Examples play a variety of roles in proving and disproving. Buchbinder and Zaslavsky (2019) have produced an a priori mathematical framework for assessing students' understanding of the role of examples when proving and disproving universal and existential statements. In this paper, I highlight three important aspects that suggest an extension of…

This study explores gender-based differences in sixth-grade students' potential for mathematical creativity through the interrelated processes of problem solving (PS) and problem posing (PP), grounded in a multidimensional framework of creativity--encompassing fluency, flexibility, and originality. A total of 346 sixth graders from public schools…

In this cross-national study, we explore the different ways of reasoning-and-proving (RP) presented in three 8th grade textbooks, one from each country: Turkey, Norway, and Slovakia. While the analysis revealed that all three textbooks contain similar numbers of problems involving some form of RP, differences exist in terms of the dominating ways…

The aim of this study is to determine the number sense skills of preschool (Kindergarten) children. In the study, survey design, one of the quantitative research methods, was used. The study group consists of a total of 114 children attending all the kindergartens (5 kindergartens) in the city center of Tunceli in the 2020-2021 school year. The…

Parental involvement in children's education has benefits throughout a child's academic career. Researchers and educators have developed parental involvement programs, the most effective being those that teach parents to understand open-ended mathematics problems, allowing time for children to think, share their mathematical understanding, and…

A 12-episode constructivist teaching experiment with two pairs of elementary preservice teachers was conducted to examine how they reason distributively and proportionally. Specifically, I studied how prospective teachers reason with ratios as multiplicative comparisons. Prospective teachers solved different problems in one specific context (Step…

The aim of this study is to investigate Norwegian primary school students' multimodal mathematical reasoning when solving combinatorial problems. The data collection took place in four small groups of altogether thirteen 8-9 years old third-graders. Our study shows a variety of approaches used to solve the given combinatorial problems, such as…

The aim of this study is to reveal the mathematical literacy skills of seventh grade students according to the PISA Mathematical Literacy Framework. In the study, a special case study from qualitative research methods was used. The participants of the study were 25 seventh grade students studying in the middle school of a public school in Giresun…

The purpose of the present study is to examine the mathematical reasoning and the argumentation process of 7th-grade students during problem-solving and their views on this process. The case study method was employed in line with the purpose. The study group was determined by criterion sampling. Considering the criteria of students' scores on the…

The purpose of this study is to investigate the reflections that arise during the implementation of mathematical modeling activities with third-grade primary school students. To achieve this goal, a case study methodology was employed. The study consisted of 9 third-grade students (average age 8), selected through purposive sampling from a public…

This study sought to understand how students activate number sense in determining the position of fractions on a number line and identify how the natural number bias and number sense influences students' thinking processes. The study utilized the Cognitive Task Analysis (CTA), involving four fifth-grade elementary students as the research…

A group of eighth-graders was presented with a two-day lab exploring graph theory as an enrichment experience. With the school's winter break looming, students were weary of solving linear equations, and this topic was intended to inject some new life into the classroom. In addition to learning about a completely new topic, they would be exposed…

We are all fascinated by loops and their formation in space. When a line cuts itself, it forms an intersection point and creates a space. This is an experimental study done by analyzing several loops, forming a concrete formulation by visualizing the patterns observed, and then proving the formulations proposed using the known standard…

In the present study, we illuminate students' multiplicative reasoning in the context of their units-coordinating activity. Of particular interest is to investigate students' use of three levels of units as given material for problem-solving activity, which we regard as supporting a more advanced level of multiplicative reasoning. Among 13 middle…

Mathematical coherence is a goal within the Common Core State Standards for Mathematics. One aspect of this coherence is how student mathematical thinking is developed across concepts. Unfortunately, mathematics is often taught as isolated ideas across grades. The multiplicative field is an area of study that needs to be examined as a space to…