A summary of recommendations for math instruction for ELs by Judit Moschokovich as presented by Understanding Language, Stanford ELL.

1. Recommendations for Math
Instruction for English Learners
Ruslana Westerlund
Adapted from Judit Moschkovich, 2012, Understanding
Language, Stanford University

3. 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.

4. No quick fixes, but principles to
consider

5. Recommendation #1
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).

6. Recommendation #2
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).

7. Recommendation #2, cont.
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.

8. True or False?
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.

9. Recommendation #3
Recognize and support students to engage with the
complexity of language in math classrooms (p. 6).
Language in Mathematical Classrooms
Multiple modes Oral, written, receptive, expressive
Multiple representations Including objects, pictures, words, symbols,
tables, graphs
Different types of written Textbooks, word problems, student
texts explanations, teacher explanations
Different types of talk Exploratory, expository
Different audiences Presentations to the teacher, to peers, by
the teacher, by peers

10. Recommendation #3, cont’d
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).

11. Recommendation #4
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)

12. True or False?
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.

13. Recommendation #5
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.

14. True or False?
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.”

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

16. References:
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