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 |
||||||||||||
Clarifying |
Read, “6 is to 8” as “9 is to 12.” Are these 2 equal ratios? |
||||||||||||
Visualizing |
= |
||||||||||||
= |
|||||||||||||
Comparing and |
= and = The renamed fractions are equal. Therefore, = This is a proportion. |
||||||||||||
Connecting to prior |
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.