When one sets out to solve a mathematics problem, a feeling of satisfaction and accomplishment comes with finding the answer and knowing it is correct. In contrast, a student performing the correct process to solve an algebra equation and getting an answer such as 3 = 0 may be left perplexed and not understanding what--if anything--he or she did…

Reading mathematics problems can frustrate students to the point of shutting down. Although Pólya's four-step plan is a well-known problem-solving framework, the author's students benefited from a more concrete and detailed approach: chunking the reading. In this article, the author describes an approach to problem solving used with eighth-grade…

Research has shown that tape diagrams are beneficial for algebra learning. However, it is unclear whether certain visual features of tape diagrams have implications for learning. We investigated, with undergraduate students and math teachers, whether tape diagrams with different visual features (color, presence of outer lines, and position of the…

Research shows that though some students can easily find the correct solutions to the problem(s) at hand, the algorithms that these students create are not always ones that would, when implemented, produce the correct solution(s). Towards shedding light on this phenomenon, the present study explicates a mechanism--accounting for features of the…

TIMSS (Trends in International Mathematics and Science Study) is a long-standing international assessment of mathematics and science at the fourth and eighth grades, collecting trend data every four years since 1995. Over 70 countries rely on TIMSS to monitor their education systems in a global context, benchmarking national curricula and…

Background: A single-case design focuses on individual performance and measures the causal relationships between variables (Kazdin, 2019). This experimental design enables researchers to measure the learning behaviors of individual participants over time across phases and assess the effectiveness of an instructional strategy in improving or…

The provision of a profitable education in Mathematics is important at a cross-curricular level, since this subject finds room in a plethora of academic paths, not limited to the most scientific or technological curricula. In particular, this applies to the security and defence area, where several skills related to mathematical reasoning, such as…

To learn mathematics, historically students had no choice but to memorize fundamental facts and apply memorized algorithms. Since 1995 in the US, all states have adopted standards to govern K-12 mathematics instruction, and in most, standards have de-emphasized memorization and emphasized reasoning based on concepts. This change assumed the brain…

The learning that happens before school entry provides children with a strong foundation on which to build new conceptual understandings. In particular, mathematical skills predict later math and reading outcomes in elementary school. This article summarizes existing research on equity-based math instructional approaches and provides a rationale…

Recent work has demonstrated that having students study worked examples and answer self-explanation prompts as part of their problem-solving practice improves learning on researcher-developed measures of mathematical proficiency. However, little work has been done to date to investigate whether these benefits translate to improvements on the types…

Nowadays, it is essential to promote an interdisciplinary approach in classrooms, integrating disciplines such as biology and mathematics. This necessitates familiarity with specific problem-solving practices employed by the expert community, such as mathematical modelling. This perspective piece explores a mathematical modelling practice to…

This paper aims to understand how primary students use gestures to solve partition tasks and to what extent these gestures may promote fraction understanding. Analysis of six selected students' answers to partitioning tasks, classroom observation, and post-lesson interviews indicates that co-thought representational gestures play a critical role.…

Research has shown that teaching mathematics through problem posing, or problem-posing based learning (P-PBL), is a student-centered instructional approach that can improve students' cognitive and affective aspects of learning. However, since textbooks continue to include very few opportunities for problem posing, researchers have been working to…

Student achievement in learning mathematics is considerably low in Indonesia. This study aims to discuss factors affecting learning achievements in mathematics in Indonesia, including direct and indirect influences, such as students' perception of teacher competence, learning anxiety, problem-solving ability, learning motivation, and mathematical…

This study examined characteristics of problem posing and its relationship with the teaching experience of elementary school mathematics teachers from ethnic minority areas in the Southwest of China. Eighty-one (N = 81) elementary school mathematics teachers responded to a task-based questionnaire and posed mathematical problems based on given…