Oscillatory electroencephalographic patterns of arithmetic problem solving in fourth graders

Numerous studies have identified neurophysiological correlates of performing arithmetic in adults. For example, oscillatory electroencephalographic (EEG) patterns associated with retrieval and procedural strategies are well established. Whereas fact retrieval has been linked to enhanced left-hemispheric theta ERS (event-related synchronization), procedural strategies are accompanied by increased bilateral alpha ERD (event-related desynchronization). It is currently not clear if these findings generalize to children. Our study is the first to investigate oscillatory EEG activity related to strategy use and arithmetic operations in children. We assessed ERD/ERS correlates of 31 children in fourth grade (aged between nine and ten years) during arithmetic problem solving. We presented multiplication and subtraction problems, which children solved with fact retrieval or a procedure. We analyzed these four problem categories (retrieved multiplications, retrieved subtractions, procedural multiplications, and procedural subtractions) in our study. In summary, we found similar strategy-related patterns to those reported in previous studies with adults. That is, retrieval problems elicited stronger left-hemispheric theta ERS and weaker alpha ERD as compared to procedural problems. Interestingly, we observed neurophysiological differences between multiplications and subtractions within retrieval problems. Although there were no response time or accuracy differences, retrieved multiplications were accompanied by larger theta ERS than retrieved subtractions. This finding could indicate that retrieval of multiplication and subtraction facts are distinct processes, and/or that multiplications are more frequently retrieved than subtractions in this age group.

Deskripsi kemampuan berpikir kritis siswa dalam pemecahan masalah aritmetika sosial di SMPN 1 Labuhan Haji Tahun Ajaran 2020/2021

The research aims to describe students' critical thinking ability in terms of social arithmetic problem problem 2020/2021. As for the indicators of critical thinking ability covering clarification, furtherment, strategy, and inference. This type of research is qualitative descriptive research with a quantitative approach. The method of data collection includes a test of the critical thinking ability of 3 items of description and interview. Based on data analysis, it could be concluded that: (1) the high category of subjects of 3 students, indicating that in the clarifying, subclassification, strategy, and inference parts can state the problem perfectly and completely (2) the only moderate number of subjects at 5 students, pointing out that in the clarifying, subclassification, strategy, and inference sections can present the problem less completely (3) next, the low number of subjects of 12 students, I will be able to explain that in the clarification,assement, strategy, and inference will be unable to declare the problem.

Oscillatory Electroencephalographic Patterns of Arithmetic Problem Solving in Fourth Graders

Numerous studies have identified neurophysiological correlates of performing arithmetic in adults. For example, oscillatory electroencephalographic (EEG) patterns associated with retrieval and procedural strategies are well established. Whereas fact retrieval has been linked to enhanced left-hemispheric theta ERS (event-related synchronization), procedural strategies are accompanied by increased bilateral alpha ERD (event-related desynchronization). It is currently not clear if these findings generalize to children.Our study is the first to investigate oscillatory EEG activity related to strategy use and arithmetic operations in children. We assessed ERD/ERS correlates of 31 children in fourth grade (aged between nine and ten years) during arithmetic problem solving. We presented multiplication and subtraction problems, which children solved with fact retrieval or via a procedure. Based on both problem size and verbal strategy reports, we analyzed these problem types separately for each operation.We found similar strategy-related patterns to those reported in previous studies with adults. That is, retrieval problems elicited stronger left-hemispheric theta ERS and weaker alpha ERD as compared to procedural problems. Interestingly, we observed differences between multiplications and subtractions within retrieval problems. Although there were no response time and accuracy differences, retrieved multiplications were accompanied by larger theta ERS than retrieved subtractions. This finding could indicate that retrieval of multiplication and subtraction facts are distinct processes, and/or that multiplications are more frequently retrieved than subtractions in this age group.

Improving Understanding of Mathematical Equivalence

Modify arithmetic problem formats to make the relational equation structure more transparent. We describe this practice and three additional evidence-based practices: (1) introducing the equal sign outside of arithmetic, (2) concreteness fading activities, and (3) comparing and explaining different problem formats and problem-solving strategies.

