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Eugenio Chandía; Patricia Fuentes Acevedo; Natalia Ruiz; Daniza Rojas; Mirian Baeza; Cristian Reyes – International Electronic Journal of Mathematics Education, 2025
The study investigates the knowledge profiles of elementary pre-service teachers (PST) concerning numbers and operations before their professional classroom practice. By validating an instrument through exploratory and confirmatory factor analyses, it identifies and categorizes the PST' performance into distinct profiles based on the mathematical…
Descriptors: Preservice Teachers, Elementary School Teachers, Mathematics Instruction, Pedagogical Content Knowledge
Julie Nurnberger-Haag; Scott A. Courtney – Electronic Journal for Research in Science & Mathematics Education, 2025
Integer arithmetic is difficult for students worldwide. Although students' integer thinking has frequently been studied, little is known about typical instructional practice for this difficult topic. Thus, to investigate what resources teachers use, we surveyed U.S. middle-grade teachers who teach negative numbers. About half the teachers said…
Descriptors: Arithmetic, Numbers, Middle School Teachers, Middle School Mathematics
Megan Rojo; Sarah G. King; Jenna Gersib; Christian T. Doabler – Learning Disability Quarterly, 2025
Competence with rational numbers is essential for mathematics proficiency in secondary mathematics. However, many students struggle with rational number concepts, and students with mathematics difficulties struggle even more. The purpose of this study was to examine the effects of an intervention that incorporated the use of explicit instruction…
Descriptors: Mathematics Instruction, Intervention, Direct Instruction, Models
Konstantinos P. Christou; Despoina Ioanna Kyrvei; Xenia Vamvakoussi – Mathematical Thinking and Learning: An International Journal, 2024
In this study, we investigated how secondary students interpret algebraic expressions that contain literal symbols to stand for variables. We hypothesized that the natural number bias (i.e., the tendency to over-rely on knowledge and experiences based on natural numbers) would affect students to think that the literal symbols stand for natural…
Descriptors: Algebra, Mathematics Instruction, Grade 8, Grade 9
Stacy K. Boote; Terrie M. Galanti; Danielle Felicien; Tara Kelly – Mathematics Teacher: Learning and Teaching PK-12, 2025
Teachers and teacher educators have been sharing strategies and resources for implementing mathematics routines in National Council of Teachers of Mathematics (NCTM) journals for years. A less commonly shared mathematics routine, especially with young learners, is "Clothesline Math" (Shore, 2017, 2018). In this routine, teachers create…
Descriptors: Mathematics Instruction, Visual Aids, Early Childhood Education, Mathematics Skills
Simon, Martin A.; Della Volpe, Daniela; Velamur, Arundhati – Mathematical Thinking and Learning: An International Journal, 2023
Development of the cardinality principle, an understanding that the last number-word recited in counting a collection of items specifies the number of items in that collection, is a critical milestone in developing a concept of number. Researchers in early number development have endeavored to theorize its development. Here we critique two widely…
Descriptors: Mathematics Instruction, Teaching Methods, Numbers, Number Concepts
Prather, Richard – Journal of Numerical Cognition, 2023
Mastery of mathematics depends on the people's ability to manipulate and abstract values such as negative numbers. Knowledge of arithmetic principles does not necessarily generalize from positive number arithmetic to arithmetic involving negative numbers (Prather & Alibali, 2008, https://doi.org/10.1080/03640210701864147). In this study, we…
Descriptors: Prediction, Mastery Learning, Mathematics Instruction, Cognitive Processes
Bowling, Tom – Australian Mathematics Education Journal, 2020
A test method is described for determining the divisibility of non-negative integers by a prime number. The test uses an integer multiplying factor that is defined for each prime, designated as [beta], to reduce the non-negative integer that is being tested by an order of magnitude in each of a sequence of steps to obtain a series of new numbers.…
Descriptors: Mathematics Instruction, Teaching Methods, Division, Arithmetic
Tunahan Filiz; Gönül Günes – International Journal of Education and Literacy Studies, 2023
This study was undertaken to systematically analyze instructional interventions employed to enhance the mathematical performance of elementary school students with math learning difficulties (MLD). Over 20 years (2003-2023), 34 articles that met the inclusion criteria were included in the analysis. The articles in the study were analyzed in terms…
Descriptors: Intervention, Mathematics Instruction, Elementary School Students, Learning Problems
Marina Vasilyeva; Elida V. Laski; Beth Casey; Spyros Konstantopoulos; Linxi Lu; Jiwon Ban; Sophia Betar; Hyun Young Cho; Muanjing Wang – Grantee Submission, 2025
This study examined the effects of training involving spatial versus nonspatial representations of numerical magnitude for promoting arithmetic fluency. The key goal was to advance theoretical understanding of the relation between spatial and math learning, while simultaneously laying the groundwork for the development of future educational…
Descriptors: Elementary School Mathematics, Elementary School Students, Elementary School Teachers, Grade 1
Suárez-Rodríguez, Mayra; Figueras, Olimpia – North American Chapter of the International Group for the Psychology of Mathematics Education, 2020
Researchers, who have studied the understanding of the density property in the set of decimal numbers, have shown that the student uses the property of the discrete of natural numbers to solve tasks related to density. So, a restructuring of concepts is necessary, that is, a conceptual change from "the discrete" to "the dense".…
Descriptors: Arithmetic, Numbers, Preservice Teachers, Mathematics Instruction
Papadopoulos, Ioannis; Gunnarsson, Robert – Educational Studies in Mathematics, 2020
When a number sentence includes more than one operation, students are taught to follow the rules for the order of operations to get the correct result. In this context, brackets are used to determine the operations that should be calculated first. However, it seems that the written format of an arithmetical expression has an impact on the way…
Descriptors: Mathematics Instruction, Elementary School Mathematics, Arithmetic, Foreign Countries
Pruitt, Kenny; Shannon, A. G. – International Journal of Mathematical Education in Science and Technology, 2018
The purpose of this paper is to consider analogues of the twin-prime conjecture in various classes within modular rings.
Descriptors: Mathematics Instruction, Numbers, Teaching Methods, Arithmetic
Orrantia, Josetxu; Muñez, David; Matilla, Laura; Sanchez, Rosario; San Romualdo, Sara; Verschaffel, Lieven – Cognitive Science, 2019
A growing body of research has shown that symbolic number processing relates to individual differences in mathematics. However, it remains unclear which mechanisms of symbolic number processing are crucial--accessing underlying magnitude representation of symbols (i.e., symbol-magnitude associations), processing relative order of symbols (i.e.,…
Descriptors: Numeracy, Numbers, Symbols (Mathematics), Mathematics Instruction
Sianturi, Iwan Andi Jonri; Ismail, Zaleha; Yang, Der-Ching – School Science and Mathematics, 2021
The purpose of this study is to compare the differences of four essential aspects (i.e., representational forms, contextual features, cognitive demand levels, and response types) embedded in mathematical problems within the topics of numbers and operations in mathematics textbooks used in Finland, Indonesia, Malaysia, Singapore, and Taiwan. This…
Descriptors: Mathematics Instruction, Problem Solving, Numbers, Arithmetic