CALIFORNIA DEPARTMENT OF EDUCATION Tom Torlakson, State Superintendent of Public Instruction...

CALIFORNIA DEPARTMENT OF EDUCATIONTom Torlakson, State Superintendent of Public Instruction

California Mathematics Council - South55th Annual Mathematics Conference

Palm Springs, October 2014

Common Core Mathematics: Building Competent and Confident Problem Solvers

The Mathematics Framework: A Tool for Teachers of

English Learners

TOM TORLAKSONState Superintendent of Public Instruction


English LearnersPresenters:Jose Dorado

Instructional Quality Commission Member and

Elementary Mathematics Specialist

Los Angeles Unified School District

Deborah Franklin

Education Programs Consultant

Curriculum Frameworks Unit

California Department of Education

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English Learners

In this session, we will delve into the Mathematics Framework and focus on the ways in which teachers can use the Framework to help

English learners thrive.

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California Common Core State Standards for Mathematics

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The Estándares Estatales Comunes de Matemáticas are a translation of the Common Core Mathematics Standards K-8.

http://commoncore-espanol.com/california-common-core-state-standards-mathematics-spanish

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The Common Core Vision for ALL Students

“All students must have the opportunity to learn and meet the same high standards if they are to access the knowledge and skills necessary in their post-school lives. The Standards should be read as allowing for the widest possible range of students to participate fully from the outset…” (Common Core State Standards Initiative)

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California’s English Learners2013-14 Data

1,413,549 (22.6 percent) of K–12 students are classified as English learners (ELs).

Another 20 percent are reclassified as English proficient.

84 percent of ELs speak Spanish. 30 different home languages are

spoken by at least 1,000 students.

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California’s English Learners2013-14 Data

The number of languages and percent of ELs varies by county, district, and school.

12 counties have a student population that is less than 5 percent ELs.

In 4 counties, 30 to 40 percent of students are ELs.

In Imperial County, approximately 42 percent of students are ELs.

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How Can the Mathematics Framework Help Teachers?

Three chapters provide guidance to help ensure that all students participate fully from the outset:Universal AccessInstructional StrategiesSupporting High Quality Common Core Mathematics Instruction

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Universal Access

“Regular and active participation in the classroom—not only reading and listening but also discussing, explaining, writing, representing, and presenting—is critical to success in mathematics.” (excerpt from the UA chapter)

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Example of speaking and listening and explaining in the classroom:

The teacher asks students to think about different ways to solve a problem.

Students use a variety of strategies to figure out the answer.

The teacher asks the students to explain their reasoning process.

Students explain their reasoning—and justify the strategies they used.

The other students critique their classmate’s reasoning and justification.

The students take responsibility for deciding whether a strategy that is presented is correct, with guidance from the teacher.

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How do we get there?

Planning for Universal AccessAssess or be aware of the language development level of English learners.Create a safe environment and encourage students to ask questions.Draw on students’ previous experiences or cultural relevance as guides.Explain concepts and procedures using multiple representations that can be displayed through drawings, manipulatives, and/or technology.

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Planning for Universal Access

Allow students to demonstrate their understanding and skills in a variety of ways.

Emphasize academic and discipline-specific vocabulary.

Provide students with language models and structures for “speaking mathematics.”

Use sentence frames (communication guides) to support academic vocabulary and language learners.

Enlist help from other teachers, curriculum specialists, and other specialists (e.g., teachers of special education and English learners).

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ActivityPlanning for Universal Access

Look over the list of suggestions (provided in the handout). Discuss with your table partners:

What strategies or approaches have you used to support English learners? Other learners?How will the CA CCSSM change the strategies or approaches you use?

After you have discussed the suggestions, please choose someone to share your comments with the whole group.

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Universal Design for Learning (UDL)

Three Principles:Principle I: Provide Multiple Means of Representation (the “what” of learning)

Principle II: Provide Multiple Means of Action and Expression (the “how” of learning)

Principle III: Provide Multiple Means of Engagement (the “why” of learning)

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New Language Demands of the CA CCSSM

The increase language demands are made explicit in several of the standards for mathematical practice.

