Transcript Document

START!
Known to New
College/Career Anchors and
Math Performance
Agenda
1.
2.
3.
4.
5.
6.
What are College/Career Anchors?
What are Math Performance
Standards?
Why are they Important?
Leading Change = Making Priorities
Broadest Impact
Plan for Success
Reading
Inference
Evidence
Analyze
Summarize
Interpret
Integrate
Evaluate
Delineate
Math
Mathematically
proficient students
can…
Explain meaning
Conjecture
Reason abstractly
Critique Reasoning
A Shift in Perspective
The CCSS for Mathematics compel a
change in the culture of traditional
mathematics classroom.
• In the typical mathematics classroom
students are “too busy covering content” to
be engaged with mathematics.
The CCSS attempt to tell
teachers when to slow down
and emphasize student
understanding of significant
mathematical ideas.
What Needs to
Change?
http://www.ted.com/talks/dan_meyer_math_cur
riculum_makeover.html
Cognitive Targets – CCSS Requires Focus
on Rigorous Elements
NAEP 2009
PISA 2009
Locating / Recalling
Accessing and retrieving
Integrating / Interpreting
Integrating and interpreting
Critiquing / Evaluating
Reflecting and evaluating
What is Changing?
1.
2.
3.
4.
5.
Textbook?
Core Curriculum?
State Tests?
RtI / ELL
Math EOCs?
CHANGE TODAY
Common Core
State Standards
The First and Most
Fundamental Change is
Depth and Rigor
O
O
c
The Foundation
Questions for
Implementation
1. What can I affect?
2. What is most important?
3. What will be most difficult, and
therefore take the most time to
change?
But what does “higher
standards” mean?
• More topics?
– No. The U.S. curriculum is already cluttered with too
many topics
• Teaching topics in earlier grades?
– No. Analyses of the standards of high-performing
countries suggest otherwise.
– In Singapore, division of fractions is a 6th grade
expectation; in the U.S. it is typically a 4th or 5th grade
expectation.
– In Japan, probability is introduced in the 7th grade; in the
U.S., it can be found anywhere throughout grades 3-6,
depending on the state.
A Shift in Perspective
Current U.S. curricula (“mile wide, inch deep”)
coupled with high-stakes testing pressures
teachers to
– “cover” at “pace”
– turn the page regardless of student needs
However, the study of mathematics should not
be reduced to merely “a list of topics to cover”
Singapore preaches, “Teach less, learn more”
Agenda
1.
2.
3.
4.
5.
6.
What are College/Career Anchors?
What are Math Performance
Standards?
Why are they Important?
Leading Change = Making Priorities
Broadest Impact
Plan for Success
Broad Impact
The College / Career
Readiness Anchors & Math
Performance Standards have
the Broadest Impact Across
All School Personnel
Define Learning
Targets
They Define Learning Targets
Which Identify Student Skills
and Skill Types
Criteria for Learning Target Statements
• Specific and Measureable
•
– Order a group fractions and label them on a
number line
Contain a performance verb that describes what
students will do to demonstrate achievement
– Order, Label
•
State the specific context in which the student
will apply that performance
– e.g. written, oral, short answer, presentation
Learning Progression
Standard: Identify the relative position of simple positive fractions,
positive mixed numbers, and positive decimals and be
able to evaluate the
values based on their position
on a number line.
Draw a basic
number line
from 0 to 10
Compare
fractions,
Identify and
decimals and
locate
the
Indicate the
mixed numbers
approximate
approximate
by identifying
location
of
Locate tenths
location of
their relative
decimals
in
Place halves in in decimal form thirds, fourths,
position on a
hundredths
on
a
Locate simple fraction form on a number
and fifths on a
number line
number
line
whole
line
on a number
number line
numbers on a
line
number line
Classifying Targets
Knowledge
Mastery of substantive subject content where mastery
includes both knowing and understanding it.
Reasoning
The ability to use knowledge and understanding to
figure things out and solve problems.
Performance
The development of proficiency in doing something where it is
the process that is important such as playing a musical
instrument, reading aloud, speaking in a second language or
using psychomotor skills.
Products
The ability to create tangible products, such as term papers, science
fair projects, and art sculptures that meet certain standards of
quality and present concrete evidence of academic proficiency.
