From whole numbers to fractions to word problems: Hierarchical relations in mathematics knowledge for Chinese Grade 6 students.

It is well established in the literature that fraction knowledge is important for learning more advanced mathematics, but the hierarchical relations among whole number arithmetic, fraction knowledge, and mathematics word problem-solving are not well understood. In the current study, Chinese Grade 6 students (N = 1160; 465 girls; Mage = 12.1 years, SD = 0.6) completed whole number arithmetic (addition, subtraction, multiplication, and division), fraction (mapping, equivalence, comparison, and arithmetic), and mathematics word problem-solving assessments. They also completed two control measures: number writing speed and nonverbal intelligence. Structural equation modeling was used to investigate the hierarchical relations among these assessments. Among the four fraction tasks, the correlations were low to moderate, suggesting that each task may tap into a unique aspect of fraction understanding. In the model, whole number arithmetic was directly related to all four fraction tasks, but was only indirectly related to mathematics word problem-solving, through fraction arithmetic. Only fraction arithmetic, the most advanced fraction skill, directly predicted mathematics word problem-solving. These findings are consistent with the view that students need to build these associations into their mathematics hierarchy to advance their mathematical competence.

Instability, changes, and internal structure of children's attitudes toward mathematics in primary school: A four-wave investigation.

The longitudinal person-oriented study aimed to explore profiles, stability, gender differences, and compositional relations of math attitudes by tracking Chinese third graders (Ntotal = 1013, Mage(T1) = 8.92 ± 0.46, Ngirls = 404) in four waves with 1-year intervals. Five profiles and unstable transitional probabilities were identified among the four waves. The relations between enjoyment to confidence and value shifted from reciprocity to enjoyment dominance, but value negatively predicted later enjoyment and confidence. Additionally, boys' advantages were significant in late elementary school (fifth, sixth grades) and girls benefited from initial positive attitudes. These findings suggest that Chinese students' math attitudes in middle childhood are unstable, shaped by internal and external environmental dynamics, and need to be further explored in cross-cultural research.

Math attitudes and math anxiety predict students' perception of teacher support in primary school, but not vice versa.

BACKGROUND: Both teacher support and math attitudes have been identified as associated with math anxiety in primary school children. However, little is known about how they are interrelated longitudinally. AIMS: The study was designed to examine the associations among perceived teacher support, math attitudes, and math anxiety in Chinese primary school students. SAMPLE: The sample included 1802 students (56.16% boys) initially in the third and fourth grades in two public schools in China. METHODS: A three-year cross-lagged panel design was conducted to examine the associations among perceived teacher support, math attitudes, and math anxiety. Moreover, a multigroup analysis was used to examine whether the associations varied by gender. RESULTS: There were reciprocal associations over time between math attitudes and math anxiety. Meanwhile, both math attitudes and math anxiety significantly predicted perceived teacher support one year later, but not vice versa. Further, the association between T1 math anxiety and T3 perceived teacher support was mediated by T2 math attitudes; the association between T1 math attitudes and T3 perceived teacher support, on the other hand, was mediated by T2 math anxiety. Moreover, there were no significant gender differences in these associations. CONCLUSIONS: Math anxiety and math attitudes objectively affected each other, and both of them significantly predicted later perceived teacher support, but not vice versa. This study demonstrates that children are not merely passive recipients of environmental influences and offers theoretical guidance for intervention practices that aim to reduce the risk of math anxiety.

How Important Are Parental Career Expectations? A Subtle and Long-Term Influence on Adolescents' Career Aspirations.

Perceived parental expectations of adolescents have been linked to many high school consequences, yet few studies have examined the relationship between perceived parental expectations and adolescents' career aspirations, and potential mechanisms that underlie these associations. To address this research gap, this study investigated the reciprocal relationship between perceived parental expectations and career aspirations, as well as the mediating role of adolescents' career exploration among Chinese adolescents. Using a longitudinal design, a total of 2540 senior high school students (51.38% girls, Mage = 17.09 ± 0.69) participated in the study. The results showed that perceived parental expectations of adolescents have no direct impact on their subsequent career aspirations. A longitudinal mediating role of career exploration was found between perceived parental expectations and career aspirations. No gender differences were found in any of the pathways. These findings provided support for helping adolescents better set their career aspirations by acknowledging the critical role of parental expectations and the mediating role of career exploration.

