In many prekindergarten classes, children begin the day by singing a song as part of their opening routine. In reflecting on opening routines in public prekindergarten classrooms across Michigan, the authors have been struck by how often small changes in teachers' routines or materials could enrich the mathematical engagement of children. The goal…

The analysis of a historical mathematical textbook constitutes a particular challenge when the original had been composed before the invention of the printing press and an even greater one when the very original might even not have been fixed as a manuscript. The analysis of such cases affords a focus on the relation between orality and written…

The paper focuses on four upper secondary students' collaborative small-group mathematical reasoning (MR) with respect to a sinusoidal function. The students were collaboratively engaged in a process of MR regarding the relationships between mathematical theoretical descriptions of parameters in the algebraic expression of the sinusoidal function…

In this article, we explore the reading and writing of mathematical poetry from our experiences as mathematics teacher educators. First, we outline how our own engagement with mathematical poetry encouraged us to incorporate it into our teaching of pre-service teachers. We describe how our initial disappointment with the mathematical content of…

Metacognitive competencies are of great importance for developing modelling competencies. However, there are assumptions about useful metacognitive knowledge and strategies for individuals working on modelling problems as well as for whole groups, but their coherence as well as their influence on modelling processes is not evaluated…

The purpose of this mixed-methods case study is to analyze the engagement levels of low-achieving high school seniors enrolled in a basic algebra course called Pre-College Algebra. The term low-achieving pertains to the class member participants enrolled in a course that is perceived and even described as the less rigorous of the choices of all…

Networked improvement communities provide a promising approach for improving education's most pressing problems. By uniting diverse practitioner experiences with expert subject knowledge and an improvement science evaluative framework, networks of multiple schools can collectively solve persistent educational challenges. However, networks have…

The main purpose of this chapter is to document the reasoning of three students, two with disabilities and one with mathematical difficulties, as they participated in and contributed to the classroom mathematical practices established by a seventh-grade class during integer instruction. The integer instructional sequence was designed to support…

Ginsburg (1977) observed that children typically develop surprisingly powerful informal (everyday) knowledge of mathematics and that mathematical learning difficulties often arise when formal instruction does not build on this existing knowledge. By using meaningful analogies teachers can help connect new formal instruction to students' existing…

The purposes of this study were to (a) explore whether early fractions understanding at 4th grade is differentially challenging for students with versus without adequate whole-number competence and (b) identify specific whole-number skill associated with difficulty in fractions understanding. Based on initial whole-number competence, 1,108 4th…

In preparing to study teacher-student interactions in mathematics classrooms in Iran, this paper as a literature review considers relevant mathematics education literature. I explore which aspects of classroom environments orient researchers to judge patterns of classroom interactions as productive. I examine patterns of classroom interactions…

Two content topics will be described. One deals with geometric measurement: length, area, and volume. These are important topics and they have not been learned very well. In particular, what types of relations can one consider when dealing with these three aspects of geometric measurement? The second topic is fractions, and different views of what…

The incorporation of subject-specific technologies in teaching and learning mathematics has been extensively investigated in different areas outside Uganda. The benefits are extensive, although the adoption of these technologies has been threatened by teachers needing help to apply them effectively for instruction. While this alone would aptly…

Although teachers are expected to teach mathematics ambitiously, it is challenging for them to do so. Given that the first year represents a critical juncture between teacher preparation and inservice teaching, it may be particularly challenging to teach ambitiously. Understanding the nuanced characteristics in lessons taught by first-year…

This study examined the impact of Classworks® Individualized Learning math instruction on second-grade students performing below the 25th percentile in math. The research, conducted during the 2021-2022 school year, involved 1,367 students from 45 schools across seven districts. A quasi-experimental design compared 941 students who had any use of…