Two complementary processes involved in mathematical modelling are mathematising a realistic situation and applying a mathematical technique to a given realistic situation. We present and analyse work from two undergraduate students and two secondary school teachers who engaged in both processes during a mathematical modelling task that required…

Overall scale scores from the National Assessment of Educational Progress (NAEP) indicate that there was only minimal improvement in the mathematics performance of high school students between 1978 and 2004. Using recently released data from the Long-Term Trend (LTT) NAEP, this study describes the content covered on the LTT NAEP and the…

This article presents features of a qualitative research study concerning the teaching and learning of school algebra using a function-based approach in a grade 8 class, of 23 students, in 26 lessons, in a state school of Athens, in the school year 2003-2004. In this article, we are interested in the inequality concept and our aim is to…

The translation principle allows students to solve problems in different branches of mathematics and thus to develop connectedness in their mathematical knowledge. Successful application of the translation principle depends on the classroom mathematical norms for the development of discussions and the comparison of different solutions to one…

The aim of this study was to examine if there is a difference in the performance on non-linear problems regarding age, gender, and solving situation, and whether the multiple-choice answer format influences students' thinking. A total of 112 students, aged 15-16 and 18-19, were asked to solve problems for which solutions based on proportionality…

Linear models are frequently inappropriately applied to various situations. When misapplied, linearity is traditionally referred to as a tendency, a misconception, or an error. Cognitive linguistic, situated cognition, and sociocultural or cultural-historical activity theory, on the other hand, suggest that linear models are adopted by learners…

Background: Many studies have looked at students' mathematics achievement in the middle and high school years and the kinds of factors that are associated with their achievement. Within this domain, however, most research utilized cross-sectional data. Cross-sectional designs have both statistical and conceptual limitations. Few studies used…

Evolving technology has played an important part in a common quadratic-function lesson. Having been mentioned repeatedly in numerous reform documents, a recurring lesson has involved changing the parameters in f(x) = ax[superscript 2] + bx + c and studying the effects on the graph. In both NCTM Yearbooks and NCTM Standards documents, technology is…

Over the past three years, the authors have conducted research in middle and high school classrooms in an effort to improve the effectiveness of robotics to teach science, technology, engineering, and mathematics (STEM) education--their focus has been on math. The authors have found that subtle changes in the design and setup of the lesson make a…

In this article, the authors examine elementary and middle school mathematics teachers' concerns about teaching Latino/a student populations across three regions in the United States: southern Arizona, northern New Mexico, and central California. Surveys were administered to 68 teachers who participated in professional development activities on…

In many of the secondary classrooms across the country, including the research site for this study, students are passively engaged in the mathematics content, and academic performance can be described, at best, as mediocre. This action research study sought to bring about improvements in student engagement and performance in the secondary…

Number Concepts; Measurement; Geometry; Probability; Statistics; and Patterns, Functions and Algebra. Procedural Errors were further categorized into the following content categories: Computation; Measurement; Statistics; and Patterns, Functions, and Algebra. The results of the analysis showed the main sources of error for 6th, 7th, and 8th…

This article examines the teacher preparation program learning opportunities afforded future lower secondary mathematics teachers and future elementary teachers who may teach mathematics. Data from U.S. participation in the recent international Teacher Education and Development Study in Mathematics are explored against international profiles to…

Students who have difficulty reading, understanding, and solving word problems because of cultural and linguistic differences present challenges to teachers who are working to help every student achieve mathematical proficiency. In many middle school classrooms, teachers emphasize traditional textbook word problems, which are meant to engage…

The purpose of this study was to investigate the preservice secondary mathematics teachers' development of pedagogical understanding in the teaching of modular arithmetic problems. Data sources included, written assignments, interview transcripts and filed notes. Using case study and action research approaches cases of three preservice teachers…