Number facts are commonly assumed to be verbally stored in an associative multiplication fact retrieval network. Prominent evidence for this assumption comes from so-called operand-related errors (e.g. 4 × 6 = 28). However, little is known about the development of this network in children and its relation to verbal and non-verbal memories. In a longitudinal design, we explored elementary school children from grades 3 and 4 in a multiplication verification task with the operand-related and -unrelated distractors. We examined the contribution (...) of multiplicative fact retrieval by verbal and visuo-spatial short-term and working memory. Children in grade 4 showed smaller reaction times in all conditions. However, there was no significant difference in errors between grades. Contribution of verbal and visuo-spatial working memory also changed with grade. Multiplication correlated with verbal working memory and performance in grade 3 but with visuo-spatial working memory and performance in grade 4. We suggest that the relation to verbal working memory in grade 3 indicates primary linguistic learning of and access to multiplication in grade 3 which is probably based on verbal repetition of the multiplication table heavily practiced in grades 2 and 3. However, the relation to visuo-spatial semantic working memory in grade 4 suggests that there is a shift from verbal to visual and semantic learning in grade 4. This shifting may be induced because later in elementary school, multiplication problems are rather carried out via more written, i.e., visual tasks, which also involve executive functions. More generally, the current data indicates that mathematical development is not generally characterized by a steady progress in performance; rather verbal and non-verbal memory contributions of performance shift over time, probably due to different learning contents. (shrink)

Three studies were conducted to examine the relation of spatial visualization to solving kinematics problems that involved either predicting the two‐dimensional motion of an object, translating from one frame of reference to another, or interpreting kinematics graphs. In Study 1, 60 physics‐naíve students were administered kinematics problems and spatial visualization ability tests. In Study 2, 17 (8 high‐ and 9 low‐spatial ability) additional students completed think‐aloud protocols while they solved the kinematics problems. In Study 3, the eye movements of fifteen (...) (9 high‐ and 6 low‐spatial ability) students were recorded while the students solved kinematics problems. In contrast to high‐spatial students, most low‐spatial students did not combine two motion vectors, were unable to switch frames of reference, and tended to interpret graphs literally. The results of the study suggest an important relationship between spatial visualization ability and solving kinematics problems with multiple spatial parameters. (shrink)

This article reports three experiments that investigated the relationship between working memory capacity and syllogistic and five-term series spatial inference. A series of complex and simple verbal and spatial working memory measures were employed. Correlational analyses showed that verbal and spatial working memory span tasks consistently predicted syllogistic and spatial reasoning performance. A confirmatory factor analysis showed that three factors best accounted for the data--a verbal, a spatial, and a general factor. Syllogistic reasoning performance loaded all three factors, whilst spatial (...) reasoning loaded only the general factor. The implications of these findings are discussed in the context of reasoning theories and contemporary accounts of the structure of working memory. (shrink)

In the field of mathematics education, one of the main questions remaining under debate is whether students’ development of mathematical reasoning and problem-solving is aided more by solving tasks with given instructions or by solving them without instructions. It has been argued, that providing little or no instruction for a mathematical task generates a mathematical struggle, which can facilitate learning. This view in contrast, tasks in which routine procedures can be applied can lead to mechanical repetition with little or no (...) conceptual understanding. This study contrasts Creative Mathematical Reasoning (CMR), in which students must construct the mathematical method, with Algorithmic Reasoning (AR), in which predetermined methods and procedures on how to solve the task are given. Moreover, measures of fluid intelligence and working memory capacity are included in the analyses alongside the students’ math tracks. The results show that practicing with CMR tasks was superior to practicing with AR tasks in terms of students’ performance onpracticed test tasksandtransfer test tasks. Cognitive proficiency was shown to have an effect on students’ learning for both CMR and AR learning conditions. However, math tracks (advanced versus a more basic level) showed no significant effect. It is argued that going beyond step-by-step textbook solutions is essential and that students need to be presented with mathematical activities involving a struggle. In the CMR approach, students must focus on the relevant information in order to solve the task, and the characteristics of CMR tasks can guide students to the structural features that are critical for aiding comprehension. (shrink)

To date, few studies have focused on mapping the mechanisms underlying children’s skills in science. This study investigated to what extent logical reasoning, spatial processing, and working memory, tapped at age 9-10-years, are predictive of physics skills at age 12-13-years. The study used a sample of 81 children (37 girls). Measures of mathematics and reading were also included in the study. Multiple regression analysis showed that spatial processing, and verbal working memory accounted for a similar amount of unique variance (4.5–4.6%) (...) while logical reasoning accounted for 5.7% variance. Physics is a multivariate discipline that draws upon numerous cognitive resources. Logical reasoning ability is a key component in order for children to learn about abstract physics facts, concepts, theories, and applying complex scientific methods. Spatial processing is important as it may sub-serve the assembly of diverse sources of visual-spatial information into a spatial-schematic image. The working memory system provides a flexible and efficient mental workspace that can supervise, coordinate, and execute processes involved in physics problem solving. (shrink)

