**ERIC Identifier:** ED414769

**Publication Date:** 1997-12-00

**Author: **Buchanan, Keith - Helman, Mary

**Source: **ERIC
Clearinghouse on Languages and Linguistics Washington DC.

## Reforming Mathematics Instruction for ESL Literacy Students.
ERIC Digest.

English as a second language (ESL) students who have had limited or
interrupted schooling in their first language--whom we refer to as literacy
students--can be overwhelmed by new experiences in ESL and content courses. They
must learn in a linguistically and culturally unfamiliar environment, construct
understanding without the background knowledge that their classmates employ to
make assumptions, and process new information. All too often, these
circumstances lead to frustration for both literacy students and their teachers.

Literacy students must have access to math content from the beginning of
their formal education. This calls for modifications in the curricula and in the
delivery of instruction. By integrating math and language teaching, innovative
courses can provide experiences that bridge gaps in literacy students' math
knowledge, expand their communicative competence in English, and ultimately
prepare them for success in future math coursework.

### CORRELATING MATHEMATICS WITH LANGUAGE SKILL BUILDING

In
response to the call for the reform of mathematics education in the United
States, the National Council of Teachers of Mathematics (NCTM) established a
Commission on Standards for School Mathematics in 1986. This led to publication
of Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989),
which included 54 standards among four divisions: Grades K-4, 5-8, 9-12, and
evaluation. The NCTM standards established five goals for mathematical literacy:
(1) that students learn to value mathematics; (2) that they become confident in
their ability to do mathematics; (3) that they become mathematical problem
solvers; (4) that they learn to communicate mathematically; (5) and that they
learn to reason mathematically (NCTM, 1989). The NCTM position statement on
language minority students (1994) further clarifies that, "Cultural background
and language must not be a barrier to full participation in mathematics programs
preparing students for a full range of careers. All students, regardless of
their language or cultural background, must study a core curriculum in
mathematics based on the NCTM standards."

The goals articulated in the NCTM standards have special implications for
math teachers who are working with literacy students. While these students have
had many experiences outside of school, most of these experiences have not
prepared them for success in formal classroom settings. Math teachers can make
math meaningful for literacy students by designing instructional activities that
build upon students' real life experiences. Lessons that provide challenging
problem-solving activities at which students can succeed help to build their
reasoning and problem-solving skills, as well as their confidence. For students
to learn to communicate mathematically, they need opportunities to hear math
language and to speak and write mathematically.

### NCTM STANDARDS AND EFFECTIVE INSTRUCTIONAL STRATEGIES FOR LITERACY STUDENTS

In 1991, NCTM produced a companion document to the
curriculum standards. Professional Standards for Teaching Mathematics, which
provides guidelines for teachers to design an environment in which all students
will develop mathematical literacy (NCTM, 1991). The guidelines require
significant changes in classrooms for literacy students. Five of these changes
are described here.

1.
Select mathematics tasks that engage students' interests and intellect.

Although the math concepts for literacy students may be at a basic level, the
interests and intellectual abilities of these students are not. Selecting tasks
that can bridge these discrepancies in ability levels is a challenge for math
teachers. For example, in a lesson on calculating percentages, younger students
might calculate the percentage of tax on a bicycle, while older students may use
their pay stubs to calculate percentages of various categories of withholding.

2.
Orchestrate classroom discourse in ways that promote the investigation and
growth of mathematical ideas. Orchestrating discourse for literacy level ESL
students requires the teacher to attend to teaching English in the content area,
which includes both the language specific to math and additional English
language skills. For example, when teaching that an obtuse angle is greater than
90 degrees, the teacher will not only have to teach the vocabulary word "obtuse"
but may also have to teach the use of the "-er" suffix to show comparison in the
word "greater."

3.
Use, and help students use, technology and other tools to pursue mathematical
investigations.

Many literacy students are unfamiliar with the basic tools associated with
mathematics such as rulers, protractors, calculators, and computers, and need
opportunities to make optimum use of these tools. When working on estimation of
lengths, for example, students can use both standard and metric measuring tools
to find things that measure approximately one centimeter, one decimeter, one
meter, one inch, one foot, or one yard. They can then use these items to
estimate the length of other objects in the classroom, check their estimates
with the actual tools, and use calculators to find the percentage of error in
their estimations.

4.
Seek, and help students seek, connections to previous and developing knowledge.

To make connections with students' prior experience, teachers must become
familiar with the backgrounds of their students. Working in collaboration with
other content and ESL teachers will help the math teacher provide connections
with the knowledge students are developing in other classes. When students are
studying data analysis and graph making, for example, the math teacher can
collaborate with science or social studies teachers to build connections with
work in those classes.

