Elementary

Measurement is a critical component of mathematics education, but research on the learning and teaching of measurement is limited. We previously introduced, refined, and validated a developmental progression – the cognitive core of a learning trajectory – for length measurement in the early years. A complete learning trajectory includes instructional activities and pedagogical strategies, correlated with each level of the developmental progression. This study evaluated a portion of our learning trajectory, focusing on the instructional component.

This article elaborates a theoretical, methodological, and analytical approach intended to highlight the materiality and reciprocity of noticing in mathematics classrooms. Drawing from highly resonant concepts from materialism and Indigenous Knowledges—two perspectives that researchers rarely bring into dialogue—this alternative approach explores the reciprocal, material, and more-than-human nature of noticing. By focusing on the role of movement in noticing, the approach discusses the indivisibility of sensing and making sense as students and teachers mobilize mathematical concepts.

In this article, we report on the development of a novel, video-based measure of teachers’ moment-to-moment noticing as knowledge-filtered perception. We developed items to capture teachers’ perception of similarity of their own teaching to the teaching shown in three short video clips of authentic classroom instruction. We describe the item design and relate teachers’ moment-to-moment noticing to their reflective noticing as measured by judgements of similarity teachers provided after viewing each video.

Background
Elementary educators are increasingly asked to teach engineering design, motivating study of how they learn to teach this discipline. In particular, there is a need to examine how teachers reason about pedagogical situations and dilemmas in engineering—how they draw on their disciplinary understandings, attention to students' thinking, and pedagogical practices to support students' learning.

Background
Students may exhibit growth mindsets, where intelligence is seen as malleable and failures prompt more effort and new approaches, or fixed mindsets, where intelligence is seen as immutable and failures indicate lack of intelligence. One's mindset in general may be different from that for a particular domain such as engineering. Having a growth mindset predicts more positive learning outcomes.

This research focuses on ways in which balance scales mediate students’ relational understandings of the equal sign. Participants included 21 Kindergarten–Grade 2 students who took part in an early algebra classroom intervention focused in part on developing a relational understanding of the equal sign through the use of balance scales. Students participated in pre-, mid- and post-intervention interviews in which they were asked to evaluate true-false equations and solve open number sentences. Students often worked with balance scales while solving these tasks.

Well-designed mathematics instruction focused on concepts and problem-solving skills associated with measurement and data analysis can build a foundational understanding for more advanced mathematics. This study investigated the efficacy of the Precision Mathematics Level 1 (PM-L1) intervention, a Tier 2 print- and technology-based mathematics intervention designed to increase first-grade students’ conceptual understanding and problem-solving skills around the areas of measurement and data analysis.

Mathematics interventions aimed at accelerating the learning of students with mathematics difficulties (MD) should be developed through a design science approach such as the Curriculum Research Framework (CRF). Precision Mathematics is a National Science Foundation-funded DRK–12 Design and Development project focused on building mathematical proficiency with the critical concepts and problem-solving skills of early measurement and data analysis among first- and second-grade students with MD.

Being nice is difficult to critique. Niceness is almost always portrayed and felt as a positive quality. In schools, nice teachers are popular among students, parents, and administrators. And yet Niceness, as a distinct set of practices and discourses, is not actually good for individuals, institutions, or communities because of the way it maintains and reinforces educational inequity.