Introducing functional thinking in year 2: a case study of early algebra teaching

Sixty-five Year 2 children with ages ranging from six to seven years participated in a teaching experiment to introduce functional thinking. The results show that young children are capable of generalising, can provide examples of relations and functions, can describe the inverse of such relationships and give valid reasons for how they found the inverse relationships. They also indicate that specific features of instruction assist this process, particularly abstracting underlying mathematical relationships, notably the materials used by the teacher and the children, the types of activities and the questions asked by the teacher. This leads to specific implications for the teaching of arithmetic in the early years

Estimating retention benchmarks for salvage logging to protect biodiversity

Forests are increasingly affected by natural disturbances. Subsequent salvage logging, a widespread management practice conducted predominantly to recover economic capital, produces further disturbance and impacts biodiversity worldwide. Hence, naturally disturbed forests are among the most threatened habitats in the world, with consequences for their associated biodiversity. However, there are no evidence-based benchmarks for the proportion of area of naturally disturbed forests to be excluded from salvage logging to conserve biodiversity. We apply a mixed rarefaction/extrapolation approach to a global multi-taxa dataset from disturbed forests, including birds, plants, insects and fungi, to close this gap. We find that 75 ± 7% (mean ± SD) of a naturally disturbed area of a forest needs to be left unlogged to maintain 90% richness of its unique species, whereas retaining 50% of a naturally disturbed forest unlogged maintains 73 ± 12% of its unique species richness. These values do not change with the time elapsed since disturbance but vary considerably among taxonomic groups

The use of mathematical symbolism in problem solving : an empirical study carried out in grade one in the French Community of Belgium

This article relates to an empirical study based on the use of mathematical symbolism in problem solving. Twenty-five pupils were interviewed individually at the end of grade one; each of them was asked to solve and symbolize 14 different problems. In their classical curriculum, these pupils have received a traditional education based on a "top-down" approach (an approach that is still applied within the French Community of Belgium): conventional symbols are presented to the pupils immediately with an explanation of what they represent and how they should be used. Teaching then focuses on calculation techniques (considered as a pre-requisite for solving problems). The results presented here show the abilities (and difficulties) demonstrated by the children in making connections between the conventional symbolism taught in class and the informal approaches they develop when faced with the problems that arc, put to them. The limits of the "top-down" approach are then discussed as opposed to the more innovative "bottom-up" type approaches, such as those developed by supporters of Realistic Mathematics Educations in particular