运算动量效应的理论解释及其发展性预测因素

了解运算偏差的形成与发展对探索算数运算系统的内在机制具有重要意义, 早期的算数运算能力是儿童理解和进行复杂数学运算的基础。运算动量偏差是指个体在进行基本数学运算时倾向于高估加法运算结果而低估减法运算结果的一种运算偏差, 主要包括三种理论解释, 即注意转移假说、启发式解释和压缩解释。鉴于运算动量效应在成年群体中相对稳定却在不同发展阶段儿童中存在不一致的证据, 数学能力的提高与空间注意的成熟可结合不同的理论解释来阐明儿童发展过程中运算动量效应的变化趋势。未来可以进一步整合多种研究任务以揭示运算动量效应的发展轨迹, 考察数量表征系统与运算动量效应间的关联, 探究运算动量效应在不同运算符号中的稳定性, 探讨不同因素共同作用对运算动量效应的影响, 并设计有关数学能力的干预措施以减少运算动量效应这一运算偏差。

The theoretical accounts and developmental predictors of operational momentum effect

As a fundamental mathematical skill, approximate arithmetic is one of the critical abilities in daily life to represent and operate on the numerosity of objects approximately. Investigating how arithmetic bias is formed and developed is important to understand the underlying mechanism of arithmetic operation. When performing arithmetic operations, individuals tend to overestimate outcomes in addition and underestimate outcomes in subtraction, such estimation bias is called the Operational Momentum (OM) effect. Currently there were three mainstream theoretical accounts (i.e., attentional shift account, heuristic account, compression account). The main differences among these three accounts are whether the spatial-numerical association is invoked and how deeply the numerical elements are processed. The attentional shift account, as the most recognized explanation mechanism, argues that the OM effect is due to spatial shifts of attention along the mental number line. When calculating and estimating numerosities, individuals first map the first operand onto the mental number line, then, according to the kind of the operation sign, the attentional focus was shifted to a new location on the mental number line with the distance of the representation of second operand on the mental number line. When performing mental arithmetic, the mental representation usually shifts positively on the mental number line along the direction of operation sign, therefore, the outcome is represented larger in addition and multiplication and smaller in subtraction and division (Katz & Knops, 2014; McCrink et al., 2007). The heuristic account is firstly used to explain the findings of the OM effect in infants, which assumes that individuals use intuitive operational logic and adopt a simple heuristic to solve the mathematical problems: addition indicates larger outcomes and subtraction indicates smaller outcomes. The compression account assumes that the OM effect is the result of the necessary compression and decompression process on the logarithmic compression of the mental number line. This account is still in the theoretical stage and needs more empirical work to verify. Furthermore, the three accounts are not mutually exclusive - some findings suggested the OM effect can be explained by multiple accounts.Early arithmetic is fundamental to the acquisition of complex mathematical concepts and advanced arithmetic operations. By reviewing recent findings of the OM effect in early development, we found many studies have demonstrated the OM effect in infants (Cassia et al., 2016, 2017; McCrink & Wynn, 2009), but it remained puzzled in later development as work in children have shown inconsistent findings. As age increases, research work with 6- to 7-year-old children observed an inverse OM effect (Knops et al., 2013), however, adult-consistent OM effect has been found in 7- to 12-year-old children and the OM effect monotonically increased with age (Jang & Cho, 2022; Pinheiro-Chagas et al., 2018). Together these show a U-shaped developmental trend in OM effect between preschoolers and school-age children. This trend may be related to the improvement of the mathematical ability and the maturation of the spatial attention. Specially, with the acquisition of the mathematical knowledge, preschool children’s mathematical ability would improve, the knowledge of the counting principle and other related mathematical concepts appear to influence the performance of the arithmetic computations. Meanwhile, the maturation of the spatial attention may influence the mapping of numerical representations onto the mental number line therefore influences the OM effect.Given the importance of the underlying mechanism of the OM effect on understanding the arithmetic operation in development, future research in developmental field should investigate: 1) the developmental trajectory of the OM effect with multiple paradigms and techniques; 2) the role of the Approximate Number System in the origin and development of the OM effect; 3) generalizability of the OM effect in complex arithmetic or even algebraic operations; 4) the joint effect of various factors (e.g., mathematical abilities and spatial attention) on the OM effect; and 5) the intervention for arithmetic bias.