Transcript (of student interest) and have the students write mathematics

Warm – up
Consider The Pattern!
1
3
7
5
9 11
. . . .
Answer the following questions:
1. What are the elements in the next row?
2. Consider the sum of the elements in the 1st row, 2nd row, 3rd
row, etc. What is the sum of the elements in the tenth row?
3. Consider the sum of the first two rows, the first three rows,
the first 4 rows, etc. What is the sum of the first ten rows?
From “Mathematics Teaching in the Middle School,” January, 1999.
1
Warm – up
Consider The Pattern!
1
3
7
5
9 11
. . . .
Describe two more patterns in this triangular set of
numbers.
From “Mathematics Teaching in the Middle School,” January, 1999.
2
Writing in the Mathematics
Classroom
The student will learn
what recent research
shows about writing in
the mathematics
classroom and will see
several examples of
how to implement
writing in their
classrooms.
3
Introduction
Should we teach thinking in a mathematics
class?
Should we teach writing in a mathematics
class?
4
Motivation
The writing process can be a medium for
learning mathematics and thus should be an
integral part of every mathematics class.
5
Research Findings
• Students who write essays explaining specific
mathematical techniques do better on traditional
exams that their peers who have been taught
traditional by methods.
• As we write we see new relationships, invent new
ideas, and learn to communicate better. Using
writing in mathematics will not only make
mathematics students better writers but will make
them better mathematics students.
continued
6
Research Findings
• the classroom environment is less threatening, and
anxiety is less likely to interfere with learning.
• students are more involved in the learning
process.
• students use higher-level skills because writing
tasks require those skills.
7
NCTM Standard - Communication
Pre-kindergarten – Grade 12
Students who have the opportunities,
encouragement, and support for speaking,
writing, reading, and listening in
mathematics classes reap dual benefits:
- they communicate to learn mathematics, and
- they learn to communicate mathematically.
8
NCTM Standard - Communication
Pre-kindergarten – Grade 12
• Organize and consolidate their mathematical
thinking through communication
- Writing in mathematics can also help students
consolidate their thinking because it requires them
to reflect on their work and clarify their thoughts
about the ideas developed in the lesson. Later, they
may find it helpful to reread the record of their own
thoughts.
9
NCTM Standard - Communication
Pre-kindergarten – Grade 12
• Communicate their mathematical thinking
coherently and clearly to peers, teachers, and others.
- the process of learning to write mathematically is
similar to that of learning to write in any genre.
Practice, with guidance, is important. So is
attention to the specifics of mathematical argument,
including the use and special meanings of
mathematical language and the representations and
standards of explanation and proof.
10
NCTM Standard - Communication
Grades 6 - 8
Communication should be focused on worthwhile
mathematical tasks. Teachers should identify
tasks that • relate to important mathematical ideas;
• are accessible to multiple methods of solutions;
• allow multiple representations;
• afford students opportunities to interpret, justify,
and conjecture.
continued
11
NCTM Standard - Communication
Grades 6 - 8
Teachers can use oral and written communication
in mathematics to give students opportunities to • think through problems;
• formulate explanations;
• try out new vocabulary or notation;
• experiment with forms of argumentation;
• justify conjectures;
• critique justifications;
• reflect on their own understanding an on the ideas
of others.
12
NCTM Standard - Communication
Grades 9 - 12
High school students should be • good critics and good self-critics;
• able to generate explanations, formulate questions,
and write arguments;
• able to use spreadsheets, geometric diagrams,
natural language and algebraic symbols;
• able to use mathematical symbols and language
correctly:
• good collaborators who work effectively with
others:
continued
13
NCTM Standard - Communication
Grades 9 - 12
Teachers should have an active role in developing
communication in grades 9 through 12 • help students become more precise in written
mathematics;
• have students read increasingly more technical
text;
• use problems that require explanations;
• regularly discuss and compare the adequacy of
those explanations;
14
Writing
Writing is a valuable way of reflecting on and
solidifying what one knows, and several kinds of
exercises can serve this purpose.
15
Writing Activities for Math
Journals
• Students keep records of feelings, questions, and
descriptions of algorithms or processes they have
learned.
