Problem+Solving

 **"I’ve** **been thinking a good deal lately about how reading and math are alike and different. Both call for bringing meaning to the printed page. In re****ading, we call this comprehension and in math, we call it sense making. When you’re reading a book, however, if you can’t figure out what a word is, it’s most often still possible to continue with the story, making sense from the context or the pictures or both. I often have the experience myself when I’m reading of not knowing the exact meaning of a word, but I just keep on reading and am able to pick up the gist of what’s going on. I don’t think the same is true about math. If you don’t understand one step in a procedure or one aspect of a problem, you can’t just continue on and be successful. It’s as if you fall off a ladder and have to start climbing again from the bottom rung. I think that’s what it’s like for students who are struggling. They miss something that is essential to their learning success, and their progress is stopped**." [|(Burns, 2002)]  It is difficult enough to get the native English speakers to understand how to problem solve in math class, but it is even more of a challenge for the ELLs who are in a classroom that is solely being taught in English. Challenges for ELLs can include conversational fluency, discrete language skills, and academic proficiency.

Some students who may seem that they are fluent English speakers may not be fluent in English as an academic language. In order to solve [|math problems]students must also be willing to keep trying various strategies without giving up AND they must know when they know the answer or when they have not found the answer yet. Teaching the language of mathematics is two- way and reciprocal. Mathematical knowledge is gained through language and knowledge can be gained through mathematics instruction.

According to Cummins our [|(BICS)] or Basic Interpersonal Communication Skills is developed before our [|(CALP)] or Common Academic Language Proficiency.(Cummins in 1979) We develop our BICS through casual conversations with friends and family, but if we are not exposed to the academic language our CALP will suffer. Our [|CALP] needs to be developed through meaningful activities in the academic setting in order for students to best understand problem solving activities. [|Rothenberg]and [|Fisher] said that we should consider the following four principles when developing our mathematics instruction for ELLs:

1. Comprehensible input 2. Contextualized instruction 3. A low anxiety learning environment 4. Meaningful engagement in learning activities

Comprehensible input in the math classroom means that students have to understand what they are hearing and what they are reading. The teacher can do the following things to assist in their students understanding:
 * intentionally speak at a slower rate
 * repeat ideas
 * pause to check for understanding
 * use gestures, real __life__ objects, graphic organizers, or other visual media

"This does not mean that teachers should simplify the mathematical goals for ELLS, only that they should monitor how well the students comprehend the information being presented." (Murrey, 2008). Contextualized Instruction means that the language of math that they learn should be done in a meaningful way that can be built on. Some teachers do this by defining vocabulary before the lesson, however it can be even more powerful to teach the definitions after the students are given the lesson and an anchor to connect the definition with. (Garrison and Mora 2003).

Students should be given tasks with multiple entry points by using cooperative groups and peer work that will to help lesson the anxiety of a whole class activity.The activity should be meaningful and engage the student through all 5 senses. The student should be given repeated opportunities to listen, speak, read, and write about mathematics.Teachers should allow for real world opportunities and make the learning interesting. Lesson planning should involve important steps for each individual student based on their particular needs. The teacher should engage and support the student before, during, and after problem solving.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">**References:**

<span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">Burns, M. (2002) //Marilyn Burns Talks About Today's Classroom// Retrieved February 25, 2012 from [|www.mathsolutions.com/documents/2005_MB_Talks_Classroom_ENC.pdf]

<span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">Murrey, D. (2008). Differentiating Instruction in Mathematics for the ELL Learner. //Mathematics Teaching in the Middle School, 14,(3),146-153// <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;"> <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">[|www.everythingesl.net]
 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">For more information on problem solving check out these websites: **

<span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">[|www.purplemath.com/modules/translat.htm]

<span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">[|www.ncte.org]