Practicing visual working memory and reasoning tasks boost children’s math skills


Young children who practice visual working memory and reasoning tasks improve their math skills more than children who focus on spatial rotation exercises, according to a large study by researchers at Karolinska Institutet in Sweden.

The findings support the notion that training spatial cognition can enhance academic performance and that when it comes to math, the type of training matters. The study is published in the journal Nature Human Behaviour.

“In this large, randomized study we found that when it comes to enhancing mathematical learning in young children, the type of cognitive training performed plays a significant role,” says corresponding author Torkel Klingberg, professor in the Department of Neuroscience, Karolinska Institutet.

“It is an important finding because it provides strong evidence that cognitive training transfers to an ability that is different from the one you practiced.”

Numerous studies have linked spatial ability – that is the capacity to understand and remember dimensional relations among objects – to performance in science, technology, engineering and mathematics. As a result, some employers in these fields use spatial ability tests to vet candidates during the hiring process.

This has also fueled an interest in spatial cognition training, which focuses on improving one’s ability to memorize and manipulate various shapes and objects and spot patterns in recurring sequences.

Some schools today include spatial exercises as part of their tutoring.

However, previous studies assessing the effect of spatial training on academic performance have had mixed results, with some showing significant improvement and others no effect at all. Thus, there is a need for large, randomized studies to determine if and to what extent spatial cognition training actually improves performance.

In this study, more than 17,000 Swedish schoolchildren between the ages of six and eight completed cognitive training via an app for either 20 or 33 minutes per day over the course of seven weeks. In the first week, the children were given identical exercises, after which they were randomly split into one of five training plans.

In all groups, children spent about half of their time on mathematical number line tasks. The remaining time was randomly allotted to different proportions of cognitive training in the form of rotation tasks (2D mental rotation and tangram puzzle), visual working memory tasks or non-verbal reasoning tasks (see examples below for details).

The children’s math performance was tested in the first, fifth and seventh week.

The researchers found that all groups improved on mathematical performance, but that reasoning training had the largest positive impact followed by working memory tasks.

Both reasoning and memory training significantly outperformed rotation training when it came to mathematical improvement.

They also observed that the benefits of cognitive training could differ threefold between individuals. That could explain differences in results from some previous studies seeing as individual characteristics of study participants tend to impact the results.

The researchers note there were some limitations to the study, including the lack of a passive control group that would allow for an estimation of the absolute effect size. Also, this study did not include a group of students who received math training only.

“While it is likely that for any given test, training on that particular skill is the most time-effective way to improve test results, our study offers a proof of principle that spatial cognitive training transfers to academic abilities,” Torkel Klingberg says.

“Given the wide range of areas associated with spatial cognition, it is possible that training transfers to multiple areas and we believe this should be included in any calculation by teachers and policymakers of how time-efficient spatial training is relative to training for a particular test.”

The researchers have received funding by the Swedish Research Council. Torkel Klingberg holds an unpaid position as chief scientific officer for Cognition Matters, the non-profit foundation that owns the cognition training app Vektor that was used in this study.

Examples of training tasks in the study

  • In a number line task, a person is asked to identify the right position of a number on a line bound by a start and an end point. Difficulty is typically moderated by removing spatial cues, for example ticks on the number line, and progress to include mathematical problems such as addition, subtraction and division.
  • In a visual working memory task, a person is asked to recollect visual objects. In this study, the children reproduced a sequence of dots on a grid by touching the screen. Difficulty was increased by adding more items.
  • In a non-verbal reasoning task, a person is asked to complete sequences of spatial patterns. In this study, the children were asked to choose the correct image to fill a blank space based on previous sequences. Difficulty was increased by adding new dimensions such as colors, shapes and dots.
  • In a rotation task, a person is asked to figure out what an object would look like if rotated. In this study, the children were asked to rotate a 2D object to fit various angles. Difficulty was moderated by increasing the angle of the rotation or the complexity of the object being rotated.

Training programs
Executive functions training

Executive functions are defined as a set of general purpose mechanisms that regulate action and cognition (Miyake and Friedman, 2012). They are commonly composed of three related, albeit separate, components: shifting, which involves moving back and forth between multiple tasks, operations, or mental sets; updating, which requires monitoring and actively manipulating working memory representations; and inhibition, which is the ability to deliberately inhibit a dominant, automatic, or prepotent response (Monsell, 1996; Miyake et al., 2000; Clair-Thompson and Gathercole, 2006; Miyake and Friedman, 2012).

These cognitive skills have been associated positively with several academic and socioemotional outcomes, such as mathematical achievement, adaptive and learning-related behaviors, and social competences (Clair-Thompson and Gathercole, 2006; Riggs et al., 2006; Brock et al., 2009; Razza and Blair, 2009; Best et al., 2011).

