Making connections within and between different aspects of mathematics is recognised as fundamental to learning mathematics with understanding. However, exactly what these connections are and how they serve the goal of learning mathematics is rarely made explicit in curriculum documents with the result that mathematics tends to be presented as a…

As a multifaceted concept, the learning of angle concepts takes years to achieve and is beset with challenges. This paper explores how the processes of constructing and validating a learning progression in geometric reasoning can be used to generate targeted teaching advice to support the learning of angle concept. Data from 1090 Year 4 to Year 10…

Although lesson study has been shown to improve the teaching and learning of mathematics, little research has focused on reasons for engaging in it from a teacher's perspective, particularly after sustained engagement with lesson study. This qualitative study reports on thirty-three teachers from the United States who were involved in twelve…

One hundred four students aged 8 to 16 worked on one Fermi problem involving estimating the number of people that can fit in their school playground. We present a qualitative analysis of the different mathematical models developed by the students. The analysis of the students' written productions is based on the identification of the model of…

Interest has long been regarded as an important motivational construct in the learning of mathematics. It has been contended that the development of interest is directed by two control systems: an emotional and a cognitive. Under the former, students are attracted to activities that are enjoyable, whereas under the latter they consciously engage…

For pre-service teachers (PSTs) who have been exposed to traditional approaches, teacher education courses can be a revelatory experience in their development as educators. This study explores if Canadian upper elementary/lower secondary (grades 4-10) PSTs change their beliefs about mathematics teaching as a result of taking a mathematics methods…

This paper explored variation of strategy use in pattern generalization across different generalization types and across grade level. A test was designed to assess students' strategy use in pattern generalization tasks. The test was given to a sample of 1232 students from grades 4 to 11 from five schools in Lebanon. The findings of this study…

This study synthesized intervention studies focusing on instruction to improve fraction skills. Seventeen studies met the inclusion criteria: being published in English-language peer-reviewed journals or dissertations between 1975 and 2014, and targeting 3rd- through 12th-grade students struggling to learn mathematics. From the "Common Core…

This mixed design study investigated the predictive and instructional uses of two different types of interim mathematics assessments given in two different districts. One district administered the same summative type of assessment three times a year, while the other district administered a different interim assessment after six-week intervals of…

This paper reported results from a generalizability study that examined the process of developing classroom practice indicators used to evaluate the impact of a school district's mathematics reform initiative. The study utilized classroom observational data from 32 second, fourth, eighth, and tenth grade teachers. The study addresses important…

Over a period of about 3 years, 3204 students in Grades 4 to 10 completed 9862 tests to identify and track their interpretation of decimal notation. Analysis of the longitudinal data demonstrates that different misconceptions persist among students to different degrees and in different patterns across the grades. Estimating the prevalence of…