Transcript Document

ELEMENTARY ACT MEETING
MATHEMATICS DEPARTMENT
SEPTEMBER 26, 2013
MATHEMATICAL
LITERACY
Warm up
Please justify that
25 / 5 = 14
Justifying work
“revision is where the real mathematics happens”
•Dr. Ravi Vakil, 2012
Warm up response
Clear Learner Objectives
• Gain an understanding of why mathematical
writing is critical.
• Tools for incorporating mathematical writing in
class
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)
In the Texas Essential Knowledge and Skills
A(2) “…. in Kindergarten-Grade 2, students build a foundation of
basic understandings in number, operation, and quantitative
reasoning; patterns, relationships, and algebraic thinking; geometry
and spatial reasoning; measurement; and probability and statistics.
Students use numbers in ordering, labeling, and expressing
quantities and relationships to solve problems and translate
informal language into mathematical language and symbols.
Students use objects to create and identify patterns and use those
patterns to express relationships, make predictions, and solve
problems as they build an understanding of number, operation,
shape, and space. Students progress from informal to formal
language to describe two- and three-dimensional geometric figures
and likenesses in the physical world. Students begin to develop
measurement concepts as they identify and compare attributes of
objects and situations. Students collect, organize, and display data
and use information from graphs to answer questions, make
summary statements, and make informal predictions based on their
experiences ”
(K-2, Texas Education Agency, 2012)
In the Texas Essential Knowledge and Skills
• A(2) “…. in Grades 3-5, students build a foundation of basic
understandings in number, operation, and quantitative
reasoning; patterns, relationships, and algebraic thinking;
geometry and spatial reasoning; measurement; and probability
and statistics. Students use algorithms for addition, subtraction,
multiplication, and division as generalizations connected to
concrete experiences; and they concretely develop basic
concepts of fractions and decimals. Students use appropriate
language and organizational structures such as tables and
charts to represent and communicate relationships, make
predictions, and solve problems. Students select and use formal
language to describe their reasoning as they identify, compare,
and classify two- or three-dimensional geometric figures; and
they use numbers, standard units, and measurement tools to
describe and compare objects, make estimates, and solve
application problems. Students organize data, choose an
appropriate method to display the data, and interpret the data to
make decisions and predictions and solve problems.
•
(3-5, Texas Education Agency, 2012)
It’s in the College and Career Readiness
Standards
(Texas College and Career Readiness Standards, 2009)
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 matters to mathematicians
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
Opinion: Support a choice. The writer must use evidence to clearly
argue his/her opinion.
Content: Provide descriptive information about a topic.
 K-2 The student uses mathematical (oral) language to express understanding by
using words, sentence stems, and full sentences to express and label
mathematical content. (progress)
 3-5 The writer must use vivid details to paint a picture for the reader.
Process: Explain the steps or procedures of something.
 K-2 The student translates informal language to mathematical language and
symbols. By developing summary statements.
 3-5 The writer must provide a clear coherent explanation of problem solving and
procedure
(Burns 2004, Russek 1998, Schmidt 1985)
Example 1a:
Mathematics Content
Writing
Example 1b:
Mathematics Content
Writing
Example 2a:
Mathematics Process
Writing
Example 2b:
Mathematics Process
Writing
Exemplars
Word problems that
focus on specific math
content
Betty’s Blocks
Elementary School
Level Exemplar
K-2
Betty loves blocks. First she made a
tower 2 blocks high. Next to it she made
a tower 4 blocks high. Next to those she
made a tower 6 blocks high. If she
continues this pattern, how many blocks
in all will she have used after she has
completed a tower 10 blocks high?
Betty’s Blocks
Student “A” response
Betty’s Blocks
Student “B” response
To the Detail
Elementary School
Level Exemplar
3-5
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
WRITING PRACTICE
TIME
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
FEEDBACK PRACTICE
TIME
Mathematical Writing Frequency
•
•
•
•
•
•
•
•
•
Daily Writing
Weekly Writing
9 Week Project
2 – 3 sentences
At least a paragraph
About 1 -2 pages
Quick write
Exit tickets
Foldable
Open ended question
Note-taking*
Parking lot
Tweet
Quick check
Journal writing
•
•
•
•
•
Writing letters
Summaries
Comic strip
Vocabulary
Big book story
Interactive math story
World scape literature
• Research project
• Steward Murphy Math
start literature series
• Math-Cliffs
• Exemplars
* Provide students opportunities to use their notes during a test to encourage
good note taking.
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.