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Erik Tillema; Joseph Antonides – Investigations in Mathematics Learning, 2024
The multiplication principle (MP) is foundational for combinatorial problem-solving. From a units-coordination perspective, applying the MP with justification entails establishing unit relationships between the number of options at each independent stage of a counting process and the total number of combinatorial outcomes. Existing research…
Descriptors: Multiplication, Mathematical Logic, Mathematics Instruction, Problem Solving
Inés Gallego-Sánchez; Verónica Martín-Molina; Isabel Caro-Torró; José María Gavilán-Izquierdo – Education 3-13, 2025
Our work investigated how six primary school students used a non-traditional method for adding and subtracting: the ABN method, a Spanish acronym for Open (method) Based on Numbers. Commognitive theory [Sfard, A. 2008. "Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing." New York: Cambridge…
Descriptors: Foreign Countries, Elementary School Students, Addition, Subtraction
Diamond, Harvey – PRIMUS, 2023
This paper presents a series of basic computational problems that are mathematically and/or graphically appealing, and provides an idea of places one might go in trying to understand what is happening, integrating mathematics, computation, and graphics. The real point of this paper is to make a case, through those examples, for computation as an…
Descriptors: Mathematics Instruction, Computation, College Mathematics, Undergraduate Study
Pellerzi, Laura Ann Weinberg – ProQuest LLC, 2023
The application of decomposition strategies (i.e., associative or distributive strategies) in two-digit multiplication problem solving supports algebraic thinking skills essential for later complex mathematical skills like solving algebra problems. Use of such strategies is also associated with improved accuracy and speed in mathematical problem…
Descriptors: Mathematics Instruction, Multiplication, Problem Solving, Learning Strategies
Andreas Brandsaeter; Runar Lie Berge – Educational Studies in Mathematics, 2025
The reasons for teaching programming in school are indeed manifold. Programming can for example be utilized as a vehicle for understanding and learning particular mathematical subject matter, or as a tool for solving mathematical problems. In this paper, however, we propose to utilize programming as a vehicle for developing mathematical…
Descriptors: Mathematics Skills, Skill Development, Competence, Programming
Hansen, Nils Kristian; Hadjerrouit, Said – International Association for Development of the Information Society, 2023
This paper aims at using a Use-Modify-Create approach to explore students' mathematical problem solving by means of computational thinking (CT) and programming activities. The data collection method is participant observation, in which the researcher also has the role as teacher, guiding the group activities. In our study, two groups of students…
Descriptors: Problem Solving, Computation, Thinking Skills, Programming
Wahid Yunianto; Guillermo Bautista Jr.; Bungkus Dias Prasetyo; Zsolt Lavicza – International Journal for Technology in Mathematics Education, 2024
As computational thinking (CT) is new to teachers, they need support on how CT integration will work. This study examines the use of a hypothetical learning trajectory (HLT) to support teachers in integrating computational thinking into mathematics lessons utilizing GeoGebra. By employing the educational design research (EDR) methodology, the…
Descriptors: Computer Software, Mental Computation, Mathematics Instruction, Educational Technology
Benjamin Tatira – Mathematics Teaching Research Journal, 2024
Solving systems of linear equations is a core concept in linear algebra and a wide variety of problems found in the sciences and engineering can be formulated as linear equations. This study sought to explore undergraduate students' development of the schema for solving systems of linear equations. The triad framework was used to describe the…
Descriptors: Mathematics Instruction, Teaching Methods, Schemata (Cognition), Problem Solving
Students' In-Moment Challenges and Developing Maker Perspectives during Problem-Based Digital Making
Ng, Oi-Lam; Liu, Minnie; Cui, Zhihao – Journal of Research on Technology in Education, 2023
We report on a case study of eight grade 5 to 6 students (ages 12-14) involved in a three-day "digital-making summer camp" focused on mathematical problem-solving through block-based programming combined with programmable electronics. Data analysis focused on the computational thinking (CT), mathematics, and problem-solving challenges…
Descriptors: Grade 5, Grade 6, Summer Programs, Camps
Bofferding, Laura; Zhu, Yi – Mathematics Teacher: Learning and Teaching PK-12, 2023
Having students solve shape puzzles, such as with pattern blocks or tangrams, is a popular way to encourage students to compose shapes in different ways and talk about the effects of different compositions (Clements et al., 2004; Clements & Sarama, 2009; Sales, 1994), meeting Common Core geometry standards in kindergarten through second grade…
Descriptors: Geometric Concepts, Puzzles, Problem Solving, Mathematics Instruction
Herman Tshesane; Hamsa Venkat – African Journal of Research in Mathematics, Science and Technology Education, 2023
Evidence in South Africa of poor performance on word problems points to particular challenges among learners relating to difficulties with, on the one hand, making sense of mathematical word problems and, on the other, moving beyond inefficient counting based calculation methods. While many studies in mathematics education in South Africa have…
Descriptors: Foreign Countries, Word Problems (Mathematics), Problem Solving, Mathematics Instruction
Marah Sutherland; David Furjanic; Joanna Hermida; Ben Clarke – Intervention in School and Clinic, 2024
This article illustrates how teachers can use number lines to support students with or at risk for learning disabilities (LD) in mathematics. Number lines can be strategically used to help students understand relations among numbers, approach number combinations (i.e., basic facts), as well as represent and solve addition and subtraction problems.…
Descriptors: Number Concepts, Arithmetic, Mathematics Instruction, Teaching Methods
Taajah Felder Witherspoon – Journal of Mathematics Education at Teachers College, 2023
The results of this study revealed students' solution strategies progressed from inefficient strategies e.g., counting on fingers to more efficient strategies with mathematical connections. These findings should enable educators to gain more insight to use Number Talks to help student develop computational fluency with numbers.
Descriptors: Mathematics Instruction, Numeracy, Computation, Mathematics Skills
Chee-Kit Looi; Shiau-Wei Chan; Longkai Wu; Wendy Huang; Mi Song Kim; Daner Sun – International Journal of Science and Mathematics Education, 2024
Limited research has been conducted on the influence of computational thinking (CT) dispositions on students' mathematics performance and engagement at the secondary or junior high school level. This study aims to bridge this research gap by developing CT-integrated mathematics lessons that incorporate CT-focused problem-solving and modeling in…
Descriptors: Foreign Countries, Secondary School Students, Computation, Thinking Skills
Antonides, Joseph; Battista, Michael T. – ZDM: Mathematics Education, 2022
Lockwood has argued that taking a set-oriented perspective is critical for successful combinatorial enumeration. To date, however, the research literature has not yet captured the cognitive processes involved in taking such a perspective. In this theoretical paper, we elaborate the constructs of spatial structuring and spatial-numerical linked…
Descriptors: Cognitive Processes, Spatial Ability, Computation, Mathematics Instruction