Dyscalculia and Line/Number-Line Bisection

 

Physical Line Bisection and Mental Number-Line Bisection: Tasks That Distinguish Students with Dyscalculia from Typically Developing Students

Quickly, and without calculating: What number lies halfway between 34 and 58?

 

Figure 1: The Cerebral Hemispheres

If you answered 44 or 45, your response was similar to that of people with typical arithmetic functioning, even though the correct answer is 46. The task you have just performed is called mental number-line bisection. In this task, people are asked to identify, as quickly as possible, the number located halfway between two numbers presented to them.

People with typical arithmetic functioning show a slight leftward bias in this task, known as pseudoneglect. This bias means that the number perceived as the midpoint tends to lie to the left of the true midpoint on the number line. In other words, the perceived numerical midpoint is slightly smaller than the actual midpoint.

Neglect is a condition in which damage to one of the brain’s hemispheres, as shown in Figure 1, produces reduced attention and awareness on one side of the visual field. A person with neglect is unable to process and perceive stimuli on one side of the body or the surrounding environment. Neglect generally appears on the side opposite the damaged hemisphere. For example, damage to the right hemisphere may lead to difficulty processing stimuli on the left side of the body.

The slight leftward bias found in mental number-line bisection occurs in people who do not have brain damage and whose arithmetic functioning is typical. It is therefore not an expression of neglect, but of pseudoneglect. The phenomenon probably originates in a slight asymmetry of attention between the two hemispheres that exists in healthy people.

The right hemisphere is more dominant than the left hemisphere in attentional functions. Because the right hemisphere is associated with the left visual field, attention is slightly biased toward the left side of the visual field. As a result, the midpoint of the mental number line is perceived as lying slightly to the left of its correct position.

This slight leftward bias in people with typical arithmetic functioning occurs not only when bisecting a mental number line, but also when they are asked to bisect a physical line, meaning a simple line rather than a number line.

What happens in students with dyscalculia? Do they also show a slight leftward bias in mental number-line bisection and physical line bisection?

This question was examined in the present study, which included 24 Israeli university students, 12 of whom had dyscalculia. The participants with dyscalculia had typical reading and attention abilities, as well as typical intelligence, as measured using Raven’s Progressive Matrices.

The students with dyscalculia performed differently from the students without dyscalculia on both tasks. In the mental number-line bisection task, the students with dyscalculia showed a greater leftward bias than the students with typical arithmetic functioning. By contrast, in the physical line-bisection task, the students with dyscalculia showed less leftward bias than the students with typical arithmetic functioning.

What accounts for the different performance of students with dyscalculia?

The researchers who conducted the study, Dr. Sarit Ashkenazi and Professor Avishai Henik, argued that the difference in performance on the mental number-line bisection task resulted from the way numbers are represented on the mental number line. In people with dyscalculia, this representation tends to be more logarithmic than it is in people without dyscalculia.

As shown in Figure 2, a logarithmic representation means that the distance between consecutive small numbers, such as 2 and 3, is greater than the distance between consecutive large numbers, such as 12 and 13. In a linear representation, by contrast, the distance between any two consecutive numbers remains constant regardless of their magnitude.

 

Figure 2: A linear scale compared with a logarithmic scale

Figure 2 shows that when people are asked to identify quickly, and without calculation, the midpoint between 4 and 16, the midpoint on a linear scale is 10, whereas the midpoint on a logarithmic scale is 8. Thus, the more logarithmic the mental representation of the number line is, the farther to the left of the true midpoint the perceived midpoint will be. In numerical terms, it will be perceived as smaller than the actual midpoint.

Children’s mental representations of numbers tend to be logarithmic. With development and learning, these representations become increasingly linear. The present study provides further evidence that the mental representation of numbers in university students with dyscalculia remains more logarithmic than it is in students without dyscalculia. The more linear the representation becomes, the better the person’s performance on various aspects of arithmetic.

The mental number-line bisection task can therefore distinguish between students with and without dyscalculia.

Ashkenazi and Henik also found differences between students with and without dyscalculia in the physical line-bisection task. Whereas students without dyscalculia showed pseudoneglect and bisected a physical line at a point slightly to the left of its true midpoint, students with dyscalculia did not show a consistent leftward bias when bisecting a physical line.

How can these differences be explained?

As noted above, the leftward bias in physical line bisection among typically functioning individuals results from an attentional asymmetry between the hemispheres. Ashkenazi and Henik proposed that people with dyscalculia may have a subtle impairment in spatial attention, and that this impairment results in a reduced leftward bias during physical line bisection.

It is important to recall that the participants in this study did not have attention difficulties. The reduced leftward bias was therefore not related to comorbidity between dyscalculia and attention or concentration difficulties.

Ashkenazi and Henik suggested that students with dyscalculia have less hemispheric asymmetry in attention than students without dyscalculia. Reduced attentional asymmetry results in a weaker leftward bias during physical line bisection.

This reduction in attentional asymmetry among people with dyscalculia may result from an impairment or functional difficulty in a brain region called the intraparietal sulcus, or IPS, particularly in the right hemisphere, as shown in Figure 3.

 

Figure 3: The IPS

There is evidence that the IPS is impaired or functions atypically in people with dyscalculia. There is also evidence that the IPS is strongly involved in physical line-bisection tasks.

Abnormalities in the right IPS have been found in women with Turner syndrome, one of the symptoms of which is dyscalculia. In a task requiring comparison between quantities, represented by groups of dots, people with dyscalculia showed reduced brain activity in the right IPS. In addition, brain stimulation applied to the right IPS of people without arithmetic impairments produces performance patterns resembling those observed in people with dyscalculia.

In summary, mental number-line bisection and physical line-bisection tasks may be able to distinguish between children and adults with and without dyscalculia. People without dyscalculia are expected to show a slight leftward bias in both tasks. People with dyscalculia are expected to show no leftward bias in physical line bisection, but a stronger leftward bias in mental number-line bisection.

Ashkenazi, S., & Henik, A. (2010). A dissociation between physical and mental number bisection in developmental dyscalculia. Neuropsychologia, 48(10), 2861–2868.