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Lauren K. Schiller; Roberto A. Abreu-Mendoza; Miriam Rosenberg-Lee – Journal of Experimental Psychology: Learning, Memory, and Cognition, 2024
Decimal numbers are generally assumed to be a straightforward extension of the base-ten system for whole numbers given their shared place value structure. However, in decimal notation, unlike whole numbers, the same magnitude can be expressed in multiple ways (e.g., 0.8, 0.80, 0.800, etc.). Here, we used a number line task with carefully selected…
Descriptors: Arithmetic, Computation, Numbers, Bias
Cheng, Chen; Kibbe, Melissa M. – Cognitive Science, 2023
Young children with limited knowledge of formal mathematics can intuitively perform basic arithmetic-like operations over nonsymbolic, approximate representations of quantity. However, the algorithmic rules that guide such nonsymbolic operations are not entirely clear. We asked whether nonsymbolic arithmetic operations have a function-like…
Descriptors: Young Children, Mathematics Skills, Arithmetic, Problem Solving
Céline Poletti; Marie Krenger; Marie Létang; Brune Hennequin; Catherine Thevenot – Child Development, 2025
Our study on 328 five- to six-year-old kindergarteners (mainly White European living in France, 152 girls) shows that children who do not count on their fingers and undergo finger counting training exhibit drastic improvement in their addition skills from pre-test to post-test (i.e., accuracy from 37.3% to 77.1%) compared to a passive control…
Descriptors: Kindergarten, Young Children, Foreign Countries, Mathematics Skills
Karen Zwanch; Brooke Mullins – Educational Studies in Mathematics, 2025
To understand the ways that manipulatives might support changes in students' reasoning about algebraic generalizations, a constructivist teaching experiment was conducted with two sixth-grade students. The students interpreted numerical situations with units of one and could construct units of units in mental activity. Initially, the students'…
Descriptors: Mathematics Education, Mathematics Instruction, Teaching Methods, Algebra
Martín Díaz, Ana; Alario-Hoyos, Carlos; Estévez-Ayres, Iria; Delgado Kloos, Carlos; Fernández-Panadero, Carmen – Education and Information Technologies, 2023
ABN (Abierto Basado en Números--Open Calculation Based on Numbers) is a method for teaching basic arithmetic operations in primary education that has become popular in recent years and that is based on the decomposition of numbers through manipulative materials that encourage mental calculation. Currently there is limited number of tools that can…
Descriptors: Mathematics Instruction, Teaching Methods, Arithmetic, Elementary School Mathematics
Schneider, Rose M.; Sullivan, Jessica; Guo, Kaiqi; Barner, David – Child Development, 2021
Although many U.S. children can count sets by 4 years, it is not until 5½--6 years that they understand how counting relates to number--that is, that adding 1 to a set necessitates counting up one number. This study examined two knowledge sources that 3½- to 6-year-olds (N = 136) may leverage to acquire this "successor function": (a)…
Descriptors: Computation, Number Concepts, Young Children, Arithmetic
Marios Pittalis – Mathematics Education Research Journal, 2025
A theoretical model describing Grade 7 students' rational number sense was formulated and validated empirically (n = 360), hypothesizing that rational number sense is a general construct consisting of three factors: basic rational number sense, arithmetic sense, and flexibility with rational numbers. Data analysis suggested that rational-number…
Descriptors: Middle School Mathematics, Middle School Students, Grade 7, Numbers
Grabner, Roland H.; Brunner, Clemens; Lorenz, Valerie; Vogel, Stephan E.; De Smedt, Bert – Journal of Experimental Psychology: Learning, Memory, and Cognition, 2022
There is broad consensus on the assumption that adults solve single-digit multiplication problems almost exclusively by fact retrieval from memory. In contrast, there has been a long-standing debate on the cognitive processes involved in solving single-digit addition problems. This debate has evolved around two theoretical accounts. Proponents of…
Descriptors: Cognitive Processes, Addition, Computation, Arithmetic
Kirkland, Patrick K.; Guang, Claire; Cheng, Ying; Trinter, Christine; Kumar, Saachi; Nakfoor, Sofia; Sullivan, Tiana; McNeil, Nicole M. – North American Chapter of the International Group for the Psychology of Mathematics Education, 2022
Students exhibiting mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient problem-solving strategies (McIntosh et al., 1997; Reys et al., 1999; Yang, 2005). Despite being highlighted in national standards and policy documents (CCSS, 2010; NCTM, 2000, 2014),…
Descriptors: Middle School Students, Number Concepts, Fractions, Arithmetic
Bonneton-Botté, Nathalie; Ollivier, Fanny; Hili, Hélène; Bara, Florence – Canadian Journal of School Psychology, 2022
Numerous studies have shown a significant positive relationship between the mental representation of hands in young children and their calculation performance. The literature indicates that certain components of manual motor skills may be critical to the quality of this relationship. The main objective of this study is to measure the benefit of an…
Descriptors: Schemata (Cognition), Psychomotor Skills, Computation, Training
Glaser, Maria; Knops, André – Journal of Numerical Cognition, 2023
The notion that mental arithmetic is associated with shifts of spatial attention along a spatially organised mental number representation has received empirical support from three lines of research. First, participants tend to overestimate results of addition and underestimate those of subtraction problems in both exact and approximate formats.…
Descriptors: Spatial Ability, Mental Computation, Arithmetic, Attention
Alena Egorova; Vy Ngo; Allison S. Liu; Molly Mahoney; Justine Moy; Erin Ottmar – Mind, Brain, and Education, 2024
Perceptual learning theory suggests that perceptual grouping in mathematical expressions can direct students' attention toward specific parts of problems, thus impacting their mathematical reasoning. Using in-lab eye tracking and a sample of 85 undergraduates from a STEM-focused university, we investigated how higher-order operator position (HOO;…
Descriptors: Undergraduate Students, STEM Education, Mathematical Formulas, Mathematics Instruction
Eleftheriadi, Artemis; Lavidas, Konstantinos; Koustourakis, Gerasimos; Papadakis, Stamatis – Educational Process: International Journal, 2023
Background/purpose: Investigation into the misconceptions of preschool students in mathematics and their differences between the ages of 4-5 and 5-6 years old helps form appropriate developmental mathematics teaching programs. However, although several studies have been conducted examining preschoolers' previous knowledge and misconceptions about…
Descriptors: Misconceptions, Numbers, Arithmetic, Age Differences
Deslis, Dimitrios; Desli, Despoina – International Journal of Science and Mathematics Education, 2023
This study investigates students' and adults' performance in judging reasonableness of computational results, namely reflecting on whether these results qualify as acceptable answers to mathematical tasks. Data was gathered via task-based questionnaires from 160 participants, evenly divided between fifth-graders and adults. Their responses to a…
Descriptors: Elementary School Students, Grade 5, Adults, Mathematics Activities
Borriello, Giulia A.; Grenell, Amanda; Vest, Nicholas A.; Moore, Kyler; Fyfe, Emily R. – Child Development, 2023
This study examined repeating and growing pattern knowledge and their associations with procedural and conceptual arithmetic knowledge in a sample of U.S. children (N = 185; M[subscript age] = 79.5 months; 55% female; 88% White) and adults (N = 93; M[subscript age] = 19.5 years; 62% female; 66% White) from 2019 to 2020. Three key findings emerged:…
Descriptors: Mathematics Instruction, Pattern Recognition, Prediction, Correlation