LINKING STANDARDS, ASSESSMENTS, AND INSTRUCTION IN MATHEMATICS Presented by Gabriela Orozco Gonzalez April 5, 2014 Stockton Common Core Seminar.
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Transcript LINKING STANDARDS, ASSESSMENTS, AND INSTRUCTION IN MATHEMATICS Presented by Gabriela Orozco Gonzalez April 5, 2014 Stockton Common Core Seminar.
LINKING STANDARDS, ASSESSMENTS,
AND INSTRUCTION
IN MATHEMATICS
Presented by
Gabriela Orozco Gonzalez
April 5, 2014
Stockton Common Core Seminar
WELCOME
Educator, I have taught K-6th Grade, currently teach 1st &
2nd Grade Combination class
Language Arts Performance Task Writer & Mathematics
Item Reviewer for the Smarter Balanced Assessment
Consortium
CTA Teacher Leadership Cohort and Professional
Learning Trainer
NEA Teacher Ambassador for SBAC Representing
California
Presentation Materials on my blog:
Commoncorecafe.blogspot.com
2
LEARNING TARGETS
Gain an awareness of the content and
structure of the Common Core State Standards
for Mathematics
Understand the meaning of the Mathematical
Practices in the CCSSM and apply the practices
to your current classroom instruction
Become familiar with a performance task and
task planner
A BALANCED ASSESSMENT SYSTEM
Common
Core State
Standards
specify
K - 12
expectations
for college
and career
readiness
Summative
assessments
Benchmarked to
college and career
readiness
Teachers and
schools have
information and
tools they need
to improve
teaching and
learning
Teacher resources for
formative
assessment
practices
to improve instruction
Interim assessments
Flexible, open, used
for actionable
feedback
All students
leave
high school
college and careerready
SIX ITEM TYPES
•
•
•
•
•
•
Selected Response
Short Constructed Response
Extended Constructed Response
Performance Tasks Focus for today
Technology-Enabled
Technology-Enhanced
THE ASSESSMENT CHALLENGE
How do we get from here . . .
Common Core
State Standards
specify K-12
expectations for
college and
career readiness
. . . to here?
All students
leave high school
college- and
career-ready
. . . and what can an
assessment system
do to help?
SMARTER BALANCED ASSESSMENTS ARE:
Standards based NOT
textbook based
Your text book is an AWESOME
resource/ reference book.
Standard
Activities that
address
Standard
Assessment
STANDARDS BASED INSTRUCTION
Standards-based education is a process for planning,
delivering, monitoring and improving academic
programs in which clearly defined academic content
standards provide the basis for content in instruction
and assessment.
Standards help ensure students learn what is
important, rather than allowing textbooks to dictate
classroom practice.
Student learning is the focus - aiming for a high and
deep level of student understanding that goes
beyond traditional textbook-based or lesson-based
instruction.
TEACHERS GUIDE INSTRUCTION
BASED ON STANDARDS
“The standards come alive when teachers
study student work, collaborate with other
teachers to improve their understanding
of subjects and students’ thinking, and
develop new approaches to teaching that
are relevant and useful for them and their
students.”
- Linda Darling-Hammond, 1997
CURRICULUM
Curriculum Mapping is a long-range plan captured in a
graphic organizer that represents a collection of Standardsbased units. It is informed by the benchmarks and curriculum
objective, student data, including an analyses of student work
and projected assessment timelines. It is a document that
should be modified based on student needs and reviewed and
revised yearly.
CCSSM PLANNING AND
IMPLEMENTATION
Planning meetings with grade level
representatives:
Examine Standards, then Prioritize
Pacing Overviews
Assessment Calendar
Unit Overviews and/or Unit Plans
Create Assessments
Revise Assessments
DESIGN AND ORGANIZATION
Standards for Mathematical Practice
Carry across all grade levels
Describe habits of mind of a mathematically expert student
Standards for Mathematical Content
K-8 standards presented by grade level
Domains:
Number and Operations
Counting and Cardinality
Operations and Algebraic Thinking
Number and Operations in Base Ten
Number and Operations—Fractions
Measurement and Data
Geometry
DESIGN AND ORGANIZATION
Content standards define what students should
understand and be able to do
Clusters are groups of related standards
Domains are larger groups that progress across grades
FOCAL POINTS & CRITICAL AREAS
Focal Points
Critical Area
PRIORITIZING THE CCSS STANDARDS
16
WEBB'S DEPTH OF KNOWLEDGE (DOK)
BLOOM'S TAXONOMY VS.
