We describe here lessons learned in designing an early algebra curriculum to measure early algebra's impact on children's algebra readiness for middle grades. The curriculum was developed to supplement regular mathematics instruction in Grades K-5. Lessons learned centered around the importance of several key factors, including using conceptual…

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…

In this report, we discuss background research on the development of student understanding of quadratic functions and present a provisional learning progression for quadratic functions and quadratic equations. We also describe task shells that are linked to the learning progression. The learning progression and task shells can be used as a…

In this paper, we propose an enriched and extended application of Harel and Sowder's proof schemes taxonomy that can be used as a diagnostic tool for characterizing secondary students' emergent learning of proof and proving. We illustrate this application in the analysis of data collected from 85 Year 9 (age 14-15) secondary students. We capture…

More and more schools are acquiring advanced manufacturing equipment. Activities that incorporate the use of this equipment for the purpose of teaching some academic content can either be designed or redesigned for other educational purposes as well. This article describes how the authors extended an activity that was initially designed to help…

This study examines two 5-year longitudinal data sets of community college students (n = 595 and n = 593) to explore factors associated with successful outcomes in developmental mathematics. Logistic regression models consider the role of demographic factors, course format, and student support structures on the likelihood of a student completing…

The study of students' use of representations is one of the main topics of physics education research and is guided by the overarching field of semiotics. In this paper we compare two semiotic frameworks, one coming from didactics of mathematics and one from physics education research; "the theory of registers of semiotic…

The literature on the association between reading comprehension and mathematics skills is complicated and conflicting. This study seeks to illuminate the nature of the association between mathematics skills and reading comprehension by incorporating potential moderators, namely components of mathematics skills, domains of content standards in…

Beginning with the class of 2023, graduating Pennsylvania high school students will need to demonstrate career or postsecondary preparedness in addition to meeting existing statewide graduation requirements. Act 158 of 2018 outlines five pathways to meeting this requirement, including two that rely exclusively on Keystone Exam performance and…