Seeking a Constructivist Geometry Textbook for Preservice Teachers

[thelema418]

I could not post this to the resource forums, so I am posting it here.

I am looking for a Geometry textbook for pre-service teachers. The text ideally should incorporate some constructivist practices and the use of technology to help visualize geometry problems. Most of the teachers will be working with middle school students in their careers, which is why this other goal of using technology and constructivist practices is important.

Thanks.

 

[micromass]

Do you mean that you want a textbook that does not use the law of the excluded middle?? Or do I not interpret your question right.
Or do you just mean a textbook that does a lot of constructions?? You will find that there is no better book than Euclid's Elements for this. It's the book that started geometry, it's been the standard math textbook for centuries and it's still worth its weight in gold.

 

[SteamKing]

'Constructivism' denotes a certain philosophy of mathematics instruction:

http://investigations.terc.edu/library/bookpapers/constructivist_learning.cfm

It differs from traditional instruction, where there is a lecturer or teacher who imparts a lesson to the students, by having the teacher act as a guide to the students who instead create knowledge based on what they already know or experience.

 

[micromass]

'Constructivism' denotes a certain philosophy of mathematics instruction:

http://investigations.terc.edu/library/bookpapers/constructivist_learning.cfm

It differs from traditional instruction, where there is a lecturer or teacher who imparts a lesson to the students, by having the teacher act as a guide to the students who instead create knowledge based on what they already know or experience.

Ah! I had no idea. Thanks SteamKing!

 

[thelema418]

Yes, that is pretty much what I mean by constructivism. It has variations in itself, yet what was previously stated is a good general description.

I have a book by Fenton that provides experiences in college algebra through instructional activities in Geometer's SketchPad (GSP). I would consider this a constructivist textbook for geometry. However, I'm not fond of the text itself and I also think it assumes a higher-level of prior understanding of the student. For example, there are parts of the book where it tells students to look up information in another book if they don't know the terminology. But if I were a student and purchased an expensive textbook to be told to look up a geometrical definition in another textbook, I'd feel like I didn't get my monies worth.

 

[thelema418]

You will find that there is no better book than Euclid's Elements for this. It's the book that started geometry, it's been the standard math textbook for centuries and it's still worth its weight in gold.

I appreciate that recommendation, and I do have access to a copy with dynamic models. I should also say that pre-service teachers are expected to know background for the Common Core State Standards in Mathematics. While some of this is classic Euclidean material, there are other aspects of geometry that were not included in Euclid's work or avoided for the sake of following the particular set of axioms.

For example, teachers would need to know about transformational and projective geometry. They should also understand the bridge between algebra and geometry. There's also constraint based geometry. In part this is because the curriculum contains these things, but it is also so the teacher has background to evaluate student's justification of mathematical ideas.