Mathematics Education

The sudden shift to online instruction caused by COVID-19 social distancing requirements prompted educators to solve new problems of technology and pedagogy. This study shares the experiences of undergraduate students in an elementary mathematics content course with learning to share visual images of their work in online classes. The authors modified the PICRAT framework (Kimmons et al., 2020) for choosing and evaluating technology in terms of pedagogical concerns and students’ opportunities for collaborative interaction to analyze the data. Spanning a two-course sequence in 2020-2021, two cohorts of students received small document cameras to broaden forms of participation, shifting from the instructor “scribing” as students verbally described their thinking during Course 1 to sharing images of their own work as they described it during Course 2. Findings focus on choosing transformative technology and will be of interest to mathematics and teacher educators concerned with equitable instruction.

This study evaluated programming and robotics (PR)-integrated geometric learning activities designed to build prospective teachers’ (PSTs’) knowledge and skills necessary for incorporating PR in elementary geometry classrooms. To identify the learning opportunities these activities provided to PSTs, the authors examined arguments PSTs generated to justify the correctness of programs designed for robots to travel along triangular paths, as well as their initial and postsurvey responses and written reflections describing their beliefs about learning and teaching mathematics with PR and demonstrating their learning experience through the PR-integrated activities. Data analysis showed three different domains of learning opportunities offered to PSTs for their knowledge development for teaching PR in mathematics classrooms: (a) developing an understanding of geometric concepts used in program design, (b) improving justifying skills of using geometric reasoning to verify the correctness of robot programs, and (c) building productive views toward learning and teaching mathematics with PR. The researchers also identified the specific knowledge and skills PSTs used to verify program correctness before testing with physical robots. Suggestions are proposed for teacher education to prepare PSTs for PR-integrated mathematics instruction.

In this research study, the authors examined the responses of 63 mathematics teacher educators (MTEs) to see what digital technology tools they used during the COVID-19 pandemic that they continue to use in mathematics or mathematics education classes that support teacher preparation for undergraduate or graduate students. MTEs used mathematical action and conveyance technology, though not exclusively, to increase collaboration, assess their students, organize their course, engage students, record student work, among other purposes and were attracted to these technologies because of their ease of use. These changes have persisted because they positively influenced the teaching, cognitive, and social presence in the MTE’s course or courses.

In this practitioner-focused article, the authors present a mathematical writing activity for preservice elementary school teachers. The products of this activity, referred to as “journals,” are detailed, representation-rich explanations of problems solved in small groups. These journals were originally exchanged across institutions in a traditional peer review process; and the addition of a computer-mediated communication platform transformed the peer reviews into interinstitutional conversations. Analysis of the journals and the conversations they sparked brought to light four opportunities to develop mathematical knowledge for teaching. Evidence in the form of journal and review excerpts suggests that the process, enhanced by the computer-mediated communication, enabled preservice teachers to deepen their understanding of foundational concepts from the elementary school curriculum, to communicate mathematics more effectively to others, to better make sense of the mathematical thinking and writing of others, and to incorporate their colleagues’ suggestions into their future writing. Suggestions and considerations for implementing this activity are discussed.