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:
  • 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).