This position paper examines the phenomenon of the McNamara Fallacy to analyse flawed conceptions of "success" in mathematics learning, normalised assessment structures and their implications for mathematics education. The established presence of the McNamara Fallacy and the ramifications of this statistical fallacy provide a foundation…

We examined high school geometry students' written work on four proof tasks where they posed a conjecture, drafted an argument, provided written critiques, then revised their argument based on peer feedback. Students' written work across the tasks was analyzed to determine whether the instructional sequence supported them in improving their…

There is a wide recognition that reasoning abstractly, constructing arguments, or critiquing arguments should be an important educational goal in the mathematical experiences of all students in the standards for school mathematics. Seeing these standards as an essential element for developing deep mathematical understanding; however, call for a…

White and Gorard make important and relevant criticisms of some of the methods commonly used in social science research, but go further by criticising the logical basis for inferential statistical tests. This paper comments briefly on matters we broadly agree on with them and more fully on matters where we disagree. We agree that too little…

In our response to Clements and Sarama (2017), we address the 5 issues that they identify as criticisms of our Research Commentary (Kitchen & Berk, 2016). As in our original commentary, we highlight concerns we have regarding the delivery of [computer-assisted instruction] CAI programs and potential misuses of CAI, particularly at Title I…

The teaching of evolution in American high schools has long been a source of controversy. The past decade has seen an important shift in the rhetoric of anti-evolutionists, toward arguments of a strongly mathematical character. These mathematical arguments, while different in their specifics, follow the same general program and rely on the same…

The development of urban students' mathematical proving ability is a goal of several curricula frameworks, including some located in the southern hemisphere. However, in achieving this goal, most curriculum frameworks do so from a Western worldview, which is characterized by competition and the role of the individual. The purpose of this study was…

In this article, three instructional situations demonstrate the value of using an "unknown" student's work to allow the advancement of students' mathematical thinking as well as their engagement in the mathematical practice of critiquing the reasoning of others: (1) introducing alternative solution strategies; (2) critiquing inaccuracies…

This manuscript focuses on practical questions in a study that describes the perceptions of four teachers at the beginning stages of Common Core Mathematics implementation in a historically underperforming school district. The overarching goal was to understand the collaborative inquiry experience in a lesson study that focused on teaching the…

Analyzing and designing productive group work and effective communication constitute ongoing research interests in mathematics education. In this article we contribute to this research by using and developing a newly introduced analytical approach for examining effective communication within group work in mathematics education. By using data from…

In this article, the author offers a "Pierce-ing," rational dissection of the notion of cultural equivalence that exposes the hypocrisy of its purveyors. He tackles three major argument lines--the Probabilities Argument, the Internal-Division Argument, and the Change Argument--and proves that it is simply very improbable that culture, in any…

In this commentary, some remarks are offered on David Pimm, Mary Beisiegel, and Irene Meglis' article "Would the Real Lakatos Please Stand up." The commentary focuses on relatively recent developments in the philosophy of mathematics based on the work of Lakatos; on theory development in mathematics education; and offers critique on whether…

Although Imre Lakatos described the work published in his book "Proofs and Refutations" as a study of mathematical methodology, work which has been responded to and criticized by philosophers and historians of mathematics more on its own terms, a significant body of writing in the 30 years since its appearance has used it as a pertinent cognate…

In their comment on D. Trafimow, M. D. Lee and E. Wagenmakers argued that the requisite probabilities to use in Bayes's theorem can always be found. In the present reply, the author asserts that M. D. Lee and E. Wagenmakers use a problematic assumption and that finding the requisite probabilities is not straightforward. After describing the…