Research on problem solving typically does not address tasks that involve following detailed and/or illustrated step-by-step instructions. Such tasks are not seen as cognitively challenging problems to be solved. In this paper, we challenge this assumption by analyzing verbal protocols collected during an Origami folding task. Participants…

It is well known that introductory physics students often have alternative conceptions that are inconsistent with established physical principles and concepts. Invoking alternative conceptions in the quantitative problem-solving process can derail the entire process. In order to help students solve quantitative problems involving strong…

A small number of studies have investigated student understanding of vector addition and subtraction in generic or introductory physics contexts, but in almost all cases the questions posed were in the vector arrow representation. In a series of experiments involving over 1000 students and several semesters, we investigated student understanding…

Using a constructivist framework, eight senior chemistry majors were interviewed twice to determine: (i) structural inferences they are able to make from chemical and physical properties; and (ii) their ability to apply their inferences and understandings of these chemical and physical properties to solve tasks on the reactivity of organic…

This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context,…

This case study examined competence in two third-grade classrooms where teachers centered children's mathematical thinking in instructional decision-making. Offering a synthesis of sociocultural characterizations of competence, and drawing from a variety of data sources including classroom video, student work and assessments, and teacher…

Researchers have documented difficulties that elementary school students have in understanding volume. Despite its importance in higher mathematics, we know little about college students' understanding of volume. This study investigated calculus students' understanding of volume. Clinical interview transcripts and written responses to volume…

The notion of temporal range is introduced and discussed in this paper. Two dimensions of temporal range are identified: mathematical temporality relating to mathematical ideas, their precursors and horizons; and a mathematical learning temporality where what students say/do provides the ground on which future learning can be built. These…

The concept of covalent bonding is characterized by an interconnected knowledge framework based on Lewis and quantum models of atoms and molecules. Several research studies have shown that students at all levels of chemistry learning find the quantum model to be one of the most difficult subjects to understand. We have tried in this paper to…

This study investigated middle school students' conceptual understanding of algebraic equations. 257 sixth- and seventh-grade students solved algebraic equations and generated story problems to correspond with given equations. Aspects of the equations' structures, including number of operations and position of the unknown, influenced students'…

In this article we explore the mechanisms through which one group of preservice teachers engage in "Collective Property Noticing"--a phenomenon in which group members integrate individual contributions such that the group, as a unit, notices mathematical properties of their collective image. Drawing on improvisational theory to help to…

When designing lessons and units of study, teachers prepare problems that will make learning accessible, challenging, and targeted to goals. Experienced teachers often can predict classroom dialogue. This sense of déjà vu is even stronger when they teach the same course several times a day. The questions from the students are familiar and almost…

Consider that colorful photographs, eye-catching illustrations, and captivating images intended to make textbooks more appealing may actually distract students from the lesson at hand. Or that asking students to simply solve math problems might not be as effective as having them explain the steps of solutions that are already worked out--even some…

The answers offered by computer algebra systems (CAS) can sometimes differ from those expected by the students or teachers. The comparison of the students' answers and CAS answers could provide ground for discussion about equivalence and correctness. Investigating the students' comparison of the answers gives the possibility to study different…

The demand for Information Systems (IS) graduates with expertise in Structured Query Language (SQL) and database management is vast and projected to increase as "big data" becomes ubiquitous. To prepare students to solve complex problems in a data-driven world, educators must explore instructional strategies to help link prior knowledge…