Engaging students: Using the undefined terms of points, line and plane

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission again comes from my former student Kevin Kim. His topic, from Geometry: using the undefined terms of points, line and plane

green line

A Point, line and plane are basic concepts for geometry. Without these concepts, students cannot go far in geometry at all. If we plot two dots and connect them, then it becomes a line. This simple concept is very important, and I will make sure my students understand the concepts of point, line and plane. Although they are simple concepts, they are being used a lot in math. Triangle, square, and rectangle cannot be learned effectively without these concepts. Also, it affects higher math other than geometry. Calculus, and one of the most complicated math topology cannot even start without these concepts. Moreover, the idea of dimensions came from these basic concepts. Therefore, it would worth teaching these simple concepts for one entire class period.


green line

In ancient Korea (About 1,200 B.C.), there was one argument between two high officers. The topic was, “does point come first, or line?”. Officer A ( Yeong-An Choi) argued “It is very simple concept that is not even worth to argue. If we plot a lot of dots, they become a line, and if we do the same thing with line, then they become a plane. So point is the smallest thing which means point comes first”. Officer B ( Sae-Yong Oh) countered that, “No, point itself is meaningless. In fact point itself is plane. Point is made of a lot of lines and lines make plane. Points are just imaginary thing to help make sense of line. So, line comes first.” The argument became too serious due to their pride, so they decided to take one’s life if the other was wrong. Both of them agreed to ask this question to the famous astronomy teacher in the capital. The problem was that the teacher did not really know the answer, but officer B’s theory made some what sense to him so he said Officer B is right, and immediately officer B Killed officer A.

(Fact: Officer B was born into an upper class family while officer A was from working class. Officer A was just promoted to a higher position than officer B, and officer B could not accept that. So, officer B planned to kill Officer A. For their gambling part, the astronomy teacher actually knew the answer, but he was already threatened by officer B. So, the astronomy teacher said officer B was right, and Officer A got killed. After 2 years, this event was reported to the king. Because of Officer B’s family, he could avoid capital punishment, but he got fired from his position, and got killed by his own father for dishonoring family.)




green line

I prefer to use technology because I believe using technology may minimize students from becoming bored. As always, I checked Khan Academy and found one good explanation about the basic language of geometry (except the teacher stammered too much….).

Also, for the engagement part, I would like to show one part of movie “Interstellar” to show how point, line and plane are interesting. (The reason that I chose math as my major was because of this concept. Before I knew this, I never passed math in middle school, and I am sure, one day, I will meet students just like me. The second reference shows the brief idea that brought me to the math field.) I would like to use more technology if possible, but showing some scenes of scientific movies is the most effective way. I am not sure if it would fit to technology part, but I would like to distribute some mini white boards so that students can actually determine what happens if they connect two points. It is very easy to erase their mistakes so they will have fun with it as I did in middle school.





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