Transcript The 8 Mathematical Practices can be grouped into 4 categories

Instructional Shifts
In
Common Core
Our focus in EGUSD for 2013-2014 is
to start implementing the Standards
for Mathematical Practice
Presented by: Elk Grove Unified School District
Outcomes for Session 3:
1. Understand the instructional shifts required by
CCSS
2. Investigate the implications of the 8
mathematical practices on our classroom
instruction
3. Where/how do I start?
Think about:
• The tasks you select
• The questions you ask
Think before you do
One of the shifts in CCSS instruction is to get
students to think about what they see, what
they know and to analyze the problem before
making decisions about what they want to do.
Here’s the task
2
83
Think about:
• student misconceptions
• the questions you ask
your students
• Multiple representations
The 8 Mathematical Practices
can be grouped into 4 categories
Compare the following using <, >, or =
justify your reasoning.
3 5
3 5  3(2.?)
>
40
2 10  2(3.?)
45  40
The 8 Mathematical Practices
can be grouped into 4 categories
Integration of SMPs
• Not “Problem Solving Fridays”
• Not “enrichment” for advanced students
• Most lie in the process of arriving at an answer,
not necessarily in the answer itself
• Every lesson should seek to build student
expertise in both Content and Practice standards
• SMPs are not meant to be taught separately,
good tasks & questions will include several math
practices
Instructional shifts
Steve Leinwand:
•Author of Accessible Mathematics: Ten
Instructional Shifts That Raise Student
Achievement.
•Principal Research Analyst at the American
Institutes for Research in Washington, D.C.
• President of the National Council of
Supervisors of Mathematics.
Listen for the instructional shifts!
Steve Leinnwand video
http://www.youtube.com/
watch?v=5gWgA4yaFrY
Leinwand Instructional Shifts (Implications for how we teach)
• Move away from teaching math as a series of steps and
procedures
• Increase critical thinking opportunities for students
• Make connections between concepts both past & future
• Show multiple methods and representations
• Create depth of understanding
• Create language rich classrooms
• Check for understanding/use formative assessment
• Place a strong emphasis on the development of number
sense
Standards for Mathematical Practice in a Classroom
Traditional U.S. Problem
Compare. Use >, <, or =
7
8
<
8
7
Same Problem with SMP integration
Which fraction is closer to 1. Using a number line,
7
8
explain why this is so.
0
(Daro, Feb 2011)
8
7
1
Teacher Talk: How are these student
expectations different?
The 8 Mathematical Practices
can be grouped into 4 categories
Write a situation that could represent this math
1
problem
then show your solution.
3
4
?
How many quarter pound hamburgers can you make
with 3 pounds of ground beef?
1 pound
1
2
3
1 pound
4
5
6
7
1 pound
8
9
10 11 12
Compare
x
3
4x
Justify your reasoning!
What questions
might you ask
yourself or your
students?
Compare the following using <, >, or =.
Justify your reasoning.
Multiple representations:
Numerically
Graphically
x3  4 x
x
3
4x
Algebraically
x3  4 x  0
x  0, 2, or  2
x( x2  4)  0
x( x  2)(x  2)  0
x  0, 2, or  2
When is x3 > 4x?
x  4x
3
x  4x
-2
x  4x
3
x  4x
3
3
0
2
2  x < 0
x2
When is x3 < 4x?
x < -2
0<x2
The next level: Analyze the regions using the graph:
Where is
x  4x  0
3
x  0 or x  2 or x  2
Where is
x3  4 x > 0
x x   2,0
Where is
 2,  
x3  4 x < 0
x x   , 2
 0, 2
x3  4 x
0
Three Key Words in the CCSS
• Focus: The curriculum must include adequate
depth. Refers to grade level standards or
“Horizontal Alignment”
• Coherence: the curriculum has logical
progressions from less sophisticated topics into
more sophisticated ones. Refers to how the
standards are organized across grade levels
“Vertical Alignment”
Rigor: The curriculum must have a
balanced approach that emphasizes
procedural fluency, conceptual
understanding and
application/modeling.
Rigor is not….
• ?
• increased number of homework problems
• taking algebra in 7th grade or taking calculus in
11th grade
• Covering more material at a faster pace
This is going to be hard and I know
you may not be ready!
http://www.youtube.com/watch?v=zOzsjEmjjHs
What does this mean for teachers?
I’m sooooooo overwhelmed! Where do I start?
1. Cut yourself some slack!
What does this mean for teachers?
2. CCSS implementation is not a light switch you
can just turn on…. It’s more of a dimmer
switch that will increasingly get brighter.
What does this mean for teachers?
3. Teacher collaboration is a must!
4. What is your mind-set? Embrace this as an
opportunity to learn.
Summing it up
If you could focus on 3 areas what would they be?
Implementing Common Core for math is
about…….
• The task you select
• Questions you ask
• Connecting content to the Standards for
Mathematical Practices.