Prospective teachers’ design of numeracy tasks using a physical distancing context

Abstract

Physical distancing, which is widely practiced limiting the spread of COVID-19, is recognized to contain mathematical thoughts that can be harnessed as a context for prospective teachers’ practices of mathematical problem posing. The goal of this study is to investigate the profile of mathematical tasks posed by prospective mathematics teachers using the context of physical distancing that meets the criteria of numeracy tasks. Data were collected from 66 mathematical tasks posed by thirty-three prospective teachers at a public university in Surabaya, Indonesia, attending an assessment course of numeracy based on a problem-posing task. To analyze, the posed tasks were first identified as solvable or unsolvable tasks and then further categorized into the domains of the level of context use and the level of cognitive processes. Results show that the level of context use embedded in the posed tasks varies from zero to first order, with only a few of the posed tasks being coded as having second-order context. Regarding the levels of cognitive processes, most of the posed tasks reach the level of understanding, with only a small number of reasoning tasks identified. Interestingly, all the tasks coded to contain second-order context are classified as reasoning tasks. Some implications regarding designing numeracy tasks using physical distancing and interventions in teacher education related to numeracy task design are discussed.

Aligning numeracy task design with SDG goals: Nutrition facts as a context for prospective mathematics teachers' problem posing

“…Therefore, the findings of this study serve as an important warning for teacher education programs to focus on improving the skills of prospective teachers in formulating numeracy tasks that meet the criteria of effective numeracy tasks. Since problem-posing is recognized as a multifaceted and complex task, addressing issues related to this phenomenon requires interventions that enhance prospective teachers' ability to use authentic contexts for mathematization, reduce reliance on excessive task information, unfamiliar terminology, vague contextual units, and inappropriate use of mathematical symbols (Crespo & Harper, 2020;Kohar et al, 2022). Additionally, engaging prospective teachers in collaborative problem-posing activities can be beneficial.…”

Preservice Teachers in Real-world Problem-Posing: Can They Turn a Context into Mathematical Modelling Problems?

“…Each created problem was first evaluated before being classified into those two domains. Unsolvable problems (tasks) include confusing language, unexplained crucial premises, insufficient contextual, numerical, figural, tabular, or pictorial information concerning the provided context (online taxi driver salary) that causes it impossible to solve was also considered to be unsolvable (Kohar et al, 2022).…”

“…For preservice teachers, posing modelling problem is not only intended to improve their modelling competences, which in this regard, Blum and Niss (1991) argued that problem-posing may be helpful for modelling since it can be viewed as a problemsolving activity, but also to improve their skills in designing problem for being implemented within their future teaching practices. While problem posing based on real-world events might be a promising strategy for encouraging students' modelling competence due to its strong connection to problem-solving (Hartmann et Research found that preservice teachers frequently struggle with posing mathematical tasks such as being limited to pose simple, one-step tasks, exercises, tasks with lower-level cognitive demands (procedures without connections), tasks with a narrow domain, even non-mathematical or unsolvable tasks, which included bare or insufficient information (Fitriana et al, 2022;Kohar et al, 2022). In addition, when confronted with real-world situations, preservice teachers often find difficulties in turning a context into modelling problems (Paolucci, 2017;Ortiz & Ferri, 2022).…”