Department of Counseling, Developmental, and Educational Psychology, Boston College, Chestnut Hill, Massachusetts, United States of America.
PLoS One. 2018 Dec 31;13(12):e0208832. doi: 10.1371/journal.pone.0208832. eCollection 2018.
Children who use advanced arithmetic strategies, such as count-on and decomposition, are more accurate when solving arithmetic problems and are more likely to later have higher levels of math achievement. The present study tested the hypothesis that instruction using linear-spatial representations would activate children's knowledge necessary for use of mental addition strategies and, thus, lead to greater accuracy on addition problems, than instruction using irregular representations of magnitude. As predicted, low-income kindergartners (n = 29) randomly assigned to practice sums up to 10 using materials that instantiated the linear-spatial features of a mental number line (i.e., discrete squares arranged in rows) demonstrated substantially more improvement in solving unpracticed addition problems than children who practiced with irregular materials (i.e., pictures of stars arranged in random arrays). This was particularly true for children with better initial numerical knowledge, which provided support for the idea that existing knowledge was activated. The use of count-on more than doubled from pretest to posttest among children in the linear-spatial condition and this mediated the difference in improvement between conditions. The importance of aligning instructional materials to relevant mental representations-consistent with the Cognitive Alignment Framework for instructional design-is discussed.
儿童使用高级算术策略，如数数和分解，在解决算术问题时更准确，并且更有可能在以后获得更高水平的数学成就。本研究检验了这样一个假设，即使用线性-空间表示的教学会激活儿童使用心理加法策略所需的知识，从而导致在加法问题上的更高准确性，而不是使用数量的不规则表示进行教学。正如预测的那样，随机分配练习使用体现心理数字线线性-空间特征的材料（即排列成行的离散方块）的低收入幼儿园儿童（n = 29）在解决未练习的加法问题方面表现出了显著的进步，比练习使用不规则材料（即随机排列的星星图片）的儿童进步更大。对于初始数值知识较好的儿童来说，这一点尤其如此，这为激活现有知识的观点提供了支持。在直线-空间条件下，从预测试到后测试，儿童使用数数的比例增加了一倍以上，这在条件改善方面存在差异。与教学设计的认知对齐框架一致，根据相关心理表现来调整教学材料的重要性被讨论。
