Broadening the sense of ‘dynamic’: a microworld to support students’ mathematical generalisation

This paper describes the design of a mathematical microworld to tackle the persistent difficulties that secondary school students have with the idea of algebraic generalization, which is a key stumbling block in secondary-school mathematics classrooms. Our focus is to characterize algebraic ways of thinking and to design both affordances of the system as well as suitable tasks and pedagogies that provide a substrate of activity and experience for the teaching and learning of algebraic generalizations. Using as reference illustrative cases of 12 to 13-year-old students' interaction with the microworld, we demonstrate the strong interplay between epistemology and the design of the microworld and draw conclusions regarding its potential to support the development of algebraic ways of thinking.

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“…Examples of these iterations and students' interactions are reported in Geraniou et al . (2009a) and Noss et al . (2009).…”

Section: The Migen Projectmentioning

confidence: 95%

Sowing the seeds of algebraic generalization: designing epistemic affordances for an intelligent microworld

Mavrikis

Noss

Hoyles

et al. 2012

Computer Assisted Learning

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“…Similar activities are often found in the UK National curriculum, and have the potential to emphasise the structural aspect of patterning rather than the purely numerical. As explained in more detail in [15] this is a key difficulty that students face.…”

Section: The Problemmentioning

confidence: 99%

Similarity-Based Grouping to Support Teachers on Collaborative Activities in an Exploratory Mathematical Microworld

Gutierrez-Santos

Mavrikis

Geraniou

et al. 2017

IEEE Trans. Emerg. Topics Comput.

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This paper describes a computer-based tool that helps teachers group their students for collaborative activities in the classroom, the challenge being to organise groups of students based on their recent work so that their collaboration results in meaningful interactions. Students first work on an exploratory task individually, and then the computer suggests possible groupings of students to the teacher. The complexity of the tasks is such that teachers would require too long a time to create meaningful groups. The paper describes the design of the tool, the algorithms and metrics used for generating the groups, the evaluation of the tool, and the pedagogical context in which the tool was designed.

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“…At this stage, the client's ResourceList has not been updated; all that has happened is that the server has notified the ResourceList that it must re-check with the server to find out the latest state of its data resource. It therefore asks the MessagesRestlet for the latest representation of its data resource 15 . The MessagesRestlet contacts the DataModel 16 in order to obtain the updated data resource content 17 .…”

Section: Implementation Overviewmentioning

confidence: 99%

The Conceptual and Architectural Design of a System Supporting Exploratory Learning of Mathematics Generalisation

Pearce

Poulovassilis

2009

Lecture Notes in Computer Science

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Abstract. The MiGen project is designing and developing an intelligent, exploratory environment to support 11-14-year-old students in their learning of mathematical generalisation. Deployed within the classroom, the system will also provide tools to assist teachers in monitoring students' activities and progress. This paper describes the conceptual and architectural design of the system, and gives a detailed technical explanation of a working proof-of-concept prototype of the architecture, motivating in particular the technologies and approaches chosen to implement the necessary functionality given the context of the project. We also discuss how the prototype will be used as a basis for developing the first full version of the MiGen system, in the context of ongoing knowledge acquisition and analysis within the project's iterative, stakeholder-centred design, development and testing methodology.

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Broadening the sense of ‘dynamic’: a microworld to support students’ mathematical generalisation

Cited by 31 publications

References 14 publications

Sowing the seeds of algebraic generalization: designing epistemic affordances for an intelligent microworld

Sowing the seeds of algebraic generalization: designing epistemic affordances for an intelligent microworld

Similarity-Based Grouping to Support Teachers on Collaborative Activities in an Exploratory Mathematical Microworld

The Conceptual and Architectural Design of a System Supporting Exploratory Learning of Mathematics Generalisation

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