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Take
Action!
Separate mathematical difficulties
from language challanges.
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The following year these same teachers had their students
participate in the creation of the word walls. Students chose words
they wished to define and illustrate and then posted their work
beside the word strips. This level of involvement made the word
walls more meaningful, and students consulted them more regularly. Students may also feel further connected to word walls if
they, too, are developing their own word banks in their notebooks
or with vocabulary flip books.
Sometimes it is difficult to separate language difficulties from
mathematical ones. For example, Brenda was being interviewed
by her teacher in the late spring.
The teacher asked her, “What is one-tenth of twenty?”
Brenda replied, “Two hundred.”
The teacher asked a related question, “What is one-tenth
of ten?”
In response, Brenda replied, “One hundred.”
The teacher, knowing that he had fish crackers in his desk
drawer, asked, “If you have ten fish in your fish tank and one out
of ten of them is a goldfish, how many of them are goldfish?” As
he asked her this question, he got the bag and laid out ten fish
crackers on his desk.
Brenda took one fish cracker and responded, “One.” When
the teacher asked about one-tenth of twenty in the same manner, Brenda was able, with some assistance as she attempted to
break the twenty fish crackers into two groups of ten, to correctly identify that the answer would be two. The teacher was
not sure if Brenda needed the real-world model or the gestures
to understand what to do or if she just didn’t understand the
phrase one-tenth of.
The teacher wondered why Brenda’s first response was
to multiply by ten rather than divide by ten and decided to
emphasize the language by saying, “Yes, one-tenth of twenty is
two.”
Brenda looked up at him a bit perplexed, but then her eyes
widened and she said, “Oh, when you wanted to know one-tenth,
you meant smaller parts, not bigger. I get it now.” The teacher
knew Brenda had made an important connection.
We need to be sensitive to language issues. According to
the National Clearinghouse for English Language Acquisition
(2007) the school population has grown 3.66 percent since
1995, while the number of limited English proficient students
has increased by 57.17 percent. Before you ask students to complete mathematical tasks, make sure that they can understand
Math for All: Differentiating Instruction, Grades 6–8
Math for All: Differentiating Instruction, Grades 6–8
© 2009 Math Solutions
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the language of the task. Consider using this checklist when
preparing tasks:
How to Support Students’ Understanding of the Language of a Mathematical Task
Preview vocabulary at the beginning of a lesson, using realia whenever possible.
Encourage students to dramatize word problems.
Ask students to summarize the task in their own words.
Have vocabulary lists available when students write about their ideas.
Use accurate mathematical terms, rather than simpler everyday terms that will need
to be relearned later; for example, use rhombus rather than diamond (Lee and
Herner-Patnode 2007).
Use pictures, models, and gestures to clarify ideas whenever possible.
Have students try out their thinking in pairs or small groups before speaking in front
of the whole class.
Map symbolic notation carefully onto everyday situations and concrete models.
Speak slowly and avoid idioms and contractions.
Pose problems in familiar contexts that students will recognize.
We also need to pay attention to particular terms that may be
problematic. For example, many mathematical terms, such as face,
plot, and similar, have a different meaning in everyday usage.
(Please see the following page for examples of words found in the
middle school curriculum that have different everyday and mathematical meanings as well as examples of mathematical words that
have everyday homophones.)
Homophones—words that sound the same but have different
spellings and meanings—can be similarly problematic. Again, teachers should give special attention to these terms (humorous examples
can be helpful). One teacher tells her students about the following
conversation and asks them to figure out what happened.
Two people leave a doctor’s office when one says, “What
was your weight?”
The other replies, “Five minutes.”
“Oh,” says the first. “Mine was one hundred thirty
pounds.”
Chapter 5
Math for All: Differentiating Instruction, Grades 6–8
© 2009 Math Solutions
Breaking Down Barriers to Learning
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Words with Different Meanings in Everyday
Life Than in Math Class
acute
altitude
center
cylinder
degree
edge
expression
face
fair
factor
graduated
identity
intercept
mass
mean
median
mode
net
odd
origin
plot
point
power
range
real
ruler
reflection
rotation
set
side
similar
table
turn
volume
yard
Mathematical Words That Have Everyday Homophones
cents/scents
complement/compliment
fair/fare
eight/ate
hour/our
one/won
plane/plain
Take
Action!
Attend to confusing pairs of words.
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pi/pie
sum/some
symbol/cymbal
week/weak
weight/wait
whole/hole
Some everyday words sound similar to mathematical terms,
including sense (cents), have (half), court (quart), and spear
(sphere). And some math terms sound alike (e.g., hundreds and
hundredths, intercept and intersect). Teachers should enunciate
these words carefully, record them when they first introduce the
words, and listen deliberately to students’ pronunciation of
them.
Rubenstein (2007) reminds us to also pay attention to those
words that are often learned in pairs and thus confused. Examples
include factor and multiple, perimeter and area, permutation and
combination, and power and exponent. One strategy she suggests
is having students learn one of the words in these pairs first and
then introducing the second term and concept only after the first
one is familiar.
Math for All: Differentiating Instruction, Grades 6–8
Math for All: Differentiating Instruction, Grades 6–8
© 2009 Math Solutions