Problem solving has been a major theme in Japanese mathematics curricula for nearly 50 years. Numerous teacher reference books and lesson plans using problem solving have been published since the 1960s. Government-authorized mathematics textbooks for elementary grades, published by six private companies, have had more and more problem solving over…

Differences exist between engineering and liberal arts students because of their educational backgrounds. Therefore, they solve problems differently. This study examined the brain activation of these two groups of students when they responded to 12 questions of verbal, numerical, or spatial intelligence. A total of 25 engineering and 25 liberal…

Intelligence is not fixed. While many of us may not be innately talented in all areas of learning, all of us are capable of learning anything. It is important that teachers help communicate this concept to students and help students to develop this growth mindset. This article first compares growth and fixed mindsets, discussing some of the…

Sorting is a fundamental computing concept. As for today, it is taught at the secondary school level. However, this kind of algorithm is an obstacle for some students due to its high level of abstraction. To prevent discouragement as well as to incorporate a fun and challenging algorithmic task, a novel tablet-based digital game,…

This study investigates prospective secondary mathematics teachers' visual representations of polynomial and rational inequalities, and graphs of exponential and logarithmic functions with GeoGebra Dynamic Software. Five prospective teachers in a university in the United States participated in this research study, which was situated within a…

Engaging learners in exploratory problem-solving activities prior to receiving instruction (i.e., explore-instruct approach) has been endorsed as an effective learning approach. However, it remains unclear whether this approach is feasible for elementary-school children in a classroom context. In two experiments, second-graders solved mathematical…

The purpose of this study was to examine effectiveness of paraphrasing interventions on mathematics word problem-solving accuracy in third grade children (N = 72) at risk for mathematics disabilities (MD). Three instructional conditions directed students' attention through paraphrasing, via writing, to different propositions within word problems.…

Teachers in primary education experience difficulties in teaching word problem solving in their mathematics classes. However, during controlled experiments with a metacognitive computer programme, students' problem-solving skills improved. Also without the supervision of researchers, metacognitive computer programmes can be beneficial in a natural…

Colleen Vale makes the case for professional learning teams collaborating together to improve their teaching and hence children's achievement. In this article she describes how this may be done. Along the way the teachers explored the idea of equivalence and the common conceptions and misconceptions held by children in their classes.

Comparison is a fundamental cognitive process that can support learning in a variety of domains, including mathematics. The current paper aims to summarize empirical findings that support recommendations on using comparison of multiple strategies in mathematics classrooms. We report the results of our classroom-based research on using comparison…

Recognizing the challenges that students face when they may lack background and experiential knowledge with regard to coins is important so that teachers can address this during instruction. Exposure to coins is one of the basic necessities to learning about the coins, but that is just the initial part of the learning sequence. Unless students are…

Our goal in this article is to discuss the importance of problems in early childhood education for the child's development and engagement with the mathematics existing in childhood culture. Our assumption is that an important task for young children's education is to create a democratic and critical environment, in which multiplicity of…

A beneficial effect of gesture on learning has been demonstrated in multiple domains, including mathematics, science, and foreign language vocabulary. However, because gesture is known to co-vary with other non-verbal behaviors, including eye gaze and prosody along with face, lip, and body movements, it is possible the beneficial effect of gesture…

Achieving practical implementation of learning by problem posing faces the issue of inefficiency due to the time needed for assessment and giving feedback to students' posed problems. As a solution of this problem, we have developed a tablet PC-based software for learning by posing arithmetic word problems named Monsakun. The software is based on…

This paper reports a study conducted in a laboratory classroom with the capability to record classroom social interactions in great detail using advanced video technology. The social interactions of student groups during collaborative problem solving were analysed based on transcript data. This analysis suggests that meaning negotiation in…