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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1answer
224 views

Learning High School Geometry in Ten Days

I would like to attempt this, as I want to place out of geometry next year. It is imperative that I do it now. How should I go about doing this? I have a copy of Elementary Geometry for College ...
12
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6answers
549 views

Can we explain to undergraduates how points make a line?

Many of my students arrive in college believing that lines are (in some way) made out of points. They also believe that points have no length. They want to know how a bunch of zero length points ...
3
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2answers
222 views

Is the Nomenclature of Triangle Congruency Proofs Consistent?

My Geometry class is doing triangle congruency proofs these days. In general, we find three pairs of congruent parts (sides or angles) in two triangles; we show that these congruencies reveal that the ...
5
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1answer
259 views

Applications of notable points and lines of a triangle

I am currently starting to teach math to highschool kids who don't do well on their own, and I'm teaching a guy about notable points and lines of a triangle (incenter, centroid, circumcenter, ...
28
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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!" (...
8
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5answers
231 views

How do you explain straightness to a 5-year-old?

How do you explain straightness to a 5-year-old? I am having a hard time trying to explain straightness to little kids. I have been asked, "How do you know that the ruler is straight?" Are there any ...
4
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4answers
166 views

How to explain how to get an end point of a segment from the other end point and it's midpoint?

I've had to try to explain the following problem: Let $PQ$ be a line segment, given $P(x_1, y_1)$ and the midpoint $M(x_2, y_2)$, find the coordinates of $Q$. I always draw a diagram and draw $\...
8
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2answers
302 views

Learning Math like Euclid

I'm posting this here as it's off-topic for the Math stack exchange, and I'm hoping there will be some educators here that can point me in the right direction. I enjoyed watching the YouTube series ...
1
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2answers
124 views

Interesting math lesson on integers, Euclid's Elements, polyhedra, prime numbers, non-Euclidean geometry, arithmetic functions or graphs

I have to deliver a lecture for secondary school, about one of these topics: integers, Euclid's Elements, polyhedra, prime numbers, non-Euclidean geometry, arithmetic functions or graphs. It should ...
11
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1answer
631 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 ...
11
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4answers
869 views

Reasons to teach Thales' theorem

In a classical course on Euclidean, compass-and-ruler geometry, Thales' theorem has always had a prominent place. However, as the Wikipedia article says, It is equivalent to the theorem about ...
8
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1answer
1k views

What is the term for the marks used to show congruence in geometric figures?

When looking at a given picture to be used in a geometric proof, often times single, double, or triple "slashes" mark off equal line segments or arcs. What is the correct term for these? I've seen ...
19
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8answers
2k views

Are there disadvantages to teaching complex numbers as purely geometrical objects?

Complex numbers are, or at least were to me, generally introduced like this: There's no number whose square is negative. That's a shame! Well, whatever - we'll make one up! Set $i^2=-1$ and declare ...
5
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2answers
142 views

How to teach mass center for young people

Could anyone recommend me some software that helps me teach about the centroid of an object? Something that was dynamic on the computer screen. Destined for 18 ...
4
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3answers
748 views

A formula for the area of a rectangle [closed]

This is a question about elementary geometry, so I think it belongs on this site. Let $d$ be the length of a diagonal in a rectangle, and let $m$ be half the perimeter. Then a formula for the area ...
6
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3answers
266 views

Wording VS mathematical notations

Is it better to write everything in words as the concepts themselves should be known? Or will some teachers in some countries prefer to be able to choose questions which also test the student's ...
16
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6answers
1k views

A text-based program to draw geometric figures

I found this question on another forum. Are there any hints how one could make pictures from geometric problems by coding? I mean, if one has a handicap in his hands and he can't use mouse very well, ...
6
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4answers
874 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 ...
12
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4answers
559 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 ...
3
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1answer
200 views

calculus without analytic geometry

How much of introductory calculus can be learned without using analytic geometry or for that matter any algebraic notations but simple euclidean geometry? Are there any resources(new ones not the old ...
3
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2answers
179 views

“A” or “The” Cartesian plane?

Which is correct terminology: "A Cartesian plane" or "The Cartesian plane"? (As in the directions for a section of homework being, "Plot a point on ______ Cartesian plane." In that context, I feel ...
7
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3answers
415 views

Will presenting non-Euclidean geometries to students before Euclidean geometry give them a better intuition about shapes on the plane?

This question is related to Is Euclid dead? or Should Euclidean geometry be taught to high school students?, but I am not asking about whether Euclidean geometry should be taught at all, but whether ...
12
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5answers
516 views

Geometry with a view towards differential geometry textbook

I am scheduled to teach an upper-division undergraduate class on "Geometry" and I get to choose more or less what that means. Common choices seem to be non-Euclidean, hyperbolic, projective, or ...
3
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1answer
87 views

Consolidating three descriptions of a parabola in precalculus

I want to present these three descriptions of a parabolic curve to my precalculus class: The graph of a quadratic function $f(x) = ax^2+bx+c$. Given a line called the directrix and a point called the ...
5
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2answers
137 views

At what educational stage are angles greater than 180 introduced?

