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f901afff-0eb1-4a58-b465-781a01ef4bee.html
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<p>Language development can be built into teachers’ instructional practice and students’ classroom experience by intentionally designing materials, teacher commitments, administrative support and professional development.</p>
<p>Our theory of action is grounded in four key concepts:</p>
<ul>
<li> Interdependence of language learning and content learning, </li>
<li> Scaffolding routines that foster students’ independent participation, </li>
<li> Instructional responsiveness in the teaching process, and </li>
<li> The central role of student agency in the learning process. </li>
</ul>
<p> </p>
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<p>Mathematical understanding and language competence develop interdependently. Deep conceptual learning is gained through language. Ideas take shape through words, texts, illustrations, conversations, debates, examples, etc. Teachers, peers, and texts serve as language resources for learning. Instructional attention to academic language development, historically limited to vocabulary instruction, has now shifted to also include instruction around the demands of argumentation, explanation, generalization, analyzing the purpose and structure of the text, and other mathematical discourse.</p>
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<p>Scaffolding provides temporary supports that foster student autonomy. Language learners can engage deeply with mathematical ideas under instructional conditions. Mathematical language development occurs when students use language to make meaning and engage with challenging problems beyond their ability to solve independently, requiring interaction with peers. These interactions should be scaffolded, so students can</p>
<ul>
<li> Make sense of what is being asked of them </li>
<li> Help organize their own thinking </li>
<li> Give and receive feedback </li>
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<p>Instruction supports learning when teachers respond to students’ verbal and written work. Eliciting student thinking through language allows teachers and students to respond formatively to the language students generate. Formative peer and teacher feedback creates opportunities for revision and refinement of content understanding and language.</p>
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<p>Students are agents in their own mathematical and linguistic sense-making. Mathematical language proficiency is developed through the process of actively exploring and learning mathematics. Language is action. In the very “doing” of math, students have naturally occurring opportunities to need, learn, and notice mathematical ways of making sense and talking about ideas and the world. These experiences support learners to expand their existing language toolkits. </p>
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<h4>Design Framework</h4>
<p>The framework for supporting English learners (ELs) in this curriculum includes four design principles for promoting mathematical language use and development in curriculum and instruction.</p>
<p>These four principles are guides for curriculum development, planning and execution of instruction, and the structure and organization of interactive opportunities for students. They also serve as guides for observation, analysis, and reflection on student language and learning. The design principles motivate the use of mathematical language routines.</p>
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<button class="os-raise-accordion-header"> <!-- Header goes here --> Principle 1: SUPPORT SENSE-MAKING</button>
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<p>Strengthen opportunities and structures for students to scaffold tasks and amplify language to make their own meaning.</p>
<p>Students need multiple opportunities to talk about their mathematical thinking, negotiate meaning with others, and collaboratively solve problems with targeted guidance from the teacher.</p>
<p>Teachers can make language more accessible for students by amplifying rather than simplifying speech or text.</p>
<p>Simplifying includes avoiding the use of challenging words or phrases.</p>
<p>Amplifying means anticipating where students might need language support to understand concepts or mathematical terms, and providing multiple ways to access them.</p>
<ul>
<li> Providing visuals or manipulatives </li>
<li> Demonstrating problem-solving </li>
<li> Engaging in think-alouds </li>
<li> Creating analogies, synonyms, or context </li>
</ul>
<p>Students are supported in taking an active role in their own sense-making of mathematical relationships, processes, concepts, and terms through amplification.</p>
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<button class="os-raise-accordion-header"> <!-- Header goes here --> Principle 2: OPTIMIZE OUTPUT</button>
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<p>Strengthen opportunities and structures for students to describe their mathematical thinking to others.</p>
<p>Linguistic output is when students communicate their ideas to others in oral, written, or visual formats. All students benefit from repeated, strategically optimized, and structured opportunities to articulate mathematical ideas into linguistic expression.</p>
<p>Opportunities for students to produce output should be strategically optimized such as:</p>
<ul>
<li> Important concepts of the unit or course </li>
<li> Important disciplinary language functions </li>
<ul>
<li> making conjectures and claims </li>
<li> justifying claims with evidence </li>
<li> explaining reasoning </li>
<li> critiquing the reasoning of others </li>
<li> making generalizations </li>
<li> comparing approaches and representations </li>
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<p>When opportunities to produce output are optimized by disciplinary language functions students will get spiraled practice in robust reasoning, precise language, and visuals.</p>
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<p>Strengthen opportunities and structures for constructive mathematical conversations in pairs, groups, or whole class.</p>
<p>Conversations are back and forth interactions with multiple turns that build up ideas about math. They scaffold students developing mathematical language because conversations provide opportunities to simultaneously make meaning, communicate that meaning, and refine how content understandings are communicated.</p>
<p>Effective conversations include opportunities for students to</p>
<ul>
<li> Pose and answer questions </li>
<li> Clarify what is being asked and what is happening in a problem </li>
<li> Build common understandings </li>
<li> Share experiences relevant to the topic </li>
</ul>
<p>Meaningful conversations depend on the teacher using lessons and activities as opportunities to build a classroom culture that motivates and values efforts to communicate.</p>
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<button class="os-raise-accordion-header"> <!-- Header goes here --> Principle 4: MAXIMIZE META-AWARENESS</button>
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<p>Strengthen the meta-connections and distinctions between mathematical ideas, reasoning, and language.</p>
<p>Language is a tool that not only allows students to communicate their math understanding to others, but also to organize their own experiences, ideas, and learning for themselves. Meta-awareness is consciously thinking about one's own thought processes or language use. Meta-awareness develops when students and teachers engage in classroom activities or discussions that bring explicit attention to what students need to do to improve communication and reasoning about mathematical concepts.</p>
<p>Meta-awareness in students can be strengthened when teachers ask students to explain to each other the strategies they used to solve a challenging problem. They might be asked:</p>
<ul>
<li> How does yesterday’s method connect with the method we are learning today? </li>
<li> What ideas are still confusing to you? </li>
</ul>
<p>These questions are metacognitive because they help students to reflect on their own and others’ learning.</p>
<p>Students can also reflect on their expanding use of language by comparing with peers the language used to clarify a mathematical concept. Students learning English benefit from being aware of how language choices are related to the purpose of the task and the intended audience, especially if oral or written work is required. Both metacognitive and metalinguistic awareness are powerful tools to help students self-regulate their academic learning and language acquisition.</p>
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