A New Way to Look at Comprehension: 


Strong Reading Comprehension Skills = Success in Math
By Bridget A. Hadley

Reading is a social process, an interactive activity, one in which readers create meaning through interactions with the text in a particular context, their own prior knowledge, as well as other readers (Weaver, 1994; Rosenblatt, 1978; Durkin, 1993).  If you agree with this statement, then you probably believe that comprehension is not only social and interactive, but also complex and abstract.  That’s a tall order.

Couple all of this with the idea that reading doesn’t just happen in the language arts classroom.  It is a necessary skill for gaining competency in mathematical thinking as well, learning in any class is enhanced with strong reading comprehension skills.  But the problem is that content area teachers seldom receive instruction in teaching children to read.

Still, the bottom line is that it is the math teacher’s job to teach students to think mathematically and to problem solve.  In order to do that, students apply many of the same cognitive processes they use when they determine meaning in printed text.  It’s everyone’s business to teach these types of thinking skills.

Step with me inside a mathematics classroom to explore reading comprehension strategies that will help improve mathematical thinking and problem solving. Some such strategies include:

·        Clarifying

·        Comparing and contrasting

·        Connecting to prior experiences

·        Inferencing

·        Predicting

·        Questioning the text

·        Summarizing

·        Visualizing

These look familiar to language arts teachers but they also have a home in the math classroom.  Here is an example of using those strategies to think mathematically.  We’ll start with the mathematical equation (and then, at the end of the article, see a word problem, from in a contextual setting).

PROBLEM:

Here are two ratios:  and  

Are they a proportion?

STRATEGY

THINKING MATHEMATICALLY

Clarifying

Read, “6 is to 8” as “9 is to 12.”

Are these 2 equal ratios?

Visualizing

 =

               
 

 =

                       

Comparing and contrasting

 =   and   =

The renamed fractions are equal.

Therefore,  =

This is a proportion.

Connecting to prior experiences

There is a quick way to check if two ratios are equal.

It is called cross products.

  6

The cross products of 72 are the same. So, this is a proportion.

Inferencing

If the simplified fractions are equal, then there is a proportion.

Therefore,  =  is a proportion because  =

Predicting

 = 6 ÷ 8 = 0.75

 = 9  ÷ 12 = 0.75

0.75 = 0.75, so there is a proportion

Questioning the

text

I know that a proportion is two equal ratios.

How can I find out if these are 2 equal ratios?

Summarizing

Two equal ratios form a proportion.

If the cross products are not the same, the two ratios are not equal.

Then there is no proportion.

The mathematical thinking demonstrated in the above examples also applies when a student encounters a word problem like this:

Suppose you place an object that weighs 6 grams on a balance scale.  You would have to place 20 paper clips on the other side to balance the weight.  If that is the case, how many paper clips would balance the weight of a 12-gram object?

One of the greatest benefits in using these common strategies in mathematical understanding, as well as text comprehension, is that their reinforcement of each other.  Students learn that reading is more than decoding:  it is gaining an understanding, being able to visualize the information presented, and using that understanding to solve a question or problem.

When students understand that comprehending what was read is integral to problem solving, they become successful problem solvers. Those who visualize mathematics in all they do can build their own repertoire of comprehension strategies over time −including visualization or imaging.  It may even be a way to help students who are strong in mathematics improve their language arts/reading comprehension skills.

Imagine looking at your world through mathematical thinking lenses. How might you describe this image?

The time 3:00 or 3 o’clock

A right angle and 2 obtuse angles

A 360° circle with one 90° angle and 2 angles whose measures total 270°

Try this one.

The time eighteen minutes past six o’clock

The sum of 15

The number 54, which is the next number in this multiplication pattern

The number 30, which is the next number in this addition pattern

You see, teachers, parents, and students can all experience “Aha!” Mathematics moments when reading for comprehension in order to problem solve.  The same tools work whether we are teaching math class, language arts class or even social studies or science.