In many scientific contexts, students need to be able to use mathematical knowledge in order to engage in scientific reasoning and problem-solving, and their understanding of scientific concepts relies heavily on their ability to understand and use mathematics in often new or unfamiliar contexts. Not only do science students need high levels of…

The purpose of this study is to design a modeling task to facilitate students' inquiries into the chain rule in calculus and to analyze the results after implementation of the task. In this study, we take a modeling approach to the teaching and learning of the chain rule by facilitating the generalization of students' models and modeling…

This study aims to explain the thinking process of students in solving combination problems considered from assimilation and accommodation frameworks. This research used a case study approach by classifying students into three categories of capabilities namely high, medium and low capabilities. From each of the ability categories, one student was…

This study describes mathematics education graduate students' understanding of relationships between sine and cosine of two base angles in a right triangle. To explore students' understanding of these relationships, an elaboration of Skemp's views of instrumental and relational understanding using Tall and Vinner's concept image and concept…

This article describes a type of professional development focused on students' thinking that occurs in middle school mathematics classrooms. This type of professional development is called "Classroom Embedded" and occurs over one or two days in a classroom with middle school students and their teacher. Teachers actively participate in…

Students engage in proportional reasoning when they use covariance and multiple comparisons. Without rich connections to proportional reasoning, students may develop inadequate understandings of linear relationships and the equations that model them. Teachers can improve students' understanding of linear relationships by focusing on realistic…

In this study, we developed a three-dimensional framework to characterize post-secondary Calculus I final exams. Our "Exam Characterization Framework" (ECF) classifies individual exam items according to the cognitive demand required to answer the item, the representation of both the task statement and the solution, and the item's format.…

This paper explores the use of animations as an approximation of practice to provide a transformational technology experience for elementary mathematics preservice teachers. Preservice teachers in mathematics methods courses at six universities (n = 126) engaged in a practice of decomposing and approximating components of a fraction lesson. Data…

In previous publications the authors of this paper identified specific relations between comprehension and convincement. On the basis of Grounded Theory, this research analyzes the changes that arise in said relations as a response to changing conditions. For their study, the authors analyze an interaction, at a distance, between a tutor and a…

Effectively launching a task involves surfacing and addressing misconceptions so that students can make progress on the task. Launching a task is supported by teachers' noticing (interpreting and responding to students' thinking). We investigated the degree to which an intervention supported improvements in pre-service secondary teachers' (PSTs')…

The reverse engineering of simple inventions that were of historic significance is now possible in a classroom by using digital models provided by places like the Smithsonian. The digital models can facilitate the mastery of students' STEM learning by utilizing digital fabrication in maker spaces to provide an opportunity for reverse engineer and…

Researchers have argued that there are strong links between primary school students' competence with fraction concepts and operations and their algebraic readiness. This study involving 162 Years 5/6 students in three primary schools examined the strength of that relationship using a test based on familiar fraction tasks and a test of algebraic…

What might arithmetic look like on an island that eschews carry digits? How would primes, squares and other number theoretical concepts play out on such an island?

We introduce Lake Wobegon dice, where each die is "better than the set average." Specifically, these dice have the paradoxical property that on every roll, each die is more likely to roll greater than the set average on the roll, than less than this set average. We also show how to construct minimal optimal Lake Wobegon sets for all "n" [greater…

In this article, we present a family of finite groups, which provide excellent examples of the basic concepts of group theory. To work out the center, conjuagacy classes, and commutators of these groups, all that's required is a bit of linear algebra.