WRITING IN MATH
MATHEMATICAL
LITERACY
Warm up (use your journal)
Please justify in writing that
25 / 5 = 14
“revision is where the real mathematics happens”
•Dr. Ravi Vakil, 2012
Warm up response
WHY WRITE IN
MATH CLASS?
Research says…
reflect on their
thinking
(Albert, 2000)
connect
mathematical
content to personal
experience
(Baxter, Woodward,
& Olson, 2005)
use both
hemispheres of the
brain
(Freitag, 1997)
take time to clarify
and deepen
thinking (Fuehrer,
2009)
Writing
allows
us to …
measure.
(Russek, 1998)
It’s part of Mathematics
“it centers on proof, argumentation,
and perspective, convincing people,
making them understand it is
central to mathematics…..as a
result it’s probably the only subject
where elegance in the writing is
essential to how we see the
subject”
- Dr. Ravi Vakil, 2012
It supports the development of Academic Language
• “There is no one-to-one
correspondence between the words
and symbols they represent.”
• “Mathematics text are conceptually
packed, have high density.”
• “Require left-to-right as well as upand-down eye movement.”
• “Use numerous symbolic devices such
as charts and graphs.”
(Wright, 2008)
Knowing where the they stand within the content is important, but learning how they acquired
the knowledge is relevant to continuing comprehension
(D’Ambrosio, 1997)
It enriches teaching practice
• Identify student
misconception.
• Improve delivery of
instructions
• Deepen classroom
questioning
Quick Glance
Writing is essential in mathematics as it:
• Increases and deepens content understanding
• Helps Identify misconceptions
• Improves lesson planning and delivery of instruction
“Writing is nature’s way of letting us see how sloppy our thinking is”
(Wolfe, 2001)
WHAT
SHOULD
MATH
WRITING
LOOK LIKE?
Types of writing
Argument/Opinion: Support a choice. The writer must
use evidence to clearly argue his/her opinion.
Content: Provide descriptive information about a topic.
Process: Explain the steps or procedures of something.
(Burns 2004, Russek 1998, Schmidt 1985)
Example 1b:
Mathematics Content
Writing
Example 2b:
Mathematics Process
Writing
Exemplars
Word problems that
focus on specific math
content
To the Detail
Mike was born on February 20, 1988, at
11:05 a.m. His birthday falls on a Friday
this year, but he will be celebrating it with
a party on Saturday, February 21, 1998,
at 3:00 p.m.
On the birthday cake she made, his
mom wants to write the exact age he will
be at the start of his party. How could
she write it?
To the Detail
Student “A” response
To the Detail
Student “B” response
Make sure your Math writing includes:





Complete response with mathematical notations.
Clear, coherent explanation.
Clear and labeled diagrams when used.
Shows understanding of the question
Identifies the elements of the question.





Includes examples and/or counter examples.
Combines words with symbols.
Uses correct mathematical notation
Provide details.
Submit neat work
(AVID 2008, Lee 2010, Crannell 2008)
“elegance in the writing is essential to how we see the subject”
Dr. Vakil
Most Importantly…
Providing descriptive feedback allows students to
learn and understand their mistakes, it also
influences and molds the way a teacher conducts
instruction.
(Barry, 2008)
Some Feedback methods
Think – WriteShare:
After allowing time
to think and
individually respond
to a questions,
provide students
with a rubric and
partner them up.
Random selection
of students:
After allowing
students to write
pick a focus group
for feedback.
Random selection
of scoring:
After allowing to
students to write,
pick up work for all
students and focus
feedback on
specific element(s).
Type of feedback
TAKE A LOOK AT ARGUMENT
WRITING IN MATH
When writing to demonstrate knowledge students show what they have
learned by synthesizing information and explaining or applying
understanding of concepts and ideas.
A claim is developed and proven using logical
reasoning and examples
What does it do:
•Deepens student’s understanding of content
•Promotes critical thinking, analytical skills, and logical
reasoning
•Prepare students for post secondary experiences
•Provides evidence of what a student knows and can
apply about a specific area of content.
A claim is developed and proven using logical
reasoning and examples
How to implement:
•Teacher encourages student to “prove” by using examples.
•Teacher models more abstract proof using real world situations.
•Student’s practice “proof” from a personal point of view.
•Teacher models a variety of “proof”.
•Students practice by creating and critiquing other’s work.
Example: Use of geometric proofs, as well as algebraic proofs
can demonstrate depth of knowledge of the topic.
Please Remember that…
“Teachers incorporate writing in math class to help students
reflect on their learning, deepen their understanding of
important concepts by explaining and providing examples of
those concepts, and make important connections to real-life
applications of the math they are learning.”
(Mathwire.com, 2013)
FINAL THOUGHT
“Every year, we buy ten cases of paper at $35 each; and
every year we sell them for about $1 million each.
Writing… well… is very important to us”
Bill Browing,
President of Applied Mathematics, Inc.