A number of studies have demonstrated strong links between students' language features (as found in spoken and written production) and their math performance. However, no studies have examined links between the students' language features and measures of their Math Identity. This project extends prior studies that use natural language processing…

Even though many of Alaska's students are getting a good education, historically Alaska has some of the largest achievement gaps in the country. Compared to other states in America, Alaska ranks at or near the bottom in reading and math scores. This document is a call to action. Thousands of Alaskans have stepped up to answer this call and have…

This paper reports an innovative approach to teaching problem solving in secondary school mathematics classrooms based on a specifically designed problem-solving module.This approach adopts the science practical paradigm and rides on the works of Polya and Schoenfeld in order to give greater emphasis to the problem solving processes. We report the…

Researchers have consistently demonstrated that multiple examples are better than one example in facilitating learning because the comparison evoked by multiple examples supports learning and transfer. However, research outcomes are unclear regarding the effects of example variability and prior knowledge on learning from comparing multiple…

The present study investigated the differences of strategy use between low-, average-, and high-achieving students when solving different multiplication problems. Nineteen high-, 48 average-, and 17 low-achieving students participated in this study. All participants were asked to complete three different multiplication tests and to explain how…

The recommendation to study statistical variation has become prevalent in recent curriculum documents. At the same time, research on teachers' knowledge of variation is in its beginning stages. This study investigated prospective teachers' knowledge in regard to a specific measure of statistical variation that is new to many curriculum documents:…

Introduction: This study has aimed to investigate the relationship between the development of working memory and performance on arithmetic activities. Method: We conducted a 3-year longitudinal study of a sample of 90 children, that was followed during the first, second and third year of primary school. All children were tested on measures of WM…

For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the…

At the start of the Kindergarten year in New South Wales (NSW) government schools, teachers gather information on several aspects of children's number knowledge to guide their teaching programs. This includes knowledge of the sequence of words used for counting, numeral identification, and using counting to solve problems. This study investigated…

This theoretical paper outlines the process of defining "mathematical giftedness" for a present study on how primary school teaching shapes the mindsets of children who are mathematically gifted. Mathematical giftedness is not a badge of honour or some special value attributed to a child who has achieved something exceptional.…

We report on an empirical study grounded in our sustained implementation over ten years of a sequence of three-term undergraduate core mathematics courses centred on microworlds. The survey study investigates students' views on 15 competencies potentially developed as they, individually or in pairs, create 12 Exploratory Objects, i.e.,…

Despite their apparent simplicity, the concepts of square numbers and square roots are problematic for high school students. I inquired into students' understanding of these concepts, focusing on obstacles that students face while attempting to solve square number problems. The study followed a modified analytic induction methodology that included…

In order to achieve the present study's goal--to understand better the phenomenon of mathematical giftedness--we performed a multidimensional examination of the mental processing in students who exhibited mathematical expertise (EM) at the secondary school level. The study included participants from the three groups: students who excelled in…

The study investigates the mathematical and the pedagogical content knowledge among in-service and pre-service first- and second-grade mathematics teachers. The sample of 300 subjects consisted of 150 first- and second-grade in-service teachers and 150 pre-service teachers studying in a college of education, 75 of whom were first-year students and…

The purpose of this article is to explore the usefulness of a video-based tool for measuring teachers' mathematical knowledge for teaching. Unique to this tool is the use of a video featuring a mathematical disagreement that occurred in an elementary classroom. The authors define mathematical disagreements as instances in which students challenge…