Transcript K – 12 Common Core Math Standards Considerations for

K – 12 Common Core California
Standards in Mathematics
Considerations for English Learners
Presented by:
Natalie Albrizzio
Secondary Math Specialist
Ventura Unified School District
Teresa Ellingson
Elementary Math Specialist
Ventura Unified School District
Common Core California Standards
• Adopted by the state of California August 2,
2010.
• Were built upon the best state standards; the
experiences of teachers, content experts, and
leading thinkers; and feedback from the
general public.
• Include a focused and coherent set of
standards that provide a consistent, clear
understanding of what students are expected
to learn.
K – 12 Domains in Mathematics
Counting
and
Cardinality
Numbers and Operations in Base
Ten
Number and
Quantity
The Number System
Fractions
Expressions and Equations
Operations and Algebraic
Thinking
K
Ratios and
Proportional
Relationships
Functions
Algebra
Functions
Measurement and Data
Statistics and Probability
Statistics
and
Probability
Geometry
Geometry
Geometry
1
2
3
4
5
6
7
8
HS
Content Standard - Elementary
Grade Level - 1
Domain
• Number and Operations in Base Ten (NBT)
Cluster
• Given a two-digit number, mentally find 10 more
or 10 less than the number, without having to
count; explain the reasoning used.
Standard
• Use place value understanding and properties
operations to add and subtract.
Content Standard - Elementary
Grade Level - 5
Domain
• Number and Operations in Base Ten (NBT)
Cluster
• Perform operations with multi-digit whole
numbers and with decimals to the hundredths.
Standard
• Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings
and strategies …relate the strategy to a written
method and explain the reasoning used.
Content Standard – Middle School
Grade Level - 6
Domain
• Ratios and Proportional Relationships (RP)
Cluster
• Understand ratio concepts and use ratio
reasoning to solve problems.
Standard
• Understand the concept of a ratio and use ratio
language to describe a ratio relationship
between two quantities.
Content Standard – High School
Conceptual Category – Algebra
Domain
• Reasoning with Equations and Inequalities (A-REI)
Cluster
• Understand solving equations as a process of reasoning
and explain the reasoning
Standard
• Explain each step in solving a simple equation as
following from the equality of numbers asserted at
the previous step, starting from the assumption that
the original equation has a solution. Construct a viable
argument to justify a solution method.
Standards for Mathematical Practice
K – 12
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.
Practice Standard #3
Construct viable
arguments and critique
the reasoning of others.
Mathematically proficient students…
are able to justify their conclusions,
communicate them to others, and
respond to the arguments of others.
Mathematically proficient students…
reason inductively about
data, making plausible
arguments regarding the
context from which the
data arose.
• http://www.askkids.com/reso
urce/Compare-InductiveReasoning-and-DeductiveReasoning.html
Mathematically proficient students…
make conjectures and build a logical
progression of statements to
explore the truth of their
conjectures.
3, 5, 7, 9….What comes next?
Can you explain why your conjecture is
reasonable?
Students at all grades can listen to or read the
arguments of others, decide whether they
make sense, and ask useful questions to clarify
or improve the arguments.
Elementary students can construct arguments
using concrete referents such as objects,
drawings, diagrams, and actions.
Later, students learn to determine domains to
which an argument applies.
SMARTER Balanced Assessment
Consortium (SBAC)
• Current plan is to begin assessing during the
2014-15 school year.
• End-of-year summative assessment; including
performance tasks which require application of
knowledge and skill.
• Optional interim assessments that include
performance tasks.
SBAC Content Specifications
• The goal for students who are English language
learners is to ensure that performance is not
impeded by the use of language that creates
barriers that are unrelated to the construct
being measured (mathematics in this case).
• A distinction has been made between language
that is relevant to the focal construct and
language that is irrelevant to the content.
SBAC intends to address issues concerning the
impact of unnecessary linguistic complexity of
mathematics items for ELL students.
What can we do now to prepare our
students?
• Current math curriculum
• SIOP (Sheltered Instruction Observation
Protocol)
• Focused Approach
• The internet
Current math curriculum - Elementary
Games
Current math curriculum - Secondary
• GLENCOE – “Writing Math”, “Critical Thinking”
and “Find the error”
• HOLT – “Think and Discuss”, “Write about it”
and “Reasoning”
• McDOUGAL LITTELL – “Writing” and “Error
Analysis”
• PRENTICE HALL – “Writing in Math”, “Error
Analysis” and “Reasoning”
SIOP
• Identify both content and language objectives.
• Use appropriate speech and provide a
thorough explanation of academic tasks.
• Teach strategies that facilitate the learning
process.
• Reduce teacher talk and promote student
elaboration of responses.
• Mastering something new through practice
and application provides a feeling of
accomplishment.
The internet
Standards and assessment information
• www.corestandards.org
• www.k12.wa.us/smarter
Math teaching resources
• www.nctm.org
• www.cmc-math.org
Examples of performance assessments
• http://schools.nyc.gov/Academics/CommonCoreLibrar
y/Work/default
• www.mathforum.org (POW’s $25 per year)
Watch a video about deductive reasoning, inductive
reasoning, and conjectures:
• http://www.askkids.com/resource/Compare-InductiveReasoning-and-Deductive-Reasoning.html
Building mathematical language
prepares students for success!!