Simple pictorial mathematics problems for children: locating sources of cognitive load and how to reduce it

Pictorial representations are often used to help children understand the situation described in a given number-sentence scheme. These static pictorial problems essentially attempt to depict a dynamic situation (e.g., One bird flies away while there are three birds still sitting on the fence). Previous research suggested that such pictorial decrease problems impose higher cognitive load on children than the corresponding increase problems, even though both are solved with addition. However, the source of this cognitive load is unclear. It could be the direction of the depicted change or the position of the unknown (start vs. end set). To address this question and disentangle the sources of the load, we presented the problems in two different formats: 1) The conventional static one-picture problems and, 2) An adapted threepicture problem-format, which depicted the dynamic change in sequential steps. We also examined whether the three-picture problem-format makes the decrease problems easier. Seventy-nine first-graders participated in this study. Results showed that, overall, problems with the position of the unknown at the end were easier to solve than the ones in which the unknown was at the start. Furthermore, three-picture decrease problems with the unknown in the last position were easier than the one-picture decrease problems, and therefore appear to be a meaningful way to make such problems easier for children to understand.</div

Pictorial representations of simple arithmetic problems are not always helpful: A cognitive load perspective

At the start of mathematics education children are often presented with addition and subtraction problems in the form of pictures. They are asked to solve the problems by filling in corresponding number sentences. One type of problem concerns the representation of an increase or a decrease in a depicted amount. A decrease is, however, more difficult to represent in paper pictorially than an increase. Within the Cognitive Load Theory framework, we expected that commonly used decrease problems would be harder and slower to solve than increase problems because of higher intrinsic cognitive load. We also hypothesized that combining the pictorial information with auditory information would reduce this load and, as a result, would lead to improved performance. We further expected that these effects would be most prominent in children who score below average on a general mathematics test. We conducted an experiment with sixty children attending the first grade of primary school, who were divided into a higher and lower mathematics-achieving group. As expected, children performed worse on the decrease problems compared to the increase problems. Also, the combination of pictorial and auditory information reduced the accuracy lag of the decrease problems compared to the increase problems. With response time this effect occurred only in the group of lower mathematics achieving children. These results are in line with the cognitive load theory framework, but we also offer an alternative explanation regarding attention

Working memory and number line representations in single-digit addition: approximate versus exact, nonsymbolic versus symbolic

How do kindergarteners solve different single-digit addition problem formats? We administered problems that differed solely on the basis of two dimensions: response type (approximate or exact), and stimulus type (nonsymbolic, i.e., dots, or symbolic, i.e., Arabic numbers). We examined how performance differs across these dimensions, and which cognitive mechanism (mental model, transcoding, or phonological storage) underlies performance in each problem format with respect to working memory (WM) resources and mental number line representations. As expected, nonsymbolic problem formats were easier than symbolic ones. The visuospatial sketchpad was the primary predictor of nonsymbolic addition. Symbolic problem formats were harder because they either required the storage and manipulation of quantitative symbols phonologically or taxed more WM resources than their nonsymbolic counterparts. In symbolic addition, WM and mental number line results showed that when an approximate response was needed, children transcoded the information to the nonsymbolic code. When an exact response was needed, however, they phonologically stored numerical information in the symbolic code. Lastly, we found that more accurate symbolic mental number line representations were related to better performance in exact addition problem formats, not the approximate ones. This study extends our understanding of the cognitive processes underlying children's simple addition skills

Nonsymbolic and symbolic magnitude comparison skills as longitudinal predictors of mathematical achievement

What developmental roles do nonsymbolic (e.g., dot arrays) and symbolic (i.e., Arabic numerals) magnitude comparison skills play in children’s mathematics? In the literature, one notices several gaps and contradictory findings. We assessed a large sample in kindergarten, grade 1 and 2 on two well-known nonsymbolic and symbolic magnitude comparison measures. We also assessed children’s initial IQ and developing Working Memory (WM) capacities. Results demonstrated that symbolic and nonsymbolic comparison had different developmental trajectories; the first underwent larger developmental improvements. Both skills were important longitudinal predictors of children’s future mathematical achievement above and beyond IQ and WM. Nonsymbolic comparison was predictive in kindergarten. Symbolic comparison, however, was consistently a stronger predictor of future mathematics compared to nonsymbolic, and its predictive power at the early stages was even comparable to that of IQ. Furthermore, results bring forth methodological implications regarding the role of different types of magnitude comparison measures

Cognitive predictors of children’s development in mathematics achievement: a latent growth modeling approach

Research has identified various domain-general and domain-specific cognitive abilities as predictors of children’s individual differences in mathematics achievement. However, research into the predictors of children’s individual growth rates, i.e., between-person differences in within-person change, in mathematics achievement is scarce. We assessed 334 children’s domain-general and mathematics-specific early cognitive abilities and their general mathematics achievement longitudinally across four time-points within the 1st and 2nd grade of primary school. As expected, a constellation of multiple cognitive abilities contributed to the children’s starting level of mathematical success. Specifically, latent growth modeling revealed that WM abilities, IQ, counting skills, nonsymbolic and symbolic approximate arithmetic and comparison skills explained individual differences in the children’s initial status on a curriculum-based general mathematics achievement test. Surprisingly, however, only one out of all the assessed cognitive abilities was a unique predictor of the children’s individual growth rates in mathematics achievement: their performance in the symbolic approximate addition task. In this task, children were asked to estimate the sum of two large numbers and decide if this estimated sum was smaller or larger compared to a third number. Our findings demonstrate the importance of multiple domain-general and mathematics-specific cognitive skills for identifying children at risk of struggling with mathematics and highlight the significance of early approximate arithmetic skills for the development of one’s mathematical success. We argue the need for more research focus on explaining children’s individual growth rates in mathematics achievement