Students need opportunities to construct definitions in mathematics. We describe a sorting activity that can help students construct and refine definitions through discussion and argumentation. We include examples from our own work of planning and implementing this sorting activity to support constructing a definition of linear function.
Erin E. Baldinger, Matthew P. Campbell, and Foster Graif
Rebecca Vinsonhaler and Alison G. Lynch
This article focuses on students use and understanding of counterexamples and is part of a research project on the role of examples in proving. We share student interviews and offer suggestions for how teachers can support student reasoning and thinking and promote productive struggle by incorporating counterexamples into the classroom.
Krista L. Strand and Katie Bailey
K-5 teachers deepen their understanding of the Common Core content standards by engaging in collaborative drawing activities during professional development workshops.
Over the past 100 years, technology has evolved in unprecedented fashion. Calculators, computers, and smart phones have become ubiquitous, yet school mathematics experiences for many children still remain without many powerful technological tools for the exploration of mathematics. We consider the evolution of some tools as we imagine a future.
M. Kathleen Heid
Technological tools for mathematics instruction have evolved over the past fifty years. Some of these tools have opened the door to explorations of new mathematics. Features of others have made access to curricular mathematics more convenient. Thoughts on this evolution are shared.
The paper discusses technology that can help students master four triangle centers -- circumcenter, incenter, orthocenter, and centroid. The technologies are a collection of web-based apps and dynamic geometry software. Through use of these technologies, multiple examples can be considered, which can lead students to generalizations about triangle centers.
When we consider the school experience from the student perspective, we are open to change our practices to embody the very principles in which we believe.
Alyson E. Lischka, Kyle M. Prince, and Samuel D. Reed
Encouraging students to persevere in problem solving can be accomplished using extended tasks where students solve a problem over an extended time. This article presents a structure for use of extended tasks and examples of student thinking that can emerge through such tasks. Considerations for implementation are provided.
A personal reflection by Ed Dickey on the influence and legacy of NCTM's journals.
NCTM has provided rich resources through the publication of practitioner journals for decades and is now leading the way once again with a digital first dynamic publication focused on the learning and teaching of mathematics. This is a rich opportunity for teachers to engage, to learn and to go.