MATH 4 ALL

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MATH 4 ALL
M4A
Division 3
November 21, 2008
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5 Points of View
How do you feel about being here today?
Think about your experience as a math student.
When did you feel least successful in mathematics?
How has mathematics education changed since you
were a student?
When did you feel most successful in mathematics?
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Friday, November 21, 2008

• Goal for the day
• Deepen your understanding of the revised program
  of studies
• Agenda
• Beliefs Affective Domain
• Changing Focus
• Mathematical Processes
• Nature of Mathematics
• Instructional Focus

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Background and Conceptual Framework
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Beliefs and the Affective Domain
Read the following sections from the Alberta
Program of Studies
Page 2 Beliefs about Students Mathematics
Learning
Page 3 Affective Domain
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How do we create that culture in our math
classrooms?
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With a partner create a slogan that captures the
importance of what you have just read.
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What is essentially the same between the 1996 and
2007 Program of Studies?
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Beliefs about Students Mathematical
understanding is fostered when students build on
their own experiences and prior knowledge.
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Problem Solving Learning through problem solving
should be the focus of mathematics at all grades.
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Mathematical Processes (7) The mathematical
processes are intended to permeate teaching and
learning.
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Goal for Students Prepare students to use
mathematics confidently to solve problems.
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Changing Focus
Conceptual Understanding Personal
strategies Algebraic Reasoning Number Sense
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Changing Focus
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Changing Focus
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How many sums?
1, 2, 3, 4, 5, 6, 7, 8 AND 9
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Possible Solutions

• 438 167
• 129 328
• 567 495 (49518)
• 576
• 342
• 918

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Determine the following sums.
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Using two fractions, how many different ways can
you make the following sum?
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Changing Focus
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Changing Focus
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Solve this question symbolically.Please record
your work.
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Did you solve it like this?
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How could you teach this in a more exploratory
way?
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1
2
3
4
5
6
7
8
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Changing Focus
Personal Strategies Construct meaningful
formulas and procedures
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How many chocolates?

• 5 x 6 6
• 3 x 6 6
• 4 x 6
• 3 x 5 9
• 3 squared 3 squared 2 x 3 Tylers Approach

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Which is larger or ?
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How did you solve it?
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Is the larger fraction.
1.5
2.5
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Changing Focus
Algebraic Reasoning Learning to model, relate
and generalize
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The Nature of Mathematics
Patterns Pre-Algebra to Algebra
3 2 5
3 1 ? 5
Grade 1 Concept of equality and record using
equal symbol Grade 2 Concept of not equal and
record using not equal symbol
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The Nature of Mathematics
Patterns Pre-Algebra to Algebra
3 2 n
Grades 3 and 4 Solve one-step equations using a
symbol Grade 5 Equations using letter variables
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The Nature of Mathematics
Patterns Pre-Algebra to Algebra
6 2 n 2
6 n
Grade 6 Preservation of Equality
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The Nature of Mathematics
Patterns Pre-Algebra to Algebra
8 2n 2
6 2n
3 n
Grades 7 to 9 Algebraic Manipulation
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How Many Blocks are in the Bag?
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How do you think grade 8 students answered this
question?

• 8 4 x 5

x 12
Why?
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Changing Focus
Number Sense
Number sense, which can be thought of as
intuition about numbers is the most important
foundation of numeracy.
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The Seven Math Processes
permeate teaching and learning
Communication C Connections CN
Mental Math and Estimation ME Problem
Solving PS Reasoning R
Technology T
Visualization V
filters for understanding
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Mathematical Processes
Example
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Communication C
Students must be able to communicate mathematical
ideas in a variety of ways and contexts.
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Connections CN
The learning brain is constantly searching for
connections.
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Mental Math and Estimation ME
Types of Calculations Used in Everyday Life

• 84.6 involved some form of mental math
• Only 11.1 involved a written component
• Almost 60 of all calculations required only an
  estimate rather than an exact answer

(According to 200 volunteers who recorded all
computation over a 24-hour period) What
mathematics do adults really do in everyday
life? - Northolt, M., McIntosh, M. (1999)
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Problem Solving PS
Learning through problem solving should be the
focus of mathematics at all grade levels. -
Alberta Program of Studies
Learning "for" Problem Solving
Learning "about" Problem Solving
Learning "through" Problem Solving
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Reasoning R

• Reasoning skills allow students to use a logical
  process to analyze a problem, reach a conclusion
  and justify or defend that solution.

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Technology T
Calculators Computers PPT, EXCEL LCD
Projectors Document Camera Digital Cameras United
Streaming Videoconferences Podcasts YouTube Blogs
etc.
Technology contributes to the learning of a wide
range of mathematical outcomes and enables
students to explore and create patterns, examine
relationships, test conjectures and solve
problems. - Alberta Program of Studies
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Visualization V
Visualization is fostered through the use of
concrete materials, technology and a variety of
visual representations. - Alberta Program of
Studies
Are these two shapes congruent?
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Mathematical Processes
As you work cooperatively on the next math task
think about the 7 processes and which ones you
are using as you work.
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Making Boxes

• You work for the ABC Toy Company.
• Your job is to discover all the different shaped
  boxes that could be used to ship exactly 24 cubes.

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Making Boxes
How many different boxes are there? (No empty
space allowed in a box) How do you know you have
found all the possibilities? What changed as the
shape of the box changed? What stayed the same?
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Making Boxes
How many different boxes are there? (No empty
space allowed in a box) 1 x 1 x 24 1 x 2 x 12 1
x 3 x 8 1 x 4 x 6 2 x 2 x 6 2 x 3 x 4
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Making Boxes
How do you know you have found all the
possibilities? Using the manipulatives as
proof The answer was the same
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Making Boxes
What changed as the shape of the box
changed? The surface area
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Making Boxes
What stayed the same? The volume
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The Seven Math Processes
Communication C Connections CN Mental Math
and Estimation ME Problem Solving
PS Reasoning R Technology T Visualization
V
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The Nature of Mathematics
permeate the curriculum strands
Change Constancy Number Sense Patterns Relationshi
ps Spatial Sense Uncertainty
'underlying big ideas'
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Change Constancy
How does the shape of the box change as the
surface area decreases?
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Number Sense
Rote Memory
versus
Automaticity

• committing isolated facts to memory one after
  another
• drill and practice

• relies on thinking, using relationships among the
  facts
• focusing on relationships

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Patterns
Working with patterns enables students to make
connections both within and beyond mathematics.
3, 5, 7,
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Relationships
of tables of chairs
1 4
2 8
3 12
4
5
Using mathematical relationships to solve
problems.
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Spatial Sense
Spatial sense enables students to create their
own representations of mathematical concepts.
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Uncertainty
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Number Sense
Students use and develop number sense as they
create personal procedures for adding,
subtracting, multiplying and dividing.
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In the Navy
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Instructional Focus
Read the following section from the Alberta
Program of Studies Page 15 - Instructional Focus
What implications does this instructional focus
have for teachers and students in a mathematics
classroom?
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AHA MOMENTS!