The contribution of logical reasoning to the learning of mathematics in primary school

It has often been claimed that children's mathematical understanding is based on their ability to reason logically, but there is no good evidence for this causal link. We tested the causal hypothesis about logic and mathematical development in two related studies. In a longitudinal study, we showed that (a) 6‐year‐old children's logical abilities and their working memory predict mathematical achievement 16 months later; and (b) logical scores continued to predict mathematical levels after controls for working memory, whereas working memory scores failed to predict the same measure after controls for differences in logical ability. In our second study, we trained a group of children in logical reasoning and found that they made more progress in mathematics than a control group who were not given this training. These studies establish a causal link between logical reasoning and mathematical learning. Much of children's mathematical knowledge is based on their understanding of its underlying logic.     

A study of retrieval processes in action memory for school-aged children: the impact of recall period and difficulty on action memory

ABSTRACT

Research in action memory for adults has shown that enacted encoding is not only retrieved more frequently but is also faster in comparison to verbal encoding. The aim of this study was to investigate retrieval processes in terms of recall period and recall difficulty for different encoding conditions in school-aged children (8-, 10-, 12-, 14-years old). The participants studied verbal tasks, subject-performed tasks and experimenter-performed tasks, and received immediate and final free-recall tests. The results revealed that older children not only outperformed younger children in terms of accuracy but also outpaced them in all recall periods. Moreover, recalls of subject-performed tasks and experimenter-performed tasks were better and faster compared with verbal encoding on both types of recall test, by increasing throughout the recall periods. These results are discussed in terms of memory strategies and information processing methods. Pedagogic implications for the use of action memory in children's learning are also considered.     

What can we learn about immediate memory from the development of children's free recall?

We ask the question: Which aspects of immediate memory performance improve with age? In two studies, we reexamine the widely held view that primary memory capacity estimates derived from children's immediate free recall are age invariant. This was done by assessing children's immediate free-recall accuracy while also measuring the order in which they elected to recall items (Experiment 1) and by encouraging children to begin free recall with items from towards the end of the presented list (Experiment 2). Across samples aged between 5 and 8 years we replicated the previously reported age-related changes in free-recall serial position functions when aggregated across all trials of the standard task, including an absence of age differences in the recency portion of this curve. However, we also show that this does not reflect the fact that primary memory capacity is constant across age. Instead, when we incorporate order of report information, clear age differences are evident in the recall of list-final items that are output at the start of a participant's response. In addition, the total amount that individuals recalled varied little across different types of free-recall tasks. These findings have clear implications for the use of immediate free recall as a means of providing potential indices of primary memory capacity and in the study of the development of immediate memory.     

Three-year-olds Remember a Novel Event from 20 Months: Evidence for Long-term Memory in Children?

Abstract

Thirty-seven 3-year-old children, who had learned a 9-action event sequence (“making Play-Doh spaghetti”) when they were 20 months old, returned to the lab to determine whether they would be able to verbally and/or behaviourally recall the event after a 12- to 22-month delay. Children originally participated in the event either one or three times and experienced different parts of the event either at three distinct locations (spatial condition) or at a single location (nonspatial condition). Results show very little evidence of long-term memory for the event after one to two years. Returning children did not verbally recall the event, and they did not perform more actions or sequence the event more accurately than controls, with the exception of the older experimental children who had a tendency to sequence the event more accurately than same-aged controls. Although the results indicate that young children's memory for novel events is not very enduring, there were individual differences in children's ability to remember the event. These differences are discussed in terms of potential differences in cognitive abilities and changing knowledge about retrieval strategies or memory.     

Racing dragons and remembering aliens: Benefits of playing number and working memory games on kindergartners' numerical knowledge

Sources that contribute to variation in mathematical achievement include both numerical knowledge and general underlying cognitive processing abilities. The current study tested the benefits of tablet‐based training games that targeted each of these areas for improving the mathematical knowledge of kindergarten‐age children. We hypothesized that playing a number‐based game targeting numerical magnitude knowledge would improve children's broader numerical skills. We also hypothesized that the benefits of playing a working memory (WM) game would transfer to children's numerical knowledge given its important underlying role in mathematics achievement. Kindergarteners from diverse backgrounds (n = 148; 52% girls; M_age = 71.87 months) were randomly assigned to either play a number‐based game, a WM game, or a control game on a tablet for 10 sessions. Structural equation modeling was used to model children's learning gains in mathematics and WM across time. Overall, our results suggest that playing the number game improved kindergarten children's numerical knowledge at the latent level, and these improvements remained stable as assessed 1 month later. However, children in the WM group did not improve their numerical knowledge compared to children in the control condition. Playing both the number game and WM game improved children's WM at the latent level. Importantly, the WM group continued to improve their WM for at least a month after playing the games. The results demonstrate that computerized games that target both domain‐specific and domain‐general skills can benefit a broad range of kindergarten‐aged children.     

Young children's spontaneous utterances of mental terms and the accuracy of their memory behaviors: a different methodological approach

The purpose of this study was to determine whether young children's spontaneous utterances of mental terms would be congruent with the accuracy of their memory behaviours, and whether the use of an incidental memory task would yield similar developmental patterns as other methodologies. It was hypothesized that if children realize that internal mental activities influence behavioural actions, then the children's behavioural actions (recall) would be congruent with their utterances. A total of 27 three‐ and five‐year‐old children spontaneously used cognitive verbs such as knowing, forgetting, remembering, thinking, guessing and betting during a recall task. The results revealed that 39% of the 3‐year‐old children's behavioural responses and 67% of the 5‐year‐old children were congruent with their spontaneous utterances. These and other findings were consistent with studies that utilized different methodologies. Copyright © 2002 John Wiley & Sons, Ltd.     

A “snapshot” of declarative memory: Differing developmental trajectories in episodic and autobiographical memory

Episodic and autobiographical memory are clearly related, yet in both the adult and developmental literatures it is difficult to compare them because of differences in how the constructs are assessed, including differences in content, levels of control, and time since experience. To address these issues, we directly compared children's and adults’ autobiographical and episodic memory using the same controlled paradigm. Participants engaged in a photo-taking activity in a museum (autobiographical encoding) and viewed others’ photographs of the same museum exhibits (episodic encoding). At test, participants classified photos as ones they took, viewed, or novel. In the autobiographical condition older children and adults performed similarly; younger children's performance was lower than adults’. In contrast, in the episodic condition both groups of children performed more poorly than adults. The findings suggest the developmental primacy of autobiographical relative to episodic memory, and that traditional episodic tasks may underestimate older children's declarative memory abilities.     

Within-session spacing improves delayed recall in children

Multiple retrievals of a memory over a spaced manner improve long-term memory performance in infants, children, younger and older adults; however, few studies have examined spacing effects with young school-age children. To expand the understanding of the spacing benefit in children, the current study presented weakly associated English word-pairs to children aged 7–11 and cued their recall two times immediately (massed), after a delay of 5 or 10 items (spaced) or not at all (control). After this encoding session with or without two retrievals, participants were tested two times for memory of all word-pairs: immediately and 30 minutes after the encoding session. Multiple retrievals significantly improved memory on the tests. However, words repeated in a spaced design were remembered at higher rates than those that were massed, while gap size between repetitions (5 or 10) did not differentially impact performance. The data show that a within-session spacing strategy can benefit children's ability to remember word-pairs after 30 minutes. Thus, asking students to recall what they have learned within a lesson is a technique that can be used in a classroom to improve long-term recall.     

Training counting skills and working memory in preschool

Previous studies have shown that early numeracy skills predict later mathematics learning and that they can be improved by training. Cognitive abilities, especially working memory (WM), play an important role in early numeracy, as well. Several studies have shown that working memory is related to early numeracy. So far, existing literature offers a good few examples of studies in which WM training has led to improvements in early numerical performance as well. In this study, we aim at investigating the effects of two different training conditions: (1) counting training; and (2) simultaneous training of WM and counting on five‐ to six‐year‐old preschoolers' (N = 61) counting skills. The results show that domain‐specific training in mathematical skills is more effective in improving early numerical performance than WM and counting training combined. Based on our results, preschool‐aged children do not seem to benefit from short period group training of WM skills. However, because of several intervening factors, one should not conclude that young children's WM training is ineffectual. Instead, future studies should be conducted to further investigate the issue.     

Effects of Motivation on Young Children's Object Recall and Strategy Use

The study was designed to examine the effects of motivation on young children's recall for object names and early-emerging mnemonic activities. Seventy-two 4-year-old children were randomly assigned to 1 of 3 instructional conditions: incidental, intentional, or motivational. Each child was shown 10 small toy objects and provided a 90 s study period prior to recall. The children's mnemonic behaviors were videotaped for subsequent coding. The children in the incidental condition were instructed to simply look at the toys while children in the intentional and motivational condition were given explicit instructions to remember. The motivational group was also told that they could keep whichever toys they remembered. A recognition memory task was employed to examine the extent to which the stimuli were encoded during the study period. The children's recall memory did not vary as a function of instructional condition. Children's use of singular versus multiple strategies was calculated, along with a weighted summary score giving most weight to the participant's use of mature mnemonic strategies. Significant differences in strategy use were found, favoring the motivational condition. Significant positive correlations were found between the weighted summary scores and object recall, and the teacher ratings of mastery motivation and object recall. Mastery motivation was found to be unrelated to the strategic summary scores, failing to mediate strategic behaviors. The results suggest that when providing incentives to remember, children apparently engaged in more effortful mnemonic processing in order to remember the items, even though a greater number of items were not recalled.     

The influence of two years of school music training in secondary school on visual and auditory memory

The present study tested the effect of an extended music curriculum (EMC) for two years in secondary school, consisting of musical instrument, auditory perception, and music theory training, on children's visual and auditory memory. We tested 10-year-old children who had just started EMC and children without EMC (T0) in visual and auditory memory and retested the same children two years later (T1) to observe the effects of school music training. Confounding variables, like intelligence, socioeconomic status, extracurricular schooling, motivation to avoid work, and musical aptitude were controlled. Prior to the beginning of the music training no differences in the control variables and the memory variables between children with and without EMC were revealed. Children with EMC improved significantly from T0 to T1 in visual as well as in auditory memory. Such an improvement was not found for children without EMC. We conclude that extended school music training enhances children's visual and auditory memory.     

Does the use of dolls facilitate children's memory of visits to the doctor?

Age differences in children's recall of salient experiences have frequently been documented, but these findings have routinely been based on studies in which verbal interviews have been employed. Because verbal interview protocols may underestimate the memory of young children, the purpose of this research was to compare the effectiveness of such an interview with two alternative protocols that involved the use of a doll. Using these contrasting protocols, 3-and 5-year-old children were asked to remember the details of a routine physical examination. Neither doll protocol facilitated 3-year-olds' recall of the features of the check-up. In contrast, 5-year-olds who were asked to demonstrate with a doll what happened in their examination showed enhanced recall. The inclusion of a doll had no effect on older or younger children's provision of elaborative detail about their visits to the doctor. Various measures of individual differences (e. g. temperament, language skill) predicted some aspects of the children's recall and elaboration. The findings are discussed in terms of the cognitive skills necessary for effective use of dolls in the assessment process, and are related to problems associated with interviewing young children who are involved in legal proceedings.     

Self-Efficacy and Memory Aging: The Impact of a Memory Intervention Based on Self-Efficacy

ABSTRACT

A multifactorial training program was developed for older adults, to improve self-efficacy and memory performance. Elements designed to raise self-efficacy were integrated into class discussions, homework readings, and practice exercises, including an emphasis on memory potential at any age, self-set goals, and opportunities for mastery. Strategy training focused on association, organization, attention, imagery, and PQRST. Significant improvements for the training group, as compared to a wait-list control group, were observed for memory self-efficacy, locus of control, name recall and story recall. Trained participants were using effective strategies more so than the control group. Final test scores were predicted by self-efficacy, condition assignment, and baseline ability (with some variation across the three tasks). These findings suggest that an integrated and comprehensive training program that incorporates principles of self-efficacy theory has great potential for improving older adults' memory ability.     

Memory development in Libyan and Dutch school children

Cross-cultural similarities and differences in memory were examined in two studies with Libyan and Dutch school children of two different grades. The first study analysed effects of word length and pronunciation speed on recall. Baddeley's phonological loop hypothesis could fully account for the somewhat larger digit span of the Dutch children. The second study investigated effects of rehearsal training on recall. Experimental groups showed a higher performance increase after training than did control groups; Libyan children with the same pretest scores as Dutch children showed higher posttest scores, which could be a consequence of sample differences in age or test-wiseness. The studies demonstrated that current theories provide more precise explanations of cross-cultural differences in structural memory features than in control processes. Implications for instructional practice are discussed.     