Prompted by the question, "How to denote angle?," I am interested to learn when students consider and reason with angles $> 180^\circ$. For example, when do they reason with an angle of $270^\...
29
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10answers
9k views

Is this homework problem on counting triangles within a 4x4 grid too vague?

My six-year old daughter was given this maths problem for her homework: Given a regular square grid of 4 × 4 dots, how many different triangles with one dot in the middle can you draw? We were ...
13
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4answers
385 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 ...
24
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7answers
3k views

Why do we care about multiple proofs of the same theorem?

I am teaching a math appreciation course to high school students who are approximately 17 years old, in their last year of high school, and who do not believe they will choose a STEM major in ...
2
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1answer
52 views

GRE Geometry Reference Request?

My brother is taking the normal GRE (not the math subject test), and I need to help him learn geometry. I know basic geometry myself, but I need a book that will present it well and will have good ...
8
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1answer
178 views

The role of “area” in a Common-Core aligned high school classroom

Some background: I recall becoming much more adept at the concepts of area and measurement during high school geometry. However, as I scour the Common Core standards, "area" only shows up in high ...
6
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2answers
195 views

How to reasonably denote lines, line segments and rays?

I'm teaching geometry at high school for the first time soon and am struggling to find a reasonable notation for lines, line segments and rays defined by two points $A$, $B$ (and a direction). At the ...
11
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2answers
670 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 ...
5
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5answers
279 views

Should the construction of triangles be taught?

Constructing triangles (or other shapes) seems to be quite an obsolete topic, and yet, they feature in almost every high school math competition, to disappear completely in college. In recent years in ...
4
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2answers
4k views

Notation of line segment and its length

I have sometimes seen a notation where $AB$ could mean either the line segment or its length. Why do the same notation can be mean both? Should one teach pupils to use for example notation $d(A,B)$ or ...
3
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1answer
98 views

Resources on 3D transforms, vectors, coordinate systems

Background: I'm helping engineers use software to create 3D geometry in a programmatic way (similar to OpenSCAD). The functions they need to call have inputs which are low-level geometry concepts: 3D ...
3
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3answers
188 views

Which math class should I take as an exchange student in the USA (OH)? [closed]

I will go to an American High School (Ohio) this summer for a year and I will probably be a junior. I got a list of all classes, but there are really many classes to choose especially math classes. I ...
-2
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1answer
111 views

symmetry of a square - is it possible pure geometric approach in didactics? [closed]

Consider a square : four points in a plane constructed with classical means (compass and straightedge). Since no point is different from others (no coordinates, no labels...) it seems that we can not ...
15
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6answers
1k views

Are precise drawings important in geometry?

In Finnish middle school (yläkoulu) the students learn to measure distances and angles, draw geometric figures and do certain calculations (area, volume, surface measure, trigonometry). There are also ...
17
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3answers
431 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 ...
3
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1answer
264 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, ...
3
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0answers
113 views

Sketching paraboloids on paper

I have to teach sketching paraboloids on paper by looking at it's equation. Last year when I taught this topic no one was interested in learning this particular thing. They felt the topic difficult ...
21
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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 ...
7
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4answers
3k views

How Can I Motivate Geometric Constructions?

When starting compass and straightedge geometric constructions in my grade 8-9 maths classes, I usually begin by mentioning a little about Euclid and the fact that constructions have been done for ...
8
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2answers
201 views

Coverage of Fundamentals of Lines and Planes

I was helping a high school student with some fundamental concepts of planes and lines, when I realized I am rusty on some definitions myself. I found some minimal coverage in his high school math and ...
11
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5answers
1k views

Rigorously defining the concept of an angle for high school students

Arriving at a rigorous definition of the concept of angle for high school students is not as easy as expected. Google search provided me with many definition that are too technical or too vague IMO. ...
11
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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 ...
7
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2answers
228 views

Experience using Khan Academy badges for basic math courses

This semester I am teaching a basic geometry course for design students (interior and industrial), which I am making strongly project-based since I believe they need to learn how to use geometry "in ...
8
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0answers
178 views

Moore method projective geometry

Has anyone written a set of Moore method notes for synthetic projective geometry? It seems like it would be well-suited, but I haven't been able to find any such thing on the Internet.
4
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0answers
72 views

What are the best expository pieces related to the Van Hiele models?

The Van Hiele model (wikipage) "is a theory that describes how students learn geometry." I would appreciate further insights into the original model, later models that expanded or re-worked it, and ...
5
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1answer
80 views

Looking for a classic paper “Vinner and Hershkowitz”

I can't find this ZDM article: Vinner, S., & Hershkowitz, R. (1983). On concept formation in geometry. Zentralblatt für Didaktik der mathematik, 83(1), 20-25. Could you help me? I was ...