Recently, Lima lamented on the 'time-consuming and tiresome' pedagogical nature of repeated integration by parts, throwing down the challenge of providing a pencil-and-paper solution to a related problem in a few seconds. Lima put forth a simple formula as an alternative. In this work, I offer a response to Lima's challenge and his formula.…

This commentary provides an overview of abduction, also known as Inference to the Best Explanation, and argues that the term and relevant problem-solving methods should be adopted by chemistry educators. Abductive reasoning, especially within the context of science and medicine, continues to be an active area of exploration for philosophers and…

While some of Paulo Freire's readers understand his pedagogy as a rejection of any and all directive teaching methods, there are many scholars who do recognise Freire's emphasis on teacher directiveness in its appropriate form. In light of this tension between directiveness and dialogue, it seems that students of Freire must inevitably come to a…

Affect and mathematical competence are each multifaceted constructs. Accordingly, the studies in this Special Issue address multiple pathways between the two in young children. This commentary highlights the variability of these pathways and asks how affective variables are specifically related to core mathematical activities such as problem…

Sternberg (2017) summarizes the history of identification of giftedness in the 20th century and presents a case for the shortcomings of measures such as IQ for problem-solving skills required in the 21st century. The Active Concerned Citizenship and Ethical Leadership (ACCEL) model is proposed to replace the outdated construct of IQ, particularly…

The editors of Mathematics Teacher appreciate the interest of readers and value the views of those who write in with comments. The editors ask that name and affiliation including email address be provided at the end of their letters. This September 2016 Reader Reflections, provides reader comments on the following articles: (1) "Innocent…

In this webinar, Dr. William Schmidt of Michigan State University discussed helpful instructional tools for promoting the higher order conceptual thinking found in the Common Core Standards. The PowerPoint presentation and webinar recording are also available.

In a cultural environment that maintains that post-secondary education ought to produce job ready graduates, the importance of the liberal arts and the competencies they teach, along with the questions they engage, often comes up for debate. In such a culture, honors may appear frivolous, elitist, and rear-guard. Angela Marie Salas defends both…

Within composition studies, transfer and rhetorical genre studies have found an especially productive partnership for exploring together whether and in what ways students transfer writing-related knowledge from one context to another. This article continues this synthesis by turning to Anne Freadman's notion of uptake to suggest a more robust…

In this paper, I comment on the set of papers in this special issue on mathematical problem posing. I offer some observations about the papers in relation to several key issues, and I suggest some productive directions for continued research inquiry on mathematical problem posing.

The push for STEM has raised the visibility of engineering as a discipline that all students should learn. With the release of the "Framework for K-12 Science Education" and the Next Generation Science Standards (NGSS), engineering now has an official place in the science curriculum. In both the "Framework" and the NGSS,…

Improving student learning is the primary goal of every teacher of algebra. Teachers seek strategies to help all students learn important algebra content and develop mathematical practices. The new Institute of Education Sciences[IES] practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students"…

Mike Rose, author of "The Mind at Work," extols both the wholesome, pragmatic qualities of handcraft and the implicit intellectual skills required of its practitioners. His recent article, "Rethinking Remedial Education and the Academic-Vocational Divide," is titled with a call to action; in these few words alone, Rose problematizes the polar…

The development of academic literacy requires students to think critically about multiple text types. Picturebooks can be rich and varied resources on which to base well-designed instruction that will facilitate thinking, discussions, connections, and problem solving in multiple content areas. From the Holocaust to ecology to grammar, picturebooks…

Recent "reform" curricula both ignore the absence of supporting data and completely misunderstand the role of problem solving in cognition. If, the argument goes, teachers are not really teaching people mathematics but rather are teaching them some form of general problem solving, then mathematical content can be reduced in importance. According…