A square chiliagonal number is a number which is simultaneously a chiliagonal number and a perfect square (just as the well-known square triangular number is both triangular and square). In this work, we determine which of the chiliagonal numbers are perfect squares and provide the indices of the corresponding chiliagonal numbers and square…

Help turn students into problem solvers. With lesson imaging, teachers anticipate how chosen activities will unfold in real time--what solutions, questions, and misconceptions students might have and how teachers can promote deeper reasoning. When lesson imaging occurs before instruction, students achieve lesson objectives more naturally and…

The New York State Education Department (NYSED) adopted a set of three standards for social and emotional learning (SEL) in August 2018. In doing so, they have paved the way for explicit instruction in and assessment of 21st-century skills. The three-goal framework selected by NYSED (2018) is modeled after the five competencies of the…

This study is virtually intended to comprehend influential Mathematical Realistic Learning Approach (MRL) upon mathematical communication aptitude of Junior High School RA Kartini Sei Rampah, to overview has the interactive learning approach, and Initial Mathematical Cognition (IMC) found upon mathematical communication power and positive…

Unlike general approaches to learning, the Causalitic-Thinking Approach, aims to construct phenomena that have more than one possible answer. However this approach requires scaffolding strategies. This study aims to investigate the strategy of developing scaffolding in learning with the Causalitic-Thinking Approach to increase students'…

We tested a method for solving Bayesian reasoning problems in terms of spatial relations as opposed to mathematical equations. Participants completed Bayesian problems in which they were given a prior probability and two conditional probabilities and were asked to report the posterior odds. After a pretraining phase in which participants completed…

One of the subjects that constitute a problem for adult students of mathematics is the understanding of fractions and proportions. These notions are interrelated with proportional reasoning which was the focal point of our study. Using a mixed methods approach, we tried to assess the proportional reasoning of adult students during problem solving.…

In this article, the authors emphasise the importance of purposeful mathematical discussion and using sequences of connected, cumulative, and challenging tasks in advancing students' spatial reasoning in the early years of schooling.

The way that individuals perceive their well-being may vary depending on their self-efficacy especially towards a difficult life situation, such as the physical disability. The aim of this study is to examine the relationships among problem solving self-efficacy, resilience self-efficacy and subjective well-being and the differentiation among…

The current study examined the effectiveness of self-explanation prompts, visual signaling cues, and a combination of the two features on middle school students' (N = 202) algebra learning. Also explored were the differential effects of features for students with faulty conceptual knowledge (evidenced by a higher prevalence of making errors during…

The goal of this study is to compare in-service and pre-service teachers' computational thinking skills and to take in-service teachers' opinions about the contribution of professional life to differentiation in this skill. The study was conducted in Turkey. The type of the study is mixed method. Quantitative data were obtained from 870…

Problem solving skills are considered an integral part of grasping the precise concepts of the programming domain for novices in introductory programming (IP) courses. But these skills are mostly covered only in early lectures of such courses or are included in just a few early chapters of some relevant textbooks. Consequently, high failure and…

The aim of this study is to examine the risk-taking behavior of adolescents in terms of attachment styles and social problem-solving. The study group consists of 637 students from 9th, 10th and 11th grade, as 276 female (43.2%) and 361 male (56.7%). In order to collect data in the study, the Delinquent Behavior Scale, the Relationship Scale, the…

Higher-order thinking skills (HOTS) mathematical problem-solving was first introduced in the Form-3 assessment (PT3) in 2014. However, to date, there have been no studies of students' ability to solve the mathematical problems in this assessment. Therefore, this study investigated the emerging patterns and problems of HOTS mathematical…

This study reports on a way to address twenty-first-century skills in mathematics education by organizing one-day mathematics challenges in the Netherlands. During such a day, students work in teams in school on an open-ended problem which aims to elicit skills like problem-solving, modeling, collaboration, and communication. The framework and the…