The aim of this study is to better understand the notion of early algebraic thinking by describing differences in grade 4-7 students' thinking about basic algebraic concepts. To achieve this goal, one test that involved generalized arithmetic, functional thinking, and modeling tasks, was administered to 684 students from these grades. Quantitative…

Pedagogical content knowledge forms the core of teachers' professional knowledge; it refers to knowledge about making subject matter accessible to students. Thus, the formation of pedagogical content knowledge constitutes a crucial issue for educational research and practice. We investigated the contributions of content knowledge and pedagogical…

The study examined differences in students' conceptual and procedural knowledge of angles among two grades and gender. Participants were 382 sixth and 376 seventh graders from a metropolitan city in Turkey. Turkish students' conceptual and procedural knowledge of angles declined from sixth to seventh grade. Gender differences were found for…

The purpose of this study was to explore the factorial structure of motivation and perception items from a student survey utilised as part of the Reframing Mathematical Futures II (RMFII) Project. Data was collected in 2017 from 442 students in Years 7 to 10 from various different States across Australia. An exploratory factor analysis identified…

The present study aimed to examine lower secondary students? images of mathematics comprised of stated attitudes to and perceived needs for mathematics, and their views about mathematicians and their work. A group of 1284 lower secondary students drew a picture of mathematicians and described their drawings. The students? drawings fell into two…

We describe mathematics classroom teaching practice in an urban Canadian prairie Cree-bilingual school using the term "Cree mathematizing," which, to us, means (re)considering Euro-Western school mathematics from the perspectives of the Cree people engaging with the content. "Cree mathematizing" takes the form of classroom…

This research focuses on the retention of students' algebraic understandings one year following a Grades 3-5 early algebra intervention. Participants included 1455 Grade 6 students who had participated in a cluster randomized trial. Approximately half of these students received an early algebra intervention as part of their regular instruction in…

For many decades, the amount of geometry curriculum worldwide has been cut, mathematics curricula have lacked diversity of geometrical phenomena, and geometry teaching has been reduced to a somewhat eclectic mix of activities. Recently, new trends have begun to counteract these tendencies by framing new curricula around fundamental ideas. The…

Although it is common for researchers to assess implementation fidelity (IF) within the context of math intervention, IF assessments are often restricted to intervention adherence. Further, the degree to which IF influences observed outcomes is commonly ignored. The current study examined the relationship between three aspects of IF and the math…

One of the most intransigent problems in mathematics education is the culturally-influenced divide between classroom practice and educational research. This paper describes our explicit attempt to bridge that divide by translating research on instructional practices linked to improving students' mathematics achievement into a brief guide outlining…

Numeracy has increasingly become a topic of importance and concern in our contemporary society. Student success in numeracy is influenced by the positive attitudes and values they hold about mathematics. This outreach project sought to foster the development of such attitudes and values through the design, implementation, and evaluation of a…

This article describes a project in which students investigate the question: What dihedral angles between pairs of mirrors in a kaleidoscope result in perfectly symmetric images? The unit culminates with students building their own kaleidoscopes. This content aligns with parts of the Common Core's standards for fifth grade (classify…

This report is based on an activity completed by 89 Grade 6 students carrying out a statistical investigation with a focus on posing an initial question given a context and then refining it for a chosen data set. Having reached a conclusion based on evidence from their data analysis, students were given additional information on the context and…

According to the design principle of progressive schematization, learning trajectories towards procedural rules can be organized as independent discoveries when the learning arrangement invites the students first to develop models for mathematical concepts and model-based informal strategies; then to explore the strategies and to discover pattern…

Grade 6 (modal age 11) students invented and revised models of the variability generated as each measured the perimeter of a table in their classroom. To construct models, students represented variability as a linear composite of true measure (signal) and multiple sources of random error. Students revised models by developing sampling…