Designing Educational Software: The Case of Grid Algebra

Hewitt, Dave

doi:10.1007/s40751-016-0018-4

Cited by 9 publications

(9 citation statements)

References 31 publications

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“…An online demonstration video can be viewed at http://www.youtube.com/watch?v=fHMZNxGa0T4. The Grid Algebra software presents interactive numerals and letters on a grid (Hewitt, ) and mathematical expressions are constructed by dragging numerals and letters around the grid according to operational rules. A demonstration video can be viewed at http://www.youtube.com/watch?v=LaH3S_0igak&t=404s.…”

Section: The Teaching Interventionsmentioning

confidence: 99%

“…An online demonstration video can be viewed at www.youtube.com/watch?v=fHMZNxGa0T4. The Grid Algebra software presents interactive numerals and letters on a grid (Hewitt, 2016) and mathematical expressions are constructed by dragging numerals…”

Section: The Teaching Interventionsmentioning

confidence: 99%

“…We compared two teaching interventions experimentally based on software developed by mathematics education researchers and readily available to teachers in the UK, namely Grid Algebra (Hewitt, ) and MiGen (Mavrikis et al ., ). Both software packages are designed to build on students’ arithmetic knowledge when introducing algebra.…”

Section: The Teaching Interventionsmentioning

confidence: 99%

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Measuring conceptual understanding in randomised controlled trials: Can comparative judgement help?

Jones

Bisson

Gilmore

et al. 2019

British Educational Res J

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An impediment to conducting high‐quality quantitative research studies in education is the paucity of valid measures of learning gains. Studies often seek to investigate students’ deep, conceptual understanding yet many measures assess only surface, procedural understanding. One reason is that the development of validated measures of conceptual understanding is resource intensive and time consuming, and success is not guaranteed. We evaluated a novel and efficient technique, based on comparative judgement, for assessing conceptual understanding. We applied the technique to a randomised controlled trial in which students were taught simple algebra based on either the Grid Algebra or the MiGen software package. The participants were Year 5 students (N = 188) drawn from four primary schools who had not encountered algebra previously. An instrument from the literature (Concepts in Secondary Mathematics and Science: Algebra Scale) and a novel comparative judgement assessment were administered following the intervention. Students in the Grid Algebra condition outperformed those in the MiGen condition on both post‐test measures. The comparative judgement technique performed similarly to the standard instrument but was far more efficient to design and implement. The technique can, in principle, be quickly applied to any target concept of interest. We conclude that comparative judgement is a valid, reliable and practical tool that could help to increase both the quantity and quality of quantitative research in education.

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Section: The Teaching Interventionsmentioning

confidence: 99%

Section: The Teaching Interventionsmentioning

confidence: 99%

Section: The Teaching Interventionsmentioning

confidence: 99%

See 1 more Smart Citation

Measuring conceptual understanding in randomised controlled trials: Can comparative judgement help?

Jones

Bisson

Gilmore

et al. 2019

British Educational Res J

View full text Add to dashboard Cite

show abstract

“…We suspect that the offer of a structured environment might well necessitate working, from the start, on larger Bwholes^than might be typical, in the way that the Gattegno chart gives equal access to much bigger numbers than would be typically dealt with in the early years of schooling and has the potential to deal with the Bwhole^of the number naming system. Hewitt's (2016) BGrid algebra^offers one example of a symbolically structured environment in that curriculum area. Like early number, algebra can often be associated with memorisation and meaningless rote learning.…”

Section: Resultsmentioning

confidence: 99%

Ritualisation in early number work

Coles

Sinclair

2018

Educ Stud Math

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In this paper, we propose a way of thinking about ritual that is new to mathematics education research and that challenges the more common approaches to ritual that dichotomise thinking and acting. We argue for a material, monist conceptualisation of ritual, which we refer to as ritualisation. In the context of early number work, we show that ritualisation can be seen as meaningful-and not simply as rote repetition lacking mathematical sophistication-particularly in relation to a symbolically structured environment. We argue that ritualisation practices can allow entry into new fields of activity and discourse, without going through a phase of merely un-thinking performance.Keywords Ritualisation . Ritual . Early number . Number naming . Symbolically structured environment Introductory theorisingThe notion of ritual has played a vital role over the last century in the study of religion and society, by scholars of anthropology, sociology and history of religion. As religious studies scholar Catherine Bell (1991) writes, the recent, more interdisciplinary research on ritual has provided insight into the Bcultural dynamics by which people make and remake their worlds^(p. 3). Not surprisingly, various approaches to the concept of ritual have emerged, each differing in their interpretation of its function and nature. Rituals Educ Stud Math

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“…In a review of the different ways in which the term 'microworld' has come to be used, Edwards (1998) proposes that a microworld can be seen as 'embodying' a sub-domain of mathematics (or science), because of the opportunity that such an environment provides Bfor students to kinaesthetically and intellectually interact with the designers' construction of these entities, as mediated through the symbol system of a computer program^(p. 74). Examples of relevant research in mathematics education include Christou et al (2007), Confrey et al (2009) and Hewitt (2016).…”

mentioning

confidence: 99%

Designing a Web-based Learning Support System for Flow-chart Proving in School Geometry

Miyazaki

Fujita

Jones

et al. 2017

Digit Exp Math Educ

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As international research confirms, many secondary school students can find it difficult to construct mathematical proofs. In this article, we explain the pedagogical and technological underpinnings of a web-based learning support system for students who are just starting to tackle deductive proving in geometry. We show how the system was designed to enable students to access the study of proofs in geometry by tackling proof problems where they can 'drag' sides, angles and triangles from the figural diagram of the problem to on-screen cells within a flow-chart proof format. When doing so, the system automatically converts the figural elements to their symbolic form and identifies any of four kinds of errors in the learners' proof attempts, providing relevant feedback on-screen. We use empirical examples from our pilot studies to illustrate how this combination of technological features and systematic feedback can support student understanding of the structure of proof and how to plan one. Finally, we point out some limitations to mathematical expression and the usage of the flow-chart format, and indicate the prospect of minimizing such limitations by adopting a learning progression for the introductory lessons concerning deductive proofs.

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Designing Educational Software: The Case of Grid Algebra

Cited by 9 publications

References 31 publications

Measuring conceptual understanding in randomised controlled trials: Can comparative judgement help?

Measuring conceptual understanding in randomised controlled trials: Can comparative judgement help?

Ritualisation in early number work

Designing a Web-based Learning Support System for Flow-chart Proving in School Geometry

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