On Wednesday, the A2I team at New Visions participated in an excellent workshop from Harold Asturias on English language learners in a mathematics classroom. Harold made some points about the difficulties English language learners face in a mathematics class that really drove home this point to me; mathematics teachers are teachers of language too.
To illustrate my point, try this mathematics problem:
This is what solving a word problem is like for children who either can't read at all, or who are illiterate in the classroom language. What about this problem instead?
Here at least the character set is familiar, and you can recognize some words of the problem too. Some of you with some knowledge of the history of mathematics may even recognize a name from the problem above and be able to find out what the text of this problem is. Note that for almost anyone trying this problem, the text of the problem is still pretty close to incomprehensible.
What about this version?
(Source: Wolfram Mathworld)
This is at least readable, but it is still a challenging piece of prose to read. Hopefully you can imagine some of the stages of understanding between the second and third versions of this problem, and how challenging this kind of problem is. (Here is another example, this time from a textbook written in Thai.)
You can have issues with language result from just regular classroom discussion. Speak the following sentence aloud:
"Please take half of the peas that I have, and give two of them to him, and leave four of them for her."
For someone who is just learning English, even though the level of difficulty of the individual words in the sentence above is low, they may still have problems decoding the meaning of just this one sentence. There are many, many other examples of "difficult to decode" sentences. Note that this problem is probably not just exclusive to English Language Learners! Many native speakers of English struggle with comprehension in both the cases I've described above.
One solution, that I have heard proposed by some, to this problem is to remove word problems from mathematics classes. I think this solution is short-sighted. As teachers of mathematics, we are not just teaching the content of our discipline, we are also teaching the language of our discipline, and word problems are a way to build a bridge between the everyday language students have, and the academic language that mathematicians use. By removing this bridge, we would shut our students out of mathematics. If we want students to learn the language of mathematics, we must build it up from the language students know.
Another solution is to build a different kind of word problem, one not so dependent on language. While I think there are benefits to this approach, we still want students to develop mathematical language. My suggestion is to use the Three Acts type problems, and write the text of the word problem together, after students have solved the problem. This way they get a chance to develop their mathematical reasoning skills, and then develop their vocabulary for that reasoning while working on the problem. Dan Meyer demonstrates a Three Acts problem with a room of mathematics teachers. Notice how he builds up the language of the problem from the language participants use to describe it. From here, it is not too far a leap to include more of the language mathematicians would use to solve this problem.
There are ways to scaffold the use of language in your classroom without reducing mathematical difficulty. You can use daily math talks to build your students' ability to discuss mathematics. You can be deliberate in your use of language and carefully introduce vocabulary as needed to discuss mathematical ideas, and build a word wall of the vocabulary you have introduced. You can give your students opportunities to problem solve together so that they can support each other's use of language.
Here are some other resources you can use to help address this issue:
What other suggestions do you have to help all of your students learn the language associated with a math classroom?
David is a Formative Assessment Specialist for Mathematics at New Visions for Public Schools in NYC. He has been teaching since 2002, and has worked in Brooklyn, London, Bangkok, and Vancouver before moving back to the United States. He has his Masters degree in Educational Technology from UBC, and is the co-author of a mathematics textbook. He has been published in ISTE's Leading and Learning, Educational Technology Solutions, The Software Developers Journal, The Bangkok Post and Edutopia. He blogs with the Cooperative Catalyst, and is the Assessment group facilitator for Edutopia. He has also helped organize the first Edcamp in Canada, and TEDxKIDS@BC.