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del Olmo-Muñoz, Javier; González-Calero, José Antonio; Diago, Pascual D.; Arnau, David; Arevalillo-Herráez, Miguel – British Journal of Educational Technology, 2022
Problem solving is often regarded as one of the most essential cognitive functions in our daily lives, and, for that reason, educational theorists have long stressed the need for its development. As cognitive flexibility is a fundamental characteristic necessary throughout the problem-solving process, the purpose of this study is to analyse…
Descriptors: Problem Solving, Arithmetic, Grade 5, Grade 6
Ngo, Vy; Perez Lacera, Luisa; Closser, Avery Harrison; Ottmar, Erin – Journal of Numerical Cognition, 2023
For students to advance beyond arithmetic, they must learn how to attend to the structure of math notation. This process can be challenging due to students' left-to-right computing tendencies. Brackets are used in mathematics to indicate precedence but can also be used as superfluous cues and perceptual grouping mechanisms in instructional…
Descriptors: Mathematics Skills, Arithmetic, Symbols (Mathematics), Computation
Price, Gavin R.; Eric, Wilkey D. – Grantee Submission, 2017
Recent studies suggest that the relation between nonsymbolic magnitude processing skills and math competence is mediated by symbolic number processing. However, less is known about whether mapping between nonsymbolic and symbolic magnitude representations also mediates that relation, and whether the mediating role of symbolic number processing is…
Descriptors: Mathematics Skills, Symbols (Mathematics), Cognitive Processes, Executive Function
Çelik, Derya – International Journal for Mathematics Teaching and Learning, 2015
Linear algebra is one of the most challenging topics to learn and teach in many countries. To facilitate the teaching and learning of linear algebra, priority should be given to epistemologically analyze the concepts that the undergraduate students have difficulty in conceptualizing and to define their ways of reasoning in linear algebra. After…
Descriptors: Algebra, Mathematics Instruction, Mathematical Concepts, Concept Formation
Wilkins, Jesse L. M.; Norton, Anderson – Journal for Research in Mathematics Education, 2011
Teaching experiments have generated several hypotheses concerning the construction of fraction schemes and operations and relationships among them. In particular, researchers have hypothesized that children's construction of splitting operations is crucial to their construction of more advanced fractions concepts (Steffe, 2002). The authors…
Descriptors: Mathematics, Experiments, Teaching Methods, Cognitive Processes
Developmental Dissociation in the Neural Responses to Simple Multiplication and Subtraction Problems
Prado, Jérôme; Mutreja, Rachna; Booth, James R. – Developmental Science, 2014
Mastering single-digit arithmetic during school years is commonly thought to depend upon an increasing reliance on verbally memorized facts. An alternative model, however, posits that fluency in single-digit arithmetic might also be achieved via the increasing use of efficient calculation procedures. To test between these hypotheses, we used a…
Descriptors: Hypothesis Testing, Numeracy, Arithmetic, Computation
Panaoura, Areti; Gagatsis, Athanasios; Deliyianni, Eleni; Elia, Iliada – Educational Psychology, 2010
In a previous article of the same journal, we have discussed the interrelations of students' beliefs and self-efficacy beliefs for the use of representations and their respective cognitive performance on the learning of fraction addition. In the present paper, we confirm a similar structure of cognitive and affective factors on using…
Descriptors: Arithmetic, Self Efficacy, Beliefs, Problem Solving
Hallett, Darcy; Nunes, Terezinha; Bryant, Peter – Journal of Educational Psychology, 2010
Previous research on children's conceptual and procedural understanding of fractions, and other arithmetic skills, has led to contradictory conclusions. Some research suggests that children learn conceptual knowledge before procedural knowledge, some suggests that they learn procedural knowledge before conceptual knowledge, and other research…
Descriptors: Mathematics Skills, Concept Formation, Foreign Countries, Arithmetic
Hecht, Steven A.; Vagi, Kevin J. – Journal of Educational Psychology, 2010
Results from a 2-year longitudinal study of 181 children from 4th through 5th grade are reported. Levels of growth in children's computation, word problem, and estimation skills by means of common fractions were predicted by working memory, attentive classroom behavior, conceptual knowledge about fractions, and simple arithmetic fluency.…
Descriptors: Student Behavior, Short Term Memory, Grade 4, Grade 5
Ketterlin-Geller, Leanne; Liu, Kimy – Behavioral Research and Teaching, 2008
The purpose of this technical report is to describe a research study exploring students' cognitive processing while solving problems related to division of fractions. Four students were interviewed using verbal protocol techniques with the intention of better understanding their cognitive processing when dividing fractions. Information gained from…
Descriptors: Protocol Analysis, Cognitive Processes, Problem Solving, Mathematics