An introduction to Chris Tisdell’s Geometry Tool (TGT) in Mathomat templates, by John Lawton publisher at OLM

 

Professor Tisdell approached us at OLM in 2021 because he was interested in the ability of the circle templates in the Mathomat to do geometric constructions in a school classroom setting. It has been a privilege and a great learning experience to be able to work with Chris and watch as he engaged with the design of the Mathomat template to achieve its greatest potential as a drawing tool. Along the way Chris completely reimagined the structure of our circle templates, resulting in the new tool that we have named Tisdell’s Geometry Tool, or TGT, in recognition of his contribution.

As the attached paper by Chris and David Bee Olmedo (Tisdell & Bee Olmedo, 2022, p.3) explains, there are many problems associated with the classroom use of compasses. These include the kinesthetic challenge of operating a compass, the poor quality of many compasses purchased by students, their lack of integration with the straightedge and safety concerns due to their sharp points. In tackling this problem Chris really did go right back to basics, in fact I believe that he managed to “get inside Plato’s head”. Building on Mathomat manufacturing know how, Chris has come up with a template design that I think Plato himself would have seen as superior to the compass and straightedge that he so famously advocated for geometric construction work 2500 years ago and which is still prevalent in classrooms today. 

The result of Chris’s design work is the arc circle template, or TGT, that is shown below. A key aspect in the design process for the TGT was Chris’s insight that all the constructions required in school curricula can be achieved using a single radius. This builds on the Poncelet-Steiner theorem, and on the work of Francesco Severi, in 1904 (Tisdell & Bee Olmedo, 2022, p.7). The Mathomat template does not have the quality problems experienced by many low-cost school compass sets, it is essentially a professional designer’s drawing template that has been adapted to school use. As a result, Chris was able to modify a very clear circle template which has a very smoothly curved drawing edge, and which is simply operated by hand for precision drawing work. The main design challenge that Chris engaged with in modifying the Mathomat circle template was the need to locate the centre of the arc for accurate and simple positioning while drawing.

The simplicity, accuracy, and safety of the TGT in geometric constructions can be seen in Chris’s geometric construction video series which are available below, and in his recent paper (Tisdell & Bee Olmedo, 2022) which can be accessed from the attached link. 

The TGT is subject to a patent application (Lawton & Tisdell, 2021), and is available exclusively in Mathomat geometry templates. The Mathomat V3 and V5 templates feature a TGT in their designs from term 1, 2022.

In the background to Chris’s video, shown below, you will see a “naked” version of the Mathomat template. In working with Mathomat, Chris found that the unprinted naked form of the template was able to focus the user’s attention onto geometric thinking and exploration more effectively than printed versions of the template. I believe that the naked version of Mathomat is effective because it separates geometry from measurement, asking students to focus only on the former during the construction process. This is consistent with Plato, who was critical of marked instruments such as protractors, arguing that unmarked compass and straightedge tools could elevate geometry (Tisdell & Bee Olmedo): “imbuing it with the eternal and incorporeal images of thought, even as it is employed by God, for which reason He always is God” (p.2). To better support this focus on geometry OLM plan to redesign the V4 geometry template so that it is a naked design, without graduations for measurement, with a larger 100mm diameter version of the TGT. More information on this new template is available in the link below.

We trust that classroom teachers and geometry students will enjoy the discovery of geometry through the creative process of drawing using the innovative new TGT feature in Mathomat.

 

John Lawton, publisher

March 2022

 

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References 

Lawton, J., & Tisdell, C. (2021). Learning aid. Australian Patent Application No. 2021221739 AusPat: A. G. IPAustralia.

Tisdell, C., & Bee Olmedo, D. (2022). Beyond the compass: Exploring geometric constructions via a circle arc template and a straightedge. Download here