During their school years, children must deal with academic and social challenges that require them to successfully implement EF. For instance, students must switch quickly from one subject to another and transition from one academic task to another and from one skill to another in response to teachers’ instructions.

They must also remember and manipulate academic information and drop irrelevant data and add new data to update their skills. Moreover, children are required to inhibit dominant, automatic responses, such as being distracted by a classmate, and instead, remain focused on the teacher. These EF skills allow children to self-regulate their behavior and their academic performance.

Given the essential role of EF in children’s successful development, numerous training programs have been developed to improve children’s EF skills. For instance, the Tools of the Mind curriculum (Bodrova and Leong, 2007) is based on activities embedded in the school curricula, such as tasks to help self-regulate private speech and dramatic role playing and facilitate memory and attention. Diamond et al. (2007) applied this approach with 4- and 5-year-old children who received the training for 1 year, during which time the teachers spent approximately 80% of each day promoting EF skills.

Another example is the play-based approach, such as the intervention developed by Traverso et al. (2015), in which children act out roles and have to collaborate to reach specified goals (30 min, 3 times per week for 1 month). In both cases, the participants of the training were preschoolers, and the results indicated improved EF skills (Diamond et al., 2007; Traverso et al., 2015). As a disadvantage, however, implementing these types of programs required psychologists and trained teachers to introduce methodological changes to the academic curricula. In addition, the implementation of these programs in primary schools may depend largely on specific reforms implemented by education policy makers.

Mathematics school-based interventions

Apart from the EF trainings, mathematics interventions have also been related to student academic improvements (Starkey et al., 2004; Bryant et al., 2008; Ehlert and Fritz, 2013). For example, Bryant et al. (2008) developed a program in which trained tutors enhanced children’s mathematical skills by having the children work in small groups where they incorporated strategies such as modeling, thinking aloud, guided practice, and error correction.

Their results revealed significant improvements in children’s math skills and achievement levels. In the case of Starkey et al. (2004), children’s math knowledge was enhanced through the implementation of three training strategies: classroom activities incorporated by the teachers into the math curriculum; teacher trainings designed to increase their understanding of children’s mathematical development and enable them to implement the intervention; and mathematics classes administered at home that involved parents and children.

Even with significant improvements, these types of training require teachers to prepare general tasks, and thus, they do not customize teaching to fit the level of each student. In contrast, computerized activities allow every child to progress at his/her own pace. Accordingly, a computerized mathematics game can be incorporated into the individual student’s routine and adapted to the child’s specific level of performance.

Children’s characteristics related to academic performance

When assessing the effectivity of any training program, it is necessary to take into account a set of children’s characteristics that have been associated with student academic achievement. Specifically, in this study, we considered three of the most researched variables as our control variables: temperament, socioeconomic status (SES), and gender.

Regarding children’s temperament, effortful control (EC) and negative emotionality (NE) have been extensively related to academic achievement (Gumora and Arsenio, 2002; Valiente et al., 2007, 2010, 2011, 2012, 2013; Neuenschwander et al., 2012). EC involves the individual differences in the self-regulatory process, such as attention, inhibition control, and activation control, whereas NE refers to children’s negative reactivity and includes emotions such as anger, sadness, discomfort, fear, and shyness. Previous findings have revealed that students’ EC contributes positively to academic performance (Neuenschwander et al., 2012; Valiente et al., 2013).

In contrast, children’s NE is negatively associated with school achievement (Gumora and Arsenio, 2002; Valiente et al., 2010, 2012). With respect to SES, there is vast literature showing the impact of family SES on student academic achievement and indicating that low-family income is related negatively to children’s academic success (Hart and Risley, 1995; McLoyd, 1998; Davis-Kean, 2005; Valiente et al., 2011; Carvalho and Novo, 2012; Hoff, 2013; Sánchez-Pérez et al., submitted; for a meta-analytic review, see Sirin, 2005). Finally, gender has yielded inconsistent results across studies (see Davis-Kean, 2005; Valiente et al., 2007; Neuenschwander et al., 2012; Sánchez-Pérez et al., 2015, for contrasting results). Therefore, we considered students’ gender, temperament (i.e., EC and NE) and SES as potential control variables.

The present study

The motivation for the present study began with the requirement of some schools to improve the academic achievement of their students, mainly mathematical skills. Given this need, and the aforementioned relevance of some cognitive abilities for students to success at school, our research group designed a computer-based training program aimed to improve children’s cognitive skills and school achievement, in a sample of typically developing school-age children.

