Who doesn't love a good story? In this article, the authors share how teachers can utilize the idea of mathematical stories to significantly enhance existing lessons. They use a creative framework to reimagine lessons as mathematical stories and make lessons more engaging for students. The authors will first describe how to think about a lesson…

In this article, the authors focus on five instructional approaches with a strong evidence base for the teaching and learning of math: (a) plan, model, and practice: systematic and explicit instruction; (b) focus on the language of math; (c) use multiple representations, including number lines; (d) build fluency; and (e) provide word problem…

This paper reports on a novel corequisite design and implementation for College Algebra at Florida International University. The corequisite course uses online, just-in-time, prerequisite assignments delivered on an open-educational platform. Students get help from near-peer learning assistants inside a math emporium environment. The course…

Based on an enactivist perspective on learning mathematics, we articulate three key processes of designing mathematics-grounding activities (MGAs) where students' mathematical thinking can be motivated and shaped with the interactions between their enactments and the evolving tasks in the activities. Then, evaluation criteria and design steps will…

Good stories, literary or mathematical, have the ability to keep the reader engaged and wanting for more. However, poorly designed stories may also elicit a negative aesthetic reaction and thereby reduce engagement. By drawing on literary theory and Dietiker's ("For the Learning of Mathematics" 33(3):14-19, 2013; "Educational…

In this theoretical paper, I use an empirically based example to illustrate particular design features of the Learning Through Activity (LTA) design framework and examine the impact of particular design principles. The LTA design framework is based on our elaboration of Piaget's construct of reflective abstraction. The example discussed here,…

Mathematical concepts have been a consensus goal for decades, yet there is little consensus on what is meant by the terms "mathematical concept" and "mathematical understanding." This article attempts to discuss these terms in a way that can be of practical use to teachers. Greater clarity on "mathematical concept"…

Mathematics teachers are increasingly being called to integrate mathematical modeling into their course sequences and curriculum (NCTM 2018; NGA Center and CCSSO 2010). Mathematical modeling is a dynamic cycle calling teachers to engage in complex instructional work that advances students' mathematical knowledge and reasoning. The modeling cycle…

Mathematics Anxiety (MA) is an increasing challenge for mathematics educators and is a barrier to mathematical learning. Through reflection on the implementation of a lesson sequence designed to elicit regular use of explicit metacognitive questions (EMQ's), this paper explores the impact of the incorporation of self-regulated learning (SRL)…

A growing body of literature examines the use of rehearsals with preservice mathematics teachers, but research on rehearsals with experienced mathematics teachers is in its infancy. There is some evidence, however, that rehearsal debrief discussions can be valuable learning experiences for practicing teachers. Experienced teachers bring a rich set…

In this article, we describe the generation of a Design and Implementation Framework for Mathematical Modelling Tasks (DIFMT) through a researcher-teacher collaboration. The purpose of the framework is to support holistic approaches to instructional modelling competency. This framework is underpinned by principles drawn from theory and praxis…

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…

Throughout the learning process, English learners should meaningfully engage with both their peers and the mathematics. How do mathematics teachers provide the "just-right" supports for English learners to insure this happens? What scaffolds are best? How do teachers make adjustments to these scaffolds based on the needs of the…

Digital curricula can constrain teachers with ready-made instructional materials. The authors used Mathematics Teaching Practices (MTPs) to modify a digital curriculum to engage students in more thoughtful and meaningful lessons. In this article, the authors visit one of their third-grade classrooms, in which they used the prescriptive digital…

This article discusses Experience First, Formalize Later (EFFL), an approach to teaching and learning that empowers students to build strong conceptual understanding of concepts, redefining how students experience mathematics class, and ultimately leading to more equitable learning opportunities. Traditional lecture-based models for mathematics…