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…

Although increasing emphasis is being placed on mathematical justification in elementary school classrooms, many teachers find it challenging to engage their students in such activities. In part, this may be because the teachers themselves have not had an opportunity to learn what it means to justify solutions or prove elementary school concepts…

Children build foundations for mathematical thinking in early play and exploration. During the preschool years, children enjoy exploring mathematical concepts--such as patterns, shape, spatial relationships, and measurement--leading them to spontaneously engage in mathematical thinking during play. Block play is one common example that engages…

Today's classrooms pose many challenges for new mathematics teachers joining the teaching force. As they enter the teaching field, they bring a wide range of mathematical experiences that are often focused on calculations and memorization of concepts rather than problem solving and representation of ideas. Such experiences generally minimize what…

The purpose of this study was to explore the predictive relationship between the level of symbolic representation in block constructions of preschoolers and reading and mathematics abilities and rate of growth in early elementary school for children with and without disabilities. Fifty-one children participated, 22 of whom had identified…

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…

Superitem test based on the SOLO model (Structure of the Observing Learning Outcome) has become a powerful alternative assessment tool for monitoring the growth of students' cognitive ability in solving mathematics problems. This article focused on developing a superitem test to assess students' algebraic solving ability through interview method.…

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…

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…

Education in an online setting is an increasingly popular method of instruction. Previous studies comparing college or high school student performance in online and face-to-face courses found, in most cases, similar achievement between conditions. However, research is lacking regarding middle school students' academic performance and attitudes…

This is a qualitative study of two English-dominant mathematics teachers, who I refer to as "monolingual" because they speak only English and do not speak competently or extensively the cultural language of their students. This study explores how these teachers plan, implement, and reflect upon lessons with respect to their bilingual,…

"Shake, Rattle, & Roll" is a new program developed by The Actuarial Foundation with Scholastic, provides dynamic real-world math content designed to build student skills while showing students the relevance of math to understanding their world and planning for their future. Math skills are increasingly important for students. According to the U.S.…

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…

In 1999, Richard Lee Colvin published an article in "The School Administrator" titled "Math Wars: Tradition vs. Real-World Applications" that described the pendulum swing of mathematics education reform. On one side are those who advocate for computational fluency, with a step-by-step emphasis on numbers and skills and the…

Formal mathematical methods remain, for most high school students, mysterious, artificial and not a part of their regular intuitive thinking. The authors develop some themes that could lead to a radically new approach. According to this thesis, the teaching of programming languages as a regular part of academic progress can contribute effectively…