difficulty that adults encounter in recognizing operands after either their addition or their simple comparison with a third number can allow us to determine if the addition has been solved by an algorithmic procedure or by retrieval of the result from memory. Indeed, if it is more difficult to recognize the operands after their addition than after their comparison, then the operation has been solved by an algorithmic procedure. On the contrary, if the difficulty is the same in the two conditions, then the addition has been solved by retrieval; a fast activity that does not imply the decomposition of the operands. Within the ongoing project, we have already extended the use of the paradigm to the domain of subtraction and we have used it in fifth graders, attesting to the fact that it is also suitable for children. I would like to postpone the remaining planned experiments described in the original project and ask the Swiss National Foundation for a one-year prolongation in order to concentrate on the experiments suggested by the reviewers. The first six experiments in the current project aims at examining potential confounds existing in our operand-recognition paradigm (ORP). The last experiment aims at extending the results we obtained on subtraction to multiplication and division problems.
Relationship between basic and complex numerical abilities
2009 - 2010
Applicant : Catherine Thevenot
This project consists of an extensive single study that would be carried out over a one-year period. It aims at providing explanation for the relationship reported in the literature between basic and more complex numerical skills. This relationship is often interpreted by researchers as evidence that an early, if not innate, solid and clear understanding of numerosity, or in other words, a good number sense, constitutes the basis for the development of complex numerical abilities such as arithmetic or mathematics. However, an alternative explanation of the relation can be put forward. It could be that individuals who have difficulties in complex numerical abilities do not engage in activities involving numbers as often as higher skilled individuals. As a consequence, their mental representation of numbers could be unclear and difficult to access due to a lack of practice. In order to shed light on the causal relationship between basic and complex numerical skills, we propose here to train not-so-good problem solvers on mental arithmetic and to examine the effect of this training on their numerical basic skills. If practicing complex numerical activities improves the clarity of number representations and the understanding of numerosity, then the hypothesis that higher level numerical abilities develop from a numerical core knowledge is not strictly true. The hypothesis that difficulty in basic numerical abilities could be the consequence of lower abilities in complex numerical abilities such as mental arithmetic could therefore be retained. On the contrary, if practicing mental arithmetic does not have any effect on more basic skills, then the hypothesis that deficits in basic numerical abilities are the consequence of a lack of exposure to numbers has to be rejected. Elucidating the question of a potential causal relationship between basic and more complex numerical abilities is fundamental in order to understand and remediate children's difficulties in arithmetic and mathematics.
Strategies in mental arithmetic: The use of the operand-recognition paradigm.
2008 - 2010
The use of the alphabet arithmetic task for the study of the automatization of counting procedures
2017 - 2018
grant-giving organisation : Chuard-Schmid Foundation
Simple arithmetic in children
2013 - 2014
grant-giving organisation : Fondation Henri Moser (Switzerland)
Simple arithmetic in children
2013 - 2017
grant-giving organisation : Marie Curie Career Integration Grant (C.I. G.)
Other partners : Jerome Prado
Relationship between basic and complex numerical abilities
2009 - 2010
grant-giving organisation : Fondation Ernst et Lucie Schidheiny
Representations and strategies in arithmetic word problem solving
2004 - 2006
grant-giving organisation : ESRC (Great Britain)
Mental models and the solution of verbal arithmetic problems
2002 - 2003
grant-giving organisation : British Council/Alliance Franco-British
Arithmetic word problems solving and mental models
2001 - 2003
grant-giving organisation : EU Marie Curie