The influence of semantic alignment on the performance of addition and division operation: age-related differences.

Semantic alignment refers to the cognitive tendency that people always seek for the matching of semantic relations between mathematical cognition and objects in specific situations. In developing individuals, language ability and mathematical ability are in the development stage, and the development of semantic consistency is more helpful to reveal the relationship between the two. From the perspective of semantic alignment, this study aims to explore the age-related difference in the effects of semantic relationship on arithmetic operations. Sixty-two children and 62 adults were recruited to perform an arithmetical verification task. The results showed that: (1) Compared with children, adults had shorter response times and higher accuracy in mathematical operations. (2) Both adults and children showed longer response times in division condition than that in addition condition. (3) Children are more affected by semantic alignment than adults in addition. (4) For addition operation, participants performed better under semantic consistent condition than under semantic inconsistent condition, but the opposite result was found for division operation. It indicated that semantic consistently promoted the addition operation and semantic inconsistently promoted the division operation. This suggests that teachers should pay attention to integrating mathematical conceptual knowledge and language context in future educational practice.

Is the Discount Really Favorable? The Effect of Numeracy on Price Magnitude Judgment: Evidence From Electroencephalography.

Attractive price promotion will induce an unreasonable willingness to purchase, especially through shopping. However, it is not clear how numeracy, one of the essential abilities for understanding and applying numbers, influences the process of purchase judgment. In total, 61 participants were recruited to perform a price promotion task using electroencephalography. The results showed that consumers with low numeracy performed worse than their peers with high numeracy at the behavioral level, and they also had lower P3b amplitude and less alpha desynchronization, regardless of price promotion frameworks. These findings provided evidence on the processing of price information and provided further insights into how numeracy impacts price magnitude judgment.

Fraction mapping and fraction comparison skills among grade 4 Chinese students: An error analysis.

BACKGROUND: Mapping fraction symbols to magnitudes is easier for students to master than comparing fraction magnitudes. Fraction mapping assesses students' understanding of part-whole interpretations of fractions; fractions represent the parts of an object or set of objects. Fraction comparison assesses students' understanding of measurement interpretations of fractions; a fraction is a single numerical quantity, not a combination of two whole numbers. AIM: To examine and compare the types of errors made by emergent fraction learners on fraction mapping and comparison tasks. SAMPLE: Grade 4 Chinese students (N = 1036; 577 boys; Mage  = 9.9 years). METHOD: We examined performance and identified errors on fraction mapping and comparison tasks. For mapping, students converted pictorial representations into fraction notation. For comparison, they chose the larger of two symbolic fractions. RESULTS: Consistent with curriculum expectations, most students successfully mapped pictorial representations to fraction notation. In contrast, few students were able to accurately compare fraction magnitudes. Within each task, students' errors were consistent across trials, suggesting that they applied systematic but incorrect procedures. However, errors were not consistent between tasks and the correlation between mapping and comparison performance was weak. CONCLUSION: Emergent fraction learners can acquire part-whole knowledge of fractions without acquiring measurement interpretations of fractions. Moreover, misconceptions about different interpretations of fractions need not overlap. Awareness of the types of errors that students make can assist educators in identifying misconceptions early so that students do not build their fraction knowledge on erroneous beliefs.

Divide and conquer: Relations among arithmetic operations and emerging knowledge of fraction notation for Chinese students in Grade 4.

