Transcript WHAT IS MATHEMATICS?

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Big Ideas for Mathematical Understanding
Importance of Mathematical Discourse
Model Strategies with Five Activities
 STUDY
OF PATTERNS AND
RELATIONSHIPS
 A WAY OF THINKING
 AN ART
 A TOOL
 A UNIVERSAL LANGUAGE
Mystery Bag #1
There are 3 colors of blocks in the bag
 The area of all the blocks is the same as
the area of 18 green blocks
 The area of the red blocks is equal to1/3
the of all the blocks
 The numbers of blocks for the 3 colors
used are consecutive whole numbers
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Partners
for Mathematics
Learning
PROBLEM
SOLVING
REASONING AND PROOF
COMMUNICATION
CONNECTIONS
REPRESENTATIONS
 What
teachers say
 When they say it
 How they say it
Careful attention to teacher discourse can
shed light on student learning in mathematics.
Most importantly, it can lead to better
teaching practices at all levels of instruction.
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Look at the problems on the screen and try
to work them out in your head.
When you think of one way to solve the
problem put a thumbs against your chest.
If you can think of another way to solve the
problem put another finger up.
If you can think of a third way, put another
finger up.
Be prepared to tell us how you solved the
problem.
1/2 + 14 x 1/2 – 3 =
Order of Operations
5.7 + 1.6 + 1.4 =
Associative
16 x 11 x 1/4 =
Commutative & Associative
6 ( 5 + 1/3 ) =
Distributive
 Distinguish
between conceptual
understanding and procedural
fluency
Conceptual understanding is
understanding the BIG IDEAS:
•Equality
•Function
•Symmetry
•Proportion
 Procedural
Fluency DOES NOT mean
Speed
 Procedural
Fluency DOES mean
Accuracy
Efficiency
Flexibility
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Mathematics is instilled in individuals by
their cultures, ethnicities, religious
practices, genders, daily experiences,
crafts, and arts.
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When language is a barrier, these
aspects are even more important to a
students’ conceptual understanding.
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Therefore…
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lessons that allow for a variety of learning
styles, prior knowledge, experiences,
cultures, and all other differences;
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opportunities to learn mathematics and
language in each lesson;
and…
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experiences that will help make
connections between prior knowledge, new
concepts, and real world application.
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The NCTM Standards emphasize the
importance of developing mathematical
language and communication in order
to understand concepts rather than
merely following a sequence of
procedures.
Five Talk Moves (strategies)
1. Re-voicing (teacher repeating)
2. Asking students to restate some else’s
reasoning.
3. “Do you agree or disagree and why?”
4. “Would someone like to add on?”
5. Using wait time.
Helps uncover misconceptions
 Helps students to improve ability to think
logically - support claims with evidence
 Gives students more to observe and
listen to; and to participate in
mathematical thinking
 Increases motivation
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In small groups, read each word
problem.
 Discuss how you would solve the
problem.
 Draw a picture to show your solution.
 Match the algorithm with the correct
word problem.
 Be ready to explain your reasoning and
justify your answer.
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 Whole-class
 Small
discussion
group discussion
 Partner
talk
Teacher facilitates and actively guides students
as they discuss a problem or concept.
Provides
students with practice in mathematical
reasoning without focusing on correct answers
Students
share thinking, steps in reasoning,
connect to what they already know, and build on
each others’ thinking
Builds
confidence for students in making sense
of complex mathematical ideas
Teacher gives a task/question for students
to discuss in groups of 3 or 4
Teacher then circulates, observes and
interjects
 Can be used as an informal assessment
 Some students may feel more secure
speaking to a small group, therefore
explore more concepts
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Teacher asks a question and gives the
students a minute or two to talk about it
with a neighbor
Students who are quiet but keeping up
can practice a response
 Students who have a question can ask
the partner and get ready to ask the
class.
 ESL students get practice and develop
confidence
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If students do not have the mathematical
vocabulary and language they will not
be able to explain their mathematical
reasoning and their justification.
Vocabulary Game –
I Have…Who Has…?
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Big Ideas
Conceptual Understanding
Procedural Fluency
Student Discourse
Math Talk Moves