Working memory and individual differences in mathematics achievement: A longitudinal study from first grade to second grade

This longitudinal study examined the relationship between working memory and individual differences in mathematics. Working memory measures, comprising the phonological loop, the visuospatial sketchpad, and the central executive, were administered at the start of first grade. Mathematics achievement was assessed 4 months later (at the middle of first grade) and 1 year later (at the start of second grade). Working memory was significantly related to mathematics achievement in both grades, showing that working memory clearly predicts later mathematics achievement. The central executive was a unique predictor of both first- and second-grade mathematics achievement. There were age-related differences with regard to the contribution of the slave systems to mathematics performance; the visuospatial sketchpad was a unique predictor of first-grade, but not second-grade, mathematics achievement, whereas the phonological loop emerged as a unique predictor of second-grade, but not first-grade, mathematics achievement.     

Semantic processing of mathematical gestures

Objective

To examine whether or not university mathematics students semantically process gestures depicting mathematical functions (mathematical gestures) similarly to the way they process action gestures and sentences. Semantic processing was indexed by the N400 effect.

Results

The N400 effect elicited by words primed with mathematical gestures (e.g. “converging” and “decreasing”) was the same in amplitude, latency and topography as that elicited by words primed with action gestures (e.g. drive and lift), and that for terminal words of sentences.

Significance and conclusion

Findings provide a within-subject demonstration that the topographies of the gesture N400 effect for both action and mathematical words are indistinguishable from that of the standard language N400 effect. This suggests that mathematical function words are processed by the general language semantic system and do not appear to involve areas involved in other mathematical concepts (e.g. numerosity).     

The trajectory of mathematics skills and working memory thresholds in girls with fragile X syndrome

Fragile X syndrome is a common genetic disorder associated with executive function deficits and poor mathematics achievement. In the present study, we examined changes in math performance during the elementary and middle school years in girls with fragile X syndrome, changes in the working memory loads under which children could complete a cognitive switching task, and the association between these two areas of function, in girls with fragile X syndrome relative to their peers. Our findings indicate that the trajectory of math and executive function skills of girls with fragile X differs from that of their peers and that these skills contribute to predicting math achievement and growth in math performance over time. Also, changes in math performance were associated with incremental increases in working memory demands, suggesting that girls with fragile X have a lower threshold for being able to perform under increasing task demands. Still, we found improvement in executive function performance between 10 and 12 years in girls with fragile X rather than a performance plateau as has been reported in other studies. The findings implicate the importance of early intervention in mathematics for girls with fragile X that addresses poor calculation skills, the supporting numerical skills, and deficits in executive functions, including working memory.     

Hand Gesture and Mathematics Learning: Lessons From an Avatar

A beneficial effect of gesture on learning has been demonstrated in multiple domains, including mathematics, science, and foreign language vocabulary. However, because gesture is known to co‐vary with other non‐verbal behaviors, including eye gaze and prosody along with face, lip, and body movements, it is possible the beneficial effect of gesture is instead attributable to these other behaviors. We used a computer‐generated animated pedagogical agent to control both verbal and non‐verbal behavior. Children viewed lessons on mathematical equivalence in which an avatar either gestured or did not gesture, while eye gaze, head position, and lip movements remained identical across gesture conditions. Children who observed the gesturing avatar learned more, and they solved problems more quickly. Moreover, those children who learned were more likely to transfer and generalize their knowledge. These findings provide converging evidence that gesture facilitates math learning, and they reveal the potential for using technology to study non‐verbal behavior in controlled experiments.     

