Number comparison and number ordering as predictors of arithmetic performance in adults: Exploring the link between the two skills, and investigating the question of domain-specificity.

Recent evidence has highlighted the important role that number ordering skills play in arithmetic abilities (e.g., Lyons & Beilock, 2011). In fact, Lyons et al. (2014) demonstrated that although at the start of formal mathematics education number comparison skills are the best predictors of arithmetic performance, from around the age of 10, number ordering skills become the strongest numerical predictors of arithmetic abilities. In the current study we demonstrated that number comparison and ordering skills were both significantly related to arithmetic performance in adults, and the effect size was greater in the case of ordering skills. Additionally, we found that the effect of number comparison skills on arithmetic performance was partially mediated by number ordering skills. Moreover, performance on comparison and ordering tasks involving the months of the year was also strongly correlated with arithmetic skills, and participants displayed similar (canonical or reverse) distance effects on the comparison and ordering tasks involving months as when the tasks included numbers. This suggests that the processes responsible for the link between comparison and ordering skills and arithmetic performance are not specific to the domain of numbers. Finally, a factor analysis indicated that performance on comparison and ordering tasks loaded on a factor which included performance on a number line task and self-reported spatial thinking styles. These results substantially extend previous research on the role of order processing abilities in mental arithmetic.

Reversibility Iteration Method to Understand Reaction Networks and to Solve Micro-Kinetics in Heterogeneous Catalysis

Solving microkinetics of catalytic systems, which bridges microscopic processes and macroscopic reaction rates, is currently vital for understanding catalysis in silico. However, traditional microkinetic solvers possess several drawbacks that make the process slow and unreliable for complicated catalytic systems. In this paper, a new approach, the so-called reversibility iteration method (RIM), is developed to solve microkinetics for catalytic systems. Using the chemical potential notation we previously proposed to simplify the kinetic framework, the catalytic systems can be analytically illustrated to be logically equivalent to the electric circuit, and the reaction rate and coverage can be calculated by updating the values of reversibilities. Compared to the traditional modified Newton iteration method (NIM), our method is not sensitive to the initial guess of the solution and typically requires fewer iteration steps. Moreover, the method does not require arbitrary-precision arithmetic and has a higher probability of successfully solving the system. These features make it ∼1000 times faster than the modified Newton iteration method for the systems we tested. Moreover, the derived concept and the mathematical framework presented in this work may provide new insight into catalytic reaction networks.