Recommendations for Math Instruction for

English LearnersRuslana Westerlund

Adapted from Judit Moschkovich, 2012, Understanding Language, Stanford University

About the Author

Judit Moschkovich is Professor of Mathematics Education in the Education Department at the University of California, Santa Cruz. Her research uses socio-cultural approaches to examine mathematical thinking and learning in three areas: algebraic thinking (in particular student understanding of linear functions); mathematical discourse practices; and mathematics learners who are bilingual, learning English, and/or Latino/a. She has conducted classroom research in secondary mathematics classrooms with a large number of Latino/a students, analyzed mathematical discussions, and examined the relationship between language(s) and learning mathematics. 

No quick fixes, but principles to consider

Focus on students’ mathematical reasoning, not accuracy in using language. Teachers should not be alarmed when they hear

imperfect language. Instead, teachers should first focus on promoting meaning, no matter the type of language students use.

Eventually, after students have had ample time to engage in mathematical practices both orally and in writing, instruction can move students toward accuracy (p. 5).

Recommendation #1

Shift to a focus on mathematical discourse practices, move away from simplified views of language. The focus of classroom activity should be on student

participation in mathematical discourse practices (explaining, conjecturing, justifying, etc.)

Instruction should move away from simplified views of language as words, phrases, vocabulary, or a list of definitions, which limits the linguistic resources teachers and students can use in the classroom to learn mathematics with understanding (p. 5).

Recommendation #2

Instruction should move away from the interpreting precision to mean using the precise word, and instead focus on how precision works in mathematical practices (p. 6). E.g. x+3 is an “expression” , x+3=10 is an

“equation”. However, attending to precision is not so much about using the perfect word; but what’s more important is to speak about precise situations.

Recommendation #2, cont.

Precise claims can be made in imperfect language and attending to precision at the individual word meaning level will get in the way of students’ expressing their emerging mathematical ideas.

True or False?

Recognize and support students to engage with the complexity of language in math classrooms (p. 6).

Recommendation #3

Language in Mathematical Classrooms Multiple modes Oral, written, receptive, expressive

Multiple representations Including objects, pictures, words, symbols, tables, graphs

Different types of written texts

Textbooks, word problems, student explanations, teacher explanations

Different types of talk Exploratory, expository

Different audiences Presentations to the teacher, to peers, by the teacher, by peers

Instruction should:a) Recognize the multimodal and multi-semiotic

nature of mathematical communication;b) Move from viewing language as autonomous

and instead recognize language as a complex meaning-making system, and

c) Embrace the nature of mathematical activity as multimodal and multi-semiotic (p. 7).

Recommendation #3, cont’d

Treat everyday language and experiences as resources, not as obstacles. Everyday language and experiences are not obstacles

to developing academic ways of communicating in math.

Instruction needs to a) Shift from monolithic views of mathematical discourse

and dichotomized views of discourse practices and b) Consider everyday and scientific discourses as

interdependent, dialectical, and related rather than mutually exclusive (p. 7)

Recommendation #4

Mathematical language may not be as precise as mathematicians or mathematics instructors imagine it to be.

Definitions are static and absolute facts to be accepted.

True or False?

Uncover the mathematics in what students say and do (p. 8). Teachers need support in developing the following

competencies (Schleppegrell, 2010): a) Using talk to build on students’ everyday language

and at the same time develop their academic mathematical language;

b) Providing interaction, scaffolding, and other supports;

c) Deciding when imprecise or ambiguous language might be okay and when not.

Recommendation #5

There is tensions around language and mathematical content and teachers are not prepared to deal with when to move from everyday to more mathematical ways of communicating, and when and how to develop “mathematical precision.”

True or False?

Classroom assessments based on mathematical discussions need to evaluate content knowledge as distinct from fluency of expression in English.

Assessments

Moschkovich, J. (2012) Mathematics, the Common Core, and language: Recommendations for mathematics instruction for ELs aligned with the Common Core. University of California, Santa Cruz

A complete list of references is available at http://ell.stanford.edu/sites/default/files/pdf/academic-papers/02-JMoschkovich%20Math%20FINAL.pdf

References: