There is an ongoing need to support students' learning of linear functions, and the study of slope makes up a foundational component of this learning. We applied techniques from systemic functional linguistics to document the meanings that were established through spoken interaction between a student and her tutors during discussions of slope. We…

Many teachers labor to distinguish between productive and unproductive struggle; they believe that struggle is productive when it engages students in thinking and communicating metacognitively, which is when students think and communicate about their problem-solving processes, strategies, challenges, and successes. One method that helps ensure…

Students in the elementary grades often experience difficulty setting up and solving word problems. Using an equation to represent the structure of the problem serves as an effective tool for solving word problems, but students may require specific pre-algebraic reasoning instruction about the equal sign as a relational symbol to set up and solve…

Texas provides a unique opportunity to examine teachers without standard university preparation, for it prepares more teachers through alternative pathways than any other state. We find two advantages for mathematics and science teachers prepared in the standard way. First, since 2008 they have been staying in the classroom longer than those who…

Student insight into algebraic formulas, including the ability to identify the structure of a formula and its components and to reason with and about formulas, is an issue in mathematics education. In this study, we investigated how 16- and 17-year-old pre-university students' insight into algebraic formulas can be promoted through graphing…

This report examines one teacher's attempts to differentiate instruction every day, in a dynamic teaching and learning environment. The report is part of a larger study that utilised a network of theories approach, coordinating the documentational approach to didactics (DAD) and Thompson and Harel's theory of meanings, to examine teachers'…

Adoption of online resources to support instruction and student performance has amplified with technological advances and increased standards for mathematics education. Because teachers play a critical role in the adoption of technology, analysis of data pertaining to how and why teachers utilize online resources is needed to optimize the design…

Title III is a federal entitlement through the Every Student Succeeds Act (ESSA) that provides supplemental resources for English Language Learners (ELL) and immigrants students who have recently arrived to the U.S. More specifically, Title III funding supports student language acquisition and academic achievement. Depending on the English…

This paper presents a mobile app, AlgeOps, created to assist students in understanding addition and subtraction of integers. The design of the app amalgamated the neutralization model (based on cancelling integers of opposite signs) and the number line model to offer a more holistic representation of integers. Furthermore, since AlgeOps presents…

The main purpose of this study is to determine ways of thinking and understanding of eight graders related to generalizing act. To carry out this aim, a DNR based teaching experiment was developed and applied to 9 eight graders. The design of the study consists of three stages; preparation process in which teaching experiment is prepared, teaching…

The aim of this study is to examine prospective mathematics teachers' skills of interpreting algebraic formulae at the student level. In this context, 84 prospective teachers studying in the senior class of the elementary mathematics teaching program of a university in Turkey constituted the participants of the study. In this study, the…

This article addresses the logistics of implementing projects in an undergraduate mathematics class and is intended both for new instructors and for instructors who have had negative experiences implementing projects in the past. Project implementation is given for both lower- and upper-division mathematics courses with an emphasis on mathematical…

Previous research has found that different presentations of the same concept can result in different patterns of transfer to isomorphic instances of that concept. Much of this work has framed these effects in terms of advantages and disadvantages of concreteness or abstractness. We note that mathematics is a richly structured field, with deeply…

Many mathematics departments have instituted transition-to-proof courses for second semester sophomores to help them learn how to construct proofs and to prepare them for proof-based courses, such as abstract algebra and real analysis. We have developed a way of getting students, who often stare at a blank piece of paper not knowing what to do, to…

This article investigates two children's intuitive thinking in solving multiplication problems from different educational backgrounds. One of the children is in a southern elementary school in the US. He was given the same problems both in first and second grades. The other child was a first grader in a southwest region of China, and she was given…