5

As for real world applications, most of the buildings around you older than 30 years were designed by an architect that manually used geometric constructions for their drawings. I learned geometric constructions in my Tech Drawing class before I learned them in maths class. Of course, CAD programs do all of that in the background now, but the reason that ...


4

I am a strong advocate for teaching constructions. At least when it comes to high school geometry. My experience in teaching geometry to freshmen and sophomore high school students has shown me how much can be gained from constructions. Of course, it also depends on how you teach it. You can micromanage it and take all the fun out of it. Or you can be ...


3

I suggest that emphasizing plane geometry problems and their solutions could be more effective than a systematic introduction to constructive geometry. For example: Alexander Shen. Geometry in Problems. MSRI Mathematical Circles Library. Volume: 18; 2016. AMS link.            Here us a ...


3

I've recently committed, in my college algebra classes, to presenting proofs for as many or all topics that I possibly can. This has made me much more aware of how often basic geometry constructions (transversals, etc.) are required. This includes: Pythagorean theorem, distance formula, midpoint formula, that any line is a linear equation, slope is constant ...


3

Conic sections would seem appropriate if you're looking to motivate some of the algebra that is on the horizon for your 7th grade students.


3

There are two websites that make geometric construction into a game. NiloCK mentioned euclidthegame.com in his comment. There is another construction game at sciencevsmagic.net, with a very different look and feel. I think some people will one enjoy one or the other much more, though I enjoy them both. I have only made it through about half the challenges on ...


2

you can use paper folding, which does not take many resources, to motivate elementary constructions. i think there is a book by johnson, d. a. published by maw that cover many basic constructions. students don need to have heard of euclid to enjoy and benefit from solving construction problems. if the teacher practices construction, then it would be easier ...


2

It might be time to show them how algebra can support or deny constructions. I would have them start looking at Gauss's proof of the constructability of the heptadecagon. This could serve as an introduction to areas of abstract algebra and beyond.


2

I question whether engagement is what is preventing students from grasping construction. I would argue that constructions are very much like geometric proofs in that they rely heavily on abstraction and formalism for something that students are already somewhat familiar with. In this thread about geometry sequencing, a colleague of mine makes the case that ...


1

I strongly believe in teaching construction problems. They can be used to stimulate lively discussions in the class. For example, see the several construction problems in Geometric Transformations, Vol I by Yaglom (MAA publication) (http://maa.org/press/ebooks/geometric-transformations-i). Also, given orthocenter, circumcenter and one of the vertices, is it ...


1

Although this has nothing to do with cross sections, it fits the physical materials: You could have the students cut out shapes to illustrate constructive proofs of the Pythagorean theorem:                       (Images from a Steven Strogatz NYTimes article.) Another constructive proof is described ...


1

Suggest posing these constructions: http://fivetriangles.blogspot.com/search/label/construction


1

I strongly recommend looking at http://www.geogebra.org it is free, available on almost every OS, and can be used to PLAY with geometric constructions. Playing with geometric constructions is probably the simplest way to "motivate" the general methods of geometric construction.


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