For example:

MP.3, “Construct viable arguments and critique the reasoning of others,” states that students will justify their conclusions, communicate them to others, and respond to the arguments of others. It also states that 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 arguments. (excerpt from UA)

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As teachers and curriculum leaders design instruction to support students’ reading, writing, speaking, and listening in mathematics, the Common Core State Standards for English Language Arts and Literacy in History/Social Studies, Science, and Technical Subjects

(CA CCSS for ELA/Literacy) and the California English Language Development (CA ELD) standards are essential resources. (excerpt from UA)

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Engaging in mathematical discourse can be challenging for students who have not had many opportunities to explain their reasoning, formulate questions, or critique the reasoning of others. Standard 1 in the Speaking and Listening strand of the CA CCSS for ELA/Literacy and

Part I of the CA ELD standards call for students to engage in collaborative discussions and set expectations for a progression in the sophistication of student discourse. (excerpt from UA)

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Standard 1 in the Speaking and Listening strand of the CA CCSS for ELA/Literacy, Grade Five:

1. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly.

a. Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. …

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Part I (Interacting in Meaningful Ways) of the CA ELD Standards, Grade Five

Critical Principles for Developing Language and Cognition in Academic Contexts:

While advancing along the continuum of English language development levels, English learners at all levels engage in intellectually challenging literacy, disciplinary, and disciplinary literacy tasks. They use language in meaningful and relevant ways appropriate to grade level, content area, topic, purpose, audience, and text type in English language arts, mathematics, science, …

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ActivityNew Language Demands of the CA

CCSSM

Read the excerpts from the standards documents (provided in the handout).

Discuss with your table partners:

How could these language expectations support mathematics instruction and learning?

After you have discussed the question, please choose someone to share your comments with the whole group.

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The newly adopted English Language Arts/English Language Development Framework is another essential resource for teachers and curriculum readers.

Look for Snapshots that connect ELA/ELD to mathematics.

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Planning Instruction for English Learners

“Every teacher must incorporate into his or her curriculum instructional support for oral and written language as it relates to mathematics standards and content. It is not possible to separate the content of mathematics from the language in which it is discussed and taught.”

(Quoted from Practical Guidelines for the Education of English Language Learners: Research-Based Recommendations for Instruction and Academic Interventions)

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The language of mathematics is not a universal language but a specialized language that requires a different interpretation than everyday language.

It is a common misconception that mathematics is limited to numbers and symbols. Mathematics instruction is often verbal or through text that is written in academic, not every day, language.

(excerpts from the UA chapter)

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Instruction should focus on: •teaching for understanding •helping students use multiple representations to comprehend mathematical concepts and explain their reasoning•supporting student’s communication about mathematics (excerpt from UA)

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Recommendations for Connecting Mathematical Content to Language1.Focus on students’ mathematical reasoning, not accuracy in using language.2.Shift to a focus on mathematical discourse practices, move away from simplified views of language.3.Recognize and support students to engage with the complexity of language in math classrooms.4.Treat everyday language and experiences as resources, not as obstacles.5.Uncover the mathematics in what students say and do. (from Judit Moschkovich, Understanding Language, Stanford University) 26


ActivityPlanning Instruction for English

LearnersAs you read the vignette, look for ways the teacher incorporated the recommendations (provided in the handout).

Discuss with your table partners: How did the teacher incorporate the five recommendations?How can you incorporate the five recommendations into your instruction?

After you have discussed the question, please choose someone to share your comments with the whole group.

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Words that mean one thing in everyday language and something different in academic English need special attention.

For example:EE: The floor is even. I looked sick and felt even worse. Even a 3 year-old child knows the answer.AE: Number: Even numbers (e.g., 2, 4, 6, etc.) Function: f (x) = f (-x)(e.g., cosine function is an even function)

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Polysemous words

These words have the same spellings and pronunciations but the meanings are different based on context.

For example:

A “table” is a structure on which one can set food and dishes but it is also something in which one can place data and information.

Homophones

Such as sum/some, whole/hole, sign/sine29



Academic language may require clarification.

For example: Name the quadrilateral figures.

Will students know that “name” in this context means to “label” the figures using the correct term that identifies each figure?

How can the teacher make clear what the task is? (And avoid answers such as Jayden, Juan, and Julia?)

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Instructional Strategies

Once again, teachers should be cognizant of potential linguistic difficulties that could be experienced by English learners and native speakers alike. (excerpt from IS)

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General Instructional Models—and whether they are explicit, interactive, or implicit

Instructional Strategies Specific to the Mathematics Classroom:Discourse in the Mathematics ClassroomStudent Engagement StrategiesTools for Mathematics InstructionExamples of Tasks and Problems Incorporating the MP StandardsReal World Problems

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Discourse in the Mathematics Classroom

Number talks are described as:

… classroom conversations around purposefully crafted computation problems that are solved mentally. … Students are given problems in either a whole-or small-group setting and are expected to mentally solve them accurately, efficiently, and flexibly. By sharing and defending their solutions and strategies, students have the opportunity to collectively reason about numbers while building connections to key conceptual ideas …

(excerpt from IS chapter)

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ActivityDiscourse in the Mathematics Classroom

Discuss with your table partners:What are the characteristics of “purposefully crafted computation problems” that could stimulate mathematical discourse?How would you design a problem and then structure the student discussion so that English learners can fully participate?