Depictive expressions of thought predate written language by thousands of years. They have evolved in communities through a kind of informal user testing that has refined them. Analyzing common visual communications reveals consistencies that illuminate how people think as well as guide design; the process can be brought into the laboratory and accelerated. Like language, visual communications abstract and schematize; unlike language, they use properties of the page (e.g., proximity and place: center, horizontal/up–down, vertical/left–right) and the marks on it (e.g., (...) dots, lines, arrows, boxes, blobs, likenesses, symbols) to convey meanings. The visual expressions of these meanings (e.g., individual, category, order, relation, correspondence, continuum, hierarchy) have analogs in language, gesture, and especially in the patterns that are created when people design the world around them, arranging things into piles and rows and hierarchies and arrays, spatial-abstraction-action interconnections termed spractions. The designed world is a diagram. (shrink)

We examined spontaneous external offloading in a study requiring participants to plan the shortest route to connect locations on maps while satisfying ordering constraints. We manipulated map difficulty (low/high) and the possibility for participants to offload cognition by allowing/not allowing them to use a pen during planning (offloading/no offloading). Participants used more types of offloading strategies in the high (vs. low) difficulty maps and showed a better performance in the offloading (vs. no offloading) condition in the high difficulty maps only. (...) However, even in the low difficulty maps, cognition was offloaded, especially when participants solved the high difficulty maps first (perseveration effect). The use of offloading strategies and offloading-supported planning performance were positively related with visual search ability, while performance in the no offloading condition was positively related with spatial working memory. Findings show that offloading strategies are spontaneously deployed in a partly adaptive way in route planning on maps. (shrink)

To our knowledge, this is one of the first studies to test different theoretical models of working memory in childhood based on a computerized assessment. We tested this across several countries: Argentina, Brazil, Canada, Italy, and UK. The present study addressed the wider macro-cultural context and how this impacts working memory. We used two economic indices to characterize the participating countries and ranked the countries based on the Global Index of Cognitive Skills and Educational Attainment. Children between 5 and 10 (...) years completed the same set of short-term and working memory tests. There were two main findings. First, there was a similar pattern in verbal working memory across countries, which suggests that this skill may be relatively consistent across different cultural groups. In contrast, the pattern for visuo-spatial working memory was different across countries, which may explained by cultural differences and educational rankings of the countries. The second main finding was that both a domain-general model and a domain-specific model provided a reasonably good fit with the data, there was the high relationship between the verbal and visuo-spatial working memory constructs across the countries in the latter model. Thus, it may be a more parsimonious choice to rely on a three-factor model. The data also suggest culture-similar patterns in a computerized assessment of working memory. (shrink)

Working memory resources are needed for processing and maintenance of information during cognitive tasks. Many models have been developed to capture the effects of limited working memory resources on performance. However, most of these models do not account for the finding that different individuals show different sensitivities to working memory demands, and none of the models predicts individual subjects' patterns of performance. We propose a computational model that accounts for differences in working memory capacity in terms of a quantity called (...) source activation, which is used to maintain goal‐relevant information in an available state. We apply this model to capture the working memory effects of individual subjects at a fine level of detail across two experiments. This, we argue, strengthens the interpretation of source activation as working memory capacity. (shrink)

Working memory resources are needed for processing and maintenance of information during cognitive tasks. Many models have been developed to capture the effects of limited working memory resources on performance. However, most of these models do not account for the finding that different individuals show different sensitivities to working memory demands, and none of the models predicts individual subjects' patterns of performance. We propose a computational model that accounts for differences in working memory capacity in terms of a quantity called (...) source activation, which is used to maintain goal‐relevant information in an available state. We apply this model to capture the working memory effects of individual subjects at a fine level of detail across two experiments. This, we argue, strengthens the interpretation of source activation as working memory capacity. (shrink)

This paper reports a study of the roles of visuo-spatial and verbal working memory capacities in solving a planning task - the five-disc Tower of London (TOL) task. An individual differences approach was taken. Sixty adult participants were tested on 20 TOL tasks of varying difficulty. Total moves over the 20 TOL tasks was taken as a measure of performance. Participants were also assessed on measures of fluid intelligence (Raven's matrices), verbal short-term storage (Digit span), verbal working memory span (Silly (...) Sentence span), visuo-spatial short-term storage (Visual Pattern span and Corsi Block span), visuo-spatial working memory (Corsi Distance Estimation), visuo-spatial processing speed (Manikin test), and verbal speed (Rehearsal speed). Exploratory factor analysis using an oblique rotation method revealed three factors which were interpreted as (1) a visuo-spatial working memory factor, (2) an age-speed factor, and (3) a verbal working memory factor. The visuo-spatial and verbal factors were only moderately correlated. Performance on the TOL task loaded on the visuo-spatial factor but did not load on the other factors. It is concluded that the predominant goal-selection strategy adopted in solving the TOL relies on visuo-spatial working memory capacity and particularly involves the active ''inner scribe'' spatial rehearsal mechanism. These correlational analyses confirm and extend results previously obtained by use of dual task methods, (Phillips, Wynn, Gilhooly, Della Sala, & Logie, 1999). (shrink)

Although various models of ethical decision making have implicitly called upon constructs governed by working memory capacity , a study examining this relationship specifically has not been conducted. Using a sense making framework of EDM, we examined the relationship between WMC and various sensemaking processes contributing to EDM. Participants completed an online assessment comprised of a demographic survey, intelligence test, various EDM measures, and the Automated Operation Span task to determine WMC. Results indicated that WMC accounted for unique variance above (...) and beyond ethics education, exposure to ethical issues, and intelligence in several sensemaking processes. Additionally, a marginally significant effect of WMC was also found with reference to EDM. Individual differences in WMC appear likely to play an important role in the ethical decision-making process, and future researchers may wish to consider their potential influences. (shrink)