Sixty (35 girls and 25 boys) 9th-grade students' conceptual understanding of the number line was qualitatively assessed through verbal explanations and visual representations. The assessment included an open-ended question focused on students' number line descriptions and the explanations coalesced around six features: sequential ordering (i.e.,…

Misconceptions occur as a result of learners' wrong beliefs and experiences, and because subsequent learning is built on these misconceptions, they cause new concepts to be learned incorrectly. Studies show that students have problems in making sense of many mathematical concepts in mathematics teaching processes and this situation can be…

Over the last years, there is a growing interest in studying students' difficulties with rational numbers from a cognitive/developmental perspective, focusing on the role of prior knowledge in students' understanding of rational numbers. The present study tests the effect of the "whole" or "natural number bias" (i.e., the…

This Brief Report presents an example of assessment validation using an argument-based approach. The instrument we developed is a Brief Assessment of Students' Mature Number Sense, which measures a central goal in mathematics education. We chose to develop this assessment to provide an efficient way to measure the effect of instructional practices…

Integer operations are typically introduced in sixth grade, but they are a consistent area of struggle among these students. This struggle also inhibits their understanding of algebraic computations involving positive and negative terms. In this article, the author provides introductory tasks and models for adding and subtracting integers that can…

A theoretical model describing Grade 7 students' rational number sense was formulated and validated empirically (n = 360), hypothesizing that rational number sense is a general construct consisting of three factors: basic rational number sense, arithmetic sense, and flexibility with rational numbers. Data analysis suggested that rational-number…

Students exhibiting mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient problem-solving strategies (McIntosh et al., 1997; Reys et al., 1999; Yang, 2005). Despite being highlighted in national standards and policy documents (CCSS, 2010; NCTM, 2000, 2014),…

The present study aimed to test the effect of the problem-posing instruction experimentally based on the extended active learning framework on the development of Turkish middle school sixth-grade students' (N = 19) problem-posing and -solving skills with whole-number operations. The training programme was completed in 13 lessons over a seven-week…

The ability to efficiently compare number symbols, such as digits, is associated with mathematics competence across the lifespan. Performance on symbolic number comparison tasks differ across age groups; young students who are developing fluency with digits improve on symbolic number comparison, and performance is better in adults than children.…

Grounded in problem-based learning and with respect to four mathematics domains (arithmetic, random events and counting, number theory, and geometry), we designed a series of programming-based learning tasks for middle school students to co-develop computational thinking (CT) and corresponding mathematical thinking. Various CT concepts and…

The purpose of this research was to develop and evaluate a number sense-based curriculum aiming to eliminate student errors due to mathematical misconceptions. A mixed method research model as one of the qualitative research approaches was adopted in this study aiming to develop a number sense-based instructional design to eliminate student errors…

This study aims to determine the effect of the cognitive conflict approach on the elimination of misconceptions in square root numbers. For this purpose, this study was conducted with 8th-grade students of a secondary school in a region of Turkey. A three tiered diagnostic test was used to determine the impact of the 5-step cognitive conflict…

This study revealed the fractional number sense form associated with daily life and the number sense of 8th-grade students with high academic success. This study aimed to determine fractional number sense which in eighth graders with high academic performance. This study has a qualitative patterned. The sample consisted of 20 students from the…

Adaptive expertise is a highly sought after, but difficult to achieve, outcome of mathematics education. Many teaching methods appear to support the development of adaptive expertise only in a small proportion of students. Game-based learning environments may be useful for supporting adaptive expertise. Therefore, we carried out a…

The potential benefits of cognitive skills in enhancing mathematics ability have been claimed by numerous researchers. Since mathematics requires a complete understanding and grasp of abstract concepts, it is essential to explore how learning with metacognitive skills affects mathematics learning. Thus, the study investigates the students'…