• Students can use stickers (red for stress, yellow for
AH’s! or bright spots, and blue for good comfort
level) when they read a mathematics assignment.
These marks can be cross referenced when writing
in their journals.
16
Writing Activities for Math
Graphic Organizers
• Compare/Contrast Venn Diagrams
• Example using
• right triangles and
• equiangular triangles.
17
Writing Activities for Math
Graphic Organizers
• Use of a diamond organizer (The Reading
Teacher, Vol. 48. No. 3, November, 1994.) to solve
the following problem.
Dr. Glandon raises rabbits. He also has rabbit pens
in which to place his rabbits. If he tries to place one
rabbit in each pen he finds that he has one rabbit
left without a pen. If he tries to place two rabbits in
each pen he finds that he has one pen without any
rabbits. How many rabbits does Dr. Glandon have?
18
Writing Activities for Math
Story Problems/Test Items
• Students write story problems to be solved by
other students using the concept currently under
study.
• Students submit items for possible inclusion on a
test.
19
Writing Activities for Math
Describe Something
• One student describes a drawing to the class while
her classmates try to draw it.
Let’s try it.
20
Writing Activities for Math
Micro Themes
Students write short essays to:
• summarize a mathematical concept;
• support a position on an issue by reasoning,
empirical evidence or some other authority;
• draw conclusions from data and discover a thesis
or general statement;
• solve a puzzle related to a mathematical concept;
• teach a concept to an imaginary learner.
21
Writing Activities for Math
Magazine Photos
Bring in photographs from magazines (of student
interest) and have the students write mathematics
problems from the content in the photos.
Problems then will be given to other students to
solve.
22
Writing Activities for Math
Post Cards
• Students write a post card about the days lesson.
Try one!
23
PLACE
STAMP
Dear Pythag,
HERE
Used your theorem today.
Really cool! Looking
forward to more tricks and
Pythagoras of Thebes
shortcuts.
22 Agora Way
QED Jim
Old Athens 5-12-13
24
Writing Activities for Math
Point of View
• Students take on the identity of a mathematical
symbol, geometric figure, etc. and write a
description of some of their experiences or pet
peeves.
25
Writing Activities for Math
Dear Euclid
• Students write answers to questions about
mathematics submitted by their classmates.
Dear Euclid, I’m a square dating a triangle. Is it
possible for me to circumscribe her? I need to know
immediately as our parents are concerned.
Polygons in waiting.
26
Writing Activities for Math
Ads/Slogans
• Students write radio or tv ads about the
mathematics topic under discussion.
• Students write a dictionary entry for a
mathematical term or process.
• Students write a mathematical slogan for a
bumper sticker.
27
Writing Prompts
• Explain in your own words the meaning of _____.
• Reflect on your participation in class today and
then complete the following statement (teacher or
student selects one).
• I learned that I (or we) . . .
• I was surprised that I . . .
• I discovered that I . . .
• I was pleased that I . . .
continued
28
Writing Prompts 2
• Explain what is most important to understand
about _____ .
• The most important thing I learned in math this
week (or today) is _______ .
• Write a letter to a classmate who could not attend
class today so that she will understand what we did
and learn as much as you did.
• What I liked most (or least) about math class
today was _______ .
29
Evaluation of Writing
Not all writing needs to be evaluated. Perhaps most
of it need not. Almost all of it should be viewed by
the teacher and often comments included.
Remember the purpose of writing in the
mathematics classroom is to improve learning.
When writing is to be evaluated consider a rubric.
A sample will be distributed for discussion.
30
Summary on Writing
• Students who write essays explaining specific
mathematical techniques do better on traditional
exams that their peers who have been taught
traditional by methods.
• As we write we see new relationships, invent new
ideas, and learn to communicate better. Using
writing in mathematics will not only make
mathematics students better writers but will make
them better mathematics students.
31
Handouts
If not previously done pass
out the handouts on:
• 500 Writing Formats, and
• Expository Writing.
32
Assignment
Prepare questions for
Wednesday – “Student
Teacher” day.
Study for the final.
33