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Rafi' Safadi; Nadera Hawa – Mathematics Teacher: Learning and Teaching PK-12, 2025
Graded Troubleshooting (GTS) is a powerful routine that teachers can use easily to engender students' metacognitive thinking and boost their understanding of mathematics concepts and procedures. This article describes a new GTS activity designed to prompt students to efficiently exploit worked examples when asked to diagnose erroneous examples…
Descriptors: Mathematics Education, Mathematics Instruction, Problem Solving, Troubleshooting
Smadar Sapir-Yogev; Gitit Kavé; Sarit Ashkenazi – Journal of Experimental Psychology: Learning, Memory, and Cognition, 2024
The solution and verification of single-digit multiplication problems vary in speed and accuracy. The current study examines whether the number of different digits in a problem accounts for this variance. In Experiment 1, 41 participants solved all 2-9 multiplication problems. In Experiment 2, 43 participants verified these problems. In Experiment…
Descriptors: Foreign Countries, Undergraduate Students, Mathematical Concepts, Multiplication
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
Angelika Kullberg; Camilla Björklund; Ulla Runesson Kempe – Educational Studies in Mathematics, 2024
The decomposition of numbers when solving subtraction tasks is regarded as more powerful than counting-based strategies. Still, many students fail to solve subtraction tasks despite using decomposition. To shed light upon this issue, we take a variation theoretical perspective (Marton, 2015) seeing learning as a function of discerning critical…
Descriptors: Subtraction, Number Concepts, Grade 2, Elementary School Students
Braithwaite, David W.; Sprague, Lauren; Siegler, Robert S. – Journal of Experimental Psychology: Learning, Memory, and Cognition, 2022
To explain children's difficulties learning fraction arithmetic, Braithwaite et al. (2017) proposed FARRA, a theory of fraction arithmetic implemented as a computational model. The present study tested predictions of the theory in a new domain, decimal arithmetic, and investigated children's use of conceptual knowledge in that domain. Sixth and…
Descriptors: Number Concepts, Numbers, Arithmetic, Fractions
Ling Zhang; Naiqing Song; Guowei Wu; Jinfa Cai – Educational Studies in Mathematics, 2025
This study concerns the cognitive process of mathematical problem posing, conceptualized in three stages: understanding the task, constructing the problem, and expressing the problem. We used the eye tracker and think-aloud methods to deeply explore students' behavior in these three stages of problem posing, especially focusing on investigating…
Descriptors: Cognitive Processes, Mathematics Skills, Problem Solving, Eye Movements
Utomo, Dwi Priyo – Journal of Research and Advances in Mathematics Education, 2020
Relational understanding constitutes students' awareness of appropriate procedures to solve problems along with logical reasoning. It is pivotal to help students solve problems in mathematics. It is necessary that the teaching of mathematics be directed to achieve relational understanding. Accordingly, students are capable of solving complicated…
Descriptors: Numbers, Problem Solving, Elementary School Students, Grade 5
Saso Koceski; Natasa Koceska; Limonka Koceva Lazarova; Marija Miteva; Biljana Zlatanovska – Journal of Technology and Science Education, 2025
This study aims to evaluate ChatGPT's capabilities in certain numerical analysis problem: solving ordinary differential equations. The methodology which is developed in order to conduct this research takes into account the following mathematical abilities (defined according to National Centre for Education Statistics): Conceptual Understanding,…
Descriptors: Artificial Intelligence, Technology Uses in Education, Number Concepts, Problem Solving
Haman, Maciej; Lipowska, Katarzyna – Developmental Science, 2023
In numerical cognition research, the operational momentum (OM) phenomenon (tendency to overestimate the results of addition and/or binding addition to the right side and underestimating subtraction and/or binding it to the left side) can help illuminate the most basic representations and processes of mental arithmetic and their development. This…
Descriptors: Preschool Children, Prior Learning, Mathematics Education, Number Concepts
Taylor Lesner; Marah Sutherland; Cayla Lussier; Ben Clarke – Intervention in School and Clinic, 2024
Building proficiency with fraction arithmetic poses a consistent challenge for students with learning difficulties or disabilities in mathematics. This article illustrates how teachers can use the number line model to support struggling learners in making sense of fraction arithmetic. Number lines are a powerful tool that can be used to help…
Descriptors: Number Concepts, Fractions, Arithmetic, Mathematics Skills
Kynigos, Chronis; Diamantidis, Dimitris – ZDM: Mathematics Education, 2022
We discuss classroom activity comprised of small groups of students collaboratively tinkering with programs of dynamically manipulable figural models, posing problems regarding their mathematical properties and behaviors. We analyzed data from students' discourse taken from two classroom interventions employing a framework of creative mathematical…
Descriptors: Creativity, Engineering, Mathematical Models, Programming
Wong, Harris; Odic, Darko – Journal of Experimental Psychology: Learning, Memory, and Cognition, 2021
Research over the past 20 years has suggested that our intuitive sense of number--the Approximate Number System (ANS)--is associated with individual differences in symbolic math performance. The mechanism supporting this relationship, however, remains unknown. Here, we test whether the ANS contributes to how well adult observers judge the…
Descriptors: Number Systems, Symbols (Mathematics), Equations (Mathematics), Problem Solving
Bajo-Benito, José Mariano; Sánchez-Matamoros García, Gloria; Gavilán-Izquierdo, José María – EURASIA Journal of Mathematics, Science and Technology Education, 2021
This paper aims to characterise an indicator of the development of the number sequence scheme among students at the level of Compulsory Secondary Education (14-16 years old students). To do so, we use a scheme development proposed by the APOS theory to characterise students' use of relations between mathematical elements when solving a…
Descriptors: Secondary School Students, Mathematics Skills, Problem Solving, Number Concepts
Obersteiner, Andreas; Alibali, Martha Wagner; Marupudi, Vijay – Journal of Numerical Cognition, 2022
Many studies have used fraction magnitude comparison tasks to assess people's abilities to quickly assess fraction magnitudes. However, since there are multiple ways to compare fractions, it is not clear whether people actually reason about the holistic magnitudes of the fractions in this task and whether they use multiple strategies in a flexible…
Descriptors: Fractions, Mathematics Skills, Learning Strategies, Problem Solving
Poloczek, Sebastian; Hammerstein, Svenja; Büttner, Gerhard – Journal of Numerical Cognition, 2022
Being able to perform computational estimations efficiently is an important skill. Furthermore, computational estimation experiments are used to study general principles in strategy development. Rounding strategies are common in computational estimation. However, little is known about whether and when children use a mixed-rounding strategy (i.e.,…
Descriptors: Children, Learning Strategies, Mathematics Skills, Computation