Using Comprehension Strategies in Math

Gloria Brown Sara Newton 2-1-07

Response to the activity

Think about this problem…

Which is best for showing the exact number of votes, the circle graph or the tally chart? Explain your answer.

Why use comprehension strategies during math

instruction?“Why do we compartmentalize

thinking and learning throughout the day?....

We should apply schema theory and metacognition to the fundamentally important problem-solving processes on which mathematical understanding rests…”

Ellin Oliver Keene, 2006

Why teach comprehension strategies during math time?

“If you want students to understand mathematical ideas, they must use both language and thought. Trying to put more thinking into the math curriculum without attention to language will be fruitless…”

Arthur Hyde Comprehending Math, 2006

Galileo said… “Mathematics is a language. The laws of nature are

written in the language of mathematics. The symbols are

triangles, circles and other geometrical figures, without whose help it is

impossible to understand a single word.”

Which comprehension strategies will we use?

• Prediction• Making

connections• Questioning• Inference• Visualization• Determining

importance• Synthesis

How can we use them to problem solve?

Teach students to become ACTIVE READERS!

PredictionStudents take prior knowledge and make an

“educated guess” about what they think the answer will be…(making a hypothesis!) Sometimes they will be asked to use information from the problem. It is important that they know that predictions must be supported!

http://mathforum.org/brap/wrap/elemlesson.html

Make a Prediction!

Predict which shape has the largest perimeter…the heart or the shamrock!

Prediction Chart

Prediction Evidence

Connections

When students have a connection to the learning, they will be more apt to internalize and own the process. Activate prior knowledge before solving math problems. Facilitate connection-making for students so they will see relevance.

Connect the problem to the learner.

There was a dog at the park. Then 5 more dogs came. How many dogs

are in the park now?

(Think about your dog, Jack, at

home!)

How can we use connections to solve this

problem?Carla wants to build a fence around

her pool. Her backyard is 45 feet long and 35 feet wide. How much fence does she need?

Before they get started…

Have a quick conversation with your students before they attack the problem about fencing and yards, activating prior knowledge about perimeter…

Try This!

Build prior knowledge by downloading “Images” from Google. This picturetook about a minute to download.

Making Connections

Ask yourself, “What does this problem have to do with me or my life? How could I use this information that I have learned?”

Use a Connections Chart Problem Connection

What is 15% of $300? I have been looking at a pair of red Gucci high- heeled shoes that cost $300. Finally they go on sale for 15% off! How much could I get them for now?

Connections ChartProblem Connection

What number can be subtracted from 32 to get 15?

The score in the Aynor-Loris football game was something like that and they won by 16 points. That gives me an estimate of the answer.

QuestioningPaired Reading and QuestionsThe questioning process slows

students’ reading and thinking down. It forces students to return to the text to find ways to solve the problems.

Pairing students as questioner and responder facilitates planning for problem-solving. Sentence-by-sentence reading, questioning, then rereading and answering focuses the students. Continued practice will foster independent strategy practice and usage.

KWC, A Questioning Strategy

What do I Know for sure?

What do I Want to do, figure out, or find out?

Are there any special Conditions, rules or tricks that I have to be aware of?

K W C

Visualization

Visualizing makes abstract ideas concrete. Lots of math concepts (time, weight, distance, length, and width) are better understood when made visual. Drawing a picture OR creating a table, graph or diagram can facilitate problem solving. Making those visuals before they begin their calculations makes it easier for students to “see” their way to the answer!

Visualization“Make a movie in your mind!”

If that does not work for your students, have them draw a pictorial representation with a study buddy.

Let’s try this:You enter the front door of a museum. You walk 66 feet

from the entrance to the back of the great hall. Next you walk another 98 feet until you reach the end of the second huge gallery room. How far have you walked?

Circle the expression that describes the problem. A. 66+98 B. 98-66 C. 98X66 D. 98/66

You have to visualize this!

How many feet on two cows and three chickens?

Visualizing with Math Literature

Movies and W-R-W-R (Hibbing & Rankin-Erickson, 2003) Movies provide a wonderful opportunity for students to gain

background understanding to intermingle with their own visualization about a story or concept. When reading a text, the addition of a movie can help students connect to new

information they may have not had background in and adapt their new thoughts, images, and feelings to the text

at hand (Gambrell & Jawitz, 1993). Hibbing and Rankin-Erickson suggest using a Watch-Read-Watch-Read (W-R-W-R) method in which students will build some background of the text, make predictions, watch part of the movie, read

more of the text, confirm understandings, make more predictions, watch more of the movie, and continue reading

the text (2003).

http://www.unitedstreaming.com

Inference

Sometimes all of the information you need to solve the problem is not “right there”.

What You Know+ What you Read

______________ Inference

Let’s infer to solve this problem.

There are 3 people sitting at the lunch table. How many feet are under the table?

What I Read: There are 3 people.What I Know: Each person has 2 feet.What I Can Infer: There are 6 feet

under the table.

How can we infer to solve this problem?

In the morning, Mary and Billy each caught one fish. Mary’s fish measured 9 decimeters and Billy’s fish measured 1 meter. In the afternoon, Mary caught another fish. It was the longest fish of the day. Which number sentence shows how long Mary’s fish was that she caught in the afternoon?

A. 9+1 B. 9-1 C. x>1 meter D. 90+1

Determining Importance

Some students cannot figure out what information is most important in the problem. This must be scaffolded through

• explicit modeling by the teacher• guided practice with a study buddy• overlearning through independent

work

Solve this!

Carlos was restocking the shelves at the grocery store. He put 42 cans of peas and 52 cans of tomatoes on the shelves on the vegetable aisle. He saw some tissues at the register. He put 40 bottles of water in the beverage aisle. He noticed a bottle must had spilled earlier so he cleaned it up. How many items did he restock?

Strategy

42 cans of peas 52 cans of tomatoestissues at the register40 bottles of waterwater that he cleaned up

importantimportantnot importantimportantnot important

Synthesizing

Journaling as a closure activity gives students an opportunity to summarize and synthesize their learning of the lesson.

Encourage students to use math word wall words in the journaling. Also, post words like “as a result”, “finally”, “therefore”, and “last” that denote synthesizing for students to use in their writing. Or have them use sentence starters like ”I have learned that…”, “This gives me an idea that”, or “Now I understand that…”

Or…have them choose 2

• I notice• I think

• I like• I learned• I wonder

What strategy could this student use to solve this

problem?

Let’s take a new look at math literature!

BibliographyAIMS solve it! k and 1 (2005). AIMS Education Foundation,

Fresno, CA.Content area guide: math (2002). Great Source, Wilmington,

Massachusetts.Harcourt math problem solving and reading strategies

workbook (2004). Harcourt, Orlando. Harvey, Stephanie & Goudvis, Anne (2000). Strategies that

work, Stenhouse, Markham, Ontario.Hyde, Arthur (2006). Comprehending math, Heinemann,

Portsmouth, NH.Math to know (2004). Great Source, Wilmington,

Massachusetts. Robb, Laura (2003). Teaching reading in social studies,

science, and math, Scholastic, New York.