Student problem posing has been advocated for mathematics instruction, and it has been suggested that problem posing can be used to develop students' mathematical content knowledge. But, problem posing has rarely been utilized in university-level mathematics courses. The goal of this teacher-as-researcher study was to develop and investigate…

In this article, the authors explain how nonfiction literature can demonstrate the nature of problem solving within disciplines such as math, science, and social studies. This literature illustrates what it means to puzzle over problems, to apply disciplinary thinking, and to develop creative solutions. The authors look closely at three examples…

Objective: To test the efficacy and tolerability of the methylphenidate transdermal formulation (MTS) against immediate-release methylphenidate (IR MPH) and placebo in a 12-hr analog classroom setting. Method: A total of nine boys ages 6 to 9 years, medicated with MPH for ADHD, complete a within-subject, double-blind study. For the purpose of the…

Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Most people…

This article describes how all students can apply the algebra skills they have learned to problem solving through investigation, along with different levels of proving the conjectures algebraically.

The Lithuanian Informatics Olympiads (LitIO) is a problem solving programming contest for students in secondary education. The work of the student to be evaluated is an algorithm designed by the student and implemented as a working program. The current evaluation process involves both automated (for correctness and performance of programs with the…

The current investigation examined the effects of behavioral history on elementary students' preference for making a choice in two studies. Previous research on choice has focused on the arrangement of current contingencies and has not accounted for the effects of behavioral history. Study 1 examined participants' preference for two options (i.e.,…

This practice guide presents five recommendations intended to help educators improve students' understanding of, and problem-solving success with, fractions. Recommendations progress from proposals for how to build rudimentary understanding of fractions in young children; to ideas for helping older children understand the meaning of fractions and…

This study examined if solving arithmetic problems hinders undergraduates' accuracy on algebra problems. The hypothesis was that solving arithmetic problems would hinder accuracy because it activates an operational view of equations, even in educated adults who have years of experience with algebra. In three experiments, undergraduates (N = 184)…

In a recent paper (Denny 2002 Eur. J. Phys. 23 449-58), entitled "The pendulum clock: a venerable dynamical system", Denny showed that in a first approximation the steady-state motion of a weight-driven pendulum clock is shown to be a stable limit cycle. He placed the problem in a historical context and obtained an approximate solution using the…

This module was initially developed for a course in applications of mathematics in biology. The objective of this lesson is to investigate how the allele and genotypic frequencies associated with a particular gene might evolve over successive generations. The lesson will discuss how the Hardy-Weinberg model provides a basis for comparison when…

We examine the Stark effect (the second-order shifts in the energy spectrum due to an external constant force) for two one-dimensional model quantum mechanical systems described by linear potentials, the so-called quantum bouncer (defined by V(z) = Fz for z greater than 0 and V(z) = [infinity] for z less than 0) and the symmetric linear potential…

A temporal contiguity hypothesis for the experience of veracity is tested which states that a solution candidate to a cognitive problem is more likely to be experienced as correct the faster it succeeds the problem. Experiment 1 varied the onset time of the appearance of proposed solutions to anagrams (50 ms vs. 150 ms) and found for both correct…

In teaching primary teacher trainees, an awareness of the characteristic features, especially commutativity and associativity of basic operations play an important role. Owing to a deeply set automatism rooted in their primary and secondary education, teacher trainees think that such characteristics of addition are so trivial that they do not need…

High schools may still be anchored to 20th century expectations, but what are the critical guideposts for a 21st century high school education? There are many specific skills and competencies that young people will need to succeed, but more than particular skills, they will need the cognitive capacity to educate themselves throughout their entire…