Japanese Mathematics Vocabulary: "We don't use this word."

I had an interesting experience several weeks ago. I recently finished my Masters Degree in Education specializing in English Language Learner Education and I am now adapting my teaching practice to help my English Language Learners. 

I realized that there was a lot of mathematics vocabulary that I didn't know in Japanese and I was limited when I was explaining something to my Japanese speaking students. So I contacted my friend who is a mathematics teacher at Kanagawa Sogo High School and has very good English. I went thought my Geometry textbook and wrote down most of the vocabulary words and a few others that I felt I would want to know in order to explain Geometry to my students in Japanese. I had somewhere around 250 words.

When we sat down and began going through the words, my friend kept saying "_________ is the word for that, but we don't use this word." I would guess that somewhere around one third of the vocabulary words that I brought, they don't use in their K-12 education. Perhaps some of this is the difference in curriculum. However my friend said that they would simply describe the word. For example we teach the word "colinear" but in Japanese schools they would simply describe the points as being on the same line or draw a picture. The same thing with coplanar, skew lines, exterior angles. and the list goes on. There isn't even a word in Japanese for a linear pair, they simply call them supplementary angles or explain that because they make a straight line, their measures would add to 180 degrees.

I walked away from our meeting wondering why we have so many vocabulary words in Geometry and mathematics in general. Because I will be teaching a Mathematics Lab next year with students from Algebra as well, I asked about some Algebra words. I again found that words like "leading coefficient" and others were not used in Japanese K-12 education. We teach students vocabulary words for concepts that we study for only one or two days. I think part of the reason is the way we were taught, so there is a culture of education that focuses on vocabulary words. 

I think Japanese education is correct when they limit the vocabulary words that they teach to the most important words that will be used throughout the course, not for a few days. Limiting the number of vocabulary words would make the mathematics more accessible to all students. However, I am afraid to do this in my practice because if I do not expose them to these words, then I will be hurting my advanced students when they go to future math classes and their teacher is using a word that I thought was unnecessary. The change has to happen in the curriculum, starting with the textbooks.

Classroom Culture: Too Focused on "The Correct Answer."

American Classroom Culture

Today we had an emergency drill and a half day, so each class was only 25 minutes long (compared to the 85 that we are used to on a block schedule). So instead of doing mathematics directly, I decided to play a game: You start out with 21 beans. Each player can take 1, 2 or 3 beans. The person who goes last, wins. It is a very simple game. I wanted the class to know that there is more to this game than just beans, so I told the students that "There is a winning strategy." and "If anyone can beat me, then I will give them a piece of candy."

As students played this game and challenged me, they were looking for the "correct strategy." Only one or two students per class figured it out, mostly by watching me and analyzing my "correct strategy." Now that I reflect on this experience, I shouldn't have said "There is a winning strategy" I should have simply said "If you can beat me, then I will give you a piece of candy." By implying that there is only one correct strategy made students focus on what I was doing instead of exploring other ways to play this game.

In addition to this, my gut instinct as a teacher is to tell everyone the "correct answer" at the end of the class period. I resisted this urge and most students left class without understanding how to win the game every time.

Japanese Classroom Culture

Several months ago I watched two classes solve a simple question. The first class was an 8th grade class and the second was a 7th grade class. The question was if you cut a cube diagonally, what is the shape of the cross section:

image from: The Electronic Journal of Mathematics and Technology, Volume 2, Number 1, issn 1933-2823. 

Retrieved from: http://lib.znate.ru/docs/index-134315.html on Sept 24, 2014

In order to solve this problem, you need to use of the Pythagorean Theorem. The 8th grade students had learned about the Pythagorean Theorem, therefore many of them figured it out. However there were groups who did not figure it out and the teacher did not give the answer at the end of the class period.

The 7th grade students haven't studied about Pythagorean Theorem. Very few students in this class solved the problems, but the teacher did not give any hints or give the answer at the end of the period. But the students still worked until the end trying to solve it.

"Correct Answer" or Process

From watching these Japanese lessons, I realized that I am too "correct answer" focused. I knew going into our bean game that I wasn't going to tell the entire class the strategy. The reason is, if students know that they will get spoon fed the answer at the end, then they loose the incentive to solve it next time. It is the process that we are more concerned about anyway, right?