Design principles of Mathpert: software to support education in algebra and calculus

Beeson, Michael

doi:10.1007/978-3-7091-6461-7_9

Cited by 33 publications

(27 citation statements)

References 10 publications

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“…Third, as an environment for developing algebraic concepts, technology is aimed to guide the development of algebraic thinking (e.g. [21]). The use of digital tools in this study is mainly on the second and third functions: conceptual understanding as a basis for a mastery of algebraic skills, and procedural skills are expected to corroborate the conceptual understanding.…”

Section: Didactical Functions Of Technology In Algebra Educationmentioning

confidence: 99%

Learning algebra on screen and on paper: The effect of using a digital tool on students’ understanding

Jupri¹,

Drijvers²,

Heuvel–Panhuizen³

2016

AIP Conference Proceedings

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Abstract. The use of digital tools in algebra education is expected to not only contribute to master skill, but also to acquire conceptual understanding. The question is how digital tools affect students' thinking and understanding. This paper presents an analysis of data of one group of three grade seventh students (12-13 year-old) on the use of a digital tool for algebra, the Cover-up applet for solving equations in particular. This case study was part of a larger teaching experiment on initial algebra enriched with digital technology which aimed to improve students' conceptual understanding and skills in solving equations in one variable. The qualitative analysis of a video observation, digital and written work showed that the use of the applet affects student thinking in terms of strategies used by students while dealing with the equations. We conclude that the effects of the use of the digital tool can be traced from student problem solving strategies on paper-and-pencil environment which are similar to strategies while working with the digital tool. In future research, we recommend to use specific theoretical lenses, such as the theory of instrumental genesis and the ontosemiotic approach, to reveal more explicit relationships between students' conceptual understanding and the use of a digital tool.

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Section: Didactical Functions Of Technology In Algebra Educationmentioning

confidence: 99%

Learning algebra on screen and on paper: The effect of using a digital tool on students’ understanding

Jupri¹,

Drijvers²,

Heuvel–Panhuizen³

2016

AIP Conference Proceedings

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“…Following Beeson's principles [4] of cognitive fidelity (the software solves the problem as a student does) and glassbox computation (you can see how the software solves the problem), domain reasoners should be organized with the same incremental and layered organization. We are following such an organization for the concepts that model knowledge, such as rewrite strategies and rules.…”

Section: Configuration and Adaptabilitymentioning

confidence: 99%

Feedback services for stepwise exercises

Heeren

Jeuring

2014

Science of Computer Programming

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Advanced learning environments such as intelligent tutoring systems for algebra, logic, programming, physics, etc. let a student practice with stepwise exercises, and support a student solving such exercises by providing feedback. These environments usually provide various types of feedback, for example about the correctness of a step, common errors, hints about how to proceed, or complete worked-out solutions. Calculating feedback is generally delegated to a dedicated expert knowledge module, also known as a domain reasoner. Existing architectural descriptions of learning environments do not precisely specify the interaction between this module and the rest of the learning system. We propose a design based on the stateless client-server architecture that clearly decouples the expert knowledge module from the learning environment. We describe a set of feedback services that support the inner (interactions within an exercise) and outer (over a collection of exercises) loops of a learning system, and that provide meta-information about a class of exercises, such as solving quadratic equations, or performing Gaussian elimination. The feedback services do not depend on a particular domain and are based on the various feedback types described in the literature.The paper analyzes which domain-specific knowledge about an exercise class is needed for implementing the feedback services. Based on this analysis, we developed a framework for implementing domain reasoners that offers generic functionality such as rewriting, simplifying, and comparing terms. We have implemented several domain reasoners in this framework, both for external learning environments and for simple prototypes. The proposed design is evaluated with these implementations, and we reflect on our experience with developing domain reasoners.

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“…Above all designed in order to be efficient, they use complex algorithms that do not match the methods taught to the students. They do not follow the principle of 'cognitive fidelity' (Beeson 1998, Nicaud et al 1999) needed in a leaming environment.…”

Section: Utility and Usability Of Cas In Mathematics Learningmentioning

confidence: 99%

User Centred Design in a Learning Environment Based on a Computer Algebra System

Lenné

Gélis

2002

Networking the Learner

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Though they have not been designed for this usage, computer algebra systems are increasingly used in leaming situations. In order to improve their didactic capabilities we study the possibility to graft mathematics interactive leaming environments onto them. We present in this paper our design approach that relies on Human Computer Interaction methods and integrates mathematics leaming knowledge. This approach has been applied to design a leaming environment, caßed Limites, that helps students to study, work out and justi:ty Iimits ofrational functions. We present the main features ofthis environment, focusing on three points: algebraic expressions manipulation, conjectures and proofs.

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Design principles of Mathpert: software to support education in algebra and calculus

Cited by 33 publications

References 10 publications

Learning algebra on screen and on paper: The effect of using a digital tool on students’ understanding

Learning algebra on screen and on paper: The effect of using a digital tool on students’ understanding

Feedback services for stepwise exercises

User Centred Design in a Learning Environment Based on a Computer Algebra System

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