TEACHING MULTIPLICATION FACTS TO STUDENTS WITH LEARNING DISABILITIES

Multiple baseline designs were used to examine the effects of an instructional package on accuracy of performance in solving multiplication facts by 3 students with learning disabilities. The instructional package included the following components: (a) a modified instructional sequence in which multiplication facts were grouped into the zeros, ones, doubles, fives, and nines categories, and those remaining; (b) identification of the category in which each fact belonged; (c) mnemonic strategies associated with solving facts in each category; and (d) steps to be completed for solving facts in each category. Results indicated that the instructional package produced substantial and immediate effects. After receiving instruction, a participant's accuracy was often 100%, and this was maintained throughout the evaluation even as other strategies were introduced. Comparable results occurred across students, demonstrating replication of the effects of the instructional package.     

数学焦虑、问题形式对乘法估算的影响

采用由研究者所修订的数学焦虑量表和自行设计的估算问题,通过对大学生被试进行团体测验,考察了在纯数字运算和应用题两种情境中数学焦虑对估算加工的影响以及估算中的问题大小效应。结果显示：（1）数学焦虑情绪在纯数字与应用题两种情境下都对估算有显著影响;（2）情境对估算准确率影响显著,纯数字情境下的估算准确率显著高于应用题情境;（3）在应用题情境估算中发现明显的问题大小效应,在纯数字情境估算中却未发现该效应。     

Preschool language and visuospatial skills respectively predict multiplication and addition/subtraction skills in middle school children

A converging body of evidence from neuroimaging, behavioral, and neuropsychology studies suggests that different arithmetic operations rely on distinct neuro-cognitive processes: while addition and subtraction may rely more on visuospatial reasoning, multiplication would depend more on verbal abilities. In this paper, we tested this hypothesis in a longitudinal study measuring language and visuospatial skills in 358 preschoolers, and testing their mental calculation skills at the beginning of middle school. Language skills at 5.5 years significantly predicted multiplication, but not addition nor subtraction scores at 11.5 years. Conversely, early visuospatial skills predicted addition and subtraction, but not multiplication scores. These results provide strong support for the existence of a double dissociation in mental arithmetic operations, and demonstrate the existence of long-lasting links between language/visuospatial skills and specific calculation abilities.     

加法和乘法算式的表征方式

探讨加法和乘法算式的心理表征方式问题 ,检验加法和乘法算式表征分离假设 :对于加法算式主要形成视觉 -阿拉伯数字表征 ,对于乘法算式主要形成听觉 -言语表征。要求 2 4位大学生 (男女生各半 )回答一位数加法和乘法问题 (例如 ,2 +3 ,2× 3) ,这些问题中的算数用阿拉伯数字 (1～ 9)呈现或者汉字数字 (壹～玖 )呈现。结果是与阿拉伯数字条件相比 ,汉字数字条件对加法问题产生更大的影响 ,这与假设一致 ,支持Campbell等人的编码复杂性假设 (Encodingcomplexhypothesis) ,但又具体化和发展了这一假设