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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15
votes
4answers
381 views

How to teach affine geometry to future high-school teachers?

This question is a follow-up to that one, where I expressed doubt about the use of abstract affine geometry in undergraduate education. However, future high-school teachers need to be able to relate ...
10
votes
5answers
215 views

Lesson-planning: Teaching probability concepts via geometry

I am intending to teach a lesson covering some topic related to "Probability via Geometry" and, if possible, I would appreciate references or materials (or good ideas) that can help me. The target ...
5
votes
2answers
138 views

Approaches to Teaching for Questions Around Partitioning Space

My students are preparing for their SATs and have problems with a certain type of questions, i.e., questions involving a geometrical figure and $n$ (usually $n = 2,3$) straight lines passing through ...
13
votes
4answers
723 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 ...
11
votes
4answers
259 views

Helping students use constructions in geometry

I work as a teaching assistant in a high school and geometry gives most students headaches. I emphasize understanding the problem by constructing lines and using elementary properties to arrive at ...
5
votes
1answer
96 views

Suitable Curriculum for Algebra through Pre-Calc students in One Class

I run a high school outreach program at UCLA called DMAP: Diversifying Mathematics And Physics (webpage: http://dmap.pbworks.com), which focuses on exposing groups underrepresented in advanced maths ...
12
votes
2answers
308 views

What prerequisites would college students need for a course based primarily on Euclid's elements?

I love Euclid's elements, and would like to base a course around them. Before I can pitch it to my supervisors, I need to know where it would fit in the curriculum. While it begins from elementary ...
1
vote
1answer
69 views

Preparation to exams [closed]

Next week I'm going to have my students write tested examinations. I need to give them problems such as . Where can I find these kind of problems to work on? Not only tangent and secant problems, but ...
10
votes
4answers
669 views

Examples of Mathematical Beauty in School Mathematics

Various branches of mathematics have mathematical beauty. Some of this are visual, such as the mandelbrot set, while others are logically sublime, such as the recursive simplicities of peano ...
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}...
9
votes
5answers
196 views

Extensions beyond Euclidian Geometry for Secondary students

My secondary geometry class is really amazing and is likely going to finish everything I have for the curriculum with a few weeks left in the school year. I was thinking to use these last few weeks ...
8
votes
3answers
753 views

Gifs of finding the volume of 3d shapes?

I'm looking for some animations (videos or gifs) of finding the volume of different 3d shapes. It would be super helpful if I could find something which stacks unit cubes into a rectangular prism to ...
9
votes
2answers
217 views

Teaching geometric transformations through fractals?

In roughly two weeks, my secondary geometry class will have reached the part of the year where we discuss geometric translations: translation, rotation, and reflection. Dilation i am going to use as ...
18
votes
10answers
5k views

A parabolic arc is not semicircular. But students think so

I'm teaching a Calc 2 class now (integration and applications) and I'm surprised that more than a handful of students seem to think the graph of $y=x^2$ on $-1\le x\le 1$ is part of a circle! Here is ...
3
votes
3answers
1k views

interesting/challenging geometric constructions for gifted secondary students

I have three students in my secondary geometry class that just destroy everything I throw at them. I tasked them with writing the word problems for their midterms and one of the three wrote simply "...
10
votes
2answers
1k views

Project/Assessment based on Flatland for Secondary Geometry Class

One of my favorite books is Flatland by Edwin Abbott, which is incredibly rich in geometric concepts especially relating to dimensionality. I would really like to assign it to my secondary geometry ...
12
votes
4answers
406 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 ...
8
votes
2answers
3k views

Notation of points with coordinates

At least in Germany, nearly all teachers and textbooks use the notation $$P(x,y)$$ for the point $P$ with coordinates $x$ and $y$. My own math professors at university always cried about this, as the ...
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: ...
19
votes
4answers
975 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 ...
4
votes
7answers
933 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 ...
6
votes
1answer
122 views

Intuitive explantion: What is a Finsler metric?

Neither of the two most evident sources, MathWorld: "Finsler Metric." Wikipedia: "Finsler Manifolds." seems to provide me with the high-level intuition that I could convey to students in ~10 minutes....
4
votes
0answers
156 views

Explaining the algebra behind a problem in computer geography

For work, I tend to have to explain quantitative ideas to people with only some informal computer science training. Yesterday, my friend wanted to draw a map on his computer and was concerned we ...
11
votes
8answers
731 views

Symmetry - practical usages

My girlfriend is studying to become a math teacher, and asked me what I have ever used symmetries for. I'm a web developer, and do some designing from time to time, so I answered that symmetry have ...
8
votes
3answers
303 views

Adoption / penetration rates for dynamic geometry software in secondary school

Dynamic geometry software (DGS) has been around for decades; Geometer's Sketchpad (not the first, but probably the most well-known commercial product) has been around since 1986. Wikipedia lists more ...
10
votes
3answers
249 views

Appropriate education level for this geometry problem

What's the appropriate education level for the following concise but non-trivial geometry problem? Points $A$, $B$, $C$ are collinear; $\|AB\|=\|BD\|=\|CD\|=1$; $\|AC\|=\|AD\|$. What is the set ...