Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a…

Geometry provides a natural window into what it is like to do mathematics. In the world of geometry, playful experimentation is often more fruitful than following a procedure, and logic plus a few axioms can open new worlds. Nonetheless, teaching a geometry course in a way that combines both rigor and play can be difficult. Many geometry courses…

The emergence of non-Euclidean geometries in the 19th century rocked the foundations of mathematical knowledge and certainty. The tremors can still be felt in undergraduate mathematics today where encounters with non-Euclidean geometry are novel and often shocking to students. Because of its divergence from ordinary and comfortable notions of…

Identifying mathematical and didactical conditions under which mathematics learners can encounter an intellectual need for defining and proving is recognized as a challenging research enterprise. This paper presents a particular configuration of conditions under which a group of pre-service mathematics teachers successfully constructed a…

In his paper, Michael Merry poses an interesting and important question: How can we navigate between two often opposing interests--that of protecting the welfare of our society's children and that of protecting their liberties by avoiding paternalism? While Merry lays out his argument with clarity and insight into the risks and harm that state…

Intervention research for couples and families managing chronic health problems is in an early developmental stage. We reviewed randomized clinical trials of family interventions for common neurological diseases, cardiovascular diseases, cancer, and diabetes, which is similar to the content of previous reviews discussed later. One overriding theme…

This article investigates the numbers [image omitted], originally studied by Catalan. We re-confirm that they are indeed integers. Using the close relationship between them and the Catalan numbers C[subscript n], we develop some divisibility properties for C[subscript n]. In particular, we establish that [image omitted], where f[subscript k]…

The current research comprises two samples that investigated the psychometric properties of the Problem-Focused Style of Coping (PF-SOC; Heppner, Cook, Wright, & Johnson) scale using two Taiwanese samples. In Sample 1 (N = 809), we investigated the structural dimensions of the PF-SOC using a principal component analysis (PCA) and confirmed…

This study looks at a mixed ability group of 21 Year 5 primary students (aged 9-10 years old) who had previously never had formal instruction using letters to stand for unknowns or variables in a mathematics context; nor had they been introduced to formal algebraic notation. Three lessons were taught using the computer software "Grid Algebra"…

This paper shows how to teach a mathematics for liberal arts class in an inquiry-based way using ideas from music to launch the mathematical activities. No musical knowledge is required to understand and teach the material. The main activity is analyzing the differences between two kinds of rhythmic palindromes. The content is mathematically…

The late-Victorian era provided aficionados of detective fiction with an abundance of short stories belonging to this literary genre. Many of these works contained some aspect of chemistry, either in the execution of a crime or in the identification of the perpetrator. In the example discussed in this article, the gas-phase reaction of hydrogen…

This paper presents guided classroom activities that showcase two classic problems in which a finite limit exists and where there is a certain charm to engage liberal arts majors. The two scenarios build solely on students' existing knowledge of number systems and harness potential misconceptions about limits and infinity to guide their thinking.…

This article presents an interview with Susan Gendron, a policy coordinator at SMARTER Balanced Assessment Consortium. In this interview, Gendron talks about the Common Core State Standards and their implications for school leaders.

This article summarizes research conducted on calculator block items from the 2007 fourth- and eighth-grade National Assessment of Educational Progress Main Mathematics. Calculator items from the assessment were categorized into two categories: problem-solving items and noncomputational mathematics concept items. A calculator has the potential to…

In considering mathematics problem solving as a model-eliciting activity (Lesh & Doerr, 2003; Lesh & Harel, 2003; Lesh & Zawojewski, 2008), it is important to know "what" students are modeling for the problems: situations or solutions. This study investigated Grade 3 students' mathematization process by examining how they modeled different…