充分加工条件下听写困难儿童的整体字形加工特点

听写困难是指儿童能够认读不能听写的现象。前期研究表明,在快速加工条件下,听写困难儿童存在整体字形加工缺陷。本研究使用学习-回忆方法,考察在充分加工条件下,听写困难儿童的整体字形加工特点。实验结果表明,在充分加工条件下,听写困难儿童不仅能够加工并形成双部件合体字的整体字形表征;而且,也能够在同字形组织水平上,形成多部件合体字的整体字形表征。因此,在充分加工条件下,听写困难儿童的整体字形加工能力正常。     

Interhemispheric cooperation and non-cooperation during word recognition: evidence for callosal transfer dysfunction in dyslexic adults

Participants report briefly-presented words more accurately when two copies are presented, one in the left visual field (LVF) and another in the right visual field (RVF), than when only a single copy is presented. This effect is known as the 'redundant bilateral advantage' and has been interpreted as evidence for interhemispheric cooperation. We investigated the redundant bilateral advantage in dyslexic adults and matched controls as a means of assessing communication between the hemispheres in dyslexia. Consistent with previous research, normal adult readers in Experiment 1 showed significantly higher accuracy on a word report task when identical word stimuli were presented bilaterally, compared to unilateral RVF or LVF presentation. Dyslexics, however, did not show the bilateral advantage. In Experiment 2, words were presented above fixation, below fixation or in both positions. In this experiment both dyslexics and controls benefited from the redundant presentation. Experiment 3 combined whole words in one visual field with word fragments in the other visual field (the initial and final letters separated by spaces). Controls showed a bilateral advantage but dyslexics did not. In Experiments 1 and 3, the dyslexics showed significantly lower accuracy for LVF trials than controls, but the groups did not differ for RVF trials. The findings suggest that dyslexics have a problem of interhemispheric integration and not a general problem of processing two lexical inputs simultaneously.     

学习困难儿童元记忆能力的实验研究

该研究以有和无意义联系的两种中文词对为材料,采用2×3×2混合实验设计,对小学三到五年级的学习困难儿童与学优儿童的JOL监测判断水平和学习时间分配之间的差异及其发展特点进行研究。结果表明：（1）学习困难儿童的JOL判断等级显著低于学优儿童;（2）在自定步骤学习过程中,随着年级增长,学习困难儿童能够根据学习材料的性质决定其学习时间的分配策略,表现出一定的元记忆控制能力,但其分配策略的有效性不高;（3）学习困难儿童的JOL监测判断水平和学习时间分配策略从小三到小五在缓慢提高;（4）学习困难儿童的JOL监测判断和学习时间分配之间存在交互影响。     

Comparing Mathematics Interventions: The Effects of Cover-Copy-Compare Alone and Combined with Performance Feedback on Digits Correct and Incorrect

The purpose of this study was to compare the isolated effects of cover-copy-compare (CCC) with the combined effects of CCC and two types of performance feedback (i.e., digits correct and incorrect per minute) on sixth grade students’ mathematics fluency and accuracy. An alternating treatments design was employed to compare treatments across 16 weeks. Participants included three general education sixth grade students whose teachers recommended them for additional help with mathematics calculation. No differentiation between treatments was demonstrated for any of the participants and individual differences pertaining to the number of sessions needed to reach and consistently perform at mastery levels were found. Follow-up data at 4 and 12 days following termination of the intervention phase indicated that all participants continued to perform at mastery levels. Generalization to a slightly more difficult mathematics skill yielded pre-intervention to post-intervention increases, albeit small. Students rated all three treatment conditions favorably.     

Awareness of a gender stereotype,personal beliefs and self-perceptions regarding math ability: when boys do not surpass girls

The negative reputation of women in mathematics and its consequences on their self-perceptions have been extensively demonstrated. However, in France and other countries, the younger the students, the less pronounced these gender differences are. The focus of this study was to explore whether children of two age groups (fourth graders and seventh graders) are aware of a math-ability gender stereotype favorable to boys, and to determine their personal beliefs on mathematics ability. The link between this gender stereotype and self-perceptions was also examined. As expected, there was not a clear-cut awareness of a math-ability gender stereotype favorable to boys. More surprising, girls in both age groups and seventh-grade boys believed that girls do better than boys. Moreover, when their gender identity was made salient, the boys who believed in girl superiority perceived their own performance in mathematics as lower. The girls, on the other hand, regardless of their age and stereotype awareness or personal beliefs, perceived their performance in math as higher when their gender identity was made salient than when it was not.