Knowledge Target Examples
• Identify sight words
• Identify similes and metaphors
• List defining characteristics of various literary
genres
• Count and group concrete manipulatives by
ones, tens, and hundreds to 1,000
Reasoning Target Examples
• Make a prediction based on evidence
• Distinguish between fact and opinion
• Evaluate information from a variety of
resources
• Classify and compare triangles by sides and
angles
Performance Target Examples
• Read aloud with fluency and expression
• Demonstrate the use of self-correction
strategies
• Find and justify the laws of exponents with
numeric bases using inductive reasoning
• Model, identify and describe square, prime
and composite numbers
Product Target Examples
• Produce a grammatically correct sentence
• Develop a proper paragraph form in a written
composition
• Compose a written composition using the
five-step writing process
• Create a design with more than one line of
symmetry
Types of Target = Level of Thinking
 Begin by analyzing the level of thinking
required by the standard
 Assess the degree of depth or complexity of
knowledge reflected in the content standards
and assessments
 Determine how deeply a student needs to
understand the content for a given
response/assessment
O
c
How to Start?
Learning Goals
1. What is Cognitive Demand?
2. What are the SKILLs
involved?
3. How do I teach it / change
my teaching?
4. What does it look it?
Assess?
A Shift in Perspective
•Too often, students view mathematics as a
trivial exercise because they are rarely
given the opportunity to grapple with and
come to appreciate the intrinsic complexity
of the mathematics.
•Despite our instincts and best intentions,
we need to stop “GPS-ing” our students to
death.
Source: Shannon, A. (2010). Common Core: Two Perspectives on Tasks and Assessments.
Presentation at the Urban Mathematics Leadership Network Retreat, June 2010.
The Standards for
Mathematical Practice
“The Standards for Mathematical Practice
describe varieties of expertise that
mathematics educators at all levels should
seek to develop in their students. These
practices rest on important processes and
proficiencies with longstanding importance in
mathematics education.” (CCSS, 2010)
The Standards for
Mathematical Practice
Source: Briars, D. & Mitchell, S. (2010). Getting Started with the Common Core State Standards.
A National Council of Supervisors of Mathematics webinar. November 2010.
The Standards for
Mathematical Practice
Conceptual
Understanding
Strategic
Competence
Adaptive
Reasoning
Productive
Disposition
Procedural
Fluency
Source: Briars, D. & Mitchell, S. (2010). Getting Started with the Common Core State Standards.
A National Council of Supervisors of Mathematics webinar. November 2010.
The Standards for
Mathematical Practice
“Encouraging these practices in students of all ages should be as
much a goal of the mathematics curriculum as the learning of
specific content” (CCSS, 2010).
1.Make sense of problems and persevere in solving them.
2.Reason abstractly and quantitatively.
3.Construct viable arguments and critique the reasoning of others.
4.Model with mathematics.
5.Use appropriate tools strategically.
6.Attend to precision.
7.Look for and make use of structure.
8.Look for and express regularity in repeated reasoning.
The Standards for
Mathematical Practice
The description of each Mathematical
Practice begins with the same first three
words:
Mathematically proficient students …
Source: Briars, D. & Mitchell, S. (2010). Getting Started with the Common Core State Standards.
A National Council of Supervisors of Mathematics webinar. November 2010.
The Standards for
Mathematical Practice
The Mathematical Practices “describe the
thinking processes, habits of mind and
dispositions that students need to develop a
deep, flexible, and enduring understanding of
mathematics; in this sense they are also a
means to an end.”
Source: Briars, D. & Mitchell, S. (2010). Getting Started with the Common Core State Standards.
A National Council of Supervisors of Mathematics webinar. November 2010.
The Standards for
Mathematical Practice
MP #1: Make sense of problems and
persevere in solving them.
•Mathematically proficient students …
•analyze givens, constraints, relationships
•and goals … they monitor and evaluate
•their progress and change course if
•necessary … and continually ask
•themselves, “Does this make sense?”
Source: Briars, D. & Mitchell, S. (2010). Getting Started with the Common Core State Standards.
A National Council of Supervisors of Mathematics webinar. November 2010.
Points of Intersection:
Content and Practices
MP #3: Construct viable arguments and
critique the reasoning of others
Consider the following subtraction algorithm:
• How could I demonstrate the idea that the
algorithm always works?
400 – 139  399 – 138
43 – 17  46 – 20
Points of Intersection:
Content and Practices
MP #7: Look for and make use of structure
Partitioning
• 8x7
• 33 + 58
Points of Intersection:
Content and Practices
MP #7: Look for and make use of structure
Example:
Understanding and interpreting the equation
of a line expressed in “Point-Slope Form”
•
y – y1 = m(x – x1)
Target : Embed
O
c
First Things First
If I cannot teach in a manner
which engages at the higher
levels of cognitive demand,
content standards do not
matter.
First Things First
The Change in Depth is
Primary
Essential
Foundational
Immediate
To Dos
1.
2.
3.
4.
5.
Training = Awareness
Direct Instruction
Daily Planning
Curriculum Tagging
Resource ID & Sharing
Lesson Modification
c
Resources
standardstoolkit.k12.hi.us
Chairman
@CurriculumInstitute.Org
O
c