Student Letter

Dear Gerardo,

It has been such an honor to have been your math teacher for the 4^th quarter of your 6^th grade year. While you were in my class, you were respectful, attentive, and did absolutely everything I asked of you. You completed your classwork as well as your homework, which I cannot say about the majority of your classmates. In fact, you held steadier than I did amongst the blurting of comments, tossing of paper, and gang pressures of your peers. Among the 26 members of your class, my last class of the day, I tried to reward the handful of you who were there to learn by… well… sitting you in the front of the room. Yes. That is all I had to offer. Still, you were patient with me, and remained respectful, attentive, and compliant through the last day of school. One of the hardest moments of that year, for me, was having had to tell you, not for the first, but the second time that you did not “pass” the EOG. I felt so guilty about your performance, that I wrote your parents a letter, even though I knew they couldn’t read it. You were going to have to translate it for them. So I wrote, in very simply language, that they should be proud of you. Only later did I realize that I didn’t need to tell them that, by your actions I should have known that they already were.

It is only now, after 5 weeks of summer school, that I realize something you already knew: Literacy in the content area is not just important, it is an absolute necessity. You already know the enormity of the literacy obstacles you face every day while coming to and English-speaking school. You knew that without meaning, all the mathematical information and formulas I was presenting to you and your classmates had nowhere in your brain to be filed, because I didn’t link it to your existing vocabulary. I knew you, as well as so many of my other English-language learning students, struggled with decoding, and I really tried (I hope you know I tried) to help you overcome those obstacles. But the truth is: I didn’t have the tools I have now. I now know that sitting you in the front of the room is not the answer. I need to get you involved in your learning. I need to give you tools such as word banks, graphic organizers, and reading partners in order for you gain mathematical fluency. It is not only the responsibility of the ESL teacher to educate you on the English language (thank you, Mr. Ford, for stepping into my classes to help our ELLs), but the responsibility of every teacher who is in connected to your education.

You were willing to be a passive learner, but I know if I had only asked more of you, you absolutely would have taken an active role in your learning. Many of your classmates would have enjoyed that type of class, as well. I have resources, strategies, and knowledge that I am eager to implement this year. I’m sorry that I didn’t have this information when you were respectfully, attentively, and compliantly sitting in my front row. I hope your 7^th grade teacher already knows what I didn’t.

Strategy #10: Personal Word Bank

This strategy is closely tied to my Strategy #9: Word Wall, except this strategy is for the student’s personal use and tailored specifically to the words they are struggling with, which may not necessarily be new vocabulary. The words are chosen by the student and written on index cards. Beers explained how she had her students keep their cards in a pencil pouch in the front of their notebook; however, my experience has been that students have trouble keeping up with a pencil, let alone a pencil pouch. As a result, I would opt for the second option: Keeping them in the room in either a personal card file, pencil pouch, or a simple envelop in a hanging file designated for that particular student (they like having a personal area in the class, even if it is just a hanging folder). Although this strategy is designed to increase word recognition, I would incorporate either a definition, or a pictorial representation of the word on the opposite side. I’m a visual learner. I like pictures. I like colors. I will encourage students to use anything they believe will help them learn the word.

Strategy 9: Word Walls

Word walls are good for non-fluent readers because, according to Beers, if students do not recognize a word out of context, they certainly won’t recognize it in context. The word wall should be created as the unit progresses so that students can see how the new vocabulary relates to the concepts being presented. Also, if the word wall was complete before the unit started, the number of items on the wall may be overwhelming. The teacher must continue to use the word in the context of the curriculum as well as post it on the word wall. Seen but not heard will do little good in familiarizing students with new vocabulary.

I am going to try something new this year with the word wall. Instead of designating a single bulletin board to math vocabulary, I’m going to use the large, colored paper to make a portable word wall. Once the unit is completed, instead of clearing the wall and starting over, I will just move it to a different part of the classroom, using that tape that the janitors hate, and continue to make a collage of word walls for each quarter. My hope is that students will see reoccurrence with some of the terminology. I’m also considering making a different group of students responsible for each of the different word walls. I want the class to take ownership of the vocabulary, but I will see 95 students every day, so selection may be difficult, since I don’t want to exclude anyone who wants to participate. I’m hoping for feedback on that…

Tool Kit Text #10

Through my membership in the National Council of Teachers of Mathematics (NCTM) I have a subscription to Mathematics Teaching in the Middle School. NCTM describes this journal as focusing on "intuitive, exploratory investigations that use informal reasoning to help students develop a strong conceptual basis that leads to greater mathematical abstraction." I have used this publication for both doing research and lesson plan ideas. For example, the latest issue features articles such as:

"Proportional Reasoning with a Pyramid"
"Tailoring Tasks to Meet Student's Needs"
"Creating Transnational Classrooms"
"Integrate Technology with Student Success"

and my favorite, of course:

"Lesson Study on the Farm," which includes extension problems

Tool Kit Text 9: The Number Line

It sounds so simple. A number line. Of course one would expect to see a number line in a room dedicated to the instruction of mathematics. However, students must be shown how to use the number line that is so prominently and proudly displayed in every math classroom in America.

Once, I developed this interactive, hands-on, constructionist lesson plan on circumference of a circle. Different, clearly numbered, stations were set up in the room with common, round objects for the students to trace, calculate the circumference using π, and compare their calculation to an actual measurement they obtained by wrapping a string around the circular object and measuring the length of the string. I even selected objects from my home whose diameters were “nice” numbers, which meant I actually traced and measured all the objects the kids would be exposed to, plus the ones that didn’t make the cut. This was a wonderful lesson that I knew the kids would enjoy, and I couldn’t wait to see their expressions when their calculation of the circumference matched the measurement. I was a genius!

The only drawback: my students couldn’t read a ruler. So much for my moment of glory.

How does this story relate to a number line? If one looks at a number line and a ruler, side by side, there isn’t much difference. Number lines help students visualize distances, differences, and the dreaded negative numbers. Number lines also help students see relationships between rational numbers, i.e. fractions and decimals, by comparing their locations on the number line.

By the end of the year, whenever the students were faced with a “compare and order” problem, and I was reviewing the answer, I would ask the class, “What is the first thing Mrs. Burch is going to do?” They would all moan in unison, “Draw a number line.”