NORMAN WEBB'S DEPTH OF KNOWLEDGE
The Common Core Standards are the cornerstones of the
Smarter Balanced assessments, Webb’s Depth of Knowledge (scale
of cognitive demand) and Blooms Revised Taxonomy (levels of
intellectual ability) are the framework and the structures that will
be used to evaluate students.
Depth of knowledge, and complexity of knowledge is the heart of
the more rigorous assessments being implemented in 2014. They
share many ideas and concepts yet are different in level of
cognitive demand, level of difficulty, complexity of verbs vs. depth
of thinking required, and the scale of cognitive demand.
17
During the planning process, refer to
the DOK Levels
18
19
rd
3
Grade Big Ideas
Standard
Activities that
address Standard
Assessment
UNDERSTANDING ASSESSMENTS
FORMATIVE: checking on learning
as students progress
SUMMATIVE: checking on learning
at the end of the learning experience
“When the cook tastes the soup, that’s
formative; when the guests taste the soup, that’s
summative.”
(Stake, 2005)
CHALLENGES
TEACHER
STUDENT
Curriculum
Collaboration
Collection of
Explain/Justify
Resources
Problem
Assessments
Professional Learning
Solving
Students experience inquiry-based methods of
understanding key concepts
Use of concrete representation when introducing new
concepts
Problem-based interactive learning should be the
foundation in teaching for understanding
Teachers implement strategies that help students develop
understanding
Utilize resources and methods beyond the adopted
textbook
Opportunities to work with small group instruction,
enrichment, etc.
PERFORMANCE TASK PLANNER
PERFORMANCE TASK PLANNER
(SECOND PAGE)
COMMUNICATION, ENGAGEMENT,
AND LEARNING
Model
Numbers
(Draw a picture or diagram, or make a list,
table, chart, or graph).
(Show how worked each part of the problem).
Words
Answer
To solve this problem, first I had to
_____________________________.
Then, I________________________.
Next, I _______________________.
After that, I ___________________.
Finally, I found out that __________
______________________________.
CCSSM AND
REAL LIFE
APPLICATIO
N
Student Problem Solving Rubric
I get a…
0
1
2
If I…
do nothing -orjust copy the prompt.
write a number sentence that doesn’t go along with the prompt.
do not write an explanation.
use numbers from the prompt with an operation included.
write an explanation telling what I did.
3
use numbers from the prompt.
write number sentences that make sense, even if they are not the right answer.
write a simple paragraph explaining what I did.
4
correctly answer most of computation that I write.
write a paragraph explaining what I did. It can have minor mistakes, but it still
makes sense. Anyone should be able to understand how I solved the prompt.
5
get the correct answer.
make more than one table, diagram, chart, etc.
write a detailed paragraph telling step-by-step what I did to solve the
problem…and include what I was thinking as I solved it! (“I did this because…”)
STUDENTS NEED TO ENGAGE WITH
Grade-appropriate materials for exposure to structures,
content, vocabulary;
Instructional-level materials that allow them to
progress;
Easy materials that allow them to practice.
If familiar/interesting, material can be more
challenging.
– More at K-12 Teachers: Building Comprehension in the Common
Core
31
TIMING MATTERS
Greater scaffolding is provided at the
beginning of tasks.
Scaffolding supports an increasing level of
complexity.
Include a plan for removing the scaffolding.
32
ADVICE
Time for Planning
Ongoing Professional Development
Follow-up Coaching
Patience and Understanding
CCSSM RESOURCES
Books
Magazines
Technology Resources
DPI Wiki
http://www.ncdpi.wikispaces.net/
http://maccss.ncdpi.wikispaces.net/home
CCSSM RESOURCES
Common Core State Standards Live Binder:
http://www.livebinders.com/edit?id=133724
Resources:
21st Century Skills
Common Core State Standards & Essential Standards
Crosswalks
Unpacking Documents
Investigations & CCSSM
Websites
MATH RESOURCES
Aegom Interactive Smartboard Lessons
www.aegom.com/
Video Resources
Annenberg Media Videos & Resources
http://www.learner.org/resources/ browse. html?discipline=6
Discovery Education/United Streaming
http://streaming.discoveryeducation.com/
MATH RESOURCES
National Council of Teachers of Mathematics (NCTM)
www.nctm.org
http://illuminations.nctm.org/
Teaching Children Mathematics Magazines
COMMON CORE RESOURCES
Tools for the Common Core Standards
http://commoncoretools.wordpress.com/
Illustrative Mathematics (CCSS Tools & Resources)
http://illustrativemathematics.org/standards
Common Core Wiki (by Drew Polly)
http://elemath.pbworks.com/w/page/30621644/common-core
National Council of Teachers of Mathematics
www.nctm.org
www.nctm.org/standards/mathcommoncore/