Bridging powerful knowledge and lived experience: Challenges in teaching mathematics through COVID-19

The coronavirus disease 2019 (COVID-19) pandemic supported an investigation of ongoing challenges as to whether and how to make mathematics relevant to learners’ lifeworlds. Given that COVID-19 created major disruptions in all learners’ lives, we developed and taught tasks that attempted to make links between their experiences of the pandemic and disciplinary mathematical knowledge. We located our investigation in current debates about the extent to which disciplinary knowledge can be linked to learners’ out-of-school experiences. We developed and analysed two tasks about COVID-19 that could support link-making and productive disciplinary engagement, and analysed one Grade 10 teacher teaching these tasks. We found that linking mathematics to learners’ lifeworlds is both possible and extremely difficult in relation to task design and how the teacher mediates the tasks. In relation to task design, we argue that teachers cannot do it alone; they need to be supported by the curriculum and textbooks. In relation to mediation, we saw that teacher practices are difficult to shift, even in the best of circumstances. We articulate the complexities and nuances involved in bridging powerful knowledge and lived experience and thus contribute to debates on how to teach powerful knowledge in relation to learners’ lifeworlds.

gPortfolios: a pragmatic approach to online asynchronous assignments

Purpose The purpose of this paper is sharing out basic guidelines and examples from an extended collaboration to move educators move online while avoiding synchronous meetings. “gPortfolios” are public (to the class) pages where students write responses to carefully constructed engagement routines. Students then discuss their work with instructors and peers in threaded comments. gPortfolios usually include engagement reflections, formative self-assessments and automated quizzes. These assessments support and document learning while avoiding instructor “burnout” from grading. gPortfolios can be implemented using Google Docs and Forms or any learning management system. Design/methodology/approach The authors report practical insights gained from design-based implementation research. This research explored the late Randi Engle’s principles for productive disciplinary engagement and expansive framing. Engle used current theories of learning to foster student discussions that were both authentic to the academic discipline at hand and productive for learning. This research also used new approaches to assessment to support Engle’s principles. This resulted in a comprehensive approach to online instruction and assessment that is effective and efficient for both students and teachers. Findings The approach “frames” (i.e. contextualizes) online engagement using each learners’ own experiences, perspectives and goals. Writing this revealed how this was different in different courses. Secondary biology students framed each assignment independently. Secondary English and history students framed assignments as elements of a personalized capstone presentation; the history students further used a self-selected “historical theme.” Graduate students framed each assignment in an educational assessment course using a real or imagined curricular aim and context. Originality/value Engle’s ideas have yet to be widely taken up in online education.