Gifted Issues Discussion homepage Forums Identification, Testing & Assessment Experiences w/ Van Hiele assessment/scale?

The more research I read regarding the Van Hiele scale the more epiphanies are coming to me. Anyone else whose children were assessed on the Van Hiele for Geometry class? It supposedly has a reasonable correlation for readiness and likelihood of success in a course requiring Euclidean Geometry proofs.

I took a look at the version used in the UCSMP study back in the early 1980's and some of the levels 4 and 5 questions definitely require some thought, especially since you only average about a minute a question.

So many thoughts are going through my head, but one of them is that I finally understand why a course in Geometry (at least the proof writing kind) rather than in Algebra is really the gatekeeper to higher level math. What I mean is that it now makes sense to me why many students can breeze through Algebra I and finally stumble in Geometry. I also feel reassured that while visual spatial skills can be especially helpful in Geometry, it really isn't the most essential skill/ability for mastering Euclidean Geometry proofs.

Any thoughts on rather level 5 on Van Hiele is a good indication of readiness for non-Euclidean Geometry?

Why is it that Geometry has proofs but Algebra doesn't? Isn't this setup just a peculiarity of the American system?

I think the best indication for non-Euclidean Geometry readiness is its predecessor, Euclidean Geometry If you don't have difficulties in Euclidean, then non-Euclidean will not be a problem.

Algebra I doesn't, but Algebra II may have some proofs, depending on a particular teacher. The problem is that in many states the sequence is Algebra I - Geometry - Algebra II, so Geometry is the first class where students stumble upon proofs
This is not just a peculiarity, unfortunately, this is one of the several major flaws in American math education.

FWIW, when I was in school, in America, in the Dark Ages, there were a ton of proofs in Algebra II. Algebra I was too far in my past for me to remember anything, but my ds was first introduced to proofs in Algebra I, here and now in the not-so-dark ages.

polarbear

ps - I tutored students in high school math for years as volunteer outreach in my community, and honestly, there seemed to be a huge mind-block about geometry - I still haven't figured it out - but I was always in demand simply because I liked geometry - and many of the extremely capable professionals I worked with who were also volunteering were convinced they couldn't "do geometry" - yet these were very sharp individuals, mostly with a background in engineering. It would have been no harder (jmo) for them to spend a few minutes looking at a geometry problem to remember how to do it than it was for them to look back at an algebra II problem, yet they were convinced that they just didn't understand geometry and didn't want to try.I *know* these folks were bright people who graduated from highly respected schools of engineering and sciences so I know they'd taken Geometry 1 and most likely didn't get a low grade in it - so why the mindset? I even had high school math *teachers* who got excited when I was willing to tutor geometry because they thought they weren't capable of answering the students questions. Sorry for the ramble… it just always confounded me wondering how this mindset developed

I couldn't beg a "why" out of a teacher in school. They were focused on the processes and the "whats." A proof without a why is like bread without a proof. Maybe people should first learn to break proofs. It seems most, if not all, of the various logic classes I've taken started with logical flaws before construction... actually maybe logic should preceed mathematical proofs.

Math department at our university has a course called Fundamentals of Mathematics. This course starts with logical puzzles .

polarbear, your son was lucky, in our district Algebra I doesn't have any proofs. Just out of curiosity, what kind of proofs did he have to do (if you remember, of course)?

Very interesting observations about geometry "block". I cannot believe that somebody with strong engineering education is incapable of solving high school geometry problem. Maybe, they just did not want to bother? After all, sometimes you have to make a drawing to solve a problem, it takes time and effort

Not sure as I am not familiar with other systems. I suspect that a lot of it has to do with age/readiness issues. At least that has come up a lot with all the research piggybacking on the original Van Hiele research. There are lots of proofs in Algebra II as well but students tend to be the same age or a year older depending on whether Algebra II comes before or after Geometry in the math sequence. I have seen proofs presented in Algebra I but generally students are not required to create a formal proof from scratch, just explain the reasoning.

Is that true for everyone regardless of their cognitive ability? That's what I don't know. Anyway, it was an interesting tidbit that level 5 indicates readiness for non-Euclidean Geometry.