In this article, the goal is to describe students' mathematical reasoning in the context of different settings of problem-solving tasks. The core of the tasks are real objects, which are presented to the students with the help of photos, a 3D model or in the environment itself. With reference to the experiential learning theory and relations to…

Research suggests some sequences of examples and problems (i.e., EE, EP) are more effective (higher test performance) and efficient (attained with equal/less mental effort) than others (PP, sometimes also PE). Recent findings suggest this is due to motivational variables (i.e., self-efficacy), but did not test this during the training phase.…

Comparative studies on paper and pencil--and computer-based tests principally focus on statistical analysis of students' performances. In educational assessment, comparing students' performance (in terms of right or wrong results) does not imply a comparison of problem-solving processes followed by students. In this paper, we present a theoretical…

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…

The looking-back stage is rarely observed in students' problem solving in spite of its recognized importance. The importance of this stage is attributed to practices of engagement with queries on verification of the obtained solution(s), comparative consideration of alternative solutions, and formulation of implications for future problem solving.…

This study invested 24 effective and 16 ineffective problem-solving kindergarten children's awareness of metacognitive self-regulated learning (MSRL) while watching other child's problem-solving behaviors. The model in a video performed a task with a trial-and-error approach and finally asked for help. After watching the video, children were asked…

The Remote Associates Test (RAT) is a word association retrieval task that consists of a series of problems, each with three seemingly unrelated prompt words. The subject is asked to produce a single word that is related to all three prompt words. In this paper, we provide support for a theory in which the RAT assesses a person's ability to…

Background: Creativity requires both divergent and convergent thinking. Previous research established that "divergent" thinking relates to mathematics performance, but generally ignored the role of "convergent" thinking and, hence, leaves it unclear how both might interact when children work on mathematical tasks. This study…

Math anxiety (MA) and math performance are generally negatively correlated (Barroso et al., 2021; Namkung et al., 2019). However, the mechanisms underlying this negative association remain unclear. According to the attentional control theory (ACT; Eysenck et al., 2007), anxious individuals experience impaired attentional control during problem…

Creativity is not only for gifted students, but also for regular ones. This case study was aimed to analyze the appropriateness of tasks and the elaboration of multiple solutions to occasion fourth-graders' mathematical creative thinking through a documentary multiple-solution counting task in a figurative setting. The data came from the written…

The aim of this study is to reveal and evaluate the attending and interpreting skills of student thinking of prospective teachers, as well as their instructional suggestions as responding skills. The current study was conducted with 29 prospective mathematics teachers (PMTs) within a qualitative design in the context of probability. First, three…

Interference of irrelevant salient variables may cause difficulties for students. This study focused on eye tracking during the comparison of perimeters task, in which area is the interfering irrelevant salient variable. There were three trial types: congruent (larger area-larger perimeter), incongruent inverse (larger area-smaller perimeter), and…

Technology can play a pivotal role in mathematics education. Qualitative methods were used to report on how a Year 1-2 teacher incorporated "Conveyance technology" (iPads), to support the teaching and learning of mathematics through student reasoning and problem-solving. The study was conducted in Australia. A single case was chosen,…

Argumentation is an important aspect in the field of education because of its impact on learning processes. At the same time, argumentation is a complex activity in terms of cognitive, relational, emotional and social dynamics. In this paper, I investigate and I describe possible difficulties encountered by children during the argumentative…

In this study we analysed what computational thinking skills pupils used when programming a small robot to solve a given problem, a simple programming task in which pupils had to select codes and put them in the correct place. Computational thinking is the process of (re)formulating a problem so that it becomes possible to use computer technology…