After you have discussed the questions, please choose someone to share your comments—and any problems you’ve designed— with the whole group.

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Supporting High-Quality Common Core Mathematics

Instruction

The planning and implementation of effective and efficient mathematics instruction that meets the needs of every student requires broad support. It is an obligation of everyone, including administrators, teacher leaders, college and university personnel, community members, and parents. (excerpt from SHQCCMI)

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Supporting High-Quality Common Core Mathematics

Instruction

Administrative Role and Support Mathematics Professional Learning for

Teachers Induction and Support for New Teachers Evaluation of Instruction Expanded Learning Time College, University and Professional Support Community and Parent Support

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Administrative Role and Support

One of the most important jobs of principals and administrators is to help create a system of collaboration among teachers for developing CA CCSSM instructional practices, recognizing that this process will take time and support.

District and school administrators, as well as school board members, need to understand what high-quality mathematics instruction looks like in order to effectively support programs of instruction. (excerpts from SHQCCMI)

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Mathematics Professional Learning for Teachers

The content of such programs must be aligned with the goals and standards for teaching mathematics in California.

…grounded in the following principles: sustained, content-embedded, collegial, and connected to practice, focused on student learning…

Mathematics professional learning should be attentive to meeting the needs of specific populations, including English learners. (excerpts from SHQCCMI)

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ActivitySupporting High-Quality Common

Core Mathematics Instruction

ReflectionWhat resources are in place to help English learners succeed in mathematics?What additional resources do you need?What is your next step?

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Next Steps for CDE

AB 899, passed in 2013, calls for modification of the CA ELD Standards to link with the CA CCSSM and the Next Generation Science Standards (NGSS). The SSPI will convene a group of experts to make recommendations by January 1, 2015. There will be at least two public hearings on the recommendations.The SBE has until August 1, 2015, to adopt or reject the modifications.Any modifications to the CA ELD Standards must be incorporated into the mathematics and the science frameworks.

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Resources The CDE Common Core Web page at

http://www.cde.ca.gov/re/cc/ is a portal to information and resources to support implementation of the California Common Core State Standards.

Use the search feature to find documents in other languages such as:Parents' Guide to Student Success (in

Spanish)California’s Common Core Standards Parents

Handbook (in over a dozen languages)Fact sheets created by CDE (in over a dozen

languages)

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Resources

The CDE CCSS Professional Learning Modules for Educators Web page at http://www.cde.ca.gov/re/cc/ccssplm.asp Mathematics: Kindergarten Through Grade Eight

Learning Progressions Mathematics: Kindergarten Through Grade Twelve

Standards for Mathematical Practice Modules on the CA ELD Standards

The CDE English Learners Resources Web page at http://www.cde.ca.gov/sp/el/er/

Understanding Language at Stanford University at http://ell.stanford.edu/

The reference list at end of the framework42


Resources

For a list of Spanish/English mathematics cognates, such as suma/sum and estimar/estimate, check out: http://www.lbschools.net/Main_Offices/Curriculum/Areas/Mathematics/XCD/ListOfMathCognates.pdf

For an overview of the CA ELD Standards and the Proficiency Level Descriptors, go to http://www.cde.ca.gov/sp/el/er/eldstandards.asp

The PLDs provide an overview of stages of English language development that English learners are expected to progress through as they gain increasing proficiency in English as a new language.

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The Estándares Estatales Comunes de Matemáticas are a translation of the Common Core Mathematics Standards K-8.

http://commoncore-espanol.com/california-common-core-state-standards-mathematics-spanish

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Here’s How to KeepUp-to-Date on Common Core

Implementation and Smarter Balanced

Subscribe to the Common Core Listserv:

[email protected]

Subscribe to the Smarter Balanced Listserv:

[email protected]

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Questions on theMathematics Framework?

Contact these CDE staff members:

Deborah Franklin, 916-319-0442,

[email protected]

Lisa Grant, 916-319-0959, [email protected]

Kristen Cruz Allen, 916-323-4867,

[email protected]

Tom Adams, 916-319-0881, [email protected]

CALIFORNIA DEPARTMENT OF EDUCATION Tom Torlakson, State Superintendent of Public Instruction...

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