K – 12 Common Core California Standards in Mathematics

Considerations for English Learners

Presented by:

Natalie AlbrizzioSecondary Math SpecialistVentura Unified School District

Teresa EllingsonElementary Math SpecialistVentura 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 MathematicsCounting

and Cardinality

Numbers and Operations in Base Ten

Ratios and Proportional Relationships

Number and Quantity

Fractions The Number System

Operations and Algebraic Thinking

Expressions and Equations Algebra

Functions Functions

Measurement and Data Statistics and ProbabilityStatistics

and Probability

Geometry Geometry Geometry

K 1 2 3 4 5 6 7 8 HS

Content Standard - Elementary

Grade Level - 1Domain• 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 - 5Domain • 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 - 6Domain• 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 reasoningStandard• 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 PracticeK – 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 #3Construct 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/resource/Compare-Inductive-Reasoning-and-Deductive-Reasoning.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 internetStandards and assessment information• www.corestandards.org• www.k12.wa.us/smarterMath teaching resources• www.nctm.org• www.cmc-math.orgExamples of performance assessments• http://schools.nyc.gov/Academics/CommonCoreLibrary/Wor

k/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-Inductive-

Reasoning-and-Deductive-Reasoning.html

Building mathematical language prepares students for success!!