Scientific ideas are often expressed as mathematical equations. Understanding the ideas contained within these equations requires making sense of both the embedded mathematics knowledge and scientific knowledge. Students who can engage in this type of blended sensemaking are more successful at solving novel or more complex problems with these…

Researchers have emphasized the importance of characterizing students' abilities to coordinate changes in covarying quantities. In this paper, we characterize three undergraduate students' coordination of covarying quantities' amounts of change during a teaching experiment. We adopt Piagetian notions of figurative and operative thought to describe…

Although it is widely known that reading plays a significant role in mathematics performance, it remains unclear how specific reading component skills and item characteristics are associated with adults' mathematics performance. The aim of this study was to investigate reading component skills (printed vocabulary, sentence processing, passage…

This exploratory study was conducted to evaluate the quality of digital math games by measuring how much the content of a digital game is aligned to the NCTM Content and Process Standards. For this purpose, this study employed a content analysis method. In total, 23 digital mathematics games have been selected and analyzed using an instrument, a…

In this article, the author presents a set of design principles that were used to construct and refine a lesson involving the TI-Nspire handheld graphing calculator through multiple enactments in high school algebra classrooms to assist students in constructing a deeper understanding of systems of linear inequalities, a high school algebra content…

In this study, we investigate a program designed for young adults with intellectual disability to learn how to calculate the value of a collection of coins and notes with procedural fluency. In the first half of the paper, we establish the importance of financial literacy for people with intellectual disability and the need to address mathematical…

The aim of this research was to explore the mathematical connections that pre-university students make when they sketch the graph of a derivative function and an antiderivative function. Also, we tried to explain the origin of the mathematical connections identified. We assume mathematical connections as a cognitive process through which a person…

The concept of a mathematical definition causes severe difficulties among students during problem solving and proving activities. Students' difficulties with the use of mathematical definitions often arise from the fact that students are often given those definitions instead of constructing them. With the aim of developing an understanding of the…

This article presents the results of our analysis of a sample of 254 Calculus I final exams (collectively containing 4,167 individual items) administered at U.S. colleges and universities. We characterize the specific meanings of foundational concepts the exams assessed, identify features of exam items that assess productive meanings, distinguish…

A basic mental model (BMM--in German 'Grundvorstellung') of a mathematical concept is a content-related interpretation that gives meaning to this concept. This paper defines normative and individual BMMs and concretizes them using the integral as an example. Four BMMs are developed about the concept of definite integral, sometimes used in specific…

In this paper, we extend the notion of noticing during the planning of a lesson to examine what and how teachers notice concerning the affordances of typical problems, such as examination-type or standard textbook questions. Teachers in examination-oriented educational systems generally use these types of problems to develop procedural skills.…

Given the recent development of mobile gaze-tracking devices it has become possible to view and interpret what the student sees and unravel the associated problem-solving processes further. It has also become possible to pinpoint joint attention occurrences that are fundamental for learning. In this study, we examined joint attention in…

In this note we describe the mathematics that emerges from the construction of an origami box. We first construct a simple origami box from two rectangular sheets and then discuss some of the mathematical questions that arise in the context of algebra, geometry and calculus.

Cyclic voltammetry (CV) is the most popular electrochemical technique for the study of electrode processes. One of the reasons for its popularity is its adjustable timescale which can vary several orders of magnitude simply by varying the rate at which the potential is scanned. Changing the scan rate affects CV features including the current,…

"Next Generation Science Standards" ("NGSS") three-dimensional learning is valuable for all students regardless of age. The "NGSS" integrate disciplinary core ideas, science and engineering practices, and crosscutting concepts, adding rigor to science teaching and learning. Though "NGSS" performance…