Elementary

Learning goals differ from performance goals. We elaborate on their function and importance as the guiding force behind maintaining cognitive rigor during mathematics learning.

Hunt, J. & Stein, M. K. (2020). Constructing goals for student learning through conversation. Mathematics Teacher: Learning and Teaching PK-12, 113(11), 904-909.

One of the most relentless areas of difficulty in mathematics for children with learning disabilities (LDs) and difficulties is fractions. We report the development and initial testing of an intervention designed to increase access to and advancement in conceptual understanding. Our asset-based theory of change—a tested and confirmed learning trajectory of fraction concepts of students with LDs grounded in student-centered instruction—served as the basis for our multistage scientific design process.

Designed to be integrated with any curriculum, each grade level includes 18-20 one-hour lessons to be conducted throughout the school year. Each LEAP lesson lasts about an hour is designed to fit within a typical daily math instructional period.

LEAP early algebra curriculum for Grades K-5. Grades 3 and 4 currently available, with the remaining books for Grades K-2, 5 in press.

Blanton, M., Gardiner, A., Stephens, A., & Knuth, E. (2020). LEAP: Learning through an early algebra progression. Didax: Rowley, MA.

This article explores how scholars have framed studies of preservice science teacher (PST) knowledge and learning over the past twelve years. We examined relevant studies between 2008

Background

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.