Download Write for Mathematics

Adapted from “Write for Mathematics”, Rothstein, Rothstein and Lauber
Write For Mathematics
Presented by:
Cynthia Cuellar
Mathematics Teaching Specialist
December MTL Meeting
The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is
supported with funding from the National Science Foundation under Grant No. EHR-0314898
Adapted from “Write for Mathematics”, Rothstein, Rothstein and Lauber
Write for Mathematics
“We believed, and still do, that knowing the vocabulary of the subject is the first layer of fluency.
To be fluent in a subject is to know how to “talk about” it or express your ideas.”
Organization includes: putting words in context, sentences, paragraphs and essays;
understanding the typical organizational structures of genres in which mathematical thinking
appears; making writing clear and appropriate for the audience
Writing = Organization + Fluency
A writer must know the language of the subject or topic and must know the different types of
organizational schema (genre) that are appropriate for specific subject-area writing.
Why Write in Mathematics?
Teachers who ask their students to write about mathematics area able to
 gain insight into their students’ mathematical thinking,
 diagnose their students’ misconceptions,
 assess students’ study habits and attitudes, and
 evaluate their own teaching technigues
McLoughlin (1998)
Advantages of teaming mathematics with writing is pointed out by Miller (1991) and points out
that “because writing leads people to think, improved mastery of mathematics concepts and
skills is possible if students are asked to write about their understanding.”
Writing in mathematics requires students to internalize important concepts as well as analyze,
compare facts, and synthesize information (Kennedy, 1980).
Students should become proficient in expressing themselves mathematically, both orally and in
writing, gaining fluency in the language of mathematics and being able to make connections
writing mathematics and from mathematics to other discipline. NCTM (2000)
The Importance of Words in Mathematics
“Words have a story”- meaning that every word belongs to a category, conveys meaning or
definition, can have expanded meaning, and has a history.
Because of the importance of words in mathematics, the first 6 strategies in the Planning Wheel
emphasizes knowing mathematical words and using them as precisely as possible.
The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is
supported with funding from the National Science Foundation under Grant No. EHR-0314898
Adapted from “Write for Mathematics”, Rothstein, Rothstein and Lauber
Strategy 1: Building Mathematical Vocabulary with Taxonomies
Taxonomies can be used to
 assess prior knowledge,
 serve as a continuous note-taking system,
 assess new knowledge,
 build mathematical vocabulary
 develop cooperative learning experiences
Taxonomies become a student’s personal thesaurus. It serves as the “holder” of terms and
represent what one already knows or is getting to know. Taxonomies serve as a foundation of
mathematical writing lessons because they provide fluency and are valuable as retrieval
systems during writing or discussion time.
Create Taxonomies as a system for “having words.” With words kids have something to say,
what they can say is what they know or are getting to know.
Strategy 2: Composing with Keywords
“Attending to words will help students learn mathematics better,” Countryman (1992).
If one accepts this premise, then we must give students frequent and continuous opportunities
to express mathematical ideas in both symbols and words.
Composing with Key Words helps students
 reflect on the meaning of mathematical words,
 clarify their understanding of these words through the process of association, and
 incorporate the words into a statement that shows how each word relates to the other
mathematical words.
Strategy 3: Metacognition
“Thinking about thinking” or “know your knowing” Costa and Lallick (2000).
Focus questions for teachers to keep in mind: “What do we want students to understand?” and
“What can they demonstrate… that they do understand?”
Focus questions for students: How did I get my answer? Is there another way to get the
answer? Is there another right answer? (Everyday Mathematics program).
The strategy of Metacognition helps students develop their thinking, reasoning, and selfevaluation skills so that they gain higher-order knowledge.
The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is
supported with funding from the National Science Foundation under Grant No. EHR-0314898
Adapted from “Write for Mathematics”, Rothstein, Rothstein and Lauber
Taxonomy
Statistics and Probability
A good way to learn the meaning
of mathematical words is to keep
track of them and use them in
writing. One way to begin a
Taxonomy in mathematics is to
think of all the words you know
related to mathematics, in this
case Statistics and Probability and
write these words next to the letter
with which the word begins.