Thorell et al. (2009) suggested that “as cognitive functions may vary in how easily they can be improved through training; focusing on specific cognitive functions and thereafter possibly use a combination of those training paradigms that have documented effects, appears to be the most rational approach” (Thorell et al., 2009, p. 107).

Following that recommendation, we included two components in our training program. One involved computerized WM tasks due to their significant improvements on children’s cognitive skills and school achievement. Moreover, because students’ math skills were the main concern of the school management team, a commercial software product that teaches and reinforces mathematical skills was introduced as the second training component. Finally, with the aim to keep students engaged in the training tasks, an external reward system was also introduced. These activities were designed to be implemented by teachers as part of the daily school activities.

A wide range of potential training effects were taken into consideration to assess the impact of the training program as a whole, but also the effects of each component of the training program (WM and math exercises, respectively) on children’s performance. On the basis of previous findings, we hypothesized that our training program will produce improvement in children’s cognitive skills such as EF and intelligence (IQ); and in school achievement, mainly math and reading skills.

Improvement in cognitive skills

There is evidence that children who performed WM, planning, and inhibitory control computerized games had positive near transfer effects similar to those of trained skills and had a positive impact on students’ school grades (Goldin et al., 2014). Interventions focused on working memory (WM) have also shown near transfer effects, such as improvements in visual (Thorell et al., 2009; Wong et al., 2014; Studer-Luethi et al., 2015) and verbal WM (Thorell et al., 2009; Wong et al., 2014) skills. Given previous findings and the well-established co-occurrence of WM and the other executive functions, namely, shifting and inhibition, we hypothesized that WM training will produce improvement in the other two EF components.

Working memory is also positively associated with intelligence. The association seems to be mediated by high-level attentional control involving the prefrontal cortex (Conway et al., 2003). Attentional control is needed to actively maintain task-relevant information in the presence of internal and external sources of distraction (Unsworth et al., 2014). A recent study has shown that training the updating component of WM through the n-back task increased participants’ IQ (Jaeggi et al., 2008). Accordingly, we hypothesized that WM training will increase children’s intelligence.

Improvement in academic achievement

Concerning academic achievement, WM training has been associated with improvement in math grades (Holmes and Gathercole, 2014), math standardized tests (Söderqvist and Bergman-Nutley, 2015), and arithmetic abilities (Bergman-Nutley and Klingberg, 2014). WM skills are likely to be required to master math competences, such as counting, mental arithmetic, measurement abilities, and space abilities (for a meta-analysis review, see Friso-van den Bos et al., 2013). Consequently, we expected to find a significant increment in mathematical skills in those children who practiced the WM activities.

Working memory training has also be shown to increase reading skills (Loosli et al., 2012; Karbach et al., 2015; Söderqvist and Bergman-Nutley, 2015) and vocabulary (Studer-Luethi et al., 2015), possibly due to the observed correlation between some reading aspects (e.g., reading comprehension and spelling) and verbal WM (Seigneuric et al., 2000; Pham and Hasson, 2014). Reading improvement may be due to the phonological storage component of WM, which has been shown to be a relevant factor for the development of a variety of linguistic abilities such as reading, vocabulary, and comprehension (Gathercole and Baddeley, 1990). Accordingly, we hypothesized that our training program would boost several aspects of children’s reading skills.

The current computer-based training program
Our computer-based training program presents several advantages not found in most of the aforementioned interventions. First, the ease with which it can be implemented in school settings and the ease by which the difficulty of the tasks can be adapted to fit the child’s ability level. Second, most of previously mentioned interventions have been conducted in lab-like environments, where it appears that the laboratory was moved to a school context.

In this sense, the training may be perceived as a supplemental, short-term activity implemented in the schools, and as such, it fails to garner teacher commitment. Our program was designed to be integrated into the school routine based on the characteristics of the school environment; thus, it did not involve moving the lab environment into the school context. The training program was conducted by designated teachers who had undergone a short training program.

Third, the tasks were designed to cover not just a specific grade, but rather several primary education grades. Moreover, because the students worked independently, the difficulty of the activities could be adapted to each child’s ability and rhythm. Fourth, in the specific case of computer-based training, it is required that children perform repetitive tasks during mid-length to long interventions.

Under such circumstances, the role of the child’s engagement is crucial for the training program to achieve the highest level of efficacy. Previous researchers have found that external rewards increase intrinsic motivation (Cameron et al., 2005) and therefore may encourage children to continue performing repetitive tasks and, consequently, gain the potential benefits. We addressed the key point of the students’ adherence to the training by including an engagement program.

reference link :

More information: Judd, N., Klingberg, T. Training spatial cognition enhances mathematical learning in a randomized study of 17,000 children. Nat Hum Behav (2021). ,


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