**Principles for Mathematics Instruction for English Language Learners**

from Stanford University, California

**Principle 1. Focus on students’ mathematical reasoning not accuracy in using language.**

- Instruction should focus on uncovering, hearing and supporting student's mathematical reasoning, not accuracy in using language. (Moschkovich, 2010).
- Recognize students’ emerging mathematical reasoning.
- Focus on the mathematical meanings learners construct, the mistakes they make or the obstacles they face (Moschkovich,&2007b).

**Principle 2. Focus on mathematical practices, not language as single words or definitions.**

- Instruction should move away from simplified views of language and interpreting “language” as vocabulary, single words, grammar, or a list of definitions (Moschkovich, 2007a, 2010).
- An overemphasis on correct vocabulary and formal language limits the linguistic resources teachers and students can use to learn mathematics with understanding.
- Instruction should provide opportunities for students to actively use mathematical language to communicate about mathematical situations.
- Instruction should provide opportunities for students to actively engage in mathematical practices such as reasoning, constructing arguments, looking for and expressing structure regularity, etc.

**Principle 3. Recognize the complexity of language in mathematic classrooms and support students in engaging in this complexity.**

Language in mathematics classrooms includes multiple:

Language in mathematics classrooms includes multiple:

- Representations (objects, pictures, words, symbols, tables, graphs).
- Modes (oral, written, receptive, expressive).
- Kinds of written texts (textbooks, word problems, student explanations, teacher explanations).
- Kinds of talk (exploratory and expository).
- Audiences (presentations to teacher, to peers, by teacher, by peers).

**Principle 4. Treat everyday and home languages as resources, not obstacles.**

- Everyday language and academic language are interdependent and related—not mutually exclusive (Moschkovich, 2010).
- Everyday language and experiences are necessarily obstacles to developing academic ways of communicating in mathematics (Moschkovich 200tia, 200tib).
- Home languages provide resources for mathematical reasoning and communication (Moschkovich 200tib, 200tic, 2009, 2011).