Start by working by yourself,
which is also called working solo
(think)
Next, collaborate (pair) with a
partner or a group. Add each
other’s words to the Taxonomy.
You will find that you “own” many
mathematical words – more than
you imagined. Owning words
means you possess knowledge;
for each word that you own, you
possess the potential for
meaning.
After you collaborate with a
partner or group, collect more
words from other groups or teams.
By doing this activity, we crosspollinate (share) and get ideas
from everyone.
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is
supported with funding from the National Science Foundation under Grant No. EHR-0314898
Adapted from “Write for Mathematics”, Rothstein, Rothstein and Lauber
Composing with Keywords
Now that you have created Taxonomies of mathematical words, you have a lot of words for
composing mathematical sentences.
Select three words from your mathematical Taxonomy on Probability.
Use all three words to compose one mathematically correct or accurate sentence.
You may change the form of the word to make your sentence work grammatically.
Example
Keywords
number, sign, even
Sentence
When we put a plus sign between two even
numbers, we can add them and get an
even number as the answer.
Adaptations
Concept
Statistics and
Probability
Concept
Statistics and
Probability
Keywords
Graph
represent
gather
Keywords
graph
axis
gather
Word Problem or Statements
After we gather data or information, we can
show or represent that data on different graphs,
such as a bar graph, line graph, or circle graph.
Sentence
I gathered information
about how much I
grew in one year and
then put this
information on a
graph that had a yaxis and an x-axis.
What My Sentence Shows or Illustrates
This is my graph that shows my growth
for one year. Some months I did not
grow at all, but then from March to April I
had a growth spurt.
Sept
Oct
Nov Dec
Jan
Feb Mar
Apr
May Jun
Jul
Aug
Your Turn
Concept
Statistics and
Probability
Keywords Sentence
What My Sentence Shows or Illustrates
The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is
supported with funding from the National Science Foundation under Grant No. EHR-0314898
Adapted from “Write for Mathematics”, Rothstein, Rothstein and Lauber
Metacognition
Metacognition means (1) knowing what you know or (2) knowing what you don’t know or (3)
knowing what you need to know. One way to express Metacognition is by using a Frame that
helps you organize your writing. Below are a variety of Frames. Each Frame has starter
phrases that must be completed and are shown in italics.
Select a term you know something about from your Statistics and Probability Taxonomy. Follow
the outline of the Frame to write what you know about that term.
Frame for term in a Zero Taxonomy
I know that I know something about zero.
First I know that zero can mean nothing or having no amount.
In addition, I know that zero is used to show place value, as in the number 101, where
zero means that there are no tens in that number.
Finally, I know that the idea of zero came from India and the Arab traders who learned
about it when they were trading in India a long time ago.
Now you know something that I know about zero.
Frame for Explanation to an algorithm
I know that I know how to add 9+6.
First I think of 9 and how much I have to go when I have 6 more.
Second, I count 10, 11, 12, 13, 14, 15. That is 6 more.
Then I write 9+6 and put the equal sign to show my answer.
Finally, I put the answer 15, after the equal sign
Frame for a response to a prompt
I know how to determine which cereal is the better value.
First, I know that an ounce equals 28.349 grams.
I also know that if I multiply 12 by 28.349, I will know how much a box of wheat flakes weighs in
grams.
Therefore, I know that a box of wheat flakes weights 349.188 grams and a box of corn flakes weighs
300 grams. If I subtract 340.188 grams from 300 grams, I find out that I get 40.188 more grams of
wheat flakes than corn flakes.
Finally, I know that you get more wheat flakes for $4.49 than you get corn flakes.
Your Turn
I know that I know…
First I know…
In addition, I know…
Finally, I know…
Now you know something that I know …
The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is
supported with funding from the National Science Foundation under Grant No. EHR-0314898