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"Mathematical ability."
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The development of situational mathematical ability lags behind the development of symbolic mathematical ability
The ability to apply mathematical knowledge to solve real-life problems is often considered one of the fundamental educational goals. However, more attention in mathematics education has been given to the development of abstract mathematical computations in symbolic form. The current investigation aims to disclose whether there are different trajectories for symbolic mathematical ability and situational mathematical ability (referred to as symbolic ability and situational ability). This cross-sectional study employed six online tasks and three offline paper-and-pencil tasks among 183 sixth-grade students in primary school and 180 seventh- to eighth-grade students in middle school. The results showed that symbolic ability, assessed through fraction division, fraction multiplication and number series completion, increased from primary school to middle school. This ability was also reflected in the procedural understanding involved in the schematic drawing of fractions and word problem composition. Their situational ability, as displayed by the construction of appropriate situations according to a prescribed arithmetic formula, decreased from primary school to middle school. The developmental patterns were consistent for both male and female students. These results suggest that the development of situational ability lags behind the development of symbolic ability. Based on the results, it is recommended that greater attention be given to the development of situational ability in mathematics education, even in higher educational stages.
Journal Article
A brain for numbers : the biology of the number instinct
\"How our intuitive understanding of numbers is deeply rooted in our biology, traceable through both evolution and development\"-- Provided by publisher.
Book
Sensorimotor mechanisms selective to numerosity derived from individual differences
We have previously shown that after few seconds of adaptation by finger-tapping, the perceived numerosity of spatial arrays and temporal sequences of visual objects displayed near the tapping region is increased or decreased, implying the existence of a sensorimotor numerosity system (Anobile et al., 2016). To date, this mechanism has been evidenced only by adaptation. Here, we extend our finding by leveraging on a well-established covariance technique, used to unveil and characterize ‘channels’ for basic visual features such as colour, motion, contrast, and spatial frequency. Participants were required to press rapidly a key a specific number of times, without counting. We then correlated the precision of reproduction for various target number presses between participants. The results showed high positive correlations for nearby target numbers, scaling down with numerical distance, implying tuning selectivity. Factor analysis identified two factors, one for low and the other for higher numbers. Principal component analysis revealed two bell-shaped covariance channels, peaking at different numerical values. Two control experiments ruled out the role of non-numerical strategies based on tapping frequency and response duration. These results reinforce our previous reports based on adaptation, and further suggest the existence of at least two sensorimotor number channels responsible for translating symbolic numbers into action sequences.
Journal Article
Creative Thinking Process of Prospective Mathematics Teacher Students in Solving Numerical Problems
Background/purpose. Creative thinking is an essential 21st-century skill in mathematics education, closely connected to logical-mathematical ability. Solving numerical problems requires students to think systematically, flexibly, and deeply beyond technical skills. In this context, the creative thinking process remains underexplored empirically. Therefore, this research aims to describe and visualize the stages of students’ creative thinking in solving numerical problems. Materials/methods. This research used a quantitative-descriptive and qualitative phenomenological method to investigate the creative thinking process. Category development was achieved through a combined concept-driven and data-driven process. The subjects were students in the Mathematics Education Research Program at Muhammadiyah University of Purwokerto, Indonesia. Students selected had taken courses relevant to numerical problems, namely the methods course. Results. Students’ creative thinking process in solving numerical problems reflected an integration of logical-mathematical intelligence skills across all stages from preparation in understanding the problem, incubation in planning, to illumination in generating strategic ideas. In the formulation and verification stages, students exhibited systematic thinking. However, limited alternative exploration and critical evaluation reduced the overall solution efficiency. These results emphasized the importance of instructional methods that promoted cognitive flexibility and metacognitive reflection throughout each stage of the creative thinking process. Conclusion. The development of students’ creative thinking in solving numerical problems required strong logical-mathematical intelligence, alternative solution exploration, and intensive metacognitive training. The results showed that curriculum design could balance theoretical and practical aspects to enhance cognitive flexibility, strengthen conceptual mastery, and support the formulation of creative numerical solutions.
Journal Article
More than visual-spatial skills: The important role of phonological awareness in mathematical abilities among Chinese primary school children
Mathematical abilities are important for children’s academic achievement during the primary education phase. Understanding which cognitive factors underlie individual differences in mathematics is essential to obtaining insights into children’s mathematical development. This study explored the roles of phonological processing skills and visual-spatial skills in arithmetic, mathematical problem solving, and mathematical reasoning among primary school children. Two hundred and fifty-one primary school children (mean age: 8.31 ± 0.89 years old), including 87 first graders, 83 s graders, and 81 third graders participated in this study. Children’s rapid automatized naming was measured using a rapid digit naming task, and phonological awareness was measured with a character rhyming task. Additionally, children’s visual perception was measured with a figure matching task, and mental rotation was measured with a 2D/3D mental rotation task. Children’s mathematical abilities were measured with three mathematics tests: calculation task, mathematical problem solving task, and mathematical reasoning task. Regression analyses and Bayesian hypothesis testing showed that phonological awareness uniquely contributed to children’s mathematical abilities, especially mathematical problem solving. The results suggest that phonological awareness serves as a key precursor of mathematical abilities during the primary education phase.
Journal Article
Relating mathematical abilities to numerical skills and executive functions in informal and formal schooling
Background
The current evidence on an integrative role of the domain-specific early mathematical skills and number-specific executive functions (EFs) from informal to formal schooling and their effect on mathematical abilities is so far unclear. The main objectives of this study were to (i) compare the domain-specific early mathematics, the number-specific EFs, and the mathematical abilities between preschool and primary school children, and (ii) examine the relationship among the domain-specific early mathematics, the number-specific EFs, and the mathematical abilities among preschool and primary school children.
Methods
The current study recruited 6- and 7-year-old children (
N
total
= 505,
n
6yrs
= 238, and
n
7yrs
= 267). The domain-specific early mathematics as measured by symbolic and nonsymbolic tasks, number-specific EFs tasks, and mathematics tasks between these preschool and primary school children were compared. The relationship among domain-specific early mathematics, number-specific EFs, and mathematical abilities among preschool and primary school children was examined. MANOVA and structural equation modeling (SEM) were used to test research hypotheses.
Results
The current results showed using MANOVA that primary school children were superior to preschool children over more complex tests of the domain-specific early mathematics; number-specific EFs; mathematical abilities, particularly for more sophisticated numerical knowledge; and number-specific EF components. The SEM revealed that both the domain-specific early numerical and the number-specific EFs significantly related to the mathematical abilities across age groups. Nevertheless, the number comparison test and mental number line of the domain-specific early mathematics significantly correlated with the mathematical abilities of formal school children. These results show the benefits of both the domain-specific early mathematics and the number-specific EFs in mathematical development, especially at the key stages of formal schooling. Understanding the relationship between EFs and early mathematics in improving mathematical achievements could allow a more powerful approach in improving mathematical education at this developmental stage.
Journal Article