Mathematical learning is important for student’s psychological development, school achievement and the training of workers in science, techonology and engineering 。 With the development of cognitive neuroscience, researchers have shown growing interests in discovering the cognitive factors that contribute to students’ mathematical achievement, and developing novel interventions and examinining the underlying neural mechanisms. Althought the various cognitive factors affecting mathematical achievement have been examined by existing studies, few studies have examined and compared these factors in a single large study, thus leaving several important questions unaddressed. First, there lacks a clear and consistent definition of general cognitive ability, and the relationship between general cognitive ability and mathematical cognitive ability, and their relationship with mathematical achievement have not been clearly understood; Second, it is largely unknown how the contributions of general cognitive abilities and mathematical cognitive abilities to mathematical achievement would change with development and school grade; Third, most of the current interventions to improve mathematical learning and learning difficulites are lab-based, which severely limits the duration, efficacy, transfer and ecological validate of these methods. To address these questions, the current study, using large sample and ecological approaches, to systematically examine the relationship between general cognitive abilities, mathematical cognitive abilities and mathematical achievement, and to develop cognitive interventions and uncover the neural mechinisms.

Study One used 9 computerized and gamified cognitive tasks to test 10660 primary and second students aged between 7-14 years old. We found that: (1) all cognitive tests showed high test-retest reliablities; (2) all cognitive abilities, including spatial short-term memory (SSTM), forward and backward verbal short-term memory (VSTM), reaction time (RT) and reasoning, are developing rapidly between 7 to 14 years old; (3) Boys outperformed girls in multiple object tracking (MOT), figural inductive reasoning (FIR), simple reaction task (SRT), and at age 13 and 14 in complex memory span (CMS), whereas girls outperformaned boys in forward and backward VSTM, and choice reaction time (CRT); (4) there exisits domain-specific and domain-genernal architecture of general cognitive abilities, and factor analysis using bifactor rotation revealed a general factor (G factor) and two specific factors (S factor), including RT and VSTM.

Study Two, based on Study One, further examined the development of mathematical abilities and its reliationship with genernal cognitive abilities, and how they jointly affected students’ mathematical achievement. Our results showed that: (1) All mathematical cogntiive abilities, including number comparison (NC), mental calculation (MC) and spatial mental rotation (MR), developed rapidly during age 7 to 14. Boys are better than girls on mental calucalation, and at age 14 mental rotation, whereas girls are better than boys on number comparison at age 8, 9, and 12, and on mental rotation on age 8 and 9; (2) The mathematical cognitive abilities were moderately correlated with each other and also showed moderate correlations with general cognitive abilities. In particular, number comparison was correlated with various working memory tasks, mental calculation was correlated with working memory and reaction time tasks, and mental rotation was correlated with figural inductive reasoning task; (3) the contribution of cognitive abilities to mathematical achievement increased with school grade; Compared to general cognitive abilities, mathemathical cognitive abilities contributed significantly higher to mathematical achievement, with mental calculation made biggest contribution, followed by mental rotation, whereas the contribution of number comparison was not significant; For general cognitive abilities, spatial short-term memory and configurnal inductive reason made high contributions.

Having revealed the cognitive factors that contributed to mathematical achievement, Study Three used functional Magnetical imaging and cognitive training to examine the effect the working memory training on math-related cognitive abilities, and the underlying neural mehcanisms. Eighteen (Experimental group) and seventeen (Control group) age matched 3rd and 4th grade primary students were recruited in this study. The experimental group were trained on several spatial working memory tasks for 2 months, using home-based, computerized, adaptive cognitive games. We found that (1) compared to the control group, working memory training could significantly improve training group’s performance on spatial working memory, backward verbal short-term memory, complex memory span and multiple object tracking, although the training group by test (pre vs. post) interaction was not significant for the later two tasks. Training also improved subjects’ mathematical achievement, but did not improve subjects’ Raven reasoning performance and mathematical cognitive abilities; (2) Working memory significantly increased the gray matter volumn and functional connectivity in the right middle prefrontal cortex, and the amount of increase was significantly positively correlated with subjects’ improvement in spatial short-term memory, and marginally significantly correlated with subjects’ improvement in backward verbal short-term memory.

Taken together, our study suggests that cognitive abilities are important factors that contributed to primary and secondary students’ mathematical achievement. The general cognitive abilities and mathematical cognitive abilities are moderately correlated; both contributed significantly to mathematical achievement, with greater contributions from mathematical cognitive abilities. Working memory training could significantly improve subjects’ general cognitive abilities that contributed to mathematical achievement and increase the gray matter volume in the prefrontal cortex. These results deepen our understanding on the factors that contribute to mathematical achievement, and provide theoretical basis for the development of cognitive diagnosis and intervention of mathematical learning. The assessment tools and intervention programs developed in this study are ready to be transformed to educational practices.