Background/purpose: The Computational Thinking ability has become a fundamental skill in the 21st century and has been integrated into educational curricula in various countries. For this curricular integration to be effective, it is essential that teachers are prepared to incorporate the development of this competency into their practices. In…

The fields of quantitative and covariational reasoning boast a wide range of powerful theoretical tools, which are described carefully in the literature. Less frequent and explicit attention, however, has been paid to writing down detailed, practical guidance for operationalizing these theoretical constructs. Some guidance is provided by…

Mathematics is not seen as an absolute corpus of well-founded knowledge anymore, but as a human activity, a social phenomenon, part of human culture that evolves historically and intelligibly in a social context. By harnessing the indigenous cultures and their knowledge systems in-depth, this article aims to evaluate how the sustainable…

This book provides prospective and practicing teachers with research insights into the mathematical difficulties of students with learning disabilities and classroom practices that address these difficulties. This linkage between research and practice celebrates teachers as learners of their own students' mathematical thinking, thus contributing…

The Better Math Teaching Network (BMTN) is a networked improvement community (NIC) of researchers and high school teachers from New England who use improvement science principles to deepen student engagement in algebra content. The BMTN began as a pilot during the 2015-16 school year and concluded in fall 2021. Key learnings from the network…

Descriptions of mathematical thinking have an extended lineage. Sometimes accurate and sometimes not, sometimes misinterpreted and sometimes not, characterizations of mathematical thought processes have inspired and at times misled people interested in designing or framing mathematics instruction. Challenges the field faces in conceptualizing…

This paper reports the results of an international comparative study conducted in Switzerland and Japan of an elementary school mathematics lesson. The principal aim of the study was to advance understanding of the cultural specificities of a mathematics lesson in its totality using concrete examples of lesson design and implementation and of how…

Research into the effectiveness of SPRING into Maths as a Tier 2 intervention is limited. This article aims to extend the evidence base for SPRING into Maths through reflective practice that links practitioner voice with theory. The article applies a theoretical lens to SPRING into Maths and provides insights into the journey of a group of…

This case study investigated the development of group cognition by tracing the change in mathematical discourse of a team of three middle-school students as they worked on a construction problem within a virtual collaborative dynamic geometry environment. Sfard's commognitive framework was employed to examine how the student team's word choice,…

Although mathematical practice has traditionally valued two distinct kinds of mathematical work--referred to by Gowers (2000) as theory building and problem solving--activity in classrooms appears to be organized largely around the latter, rather than the former. This study takes up the question of whether there is a customary role for theory…

This article and my career as an educational researcher are grounded in two fundamental assumptions: (a) that research and practice can and should live in productive synergy, with each enhancing the other, and (b) that research focused on teaching and learning in a particular discipline can, if carefully framed, yield insights that have…

This article outlines a problem-centered approach to the topic of canonical matrix forms in a second linear algebra course. In this approach, abstract theory, including such topics as eigenvalues, generalized eigenspaces, invariant subspaces, independent subspaces, nilpotency, and cyclic spaces, is developed in response to the patterns discovered…

The National Council of Teachers of Mathematics (NCTM) has called for changes in mathematics teaching from a procedural to conceptual focus since 1980, yet the way mathematics is taught in many classrooms continues to contradict the recommended practices. The pervasiveness of this challenge has led some educators to suggest changes in university…

"Success stories," i.e., cases in which mathematical problems posed in a controlled setting are perceived by the problem posers or other individuals as interesting, cognitively demanding, or surprising, are essential for understanding the nature of problem posing. This paper analyzes two success stories that occurred with individuals of different…

Comparing multiple solutions to a single problem is an important mode for developing flexible mathematical thinking, yet instructionally leading this activity is challenging (Stein, Engle, Smith, & Hughes, 2008). We test 1 decision teachers must make after having students solve a problem: whether to only verbally discuss students' solutions or…