To further understand student thinking in the context of combinatorial enumeration, we examine student work on a problem involving set partitions. In this context, we note some key features of the multiplication principle that were often not attended to by students. We also share a productive way of thinking that emerged for several students who…

The aim of this study is to analyse how mathematical problem solving is represented in mathematical textbooks for Swedish upper secondary school. The analysis comprises dominating Swedish textbook series, and relates to uncovering (a) the quantity of tasks that are actually mathematical problems, (b) their location in the chapter, (c) their…

School psychologists are tasked with ensuring treatment integrity because the level of intervention implementation affects decisions about student progress. Treatment integrity includes multiple dimensions that may impact the effectiveness of an intervention including adherence, dosage, quality, and engagement. Unfortunately, treatment integrity…

The Puppy Love problem asked fifth and sixth grade students to use their prior knowledge of measures of central tendency to determine a data set when given the mean, mode, median, and range of the set. The problem discussed in this article is a task with a higher level of cognitive demand because it requires that students (1) explore and…

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…