Collaborative learning is a group learning paradigm in which individuals or students work together to solve problems or complete tasks, exemplifying the essence of collective educational efforts. There are a lot of collaborative learning methods available; however, finding one that is suitable for the complex nature of mathematical problem-solving…

Problem posing engages students in generating new problems based on given situations (including mathematical expressions or diagrams) or changing (i.e., reformulating) existing problems. Problem posing has been at the forefront of discussion over the past few decades. One of the important topics studied is the process of problem posing as…

The growing use of programming in mathematics classrooms presents a challenge linked to implementation in general and task design in particular. This article presents design ideas for mathematical problems incorporating programming in which the focus remains mainly on learning mathematics and less on learning programming. The article starts by…

The main aim of this paper is to propose a critical view of the application of Toulmin's model of argument to mathematics education, focusing on aspects that have strong teaching implications. It is claimed that Toulmin's description of arguments in mathematics, in particular as regards the relations between form and meaning, is misleading and out…

The present study aimed to describe teachers' instructional flows when implementing a mathematical problem-posing task using scriptwriting technique. With matchsticks, a growing pattern that increases by a constant unit was created and presented to the teachers as a problem-posing situation. We analyzed the instructional flows in 50 scripts,…

Combinatorial proofs of binomial identities involve establishing an identity by arguing that each side enumerates a certain set of outcomes. In this paper, we share results from interviews with experienced provers (mathematicians and upper-division undergraduate mathematics students) and examine one particular aspect of combinatorial proof, namely…

Mathematical flexibility is thought to be a critical component of mathematical proficiency, and the term "mathematical flexibility" has been used by teachers, researchers, and policy makers for more than 2 decades. Although there seems to be consensus on the importance of mathematical flexibility as a construct, the way it is defined and…

Background: The sophistication of young children's arithmetic problem-solving strategies can be influenced through experience and instructional intervention. One potential pathway is through encountering story problems where the location of the unknown quantity varies. Aims: The goal of the present study is to characterize how arithmetic…

The invention of problems is a fundamental competence that enhances the didactic-mathematical knowledge of mathematics teachers and therefore should be an objective in teacher training plans. In this paper, we revise different proposals for categorizing problem-creation activities and propose a theoretical model for problem posing that, based on…

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 article features a fifth grade mathematics exploration planned to facilitate students' productive struggle. The exploration was a catalyst for a team of educators to unpack the teacher's experience when facilitating students' productive struggle. The team called this "teacher productive struggle" and shares about the construct…

Research has shown the importance of helping students, especially those with mild-to-moderate learning disabilities, to offload information during problem-solving. When students can get their thoughts onto paper, number line strategies can help them develop a firm foundation in mathematical problem-solving while understanding the relationships…

Many gifted students fail to be diagnosed, preventing them from receiving an education that is adapted to their characteristics, with activities that challenge their minds. Mathematics is one of the subjects in which they can demonstrate talent, where they often exhibit high skills in solving problems, handling numbers and performing spatial…

Problem solving and proofs have always played a major role in mathematics. They are, in fact, the heart and soul of the discipline. The using of a number of different proof techniques for one specific problem can display the beauty, and elegance of mathematics. In this paper, we present one specific, interesting geometry problem, and present four…

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…