Tennessee educational leaders initially implemented Response to Instruction and Intervention for the same reason other states across the nation adopted the framework; to identify students with specific learning disability. In 2014, Tennessee restructured the Response to Instruction and Intervention model to move from the traditional three-tiered…

This study examined the practices of a mathematics coach by analyzing coaching moves over multiple coaching cycles with two teachers. The coach, guided initially by a content-focused model of coaching (West & Staub, 2013), engaged teachers in cycles that consisted of co-planning, teaching, and debriefing conversations to help teachers reflect…

This document draws together work from several initiatives to establish Minimum Proficiency Levels (MPLs) for reading and mathematics, for global use in pursuit of the Sustainable Development Goal in Education, SDG 4.1, with a specific focus on indicator 4.1.1. Three educational levels are referred to in this paper as 'end of lower primary', 'end…

Number system knowledge (NSK) is broadly defined as the understanding of number relationships and is an essential mathematics skill for young elementary school-aged students. NSK instruction that emphasizes connections between number sense and spatial reasoning could be a critical anchor for second-grade students to stay rooted in their conceptual…

As major sources of information, curriculum materials (CMs) have generally served teachers and students by providing instructional and learning support. The impact of CMs on teachers' pedagogical practice and learners' engagement and success had been fairly documented. However, just as the use of CMs is influenced by teachers' orientations and…

Practices within research mathematics can and do serve as models for mathematics education. However, typically such inspirations impose a devastating narrowness in relation to reflections on mathematics. This narrowness I refer to as the "banality of mathematical expertise". Reflections on mathematics can be expressed through a…

It is commonplace in the educational literature on mathematical practice to argue for a general conclusion from isolated quotations from famous mathematicians. In this paper, we supply a critique of this mode of inference. We review empirical results that show the diversity and instability of mathematicians' opinions on mathematical practice.…

Spurred by Kilpatrick's (1987) "Where do good problems come from?", this study explores problem-posing triggers of experienced problem posers for mathematics competitions. Triggers are conceived as instances of noticing, where an impulse draws a poser's attention and "triggers off" a mathematical re-action, one of the outcomes…

Long have we known that reasoning abilities are linked to learning, and specifically to learning mathematics. Even intelligence, considered a controversial construct, plays a significant role in the research on the explanation of academic performance. This article intends to highlight some important cognitive abilities or dimensions relevant to…

There is a growing knowledge base in mathematics education highlighting the importance of teachers' cognizance about what and how they are noticing, namely considerations about their attending, interpreting, and decisions to respond on the basis of students' thinking. However, less focus has centered on those in teacher leader positions and how…

When a number sentence includes more than one operation, students are taught to follow the rules for the order of operations to get the correct result. In this context, brackets are used to determine the operations that should be calculated first. However, it seems that the written format of an arithmetical expression has an impact on the way…

In the first main section of this thesis, I investigate superirreducible polynomials over fields of positive characteristic and also over [set of rational numbers] and [set of integers]. An n-superirreducible polynomial f(x) is an irreducible polynomial that remains irreducible under substitutions f(g(x)) for g of degree at most n. I find…

The purpose of this study was to determine faculty members' self-reported use and implementation of good practices in their developmental mathematics classrooms. Participants in this study were full-time or part-time (adjunct) mathematics instructors that taught developmental mathematics courses at two-year colleges. Participants completed a…

Analyses were conducted with second graders, drawn from an ongoing multi-cohort randomized controlled trial (RCT), who had been identified for RCT entry based on comorbid reading comprehension and word-problem solving difficulty. To estimate pandemic learning loss, we contrasted fall performance for 3 cohorts: fall of 2019 (pre-pandemic; n = 47),…

This study investigated the effect of the use of content-specific material-based activities on children's mathematical skills, and changes in emotions for both sides with the help of math workstations to serve as responsive partners in delivering quality mathematics education to children and teachers. A total of 20 female kindergarten teachers and…