How do whole number arithmetic skills support students' understanding of fraction magnitude during the emerging stages of fraction learning? Chinese students in Grade 4 (N = 1038; Mage = 9.9 years; 55.6% boys) completed assessments of whole number arithmetic skills (i.e., addition, subtraction, multiplication, and division), fraction mapping (i.e., connecting visual fraction representations to fraction notations), and fraction comparison (i.e., comparing magnitudes of fraction symbols). We found that division skills uniquely differentiated students who had a basic understanding of fraction notation (mappers) from students with no understanding of fraction notation (non-mappers). Furthermore, we found that division mediated the relations between all three other arithmetic operations (i.e., addition, subtraction, and multiplication) and fraction mapping performance for the mappers. For fraction comparison, there was evidence of the whole number bias for the majority of students. The current results highlight the importance of the mastery of division skills and its dominance in predicting individual differences in fraction mapping for Chinese students in Grade 4.

How numerical surface forms affect strategy execution in subtraction? Evidence from behavioral and ERP measures.

In this study, to investigate the influence of numerical surface forms on strategy execution in subtraction and addition, 25 college students were required to perform a mental arithmetic task. Behavioral and electroencephalography responses were recorded to explore the stages of strategy execution. Arithmetic problems were presented within 11-20 by Arabic, Chinese and English numerals, respectively. The results showed that, compared with Arabic and Chinese numerals, participants had longer RTs under the condition of English numerals. English numerals induced stronger N100, P200 and P300 amplitudes, and longer latency in P200 and P300 amplitudes than in other conditions. These findings indicated that numerical surface forms affected the execution of mental arithmetic strategies, with Chinese and English numerals being processed deeper in the brain. Especially, the English digital word form occupied more psychological resources, and it was activated more in the frontal area and the parietal area, which would obviously hinder the processing of arithmetic information.

How Parenting Styles Link Career Decision-Making Difficulties in Chinese College Students? The Mediating Effects of Core Self-Evaluation and Career Calling.

The purpose of this study was to explore the relationship between parenting styles and career decision-making difficulties in college students, and uncovered the mediating roles of core self-evaluation and career calling. A total of 1,127 undergraduates were recruited to complete the questionnaires about parenting styles, core self-evaluation, career calling, and career decision-making difficulties. The results showed that: (1) Positive and negative parenting styles could positively predict career decision-making difficulties in college students. (2) Core self-evaluation and career calling mediated the relationship between parenting styles and career decision-making difficulties. Sequential dual mediators only found in which positive paternal and maternal parenting styles predict career decision-making difficulties through core self-evaluation and career calling. (3) Further analysis revealed gender difference in the relationship between parenting styles and career decision-making difficulties. The relation between paternal positive parenting style and career decision-making difficulties was significant in male students, but absent in female students; the relation between maternal positive parenting and career decision-making difficulties and the relation between paternal negative parenting and career calling were significant in female students, but absent in male students; and the relation between career calling and career decision-making difficulties was greater in male than in female. The current study expanded and deepened those existing understandings about the relationship between parenting styles and adolescents' career decisions, so as to further reveal its internal mechanism and provide more reasonable suggestions and targeted guidance for career counseling.

The influence of mouth opening and closing degrees on processing in NimStim facial expressions: An ERP study from Chinese college students.

The degree of mouth opening and closing is one of the most important attributes of expression, reflecting the intensity of facial expression and can assist people to recognize the expression more accurately. The NimStim set of facial expressions contains the open and closed expression pictures of the same actor. Although this expression set has been widely used, there is little research on the intensity effect of this set. In this study, 32 Chinese college students were recruited in to view the pictures passively in an ERP experiment, aiming to investigate the intensity effect in the NimStim set (mouth open, mouth closed) of anger, disgust, sad, happy and neutral expression in electrical physiological aspects of the reaction. Our results reported that intensity of expression early affected in VPP and mainly affected in LPP with the open mouth having a larger activity. And there was no intensity effect found in P1, N170 and EPN. Notably, culture and social environment may influence the intensity effect of different emotions. In future, researchers should use methods that ensure subjects pay more attention to the intensity effect of the NimStim facial set.

Non-symbolic representation is modulated by math anxiety and cognitive inhibition while symbolic representation not.

