Problem posing, by which learners create new problems by themselves, is an important activity in mathematics education. However, novice learners have difficulty in posing problems, particularly when formulating appropriate solution structures of problems. Although they are provided with example problems that can serve as hints for composing novel…

A standard example used in introductory combinatoric courses is to count the number of five-card poker hands possible from a straight deck of 52 distinct cards. A more interesting problem is to count the number of distinct hands possible from a Pinochle deck in which there are multiple, but obviously limited, copies of each type of card (two…

Scientific reasoning and scientific argumentation are highly valued outcomes of K-12 and higher education. In this article, we first review main topics and key findings of three different strands of research, namely research on the development of scientific reasoning, research on scientific argumentation, and research on approaches to support…

The ability to address and solve problems in minimally familiar contexts is the core business of research mathematicians. Recent studies have identified key traits and techniques that individuals exhibit while problem solving, and revealed strategies and behaviours that are frequently invoked in the process. We studied advanced calculus students…

Science education is criticized because it often fails to support problem-solving skills in students. Instead, the instructional methods primarily emphasize didactic models that fail to engage students and reveal how the material can be applied to solve real problems. To overcome these limitations, this study asked participants in a general…

Using errors as a method of learning has been made explicit through a two-staged peer review and discussion. During organic chemistry discussion sessions, quizzes are followed by a structured peer review designed to help students identify and discuss student errors. After the face-to-face discussion, a second stage of review involves analyzing and…

The author explores concrete ways to help students learn more and have fun doing it while they support each other's learning. The article specifically shows the relationships between cooperative learning and deep learning. Readers will become familiar with the tenets of cooperative learning and its power to enhance learning--even more so when…

Behavioral and neuroimaging findings indicate that distinct cognitive and neural processes underlie solving problems with sudden insight. Moreover, people with less focused attention sometimes perform better on tests of insight and creative problem solving. However, it remains unclear whether different states of attention, within individuals,…

Research on toddlers' mathematical knowledge is sparse. Studies on children's mathematical competencies before school age have mostly focused on older children. Few of the previous studies have included large groups of toddlers, few have been conducted in natural settings, and few have been directed at a broad field of mathematical knowledge. The…

Change theories and Organization Development strategies have long followed the problem-solving approach of looking at organizations, identifying the weaknesses and introducing interventions to "stop doing the wrong things." In its simplest form, this approach has been successful in a variety of situations and has a popular following. Consultants…

A flipped classroom approach was implemented in an undergraduate fluid mechanics course. Students watched short, online video lectures before class, participated in active in-class problem solving sessions (in pairs), and completed individualized online quizzes weekly. In-class activities were designed to develop problem-solving skills and teach…

The "What's the "matter" With XOD" activity addresses students' misconceptions and refines their ideas about phases of matter. This activity introduces the characteristics for solids, liquids, and gases, and begins a discussion about physical and chemical changes and how matter can cycle through different phases. Depending on class size and…

In the middle years of school, it is important that mathematics is challenging, engaging and focuses on worthwhile mathematics. In this article, Anne Roche describes a lesson that seemed to have all three of these characteristics, as students grappled with issues of scale to create a fun run, given a range of challenging mathematical constraints.…

The results of international comparative studies have shown that relationships exist between metacognition and cognitive activation and learning success. Since 2007 we have been carrying out projects in Indonesia to improve cognitive and metacognitive activities of pupils of year 7 and their teachers. These activities are to contribute to the…

In this study, the authors employed a quasi-experimental research design to examine the efficacy of a cooperative learning pedagogy (i.e., think-pair-share exercises) integrated into sections of microeconomic principles. Materials, exercises, and assessment instruments for all study sections are identical except for the nature of the…