Generalization strategies in finding the nth term rule for simple quadratic sequences

In this study, we identify ways in which a sample of 18 graduates with mathematics-related first degrees found the nth term for quadratic sequences from the first values of a sequence of data, presented on a computer screen in various formats: tabular, scattered data pairs and sequential. Participants’ approaches to identifying the nth term were recorded with eye-tracking technology. Our aims are to identify their strategies and to explore whether and how format influences these strategies. Qualitative analysis of eye-tracking data offers several strategies: Sequence of Differences, Building a Relationship, Known Formula, Linear Recursive and Initial Conjecture. Sequence of Differences was the most common strategy, but Building a Relationship was more likely to lead to the right formula. Building from Square and Factor Search were the most successful methods of Building a Relationship. Findings about the influence of format on the range of strategies were inconclusive but analysis indicated sporadic evidence of possible influences

Mathematics teaching: professional knowledge and cognitive load theory

Mathematics teaching: professional knowledge and cognitive load theor

Mathematics

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Ecosystem type drives tea litter decomposition and associated prokaryotic microbiome communities in freshwater and coastal wetlands at a continental scale

Wetland ecosystems are critical to the regulation of the global carbon cycle, and there is a high demand for data to improve carbon sequestration and emission models and predictions. Decomposition of plant litter is an important component of ecosystem carbon cycling, yet a lack of knowledge on decay rates in wetlands is an impediment to predicting carbon preservation. Here, we aim to fill this knowledge gap by quantifying the decomposition of standardised green and rooibos tea litter over one year within freshwater and coastal wetland soils across four climates in Australia. We also captured changes in the prokaryotic members of the tea-associated microbiome during this process. Ecosystem type drove differences in tea decay rates and prokaryotic microbiome community composition. Decomposition rates were up to 2-fold higher in mangrove and seagrass soils compared to freshwater wetlands and tidal marshes, in part due to greater leaching-related mass loss. For tidal marshes and freshwater wetlands, the warmer climates had 7–16% less mass remaining compared to temperate climates after a year of decomposition. The prokaryotic microbiome community composition was significantly different between substrate types and sampling times within and across ecosystem types. Microbial indicator analyses suggested putative metabolic pathways common across ecosystems were used to breakdown the tea litter, including increased presence of putative methylotrophs and sulphur oxidisers linked to the introduction of oxygen by root in-growth over the incubation period. Structural equation modelling analyses further highlighted the importance of incubation time on tea decomposition and prokaryotic microbiome community succession, particularly for rooibos tea that experienced a greater proportion of mass loss between three and twelve months compared to green tea. These results provide insights into ecosystem-level attributes that affect both the abiotic and biotic controls of belowground wetland carbon turnover at a continental scale, while also highlighting new decay dynamics for tea litter decomposing under longer incubations