The Queensland Certificate of Education (QCE) system is Queensland's senior school qualification. To support the introduction of the system in 2019, existing senior syllabuses were redeveloped and a new senior assessment model was established, this included the implementation of a mandatory high-stakes assessment task, the Problem-solving and…

Mathematical knowledge for teaching (MKT), defined by Ball ("Elementary Journal," 93, 373-397, 1993) as knowledge that is needed to teach mathematics, has been used as a framework by researchers to interrogate various aspects of teaching and learning mathematics. In this article, which draws from a larger study, we show how an in-depth…

Teaching through Problem Solving (TtPS) is an effective way to teach mathematics "for" understanding. It also provides students with a way to learn mathematics "with" understanding. In this article, the authors present a definition of what it means to teach through problem solving. They also describe a professional development vignette that…

This book's 28 chapters are adapted and updated from articles published in NCTM's "Journal for Research in Mathematics Education" between 2000 and 2010. The authors have rewritten and revised their work to make it clear, understandable, and--most of all--useful for mathematics teachers today. To help teachers even more, these articles…

Reasoning and sense making are at the heart of mathematics teaching and learning throughout the K-12 mathematics curriculum. Focusing on these skills gives students the opportunity to analyze, interpret, and critically think about the mathematics they learn. The terms "reasoning" and "sense making" are frequently used to describe the wide range of…

This paper presents the results of a study designed to facilitate teacher candidates' shift from students of mathematics to teachers of mathematics. We develop a series of tasks each of which encourages candidates to reconsider rich tasks from increasingly teacher-centric points of view. The results show that using authentic high school student…

Illustrates how engagement in worthwhile mathematical tasks can provide rich opportunities for professional development. Presents different solution strategies for the effective tax rate problem. Emphasizes that, to help students recognize differences among the preceding arguments, teachers need to recognize reasoning based on part-whole…

This article describes how the design of digital learning objects can spark professional learning. The challenge was to build learning objects that would help experienced special education teachers, who had been teaching in math classes, to demonstrate their proficiency in middle and secondary school mathematics on the PRAXIS examination. While…

Technology has revolutionized the way mathematics and science are taught and few innovations in mathematics education have had as much impact as the graphing calculator. Fourteen classroom teachers were brought together during the summer of 1997 and during a week-long workshop, the teachers collaborated to develop a resource guide for integrating…