# How to embed English into Calculus lessons

I am teaching abroad to non-native English speakers with a large variance of language skills.

I teach both pre-calculus and AP calculus (AB & BC). For both of those classes I define the new terms. I use word problems, have them read from the textbook, take notes in English during class, have the students speak English in class, and teach the class in English.

I am asking this question because my CP told me I need to embed more English into my lesson, so the students learn English.

So what are some techniques to embed English into a mathematics lesson, and what skills and lessons have you learned from teaching mathematics in an ESL environment?

• What does "CP" stand for? – J W Nov 1 '14 at 7:42
• Center Principle. – El Santi Nov 1 '14 at 15:43

I teach in an ESL environment where students come from a variety of countries. I try to be particularly sensitive to differences in notation/convention in mathematics, which seem to come up most often in the notation for the decimal point, what sign to use for multiplication and how logarithms are written.

I have also learned to take my time and avoid using too much idiomatic or low-frequency vocabulary. I usually state difficult points twice, often reformulated slightly the second time, to give students a second chance to understand. Of course, this applies to a non-ESL environment too, but it is especially important when students are struggling to follow the subtleties of mathematics in a second or foreign language.

That said, I do not attempt to turn my mathematics lessons into English lessons, apart from the occasional remark. I do, however, mention when mathematical English usage differs from everyday English usage, a classic example being the word "series." I would also say that getting students to work in small groups to solve problems will provide practice in speaking English. You can also set written assignments requiring students to write in full English sentences and not just the symbolic language of mathematics. For the latter, Kevin Houston's How to Write Mathematics may come in handy.

• Do you use worksheets? I teach Chinese students and their reading English ability is higher than there spoken English, but the issue I mostly have is that when either American notation differs from Chinese, or I teach an aspect of mathematics that is not well covered in their Chinese classes. I don't have the problem of using a period or comma for decimal notation, but for natural Log I do. However, they do get confused when talking about the $x$ for an inverse and confuse it with the $x$ of the function. – El Santi Nov 1 '14 at 15:42
• I do not use worksheets much, although I may change this at some stage. However, I have experienced the same regarding reading ability being better than speaking with many Chinese students. – J W Nov 1 '14 at 21:31

One way to teach English along with calculus is to assign so-called "word problems." (E.g. if g is the acceleration due to gravity, how do you integrate/differentiate to get Newton's Law.)

It's a situation where students have to "translate" from English to math. Then they have to do the math.

• That works for the better students of the class, the other students just copy. – El Santi Nov 3 '14 at 6:17

Well, apart from what you are already doing, there are not too many things you can do. You teach mathematics in English during Math class. And your students learn the grammar, general vocabulary, etc. during English class. And this is something your principal should understand. Depending on the level of your students, it will be also allowed to use their native language to explain some misunderstandings.

However, you could satisfy your principal if using, for example, short video fragments taken from films, TV series, Youtube, etc. Take a look to these sites, they are just a sample of what you can find:

The Math Behind Numb3rs

Simpsons Math

The main idea is to create a problem or situation with a real-life context, or easily imaginated by the students. That is where the fragments help. They provide a visual anchor where develop further mathematics. Sometimes an explicit problem will also be set from an scene (it's a classic the movie Die Hard: With a Vengeance, where some problems are proposed to Bruce Willis).

By this way you will not only satisfy your principal, but also improving your teaching practice.

• I like thoses resources, not only does it introduce mathematics but it is also "cool". Thanks. – El Santi Nov 2 '14 at 2:55
• You're welcome. Keeping motivation high is also a basic. And this kind of activities helps. – Pablo B. Nov 2 '14 at 7:36