The purpose of this series is to help teachers become better teachers of Problem Solving. The first post of the series introduced classroom procedures that challenge all students and keep them engaged.
The purpose of the second post is to make sure that students’ problem solving scores are not a reflection of their reading comprehension or their language acquisition levels.
Within any class, you have a range of reading levels. The criteria for text leveling is complicated and best explained by reading books such as those written by Fountas and Pinnell.
Assuming you don’t have time to digest 200+ academic pages in the next few days, I’ll give you my personal version of Cliff Notes. When reading a passage for Problem Solving, students usually struggle with vocabulary, text density, and sentence structure.
Compare this example of a high second grade reading passage…
From _Leveled Books for Readers_ Grades 3-6 by Gay Su Pinell and Irene C. Fountas.
…with an example of a second grade Problem Solver:
From _The Problem Solver_ Grade 2 by Creative Publications.
Notice the difference in text density. The words are a whole lot closer together and there are no pictures to help.
What about vocabulary? Do students know that a market is a store where you buy food? Do they all know that groceries are food? Is Pep Flakes a person (after all, it is capitalized like Eddie and Gina).
Notice the sentence structure: “In the time it takes Eddie to pack one bag, Gina packs 5 bags.” Even your high second grade readers may struggle with this passage.
How do you know whether or not students understand?
Most of the time, you can predict which students will have trouble with the passage. If you’re unsure, simply say to the student, “Tell me about the problem.” If the student starts reading it verbatim, it is likely that he or she isn’t comprehending.
Students should be able to make bullet points, draw a picture, or retell the problem in their own words. What if they can’t?
Below are some solutions. In both the Non-Tech and Tech ideas sections, suggestions are organized from lowest-intervention to highest-intervention.
Highlight: Ask students to take out highlighters and mark important words. Some students will automatically highlight the people, the numbers, and the “all day.” Many students will highlight the whole thing. When asked why, they will smile at you and say, “All the words are important.” If this happens, you can try colored pencils.
Colored Pencils can be used for many purposes. One of the first things to do is have students find the question mark. The sentence with the question mark should be underlined red. Use one color to connect a person to his/her action. Use another color to connect another person to his/her action. In the example above, everything connected to Gina might be green and everything connected to Eddie might be blue.
Uncover one line (or one sentence) at a time. Many students must be explicitly told that reading math problems is different than reading library books. Use a wide bookmark to cover the whole paragraph. Move the bookmark down so that only one line shows. The student draws what is in that line or explains the line to the teacher. Do the same with the second line. Then the third…
Sketch or draw out the story. Ideally, the students do the drawing. No matter what, students should be able to tell the story in their own words. Again, consider using word cards or putting important words on post-it notes or index cards.
Act out with people or puppets. One student becomes Gina. The other is Eddie. Make sure the students can tell the story in their own words. To help them, you might give the students index cards with important words. Students must use those words when they tell the story.
Students view the problem through a window of colored cellophane. Given the density of the text, your ADD and ADHD students may not be able to maintain focus in such a small area. The colored window helps them focus and read.
Rewrite the problem in a simpler way. How simply can you tell the story?
Student to student translation. If students are completely new to English Language Learning, the whole school experience is one big pantomime. They want to show teachers what they know, but frustration levels build as they struggle and struggle and struggle for a five- to seven-hour block of time. Because these students need to learn the words, put a post-it above the important words. Include a picture, the English word, and the word in their language. Let them solve the problem. The next day, erase the foreign translation and have the students match the pictures to the English words and say the words. But let them have access to the mathematics for this one hour per day.
Visuwords.com is one of my favorite pages. Let students play with it and plug in words they don’t understand.
Flip the problem. Much has been written about the Flipped Classroom. In it’s pure form, students watch lecture videos as homework and then do work in class that builds off those lectures. While I’m not a fan of flipping classrooms, flipping a lesson or two has a place in education. Make the story into a video. Let students watch it over and over as many times as they need. Make a “Part 2″ to challenge those that catch on quickly. This way, both the native English speakers and second language learners are watching videos.
Use an Interactive White Board (IWB). Make a picture of Gina and a picture of Eddie. Make trash bags and set them to infinite clone. Guilde students to tell the story.
Google Translate. Students can’t use Google translate forever. I get that. But sometimes they are so exhausted from previous hours in English that they look forward to simply dealing with numbers. Use the translate strategy as a last resort and have students keep a running list of words/phrases on post-its or an electronic format of choice. Remember, you want to see what they can do mathematically.
If you want to better understand the struggles of language learners, spend a month of your summer in a language immersion experience.
About 10 years ago, I took some Spanish classes in Madrid. Many class periods, I felt like I had rocks in my mouth and in my head. I knew what I wanted to say, but I had to struggle word by word to communicate.
One day was a particularly good Spanish day. The teacher was talking (in Spanish) about schools. I smiled and sat up proudly. Talk to me about education, I thought.
I fully understood his stories about homework and the pressures of college entrance exams. I sat up even taller and started asking semi-intelligent questions. The words just seemed to flow.
Then the conversation moved to test scores. The teachers said that his first exam score was a 10,15 and the next was a 12,8.
My thoughts began to spiral…His first score was 10,15. Those must be two scores. But he said they were one score. I missed at least the next ten minutes of conversation because I was trying to get to the root of my misunderstanding.
I raised my hand for clarification. He said the same thing, only slower. His first score was 10,15 and his second was 12,8.
I asked again. He said the same thing, this time slower and louder.
As my frustration built, my Spanish fluency deteriorated.
I re-asked the question as many ways as my broken Spanish would allow. One particular classmate looked at me like I was stupid. I felt stupid.
Later that day I passed a bank. The sign advertised car loan interest rates at 3,9%. In Spain, decimal points were commas and commas were decimal points. Duh. Just that little piece of knowledge could make or break my confidence. And, from the perspective of the teacher, I appeared to have spent at least 10 minutes daydreaming.
I often reflect on how I, a 28-year-old (at the time) with a Master’s degree, felt like the class dummy. As I walked out of the classroom, I could force positive self-talk based on the knowledge that I had successfully worked through a post-graduate degree. What about elementary- and middle-school kids? When they feel dumb, who helps provide evidence that they are smart?
This year, I noticed the sweetest of students get flustered. The frustration happened whenever we talked place value. This seemed strange – she easily caught on to every other aspect of math.
I pulled her aside and made a place value chart. I could see her working to process the numbers. She then looked up at me with pleading eyes and said, “Mrs. A., we didn’t have hundred-thousands in my other school. That is a lakh.” Duh. The Indian number system is different.
The Chinese numeration system also differs from the Western system. When asked whether they think about mathematics in Chinese or English, my bilingual Chinese-English speakers almost always claim that they prefer to think about mathematics in Chinese.
You must know the child, his/her frustration levels, and the culture from which he/she comes.
Whether you know it or not, you are a reading teacher and a language teacher. Once that becomes clear, problem-solving instruction becomes easier.
What other strategies can assist comprehension of math problem solvers?
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photo credit: 4-6 via photopin cc
Additional Reading from the National Council of Teachers of Mathematics (NCTM)
Giving Voice to English Language Learners in Mathematics
Teaching Mathematics to English Language Learners
Research Findings Involving English Language Learners and Implications for Tchg.
Problem-Solving Support for English Language Learners
Issues of Language: Teacher Insights from Mathematics Lessons in Chinese by Cynthia Anhalt; Matthew Ondrus; Virginia Horak (Mathematics in the Middle School, August 2007, Volume 13, Issue 1, Page 18).