The present study aimed to investigate whether there are basic numerical processing deficits in high math anxiety (HMA) individuals and examine the effects of cognitive inhibition on the performance of high and low math anxiety (LMA) individuals. 35 undergraduate students were recruited to perform a numerical comparison task, a numerical Stroop task, a dot comparison task, and a dot Stroop task. Results showed the following: (1) Compared with LMA group, HMA group reacted more slowly and exhibited more fixation counts in non-symbolic representation task. (2) Inhibition condition significantly increased HMA individuals' fixation durations, whereas the fixation durations of LMA individuals were similar between inhibition and non-inhibition condition. The results demonstrated that MA might temporarily occupy individuals' working memory resources. (3) In non-symbolic representation task, the effect of numerical ratio on fixation counts was larger for HMA group than that for LMA group under inhibition condition, indicating MA might arise from a basic level deficit in numerosity processing.

Arithmetic Skill May Refine the Performance of Individuals with High Math Anxiety, Especially in the Calculation Task: An ERP Study.

As a global phenomenon, the theme of math anxiety has received increasing attention. The present study aimed to investigate the relationship between math anxiety and performance and determine the role of arithmetic skill in two different tasks. Fifty-seven college freshmen were recruited to perform a comparison task and a calculation task. Only main effect of arithmetic skill was found on the behavioral level. In the comparison task, participants with high math anxiety (HMA) showed faster latencies and greater amplitudes of N1 and longer P3b latency relative to their counterparts with low math anxiety (LMA). Number, as a negative stimulus, occupied attentional resources and delayed the speed of cognitive processing for individuals with HMA. Furthermore, among those with HMA, individuals with high arithmetic skill showed larger amplitudes and shorter latencies of P2 compared with those with low airthmetic skill in the calculation task. Thus, arithmetic skill could refine the performance efficiency of individuals with HMA, especially in the calculation task. These results suggest that educational interventions emphasizing control of negative emotional responses to math stimuli will be more effective when considering different populations of mathematically competent individuals.

Cognitive Switching Affects Arithmetic Strategy Selection: Evidence from Eye-gaze and Behavioral Measures / La conmutación cognitiva afecta la selección de estrategia aritmética: Evidencia de patrones de mirada y medidas conductuales

Although many studies of cognitive switching have been conducted, little is known about whether and how cognitive switching affects individuals’ use of arithmetic strategies. We used estimation and numerical comparison tasks within the operand recognition paradigm and the choice/no-choice paradigm to explore the effects of cognitive switching on the process of arithmetic strategy selection. Results showed that individuals’ performance in the baseline task was superior to that in the switching task. Presentation mode and cognitive switching clearly influenced eye-gaze patterns during strategy selection, with longer fixation duration in the number presentation mode than in the clock presentation mode. Furthermore, the number of fixation was greater in the switching task than it was in the the baseline task. These results indicate that the effects of cognitive switching on arithmetic strategy selection are clearly constrained by the manner in which numbers are presented

Aunque se han realizado muchos estudios sobre el cambio cognitivo, se sabe poco acerca de si el cambio cognitivo afecta el uso de las estrategias aritméticas por parte de las personas y cómo lo hace. Utilizamos las tareas de estimación y comparación numérica dentro del paradigma de reconocimiento de operandos y el paradigma de elección / no elección para explorar los efectos del cambio cognitivo en el proceso de selección de estrategia aritmética. Los resultados mostraron que el rendimiento de los individuos en la tarea de referencia fue superior al de la tarea de cambio. El modo de presentación y la conmutación cognitiva influyeron claramente en los patrones de la mirada durante la selección de estrategia, con duraciones de fijación más largas en el modo de presentación numérica que en el modo de presentación de reloj. Además, el número de fijaciones fue mayor en la tarea de conmutación que en la tarea de línea de base. Estos resultados indican que los efectos del cambio cognitivo en la selección de la estrategia aritmética están claramente limitados por la forma en que se presentan los números

The Central Executive Mediates the Relationship Between Children's Approximate Number System Acuity and Arithmetic Strategy Utilization in Computational Estimation.

