Barlow et al. (2018) discussed three types of mistakes worthy of inspection: procedural errors, inappropriate solution processes, and misconceptions. Here, the authors focus on procedural errors, as these often led the teachers in their professional development project to limit their inspection of mistakes to correcting. Despite this narrow focus,…

The National Council of Teachers of Mathematics's "Principles to Actions" (NCTM, 2014) cites posing purposeful questions and eliciting and using evidence of student thinking as effective mathematics teaching practices. Interviewing students creates opportunities for teachers to develop these practices. Through interviewing, they can try…

This article describes the two types of reasoning in fraction conceptions that students often use, "gap" and "missing piece," and one that the authors aspire their students to reach, "residual." Each of these types of reasoning are underpinned by a different conception of fractions. Students who use "gap…

For students to develop adequate conceptual understanding about fractions, they require experiences that afford them opportunities to think flexibly about multiple interpretations of fractions. This article presents a sequence of lessons designed to offer such experiences for students in Years 3 and Year 4. The lessons adopt a challenging tasks…

The teaching of measurement concepts typically follows a learning sequence of: (1) identifying the attribute, (2) comparing and ordering, (3) measuring using non-standard units, (4) measuring using standard units, and (5) applications. This sequence is entrenched in many curricular documents and textbooks (Australian Curriculum Assessment and…

Teachers have long struggled with the tension between ensuring a rigorous education for all their students and the reality that students arrive at the start of a school year with vastly different skills and conceptual understandings. The tension can be even more acute in math, which relies heavily on students mastering foundational concepts in…

This article examines action research findings within a fourth-grade mathematics classroom. The researcher explores the effects of positive communication to family members on the engagement of learners receiving Tier 2 behavioral support, as well as potential considerations for building young learners' mathematical identities.

As they do their work, physical therapists apply mathematical ideas. Teachers can use some of those applications to inspire students' discovery of new concepts. In particular, the joints of the human body provide a way to represent angles that is accessible to all students and can be understood in the elementary grades. Used with fourth graders,…

Area models are an important strategy for representing and solving multiplication problems under the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010). The hands-on task presented in this article, featuring differentiation and open-ended learning, sets up students to discover area models for themselves. Organized around…

Usable Math available at https://usablemath.org/ is being designed as an open online tutor for elementary school math students and teachers in the USA. It provides interactive problem solving for 3rd through 6th grade students who are learning mathematical reasoning and computation skills through word problems. Using the system, students and…

Reinhart's (2000) article "Never Say Anything a Kid Can Say!" shared the lessons he learned as he journeyed from a teacher-centered model of instruction to one that puts students at the center of the teaching and learning process. Within his narrative, he itemized the strategies he used and learned from, balanced recommendations with…

Explore the impact technology has on mathematical identity and agency when students use mathematical action technology to engage in cycles of proof and support case-based reasoning. This article showcases a mathematics task used in a fourth-grade class that allowed students to develop their conceptual understanding of division. The authors…

We offer this synthesized framework as a tool to reveal mathematical activity in a non-formal makerspace. In particular, we connect research at different grain sizes to illustrate and explain how mathematics plays a crucial, if often implicit, role in this activity. We begin with describing the Approximate Number System and the Ratio-Processing…

The authors describe a 'Geometry chat' as an instructional strategy analogous to 'Number talks' in which students decompose and recompose shapes rather than break numbers apart and then put them back together.

To support continuous professional development model in the teaching and learning of mathematics, many districts and schools have begun hiring elementary mathematics coaches and/or specialists (MCSs). However, limited large-scale empirical research exists that determines how the use of MCSs affect student learning and achievement. Kristin E.…