Over the last two decades, students in Singapore consistently scored above students from other nations on the Trends in International Mathematics and Science Study (TIMSS; Provasnik et al., 2012). In contrast, students in the United States have not performed as well on international and national mathematics assessments and students with…

The purpose of this study was to examine child-level pathways in development of prealgebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early…

In this dissertation, the following "network computing problem" is considered. Source nodes in a directed acyclic network generate independent messages and a single receiver node computes a target function f of the messages. The objective is to maximize the average number of times f can be computed per network usage, i.e., the "computing…

Quite a number of interesting problems in probability feature an event with probability equal to 1/e. This article discusses three such problems and attempts to explain why this probability occurs with such frequency.

The method of "Double False Position" is an arithmetic approach to solving linear equations that pre-dates current algebraic methods by more than 3,000 years. The method applies to problems that, in algebraic notation, would be expressed as y = L(x), where L(x) is a linear function of x. Double False Position works by evaluating the described…

Diophantine equations constitute a rich mathematical field. This article may be useful as a basis for a student math club project. There are several situations in which one needs to find a solution of indeterminate polynomial equations that allow the variables to be integers only. These indeterminate equations are fewer than the involved unknown…

In the United States, people's collective definitions, perceptions, and myths about creativity have, at best, produced an uneven understanding of what it means to be a creative person. This article aims to clarify meanings associated with the broad term "creativity" and identify some observable processes associated with it. Part of the problem in…

A physics teacher assigns problems to his or her students not to keep them indoors during sunny days, but to strengthen and deepen their understanding of the universe. Every problem has not only an answer, but also a "moral to the story"--a reason why that question and that answer are interesting and probing. It is an unfortunate fact that our…

The problem of a ladder leaning on a wall has been a staple of introductory physics for years. It is discussed in numerous physics textbooks and in journals. Now, it even has an Internet presence. Postings from students seek help for "ladder on a wall" problems. A quick review of those postings would show that they all deal with frictionless…

It has been suggested that verbally sophisticated individuals engage in a series of precurrent behaviors (e.g., covert intraverbal behavior, grouping stimuli, visual imagining) to solve problems such as answering questions (Palmer, 1991; Skinner, 1953). We examined the effects of one problem solving strategy--visual imagining--on increasing…

Design tasks are omnipresent in our everyday lives. Previous research shows that reflective thinking is one of the critical factors in solving design problems. Related research has attempted to capture designers' reflective thinking process. Yet a close inspection of designers' reflective thinking taking place during their design process demands…

Learning physics requires understanding the applicability of fundamental principles in a variety of contexts that share deep features. One way to help students learn physics is via analogical reasoning. Students can be taught to make an analogy between situations that are more familiar or easier to understand and another situation where the same…

Charter school research has examined the relationship between charter school mission and issues of school accountability. However, there is a lack of research focusing on how charter school leaders frame and solve problems regarding multiple accountability demands. Given this gap, I investigate the question: How do charter school leaders…

Purpose: This study investigated understanding of mathematical equivalence in children with and without specific language impairment (SLI). Method: A total of 34 children (ages 8;1 [years;months] to 11;7), including 9 with expressive SLI (E-SLI), 8 with expressive and receptive SLI (ER-SLI), and 17 age-matched typically developing (TD) children…

We investigated how students use the representation of data in a given example appearing in an interactive diagram (ID) and how they create additional examples with the ID. Students who worked with the ID that offered limited representations and tools ("illustrating ID") looked for ways to bypass the designed constraints: they changed the…