Cultural Differences in Susceptibility to Stereotype Threat: France versus India

Objectives Negative aging stereotypes make older adults perform below their true potential in a number of cognitive domains. This phenomenon, known as Age-Based Stereotype Threat, is currently viewed as a powerful factor contributing to an overestimation of cognitive decline in normal aging. However, age-based stereotype threat has been investigated almost exclusively in Western countries. Whether this phenomenon is universal or culture-specific is unknown. Method Here, we first ran a pilot study (N = 106) in which we assessed French and Indian participants’ attitudes towards aging. Then, we assessed stereotype threat effects on arithmetic problem-solving performance and strategies in French and Indian older adults (N = 104). Results We found that French older adults have more negative implicit attitudes towards aging than Indian older adults. We also found that culture modulates age-based stereotype threat effects. Whereas French older adults experienced stereotype threat on both selection and execution of strategies on all arithmetic problems, Indian older adults experienced this threat only in their strategy selection on harder problems. Most interestingly, cultural differences emerged on arithmetic problems under stereotype threat condition, where otherwise no cultural differences were found in the control condition. Discussion Our findings have important implications for understanding how cultural contexts change aging effects on human cognition and age-related difference in cognitive performance.

What we count dictates how we count: A tale of two encodings

We argue that what we count has a crucial impact on how we count, to the extent that even adults may have difficulty using elementary mathematical notions in concrete situations. Specifically, we investigate how the use of certain types of quantities (durations, heights, number of floors) may emphasize the ordinality of the numbers featured in a problem, whereas other quantities (collections, weights, prices) may emphasize the cardinality of the depicted numerical situations. We suggest that this distinction leads to the construction of one of two possible encodings, either a cardinal or an ordinal representation. This difference should, in turn, constrain the way we approach problems, influencing our mathematical reasoning in multiple activities. This hypothesis is tested in six experiments (N = 916), using different versions of multiple-strategy arithmetic word problems. We show that the distinction between cardinal and ordinal quantities predicts problem sorting (Experiment 1), perception of similarity between problems (Experiment 2), direct problem comparison (Experiment 3), choice of a solving algorithm (Experiment 4), problem solvability estimation (Experiment 5) and solution validity assessment (Experiment 6). The results provide converging clues shedding light into the fundamental importance of the cardinal versus ordinal distinction on adults’ reasoning about numerical situations. Overall, we report multiple evidence that general, non-mathematical knowledge associated with the use of different quantities shapes adults’ encoding, recoding and solving of mathematical word problems. The implications regarding mathematical cognition and theories of arithmetic problem solving are discussed.

Are content effects out of sight? An eye-tracking study of arithmetic problem solving

General, non-mathematical knowledge about the entities described in an arithmetic word problem may interfere with its encoding. We used behavioral and eye-tracking measures to investigate how the use of specific quantities may foster a cardinal representation of the numbers mentioned in a problem, whereas other quantities may favor an ordinal representation instead. We asked 50 pre-service teachers to complete a solution validity assessment task. We compared participants’ gaze patterns on isomorphic problems to gather insights into their encoded representations. On problems featuring cardinal quantities, we found that specific sentences describing elements relevant in a cardinal understanding of the problems but irrelevant otherwise were looked at longer and were the focus of a higher number of backward eye movements. Additionally, an increase in pupil dilation on correctly solved cardinal problems supported the idea that participants need to engage in a recoding process when facing semantic incongruence.

When adding is right: Temporal order judgements reveal spatial attention shifts during two-digit mental arithmetic

Recent research suggests that addition and subtraction induce horizontal shifts of attention. Previous studies used single-digit (1d) problems or verification paradigms that lend themselves to alternative solution strategies beyond mental arithmetic. To measure spatial attention during the active production of solutions to complex two-digit arithmetic problems (2d) without manual motor involvement, we used a temporal order judgement (TOJ) paradigm in which two lateralised targets were sequentially presented on screen with a varying stimulus onset asynchrony (SOA). Participants verbally indicated which target appeared first. By varying the delay between the arithmetic problem presentation and the TOJ task, we investigated how arithmetically induced attention shifts develop over time (Experiment 1, n = 31 and Experiment 2, n = 58). In Experiment 2, we additionally varied the carry property of the arithmetic task to examine how task difficulty modulates the effects. In the arithmetic task, participants were first presented with the arithmetic problem via headphones and performed the TOJ task after the delay before responding to the arithmetic task. To account for spontaneous attentional biases, a baseline TOJ was run without arithmetic processing. Both experiments revealed that addition induces shifts of spatial attention to the right suggesting that visuospatial attention mechanisms are recruited during complex arithmetic. We observed no difference in spatial attention between the carry and noncarry condition (Experiment 2). No shifts were observed for subtraction problems. No common and conclusive influence of delay was observed across experiments. Qualitative differences between addition and subtraction and the role of task difficulty are discussed.