Questions tagged [geometry]

For questions related to geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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13
votes
4answers
722 views

Wiggins' question #12

There's an interesting read: Conceptual Understanding in Mathematics by Grant Wiggins. In that text the author proposes "a test for conceptual understanding" which should be given "to 10th, 11th, and ...
6
votes
3answers
591 views

In what curricula are “rectangles” defined so as to exclude squares?

Most contemporary curricula define the word "rectangle" inclusively, so that all squares are automatically rectangles. Are there curricula in which this convention is not followed? That is, are ...
9
votes
4answers
1k views

Secondary Geometry Curriculum Sequencing?

I am currently student teaching, and the main class that I am focusing on is a secondary geometry class. I am currently following my classroom mentors curriculum sequence which looks something like: ...
11
votes
2answers
640 views

Physical vs. Virtual manipulatives in the high school classroom

I notice that geometry students frequently have difficulty with representations of 3-dimensional objects in 2 dimensions. Today, we worked with physical manipulatives in order to help visualize where ...
38
votes
33answers
14k views

Real-world examples of more “obscure” geometric figures

As part of my secondary geometry class I like to hook students by presenting real-world examples (usually images I find online or have taken myself) of different geometric shapes from real life. For ...
28
votes
10answers
4k views

Is Euclid dead? or Should Euclidean geometry be taught to high school students?

Apparently Euclid died about 2,300 years ago (actually 2,288 to be more precise), but the title of the question refers to the rallying cry of Dieudonné, "A bas Euclide! Mort aux triangles!" (...
20
votes
10answers
4k views

Pi or Tau? How should the circle constant be taught?

Tau ($\tau = 2 \pi$) has more merits in its application, but pi is the established standard in industry and education. Is the trade-off of teach-ability of circle concepts worth the subsequent ...
6
votes
4answers
801 views

Integrate Coding into the Geometry Curriculum

My supervisors want to see coding integrated into the ninth grade Geometry class. This class is mostly concerned with proofs--not too much algebra. These students know a decent amount of the visually ...
19
votes
4answers
972 views

Teaching manifolds to high schoolers

I would like to introduce the concept of a manifold to a high school student. This person isn't familiar with the axioms of set theory nor topology. However, despite these deficits, I would like to ...
17
votes
11answers
1k views

Should we teach abstract affine spaces?

In France at least, there is quite an ancient tradition of teaching abstract affine spaces (e.g. as a triple $(\mathcal{E}, E, -)$ where $\mathcal{E}$ is a set, $E$ is a vector space and $-:\mathcal{E}...
8
votes
6answers
258 views

Book recommendations on mathematics education focusing on geometry

I will be teaching Euclidean geometry to future teachers, and I am feeling a bit lost (I know geometry, but I am not that familiar with mathematics education). Is there some recent (as concise as ...
17
votes
2answers
526 views

Impossibility of trisecting the angle, doubling the cube and alike, what are reasons for or against discussing them in a course on algebra?

When I taught courses on algebra giving a first exposition to Galois theory I usually included some discussion of classical results showing the impossibility of constructing certain points with ruler ...
16
votes
3answers
394 views

Evidence for or against the claim that some students are “algebra people” and others are “geometry people”

Where I live and work, there is a widely-accepted and often-repeated claim that there are two kinds of students: "algebra people" and "geometry people". This claim sometimes gets expressed in ...
12
votes
4answers
516 views

What is currently called geometry in high school?

I've encountered classes of 25 or so undergraduates in which more than half -- maybe two-thirds -- of the students claim to have had a high-school geometry course but none has seen a proof of the ...
12
votes
4answers
403 views

Is there an elementary way to explain that a map of the earth cannot preserve distances?

I am teaching a short "topics in geometry" course to future high school math teacher in France. I plan to cover some spherical geometry. I will be treating the following topics: volume of the ball ...
4
votes
7answers
932 views

Fun Activities/Games Before a Break/Between Units for Secondary Geometry

I have been planning ahead and it looks like i will have a solid three to four days before the winter break where we wont really be in a unit. We will have just finished a unit and i do not want to ...
2
votes
1answer
222 views

Are kindergartners supposed to be steered from squares being rectangles?

Question 1: What are the literature, status, debates, references, etc regarding this matter please? Apparently, some (woohoo weasel words!) consider that squares are rectangles too advanced a topic ...
13
votes
4answers
364 views

Simpler explanation for finding the vertex of a parabola

I'm tutoring a Grade 11 Math student in BC, Canada, and we're going over parabolas. He's having difficulty with finding the vertex of a parabola - not how to find it, but WHY it works. And I'm having ...
11
votes
4answers
1k views

Phrasing the Van Hiele levels in student-friendly language

I teach high school geometry and see many of my students fall in to the trap of "it looks like it, so it's true" -- a Van Hiele Level 0 to 1 thought process. For instance, when talking about parallel ...
10
votes
1answer
563 views

How to denote angle?

I'm teaching mathematics on my free time for young pupils. Once I have seen that they denote angles like $\angle ABC$. But sometimes I have difficulties to understand whether they mean an angle or its ...
3
votes
1answer
246 views

Geometric Algebra Resources

Geometric Algebra brings together algebra, geometry, vectors, complex numbers, and linear algebra. It provides a single unification of all elementary math and serves as an excellent basis for physics, ...