Studies investigating the relationship between working memory (WM) and approximate number system (ANS) acuity in the area of arithmetic strategy utilization are scarce. The choice/no choice method paradigm was used in the present study to determine whether and how ANS acuity and WM components affected strategy utilization. The results showed that the central executive (CE) mediated the relationship between ANS acuity and strategy utilization. Furthermore, quantile regression analyses revealed that the association between CE and strategy choice was robust from the first to highest quantile. Notably, the relationship between ANS acuity and strategy choice was significant at the median and higher quantiles (i.e., 0.5, 0.75, and 0.85 quantiles), but not significant at lower quantiles (i.e., 0.15 and 0.25 quantiles). These results suggest that domain-general skills play a crucial role in the relationship between children's ANS acuity and mathematical ability. The impact of ANS acuity and CE on strategy choice was dependent on the distribution of the strategy utilization level. These results provide a further understanding of the utilization of cognitive strategies.

The Effect of Central Executive Load on Fourth and Sixth Graders' Use of Arithmetic Strategies.

In the present study, we set out to investigate whether and how central executive load constrains the strategies that children use during arithmetic processing. Using a dual-task paradigm accompanied by the choice/no-choice method, we tested 233 children (115 6th graders, 118 4th graders). Results showed that the impact of central executive load on reaction times and accuracy scores related to strategy use increased with the magnitude of the demands of the central executive, with central executive load playing an important role in strategy use. Sixth graders performed better than 4th graders in the application of appropriate strategies. Children's adaptability with respect to strategy choice was affected by the type and magnitude of the central executive load; children showed better adaptability under the no-load condition and the inconsistent/low load condition than under conditions with greater load. Grade level affected children's adaptability with respect to strategy choice, with 6th graders exhibiting significantly better performance than 4th graders. These results confirm that the development of central executive skills contributes to children's overall strategy use and adaptability. These findings have important implications for understanding the category specificity of central executive working memory in arithmetic cognition and the mechanisms of strategy development in childhood.

Age-Related Differences of Individuals' Arithmetic Strategy Utilization with Different Level of Math Anxiety.

The present study used the choice/no-choice method to investigate the effect of math anxiety on the strategy used in computational estimation and mental arithmetic tasks and to examine age-related differences in this regard. Fifty-seven fourth graders, 56 sixth graders, and 60 adults were randomly selected to participate in the experiment. Results showed the following: (1) High-anxious individuals were more likely to use a rounding-down strategy in the computational estimation task under the best-choice condition. Additionally, sixth-grade students and adults performed faster than fourth-grade students on the strategy execution parameter. Math anxiety affected response times (RTs) and the accuracy with which strategies were executed. (2) The execution of the partial-decomposition strategy was superior to that of the full-decomposition strategy on the mental arithmetic task. Low-math-anxious persons provided more accurate answers than did high-math-anxious participants under the no-choice condition. This difference was significant for sixth graders. With regard to the strategy selection parameter, the RTs for strategy selection varied with age.

Separate pathway characteristics of numerical surface form processing: evidence from operand-related error effects.

Two perspectives compete to explain how the surface form of digits affects cognitive processing of numerical magnitude; one argues for a common pathway and the other for separate pathways. This study examined the operand-related error effect in simple multiplication operations using different combinations of visually presented Arabic digits and auditorily presented Mandarin number words. The study suggested two conclusions, both consistent with the separate pathway perspective. First, the numerical surface form (Arabic digits, spoken Mandarin number words) affected retrieval. That is, surface properties were maintained as specific codes throughout processing. Second, the phonological code activated by spoken Mandarin number words interfered with activation of answers during retrieval.

Distractors interfere with numerical estimation in Chinese college students as a function of field-dependent or field-independent cognitive style.

Field-dependent/independent groups' numerical estimation was assessed with respect to different distractors. Participants were 81 college students with field-dependent or field-independent cognitive styles. Cognitive style had a significant main effect on reaction without distractors. When the number of distractors was double the number of targets, the estimation accuracy of the field-dependent and field-independent groups differed. Under this double-distractors condition, both the field-dependent and field-independent participants used logarithmic representation more than linear representation in their numerical estimations, but no significant between-group differences were found.