This article presents several activities suitable for a transition to proofs course. In addition, this article surveys literature in support of active learning in the transition to proofs course and discusses how these activities have been successfully implemented in one such course.

In activities based on proof without words (PWW), we developed, students are given a PWW--a diagram that alludes to the proof of a mathematical theorem. The students work collaboratively to construct a proof alluded by the PWW, and then each student writes and submits a proof attempt. In a 3-year design-based study, we investigate and develop…

Technology integration in K-12 mathematics has received increased attention in the last decade as new mathematical technologies have been developed and implemented more often. There is a need for further research on these technologies and for effective implementation practices of technology in mathematics education in general. in practice,…

Developmental mathematics has been under the radar within higher education for some time. The reality is that there are many proven best practices in developmental math. Unfortunately, there are many obstacles that prevent student success. Moreover, the high rates of attrition and failure have led state legislators and college administrators to…

Chris Brough and Nigel Calder share two scenarios in which students co-constructed their curriculum through generating their own problem solving and mathematical investigations. This article is a valuable exploration of the benefits of teachers working in partnership with their students.

Although many researchers have examined knowledge building in traditional settings and distance learning, few have examined middle school students' building of mathematical knowledge using mobile phones. The present study uses two well-known models of knowledge building to carry out the examination: the interactive analysis model of knowledge…

It is often claimed that working and talking with partners while carrying out maths activities is beneficial to students' learning and the development of their mathematical understanding. However, observational research has shown that primary school children often do not work productively in group-based classroom activities, with the implication…

In this article we analyze the dialogic learning of one pair of students in order to investigate how these students cope with a collaborative learning situation in the classroom. Our aim is to substantiate the claims that not only are young students (8 year olds) capable of solving mathematical problems collaboratively, but that they also take an…