If you’re wondering what the first 3 weeks of a math class for primarily refugee ELL students who don’t speak any English and several possible languages (arabic, spanish, kinyarwanda, somali, swahili, kirundi, etc) – it looks like this:

Here are some thoughts and explanations and etc:

• In the absence of being able to communicate in a common spoken language, I’ve been working on developing a common visual language to describe mathematics. Two places where I was already familiar with this were: positive and negative numbers, and place value. Which is what you’re looking at.
• I decided to teach integers using physical tokens (closed circles are positive, open circles are negative) rather than a number line approach – I think in my mind I briefly rationalized that it would take less words to describe what’s happening than if I used the number line. My approach is very similar to Kate Nowak’s from this video.
• Positives & Negatives segued very nicely to place value – the inconvenience of drawing 50 dots leads to the desire to represent numbers in groups of 10s.
• These students can explain their answers to each other with only the words “open. negative. closed. positive”, which is awesome. Actually, This is an interesting pedagogical problem: imagine you are teaching a new topic to students who don’t know any of the words you’re about to use. What is the minimum number of words you need in order to communicate the idea (you are allowed infinite body gestures and pictures) and what are the minimum number of words needed so students can explain their answers to each other.
• Now that we know place value, I can check in on how well they understand multi-digit addition & subtraction. Carrying and Borrowing mean even less when students don’t even know the words – visually regrouping is a better way to communicate.

When I’m not teaching full-group lessons, students need something with a low language threshold, based in a visual language, and differentiated so students with a strong mathematical background from their own country can advance while the students with a weak background can get feedback and work on the problems they need.

There’s actually a pretty stellar solution to this problem that hopefully doesn’t cause too many ideological waves: it’s Khan Academy. I don’t know if Khan Academy realizes it or if they do this intentionally, but they’ve got some pretty stellar exercises for students with a low language threshold that need to learn both the language and the math at the same time. I’m thinking specifically of their Early Math exercises, focusing almost exclusively on the connection between symbol and language. And their videos, while not always great in content or pedagogy, usually have several options for translation, which helps students make connections between the words in their languages and the equivalent word in English.

They’ve also got some pretty clever exercises in the early math grades that emphasize connections between pictures and mathematical symbols, especially with some of their fraction exercises. I’ve been going through and vetting exercises specifically to avoid wordy exercises and to try and hit as many visual exercises as I can so I can use the visual language later to help them understand something.

So – if you’ve got a group of students who don’t speak English and are at varying degrees of mathematical ability, strategic use of Khan Academy is a pretty good idea.

More updates to come. This class is tons of fun.