Effective Teaching Strategies for Dyscalculia and Learning Difficulties in Mathematics

Perspectives from Cognitive Neuroscience

Marie-Pascale Noël, Giannis Karagiannakis

• Publisher: Routledge
• Year: 2022
• ISBN:
  9781000548778
• Edition: 1
• Topic: Education
• Subtopic: Education General

Effective Teaching Strategies for Dyscalculia and Learning Difficulties in Mathematics provides an essential bridge between scientific research and practical interventions with children. It unpacks what we know about the possible cognitive causation of mathematical difficulties in order to improve teaching and therefore learning.

Each chapter considers a specific domain of children's numerical development: counting and the understanding of numbers, understanding of the base-10 system, arithmetic, word problem solving, and understanding rational numbers. The accessible guidance includes a literature review on each topic, surveying how each process develops in children, the difficulties encountered at that level by some pupils, and the intervention studies that have been published. It guides the reader step-by-step through practical guidelines of how to assess these processes and how to build an intervention to help children master them.

Illustrated throughout with examples of materials used in the effective interventions described, this essential guide offers deep understanding and effective strategies for developmental and educational psychologists, special educational needs and/or disabilities coordinators, and teachers working with children experiencing mathematical difficulties.

1 The bases of a cognitive intervention for math learning difficulties or dyscalculia

DOI: 10.4324/b22795-1

1.1 What is dyscalculia or math learning disability?

Educational systems all over the world put a lot of emphasis on developing children’s numerical skills as having some mathematical abilities is crucial for success in modern societies (Ancker & Kaufman, 2007). Yet, not everyone is able to master even the basics of mathematics. For instance, in Minnesota, 21% of 11-year-olds leave primary school without reaching the mathematics level expected of them, and 5% fail to attain even the numeracy skills expected of a 7-year-old (Gross, 2007). These difficulties are usually called ‘Mathematical learning difficulties’ or ‘Math learning disabilities’. When these difficulties are severe, persistent, and not due to poor intelligence or inadequate schooling, they are called ‘developmental dyscalculia’.

The prevalence of dyscalculia is about 6%. For instance, Gross-Tsur, Manor, and Shalev (1996) tested 3,029 Israeli fourth-grade children and detected dyscalculia using 2 main criteria: having an intelligence within the normal range and scoring on a math test lower than the average performance obtained by children 2 years younger (i.e., second-grade children). They found that 6.5% of the children met these criteria. Similarly, in a recent study of 2,421 primary school children, Morsanyi, Bers, McCormack, and McGourty (2018) identified persistent and severe difficulties with mathematics in 6% of the sample. Yet, many of these learning difficulties remain undetected (Barbaresi, Katusic, Colligan, Weaver & Jacobsen, 2005).

Most of the time, these problems are persistent. For instance, Shalev, Manor, Auerbach, and Gross-Tsur (1998) followed the fourth-grade children who were detected as dyscalculic in the study mentioned above over a period of three years. They found that nearly all of them still scored low on a math achievement test (below the 25th percentile) and about half of them had still very severe difficulties (they scored below the 5th percentile). These mathematical learning difficulties persist even into adulthood, and it is estimated that a fifth of adults from England have numeracy skills below the basic level needed for everyday situations (Williams et al., 2003). The difficulties encountered by people with dyscalculia are multiple and may concern, among other things, the mastery of the numerical codes (reading and writing Arabic numbers, understanding the base-10 system), the storage of arithmetic facts in long-term memory (for example, remembering that 5 + 4 = 9, 8 × 3 = 24), performing the calculation procedures, or solving mathematical word problems. In their everyday life, most of them complain about difficulties such as checking the money returned or giving the correct amount (coins) of money in shops, following the proportions indicated when following a cooking recipe, or converting between measurement units such as understanding that quarter to 6 pm is the same time as 5:45 pm.

1.2 What are the causes of these learning difficulties?

Besides global factors such as low socio-economic status, affective difficulties, low intelligence, and so on, research in cognitive science has tried to identify the most basic numerical processes that are the corner stones of all further mathematical learning and which, if impaired, could lead to mathematical learning difficulties.

1.2.1 A basic number processing deficit

One of the most dominant hypotheses in the field is an impaired ‘approximate number system’ (also called ANS). Indeed, babies are born with an innate ability to detect, in an approximate way, the numerosity or the number of items in a set (see Chapter 2). The underlying representation is called the approximate number system. This is a non-verbal representation that supports an intuitive and approximate sense of number in humans as well as in many other animal species (e.g., rats, chimps). According to Wilson and Dehaene (2007) and Piazza et al. (2010), impairment at the level of this approximate number system would explain the appearance of mathematical learning difficulties as this would be the basis of all further numerical development. One way to measure this is to show two collections of objects (e.g., dots) arranged randomly and for a brief moment only (e.g., less than two seconds) in order to prevent any counting and ask the person to select the larger collection among the two. Research has found that the ability to detect the larger set among two (without counting) measured in preschool selectively predicts performance on school mathematics at six years of age (Mazzocco, Feigenson & Halberda, 2011a). Second, it has also been shown that children with mathematical learning difficulties or dyscalculia have lower performance than typically achieving children in such tasks (e.g., Piazza et al., 2010; Mazzocco, Feigenson & Halberda, 2011b). Yet, several other researches failed to replicate these results (for a review, see De Smedt, Noël, Gilmore & Ansari, 2013).