Impaired Visuospatial Short-Term Memory in Children with ADHD

Previous studies provide clear evidence that visuospatial memory performance in children with attention-deficit/hyperactivity disorder (ADHD) is significantly lower than in typically developing children. In the present study, we investigated a major cause of their low performance using a spatial span test. Possibly, inattention resulting from lack of motivation or interest causes their low performance so that they do not correctly encode targets to be remembered. On the other hand, a deficit in temporary maintenance per se may cause their low performance; that is, their inefficient use of rehearsal during a retention interval may lead to memory traces’ fast decay. Results in this study indicated that children with ADHD could sustain attention during the encoding phase. Furthermore, their performance at delayed recall was significantly lower than immediate recall, but delayed recall did not affect typically developing children's performance. These results provide evidence for the likelihood that a factor causing children with ADHD difficulty in temporarily maintaining visuospatial information is fast decay of memory traces as a result of inefficient use of rehearsal, not inattention in the encoding phase.     

Own-age biases in verbal person memory

Two experiments examined own-age biases in younger adults', older adults', and children's verbal person memory. In line with findings from face recognition studies, Experiment 1 showed that younger adults had a better recall of own-age than of other-age targets, while older adults were unaffected by target age. Participants' self-reported interest in targets did not predict target memory. Experiment 2, which examined children's and younger adults' memory of own- and other-age targets, showed an own-age advantage in children's but not in younger adults' verbal person memory. Differences in expertise of own-/other-age targets, in combination with a development of expertise throughout the Hfespan, may account for the findings, although alternative explanations should be considered. Implications for theory and practice are discussed.     

Contrasting Memory for Temporal-Source and Memory for Content in Children's Discrimination of Repeated Events

The current studies examined the separate roles that memory of temporal-source and memory of content play in children's discrimination of occurrences of a repeated event. The studies were also designed to determine the impact of age and retention interval on each of these components. In Experiment One, 4- to 5- versus 6- to 8-year-old children experienced six occurrences of a repeated event; each occurrence had the same underlying structure; however, a different version or instantiation of each item was included in each occurrence of the event. At either 1 or 6 week delay, the children were asked to recall which instantiation of the item was included in the final occurrence. In Experiment Two, children were required to recall as many instantiations as they could, prior to making a decision about which instantiation was included in the final occurrence. The results indicated that: (a) children's capacity to correctly identify the final instantiation declined over time and increased with age; (b) children's capacity to provide an instantiation that was temporally close to the final occurrence declined over time and increased with age; and (c) children's ability to remember the source of an instantiation decreased over time irrespective of any loss of memory for content. The results were discussed in relation to current theories of memory and children's eyewitness memory. © 1997 John Wiley & Sons, Ltd.     

Phonological similarity and lexicality effects in children's verbal short-term memory: Concerns about the interpretation of probed recall data

Probed recall tasks are often used to assess aspects of children's verbal short-term memory development because they are not subject to potentially confounding output effects. However, the marked recency effects that are observed in probed recall means that these tasks are potentially insensitive to experimental manipulations when later serial positions are probed. This clouds the interpretation of data from probed recall studies in which children of different ages are presented with to-be-remembered lists of different lengths. In two experiments we examined the magnitude of phonological similarity and lexicality effects in both 5- to 6- and 8- to 9-year-old children. In each case performance on probed recall tasks was contrasted with that seen on tests of serial recognition. The results indicated that probed recall tasks are potentially less sensitive to experimental manipulations in younger than older children. However, comparable effects of both phonological similarity and lexicality were seen in both age groups using serial recognition procedures. These findings have implications for the interpretation of other studies that have examined the development of verbal short-term memory using probed recall and for theoretical accounts of the development of phonological similarity and lexicality effects in children.     

‘I Remember When I Learned That!’ developmental and gender differences in children's memories of learning episodes

Eighty 4‐ to 9‐year‐old children answered factual knowledge questions in math, science and social studies during one‐on‐one interviews. Children indicated whether they had known or guessed each answer, and whether they (a) remembered the moment they learned the answer (episodic response) or (b) did not remember. For episodic responses, children provided memory narratives of learning episodes. One third of children's responses identified a learning episode. There was a developmental trend in which older children were more episodic than younger children, and when children knew and provided correct answers, there was a gender difference in which females were more episodic than males. Developmental and gender differences in the characteristics of memory narratives were also apparent. Copyright © 2010 John Wiley & Sons, Ltd.