American High School Mathematics: What is Geometry? | An important year for developing shapes and thinking skills
- Manami Fujita
- 6月4日
- 読了時間: 5分
Among the mathematics studied in American high schools, the year of " Geometry " is said to be a particularly memorable one.
In this subject that deals with geometry, students not only learn about the properties of shapes, but also develop the logical ability to consider "why things are the way they are."
In Japan, geometry is taught in two parts at junior high and high school, but in America, Geometry is studied in depth over the course of a year as a separate subject.
In this article, we will provide a clear introduction to the content of Geometry taught in American high schools, the teaching style, and skills that will be useful in the future .
Please also refer to the article "The reality of high school life in America: Differences from Japan revealed through personal experiences."
The Position of Geometry in American High School Mathematics
In American high schools, math is taught in a grade-level progression. Most schools follow this pattern:
9th grade (equivalent to third year of junior high school) : Algebra I
Grade 10 : Geometry
Grade 11 : Algebra II
Grade 12 : Electives such as Pre-Calculus, Calculus, or Statistics
Geometry is positioned as a basic subject in the second year , and after becoming familiar with mathematical formulas in algebra, students step up into the world of "shapes" and "logic."
The unique feature of this program is that it allows students to learn about a world that is difficult to see through numbers alone in a visual way through shapes.
What do you learn in Geometry?
Geometry in American high schools is not just a class about memorizing shapes.
We place emphasis on the ability to think for yourself and explain "why something is the way it is." The main contents are as follows:
● Basics and definitions of shapes
What are points, lines, and planes?
The relationship between parallel lines and angles (alternate angles and corresponding angles)
Congruence conditions for triangles (SSS, SAS, etc.)
● Properties of triangles and polygons
Sum of the interior angles of a triangle
Special triangles (right angles, isosceles, equilateral triangles)
Polygonal structure and properties
● Circles and their surroundings
Properties of chords, arcs, and tangents
Circular Angles and Central Angles
Theorems about circles and their applications
● Calculation of area and volume
Area formula for plane figures (rectangles, triangles, circles, etc.)
Volume and surface area of solid figures (cylinders, cones, spheres, etc.)
● Coordinate plane and moving shapes
Handling points and lines with coordinates
Transform, rotate, reflect, scale, etc.
● Logic and Proof
Propositions and their converses, contrapositives, and contrapositives
How to write proofs (two-column proofs and text explanations)
Rather than simply "memorizing formulas and doing calculations," this is a subject that requires students to think "why something is said?" and be able to explain it in their own words.
Characteristics of the teaching style: Emphasizing "ways of thinking" rather than answers
Geometry classes in American high schools typically have a student-led learning style .
Rather than teachers teaching one-sidedly, there is plenty of time for students to converse and explore with each other.
for example:
Group discussion : learning by sharing ideas
Activities to actually create shapes : Experience shapes using origami and geoboards
Attitude of valuing "why?" : Understanding theorems and formulas through trial and error
For example, when asking the question "Why is the sum of the interior angles of a triangle 180 degrees?", the process of students discovering the reason for themselves by cutting paper, drawing diagrams, and discussing in groups is valued.
There are many creative ways to enjoy the fun of "discovering things for yourself."
The power of Geometry and the next steps
The skills you acquire in Geometry will carry over to future studies. In particular:
Ability to think logically
Ability to explain using diagrams and words
The ability to visualize space
This will be useful not only for Algebra II and Pre-Calculus, which you will learn next, but also for subjects such as science, programming, design, and architecture.
Geometry is also an essential foundation for those aiming to work in the STEM (science, technology, engineering, and mathematics) fields in the future.
Learning styles vary by state and school
Since educational policies vary from state to state in the United States, the content of Geometry classes also varies slightly.
Many States: Common Core-aligned curriculum
Some states (e.g. Texas) adopt their own standards
Some schools have introduced "Integrated Math" which combines algebra and geometry.
In other words, where and how much of Geometry you learn will vary depending on the region and school.
However, they all share the same core theme of "developing the ability to think logically using shapes."
Support system for difficult children is also available
Geometry is a field where we often hear people say, "I can give you the answer, but I don't know how to explain it..." However, we have a support system in place for such situations.
After-school tutoring and support within the school
Free online learning materials such as Khan Academy and IXL
Apps like GeoGebra for visually learning shapes
Individualized Education Programs (IEPs) are available if needed.
If you feel like you don't understand something, the key is to use these resources without forcing yourself, and gradually deepen your understanding.
Geometry will also be useful for college entrance exams and future jobs!
Geometry is almost a requirement for college entrance exams in the United States.
Geometry questions also appear in standardized tests such as the SAT and ACT.
Furthermore, for those aspiring to become engineers or architects in the future, the ability to understand shapes and space will be a direct asset in their work.
The ability to think logically and explain things in a coherent manner will be a valuable asset in any field.
Summary: A year of learning to "think" through shapes
The geometry taught in American high schools is not just a class on shapes.
This is an important year in which you will carefully develop the ability to think "why is it like this?" and explain it in your own words .
By learning about the properties of shapes, the way you see the visible world will change and the scope of your thinking will broaden.
If you are planning to attend high school in the United States, we encourage you to enjoy Geometry with a positive attitude.
You will discover the depth of mathematics and the fun of thinking for yourself.
American Homework Support provides study support for children living in the United States.
Article author ( Manami Palmini)  Lecturer History
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