Transcript Common Core High School Mathematics: Transforming Instructional Practice for a New Era 1.1

Common Core High School Mathematics:
Transforming Instructional Practice for a New Era
1.1
Agenda
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Introductions and administrative details
MKT Assessment
CCSSM background
On the rebound
Reading MP1 and MP2
Break
Selling Shoes
Reading A-CED.1-4 and A-SSE.1
Homework and closing remarks
1.2
Welcome
• Where do you teach?
• What do you teach?
• How long have you been teaching?
• What is your experience/background with the
CCSSM?
• What do you hope to learn about the CCSSM
from this project?
1.3
Professional Norms for Our Work
Start on Time  End on Time
Name Tags
Silence cell phones.
No texting or Wi-Fi.
Attention signal
Raise hand!!
No sidebar
conversations . . .
Breaks
Common Core Leadership in Mathematics (CCLM),
Milwaukee Project
Food
• Snack sign up
• Lunch $$$
1.4
Restrooms
Learning Intentions & Success Criteria
Learning Intentions:
We are learning to deepen our understanding of the
Common Core State Standards and the implications for
teaching and learning mathematics.
Success Criteria:
We will be successful when we can describe how the
content standards and math practice standards are
evident in the implementation of a mathematical task.
1.5
Activity 1:
CCSSM Background
1.6
Focus: Unifying themes
and guidance on “ways of
knowing” the mathematics.
CCSSM Design Principles
Coherence: Progressions
based on mathematics and
student learning.
Understanding: Deep, genuine
understanding of mathematics and
ability to use that knowledge in
real-world situations.
Image: www.kidsgeo.com/geology
1.7
MPES Conference 2011/D. Huinker
CCSSM New Structure & New Terminology
Standards for
Mathematics Content
Standards for
Mathematical Practice
• Make sense of problems &
persevere in solving them
• Reason abstractly & quantitatively
• Construct viable arguments &
critique the reasoning of others
• Model with mathematics
• Use appropriate tools strategically
• Attend to precision
• Look for & make use of structure
• Look for & express regularity in
repeated reasoning
1.8
K–8 Standards
by Grade Level
High School Standards
by Conceptual Categories
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– Domains
– Clusters
– Standards
2. Reason abstractly and quantitatively.
3. Construct viable arguments and
critique the reasoning of others.
6. Attend to precision.
1. Make sense of problems and
persevere in solving them.
Standards for Mathematical Practice
4. Model with mathematics.
5. Use appropriate tools strategically.
7. Look for and make use of structure.
8. Look for and express regularity
in repeated reasoning.
William McCallum, The University of Arizona
1.9
Reasoning
and
Explaining
Modeling
and
Using Tools
Seeing
Structure and
Generalizing
K-8 Domains & HS Conceptual Categories
K
1
2
3
4
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HS
Counting
&
Cardinality
Algebra
Expressions and
Equations
Number & Operations in Base Ten
The Number System
Number &
Operations
Fractions
Ratios &
Proportional
Relationships
Measurement & Data
Functions
Statistics & Probability
Geometry
William McCallum, The University of Arizona
Number
and
Quantity
1.10
Modeling
Operations & Algebraic Thinking
CCSSM: Wisconsin
• Adopted CCSSM on June 2, 2010
• Governing member of the Smarter Balanced
Assessment Consortium (SBAC), with
assessments to be rolled out in the 2014-2015
school year
1.11
CCSSM: Sample Assessments
• SBAC website
http://www.smarterbalanced.org/
• Partnership for Assessment of Readiness for
College and Career (PARCC) website
http://www.parcconline.org/
• Illustrative Mathematics
http://www.illustrativemathematics.org/
1.12
Activity 2:
On the Rebound
• In small groups, conduct several trials where
you drop a ball from a known initial height, and
measure the rebound height.
• For each ball, collect at least 5 pieces of data,
with 5 different initial heights, and record your
results as ordered pairs
(Initial height, Rebound height).
• Plot your results on grid paper.
1.13
Activity 2:
On the Rebound
• For each of the balls you used, create an equation
that predicts the rebound height for any given initial
height.
• For each ball, suppose that it is dropped from an
initial height of 2 meters. How high does your
equation predict will it rebound on the first bounce?
• How could you use your equation to predict the
rebound height on the 4th bounce?
• Check your predictions for the 4th bounce by dropping
each ball.
1.14
Activity 3:
Reading MP1 and MP2
• Read the Standard for Mathematical Practice.
MP1. Make sense of problems and persevere
in solving them.
• Turn and talk: how did you see this practice
standard in the activity you have just
completed?
1.15
Activity 3:
Reading MP1 and MP2
• Read the Standard for Mathematical Practice.
MP2. Reason abstractly and quantitatively.
• Turn and talk: how did you see this practice
standard in the activity you have just
completed?
1.16
Break
1.13
Activity 4:
Selling Shoes
Imagine that you have a summer job selling
shoes, and your manager (recognizing your
mathematical ability) asks you to design a poster
that will tell a salesperson what length of
shoelace to select, for shoes with up to 15 pairs
of lace holes.
Your poster should show the relation between the length of
shoelace and the number of lace holes in words, a table, a graph,
and a rule.
1.18
Activity 4:
Selling Shoes
How did you see MP1 and MP2 in this activity?
MP1. Make sense of problems and persevere in
solving them.
MP2. Reason abstractly and quantitatively.
1.19
Activity 5:
Reading A-CED.1-4 and
A-SSE.1
• Read these content standards from the Algebra
conceptual category.
• Turn and Talk: How did you see these content
standards in the activity you have just
completed?
S-ID. Summarize, represent, and interpret
data on two categorical and quantitative
variables.
1.20
Learning Intentions & Success Criteria
Learning Intentions:
We are learning to deepen our understanding of the
Common Core State Standards and the implications for
teaching and learning mathematics.
Success Criteria:
We will be successful when we can describe how the
content standards and math practice standards are
evident in the implementation of a mathematical task.
1.21
Activity 6:
Homework & Closing
Remarks
Homework (to be included in journal):
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Day 1 Math Task: Bernardo and Sylvia play a game
Day 1 Class Reflection
1.22