Critical thinking is a fundamental competence in 21st-century education, particularly in mathematics, where students frequently encounter contradictory information that requires logical reasoning and reflective judgment. This study explores the stages of critical thinking among junior high school students when solving contradictory mathematical…

The development of proportional reasoning is crucial for higher-level mathematical skills. Various studies have demonstrated that the numerical structures of problems have an impact on the strategies used to solve direct proportional problems. This research was conducted to determine eighth grade students' strategies for solving inverse…

A teacher-researcher searched for and defined theoretical principles in the literature that could be used as a basis for teaching high-school students who were struggling in mathematics (in a regular-level mathematics classroom) and could offer a framework to design tasks to encourage a problem-solving, thinking classroom. After identifying 13…

Background: Problem-solving as a vehicle to develop independent thinking skills is mostly underestimated and is often either overlooked or not given adequate attention within the existing South African mathematics curriculum. Consequently, numerous learners often display limited skills or lack skills to adequately crack Mathematics problems by…

Students often instrumentally use variables and unknowns without considering the variational thinking behind them. Using parameters to modify the coefficients or unknowns in equations or systems of linear equations (without altering their structure) involves consciously incorporating variational thinking into problem-solving. We will test the…

This study examines the attitudes and opinions of 161 students, future primary school teachers, in Romania towards mathematical word problems during the 2023-2024 academic year. The investigation aimed at identifying their views on the importance, utility, and challenges of word problems. The results indicate that most students recognize the…

This study focused on capturing the research landscape of past studies related to mathematics problem solving in elementary education from 1969 to 2021 through a bibliometric analysis. All the 159 bibliographic data involved were extracted from the Scopus database. The findings show an increasing trend in publication and citation over the years.…

Modernizing mathematics refers to the idea that teachers should rethink how mathematics has traditionally been taught in schools by making rich tasks and collaboration the focus of instruction and promoting opportunities for active learning. "Modern Math Tasks to Provoke Transformational Thinking" presents carefully crafted tasks that…

A new classification for semantic structures of one-step word problems is proposed in this paper. The classification is based on illustrations of word problem situations in Common Core State Standards (CCSSM, 2010) and related historical studies (e.g. Weaver, 1973, 1979, 1982), as well as conceptual elaborations of embodied and grounded nature in…

This paper describes the design, implementation, and results of a training action with prospective primary education teachers, focusing on the creation of problems involving proportional and algebraic reasoning. Prospective teachers must solve a proportionality problem using both arithmetic and algebraic procedures, and then vary it to motivate…

Creative thinking transforms existing information, either from long-term memory or external sources, into new representations and innovative ideas. Creative thinking is an activity that processes received information to produce new representations and innovative ideas. Developing this skill is essential for students; however, recent research has…

Whole number computations are a critical skill that serves as a foundation upon which higher-order concepts in mathematics are taught to children. To facilitate their instruction, educators often use multiple representations to support a child's cognition. Representations with physical manipulatives are widely studied through a graduated…

This paper deals with a set of geometrical problems for mathematical problem-solving at different difficulty levels. All of these are presented as national flags and one has to investigate invariant area proportions when changing the locus of any corner of the flag. This dynamic element suggests the usage of dynamical geometry environments.…

The basic notions of combinatorics, including systematic listing and permutations, are important topics of mathematics that are recommended to be learned eventually from elementary schools. However, there is little research in mathematics education regarding elementary students' combinatorial strategies. The purpose of this research is to…

Students are required to have the ability to implement mathematics in solving everyday life problems. A good solving process will produce an excellent solving ability. The existing problem-solving stages cannot be used in solving problems with the Higher Order Thinking Skills (HOTS) category. The aims of this research are 1) to know students'…