Then, other research argued that it is not so much this approximate number system that is the basis of further learning in mathematics but rather, the child’s ability to connect number symbols (e.g., number words such as ‘five’ or Arabic numbers such as ‘5’) to their meaning, i.e., to the numerical magnitude they represent (Rousselle & Noël, 2007; Noël & Rousselle, 2011). Indeed, symbolic numbers allow us to go beyond an approximate representation of the numbers’ magnitude and to activate a precise number representation, and mathematics requires such a precise representation. Many studies have found that performance in math tests correlates more strongly with the ability to detect among two Arabic numbers which is the bigger than to do a similar task but on sets of items, also called non-symbolic items. In particular, Schneider, Beeres, Coban, Merz, Schmidt, Stricker, and De Smedt (2017) reviewed the studies measuring the association between symbolic (Arabic digits) and non-symbolic (dots) magnitude comparison tasks and math performance and found a stronger association with the symbolic than with the non-symbolic tasks. Also, several studies have reported that people with dyscalculia are especially impaired in symbolic number comparison relative to their typically achieving peers, and not so much in non-symbolic comparison (see for instance, the meta-analysis of Schwenk, Sasanguie, Jörg-Tobias, Kempe, Doebler & Holling, 2017).

Another type of number magnitude processing that has been invoked as a possible cause of dyscalculia is subitizing. Subitizing refers to the fast and accurate identification of the number of items in a small set (usually, between one and four items). A few studies have indeed observed impairment in this process in children with mathematical learning difficulties (e.g., Moeller, Neuburger, Kaufmann, Landerl & Nuerk, 2009; Schleifer & Landerl, 2011; Ashkenazi, Mark-Zigdon & Henik, 2013).

Finally, recent research has been considering another basic aspect of numbers: their ordinal value. This refers to the order of the numbers in the counting sequence. Thus, children with mathematical learning difficulties are slower than typically achieving children to recite the number sequence (Landerl, Bevan & Butterworth, 2004). Furthermore, the ability to judge whether three numbers are presented in ascending order (e.g., 2 3 6), descending order (e.g., 6 3 2), or not in order (e.g., 3 2 6) is a very strong predictor of mathematical achievement, even stronger than number magnitude comparison tasks (Lyons & Beilock, 2011; Morsanyi, O’Mahony & McCormack, 2017), and people with dyscalculia seem to be impaired in this process (Rubinsten & Sury, 2011). Yet, more recent research suggests that this difficulty is not specific to the numerical domain. Indeed, non-numerical order tasks, such as judging the order of months or letters, also correlate with math performance in adults (Vos, Sasanguie, Gevers & Reynvoet, 2017 or Morsanyi, O’Mahony & McCormack, 2017) and can predict first-grade children’s math abilities one year later (O’Connor, Morsanyi & McCormack, 2018). Finally, difficulties in both numerical and non-numerical order tasks are observed in people with dyscalculia (Morsanyi, van Bers, O’Connor & McCormack, 2018). These order difficulties would also be observed in short-term memory as people with dyscalculia are particularly impaired in the retention of the serial order of the items rather than the retention of the items themselves (Attout, Salmon & Majerus, 2015; De Visscher, Szmalec, Van der Linden & Noël, 2015).

Yet, more and more recent works point to the fact that dyscalculia is not a homogeneous profile characterized by a single underlying cause but rather that different profiles of dyscalculia exist. For instance, Skagerlund and Träff (2016) showed that some mathematical learning difficulties result from weaknesses with symbolic number processing, others with both symbolic and non-symbolic number processing, and that more general cognitive deficits can also be the cause of some mathematical learning difficulties (Träff, Olsson, Östergren & Skagerlund, 2017). Szucs (2016) distinguished people with mathematical learning difficulties depending on whether or not they have associated reading problems: people with learning difficulties both in mathematics and in reading would be characterized by weak verbal short-term and working memory while isolated mathematical learning difficulties would be linked to weak visual-spatial short-term and working memory. Using another way to distinguish among people with mathematical learning difficulties, De Visscher, Szmalec, Van der Linden, and Noël (2015) found that a hypersensitivity to similarity interference in memory could be the cause of pure arithmetic fact dyscalculia (i.e., people who have difficulties storing in memory the answer of small calculations) while impaired order processing would lead to more global dyscalculia. Other researchers did not make any a-priori distinction but ran cluster analyses (i.e., a certain type of statistical analysis) to find different subgroups of people with mathematical learning difficulties. Thus, Bartelet, Ansari, Vaessen, and Blomert (2014) found six distinguishable clusters of children with mathematical learning difficulties: (1) those with a weak mental number line, (2) those with a weak approximate number system, (3) those with spatial difficulties, (4) those with difficulties in accessing number magnitude from symbolic numbers, (5) those without any numerical cognitive deficit, and (6) a garden-variety group.

Currently, many authors agree ...