Reading and the Mathematics OGT

The answers to the question of how to succeed on the mathematics OGT are not simple ones. Indeed some very wise people have grappled with the issue without coming up with always successful suggestions. But we do know that success on the mathematics OGT requires that students carefully read and understand the problems. Unfortunately this will be a new focus for some of the students. Mathematics teachers need to think carefully about how they can help their students understand the problems on the test. Historically students have had difficulty with word problems. Word problems require reading--and understanding.

A background story. When my only child was in first grade, I became worried about her reading. I am ashamed to admit that I was worried because I had a colleague who had a daughter, also in first grade, who was an avid reader. My child was not an avid reader. My colleague often had tales of having to make her child stop reading and come to dinner or of finding her in her room after bedtime with a flashlight under the covers reading a book. My child did not defy me in order to read--and I was worried. At the first parent-teacher conference I expressed concern to the teacher. She looked puzzled and said my child was doing fine--better than fine actually--and I did not need to worry. But I didn't believe her. I worried all year; I kept checking with the teacher, and she kept telling me things were going well--but my child was not captured by reading and I knew it.

A few months into her second-grade year, I came home from work and she did not meet me at the door--which was unusual. When I located her, she was in her room on her bed--with a book! I asked her what she was reading, and she looked up and said, "Oh Mom--it's wonderful. It's like a movie." Of course, my worries (about reading) were over. My child was creating mental images as she read. She was understanding what she read.

Those two things--creating mental images and understanding--are crucial to being able to do word, or "story," problems. Most students (and many teachers) will tell you that they don't like that type of problem and just want to work with numbers in mathematics; words, they think, don't belong. Unfortunately, some commonly used teaching techniques actually exacerbate the problem. There is something called the "key word method" wherein students are taught such gems as the word of means "multiply." Well, of means "multiply" if the question says "What is 2/3 of 30?" But if the problem says "What part of 30 is 20--it doesn't mean "multiply."

In attempting to help students, teachers have students circle the "key words" and numbers. I have actually heard teachers say: "That way you don't have to read the whole problem." This of course does not help students form mental images, much less understand the problem.

There is no algorithmic way to be sure that students "can do" word problems. Rather students need to read, form mental images, and understand the problems. When I was in the classroom, I often asked students to "understand what the problem is asking." As one step in that understanding, I always asked students to read the problem through one time with their pencils down. Then I asked them to read it again and take notes--if possible, draw a picture of the scenario presented in the problem. I asked them to think about what the problem was asking.

Did this strategy work? Not always and almost never immediately. But over time students came to understand that there was meaning in the problem. They came to understand that their job was not to pick out the number and guess what operation to do.

This strategy is useful on OGT items for several reasons. One is that often mathematics items follow a format that is different from that of reading items. Consider the two problems below.

A state game warden has been observing deer during a particularly severe winter. She recorded that 14 of the 96 deer she observed throughout the state appeared to be suffering from malnutrition. The state has an estimated deer population of 600,000.
Based on her observations, approximately how many deer would she predict are suffering from malnutrition?
1. 14,000
2. 72,000
3. 88,000
4. 96,000
ODE commentary can be found at item 11, March 2005 OGT
Alanis is moving and needs to pack two mirrors. The larger mirror fits in a box that is 18 inches wide by 20 inches long. Her smaller mirror is similar in proportion to the larger mirror. Alanis determines that the width of the smaller box needs to be a minimum of 9 inches.
What should be the minimum length of the box to hold the smaller mirror?
1. 2 inches
2. 6 inches
3. 9 inches
4. 10 inches
ODE commentary can be found at item 28, Spring 2004 OGT

Both examples begin with a context or "story" (albeit one could argue not a very interesting one). Then the question is asked. This is a very typical order in mathematics problems: story followed by question. And it almost guarantees that a test item must be read multiple times. The implication is that rereading is a strategy that all students should be able to use. Since reading in mathematics class--even reading problems--seems an anathema to students, it is critical that mathematics teachers stress reading for understanding and not try to find ways to help students solve problems without reading.

While the test items above measure benchmarks from different standards, successful completion of both problems relies on proportional reasoning, and there were remarkably similar student results for the two problems. Sixty-eight percent got the first one right, and sixty-seven percent got the second one right. Those results are noteworthy for a couple of reasons. First, the arithmetic in problem 1 is significantly more difficult than in problem 2, and, second, the kind of visualization is different. While many, perhaps most, students would have difficulty visualizing 96,000 deer (let alone 600,000), they can visualize "a bunch" of deer. The visualization of the packing box is different. It requires a kind of spatial thinking where the student visualizes a three-dimensional object.

Without more information, it is impossible to know exactly why nearly one-third of the students missed each of these questions, but it is clear that reading and understanding the question is an important prerequisite for being successful on the OGT. Can you do mathematics without reading? No! You may be able to do arithmetic without reading, but you will never be able to do mathematics.

The ORC offers a variety of National Assessment of Educational Progress (NAEP) assessments around proportion that should help teachers determine if their students grasp the concepts involved in proportionality--or if they have difficulty understanding word problems.

NAEP Assessment Item, Grade 8: How Many Defective Batteries in a Sample of Batteries

ORC# 1824

Resource Information

Resource URL: http://nces.ed.gov/nationsreportcard/itmrls/portal.asp?questionl...

Resource Type: Assessment Resource

Discipline: Mathematics

Ohio Standards Alignment: Grades 6–12

Professional Commentary: This item asks students to predict the number of defective items in an entire shipment if the number of defective items in a random sample is known. This multiple-choice question is a sample test item used in grades 8 and 12 in the 1992 National Assessment of Educational Progress (see About NAEP)....

Reading and the Mathematics OGT

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