Connecting the equals sign

Children tend to view the equals sign as an operator symbol bereft of the rich relational properties of equality statements. It has been argued by some that this restricted view of the equals sign is due to cultural or cognitive factors. We suggest a significant factor is that rich relational meanings lack relevance within the context of paper-based arithmetic. One possible way to allow learners access to relational meanings is through interaction with technologically supported utilities for the equals sign. We report upon a trial in which two students draw on existing and emerging notions of mathematical equivalence in order to connect an onscreen = object with other arithmetical objects

Three utilities for the equals sign

We compare the activity of young children using a microworld and a JavaScript relational calculator with the literature on children using traditional calculators. We describe how the children constructed different meanings for the equal sign in each setting. It appears that the nature of the meaning constructed is highly dependent on specificities of the task design and the tools available. In particular, the microworld offers the potential for children to adopt a meaning of equivalence for the equal sign

Putting the learning back into e-learning

The design of web-based learning environments is primarily focused on the production and delivery of content to a learner. The principles of constructionism are intended to guide the development of learning environments where the learner has more control. In this paper, we describe characteristics of constructionist and learning environments that can foster the learning of mathematics. Our experiences are drawn from the development of microworlds for an e-museum. Reflecting on this process turns out to provide some fresh insights into how e-learning environments might be re-conceptualised in the future

Computational modeling and children's expressions of signal and noise

Previous research has demonstrated how young children can identify the signal in data. In this exploratory study we considered how they might also express meanings for noise when creating computational models using recent developments in software tools. We conducted extended clinical interviews with four groups of 11-year-olds and analysed the videos of the children’s activity through a process of progressive focusing. In this paper we explain the design of our tasks and report how the children’s expressions for noise, supported by the need to communicate with the software, developed from specific values to verbal expressions of uncertainty such as ‘around’, to offering ranges of values. We consider the opportunities and constraints of such an approach, which we call ‘purposeful computational modelling