Research findings have established common student misconceptions for literal symbolic representations of variables but lack corresponding findings of when or how these misconceptions arise. This article reports findings from an exploratory study of U.S. grade 4-6 students' conception(s) for various representations of unknown addends commonly found…

In this article, a mathematics teacher educator presents an activity designed to pique the interest of prospective secondary mathematics teachers who may doubt the value of learning abstract algebra for their chosen profession. Herein, he contemplates: what "is" intended by the widespread requirement that high school mathematics teachers…

Algebra I is a crucial course for middle and high school students for successful STEM related coursework. A key issue is whether students should take Algebra I in 8th versus 9th grade. Large-scale policy studies show conflicting results, and there are few (particularly longitudinal) individual difference studies. Here, 53 students were assessed in…

The "IDRA Newsletter" serves as a vehicle for communication with educators, school board members, decision-makers, parents, and the general public concerning the educational needs of all children in Texas and across the United States. The theme of this issue is "College Preparation." Contents include: (1) Texas Public School…

College algebra students face one of the highest failure rates in the U.S. The purpose of this research project was to investigate the impact graphic calculators had on college students' final grade after completing a required college algebra course. Using constructivism as a theory and a quantitative, quasi-experimental approach, the researcher…

The role of the community college is constantly evolving. At its inception in the early 1900's, the community college's broad focus was to provide quality, affordable education to the members of the community the college serves. Today, that focus remains the same, but has also morphed into one that meets the specific needs of its students. One of…

Within the social nature of teaching and learning mathematics, language can be viewed as the principal resource for making meaning in the classroom. However, research has shown that facilitating classroom discourse can be a key challenge for prospective teachers. In response to this concern, my dissertation offers case studies of three secondary…

Mathematics teacher professional-development (PD) programs based on Cognitively Guided Instruction (CGI) have been developed and implemented with tens of thousands of elementary mathematics teachers worldwide since the 1980s. Starting with a focus on addition and subtraction on whole numbers in the first CGI PD program, the content of these…

As one-to-one computer initiatives become more prevalent in schools across the state of Missouri, school leaders are faced with the challenge of determining whether one-to-one initiatives are achieving the desired academic results. Studies show that there is a connection between one-to-one initiatives and increased student engagement; however, in…

This study aims to explore the conceptualisations of function that some students express when they are responding to fictitious students' statements about functions. We also asked them what is meant by "function" and many voluntarily used examples in their responses. The task was developed in collaboration with teachers from two…

GeoGebra is a free tool that has the potential to change both how and what is taught in mathematics. GeoGebra allows teachers and students to explore various mathematical ideas either through the full applet (https://www.geogebra.org/graphing) or by sharing applets via GeoGebra's Materials site (https://www.geogebra. org/materials/). It has many…

The paper describes how designers used the construct of learning trajectories to create a tool, Math-Mapper 6-8, to help scaffold curricula toward increased learner-centered coherence. It defines "learner-centered curricular coherence" as "an organizational means to promote a high likelihood that each learner traverses one of many…

In this article the authors analyze the written solutions of some first year undergraduate mathematics students from Victorian universities as they answered tutorial exercise questions relating to complex numbers and differentiation. These students had studied at least Mathematics Methods or its equivalent at secondary school. Complex numbers was…

This article draws on some ideas explored during and after a writing workshop to develop classroom resources for the reSolve: Mathematics by Inquiry (www.resolve.edu.au) project. The project develops classroom and professional learning resources that will promote a spirit of inquiry in school mathematics from Foundation to year ten. The…

This paper reports on findings of a research study that investigated in-service secondary school teachers' perceptions and interpretations of students' errors in mathematics. The study used a survey research design in which a questionnaire with two sections was used to collect data. The first section sought to find out the teachers' perceptions of…