In this paper, we present a set of activities for an introduction to solving counting problems. These activities emerged from a teaching experiment with two university students, during which they reinvented four basic counting formulas. Here we present a three-phase set of activities: orienting counting activities; reinvention counting activities;…

This research is reviewing students' process of decision making intuitively, analytically, and interactively. The research done by using discount problem which specially created to explore student's intuition, analytically, and interactively. In solving discount problems, researcher exploring student's decision in determining their attitude which…

This work aims to demonstrate the use of Excel spreadsheets for solving L-L extraction problems. The key to solving the problems successfully is to be able to determine a tie line on the ternary diagram where the calculation must be carried out. This enables the reader to analyze the extraction process starting with a simple operation, the…

Purpose: Statistics shows terrifying tendencies in people' unwillingness to develop themselves by reading books. The situation is even more serious if we look at companies and their employees. People want to be specialists, but in fact reading culture in companies is rare. Many actions which are undertaken to reverse this trend may lead to sales…

Teachers and students commonly use various concrete representations during mathematical instruction. These representations can be utilized to help students understand mathematical concepts and processes, increase flexibility of thinking, facilitate problem solving, and reduce anxiety while doing mathematics. Unfortunately, the manner in which some…

The interaction analysis presented by Kim and Roth examines nine students, their teachers, the learning task and materials in a mixed second and third grade science classroom during the school day. In the research narrative readers are introduced to two resourceful and creative groups of students as they work on a task assigned by their…

The existing literature indicates that interactive-engagement (IE) based general physics classes improve conceptual learning relative to more traditional lecture-oriented classrooms. Very little research, however, has examined quantitative problem-solving outcomes from IE based relative to traditional lecture-based physics classes. The present…

This article argues for a shift in how researchers discuss and examine students' uses and understandings of multiple representations within a calculus context. An extension of Zazkis, Dubinsky, and Dautermann's (1996) visualization/analysis framework to include contextual reasoning is proposed. Several examples that detail transitions between…

South Africa has opened up access to higher education over the past 20 years. The massive increase in enrolments (with almost 70% first-generation students) substantially affects progress and graduation rates in Science programmes in higher education. First-year students in Science realise that university mathematics requires knowledge and skills…

In this undergraduate analytical chemistry experiment, students quantitatively assess the antibacterial activity of essential oils found in thyme leaves ("Thymus vulgaris") in an authentic, research-like environment. This multi-week experiment aims to instill green chemistry principles as intrinsic to chemical problem solving. Students…

The Assessment and Teaching of 21st Century Skills (ATC21S™) project undertook a research and development plan that included conceptualization of 21st century skills and assessment task development. Conceptualization focused on the definition of 21st century skills. This article outlines the particular case of one of these skills, collaborative…

The "Wisdom of Crowds" hypothesis has been introduced into many fields, but not into education. Groups with diverse knowledge and skills make better decisions than homogenous groups or expert groups. Diversity adds different points of view, which improve the problem solving ability of the group. The increased use of social networks makes…

A problem-solving scaffold approach to synthesis was developed and implemented in two intervention sections of Chemistry 2211K (Organic Chemistry I) at Georgia Gwinnett College (GGC). A third section of Chemistry 2211K at GGC served as the control group for the experiment. Synthesis problems for chapter quizzes and the final examination were…

The article opens with a Geoboard Triangle Quest in this form: "How many noncongruent triangles can be constructed on a 4 × 4 geoboard? How do you know? Justify your answer with significant supporting work." The use of advanced digital technologies as tools for problem solving receives much attention in the methods classes if the…

The purpose of the study was to determine whether there was any significant difference in speed, accuracy, retention and transferability between the Decomposition (DEC) and the Base-Complement Additions (BCA) algorithms for performing compound subtraction in non-decimal bases. Fifty-nine students with a mean age of approximately 15 years from two…