5.
Guide individual, small-group, and whole-class work.

Literacy math students benefit from a variety of instructional settings in
the classroom. The teacher must guide students through individual, small-group,
and whole-class activities. The introduction of a new set of vocabulary or
manipulatives to the whole class, for example, can build listening and
responding skills. Small-group work allows students to use language to talk
about the math tasks at hand while they solve nonroutine problems. Individual
work settings ensure that all students process lessons at their own rate of
learning.

### DESIGNING APPROPRIATE CURRICULA

In order to revise math
curricula for literacy students, schools must address such as these:

*
Who are our literacy students, and why are they unsuccessful in our present math
courses?

*
What is the most efficient way for students with limited time in school to learn
what their classmates already know?

*
How should math teachers incorporate language into daily lessons?

*
Why is it appropriate to separate literacy students from other math students for
a time?

*
How should literacy students' understanding of math be assessed?

Responses to these questions should be used to guide curriculum development
by educators from both math and ESL/bilingual backgrounds who are knowledgeable
about both the school district's math objectives and the needs of second
language learners from various age groups. Math instructors judge the relative
importance of existing instructional objectives and, along with ESL/bilingual
personnel, develop specific teaching strategies.

Clustering
Objectives

Literacy math classes aim to teach a number of years of conventional math
classes in a condensed period of time. In many cases, it is appropriate to
cluster similar learning objectives across grade level boundaries. These
clusters of objectives make the most efficient use of students' time in the
literacy math class and also recognize that, often, older students do not
require as much time to master objectives normally taught in earlier grades. In
addition to saving class time, the clustering of objectives reduces the
artificiality of structuring lessons where, for example, students only solve
problems that involve numbers less than 100 and do not require regrouping.

Clustering objectives also offers opportunities to integrate a variety of
math strands into one lesson. In a geometry unit, for example, a group of
students may estimate the cost of carpeting the classroom. The objectives for
the lesson would read, "Identify the space inside a plane shape as its area.
Find the area of simple polygons." In order to carry out the activity, students
also demonstrate their understanding of these objectives: measure lengths of
objects using customary units; multiply whole numbers, regrouping as necessary;
multiply whole numbers by decimal numbers. These math skills are being used by
students in a real life setting to solve a problem while mastering another
objective. The teacher can assess mastery of the previously taught content and
reteach where necessary while continuing to move through the curriculum.

Three
Important Variables

The essential math objectives identified by local school jurisdictions should
remain unchanged for literacy math students. In literacy math curricula,
however, the objectives are clustered and condensed, modifying the scope and
sequence. Next, specialized teaching strategies are developed. All the
strategies take into account students' ages, English proficiency, and
developmental levels.

"Students' Ages." Innovative strategies need to be developed for 17 year-old
students with beginning English skills, as well as for fourth graders whose
first school experience is in an American setting. Older students benefit
particularly from math curricula that take into account their previous life
experiences, such as problems involving money or their new school environment.
For example, high school students who are studying ordinal numbers could be
given practice identifying the periods of their school schedules or explaining
the order of their lockers in the hallways.

The fourth grade math literacy student faces a smaller developmental gap with
peers, yet may still need a period of specialized instruction. The texts and
materials that native English speakers use to learn about ordinal numbers may
not interest a student whose previous learning experience has never originated
in books. Instruction with concrete experiences, especially incorporating math
manipulatives, are effective bridges to formal math class education for literacy
math students of all ages.

"Students' English Proficiency." In a lesson on ordinal numbers, beginning
proficiency students could complete an oral activity combining their
understanding of colors with identification of the order of colored objects
demonstrated by the teacher on an overhead projector. More advanced students
could describe the exercise in writing. In general, less proficient learners
depend more on the teacher or other students to model expected work and class
behavior. A literacy math classroom will have a different look because it is
enriched with extra attention to language. Charts with important vocabulary and
language structures fill the walls, along with writing by the teacher and
students.

"Students' Developmental Levels." Multiple learning strategies are necessary
to reach both those students who show understanding of objectives after just a
few activities and those who may need continued reinforcement. Literacy math
teachers report that they are constantly revising curricular objectives to break
them into smaller, simpler pieces, and revising directions to incorporate
previously studied vocabulary and activities. Many teachers also modify their
overall teaching plan by spiraling out of an objective before it has been
mastered by many in their classes, then returning to it after a period of time
spent working in another area. For example, after a week spent on a unit on
mental math and estimation, the teacher could redirect the class with
individualized lessons on operations, incorporating the estimation skills
students learned in order to predict their answers. When they return to the
estimation unit, the practical value of the lesson will be clear.

### ASSESSING LITERACY MATH STUDENTS' PROGRESS

Just as
mathematics content and instruction change to meet the needs of literacy
students, teachers need to find different ways to assess literacy students'
progress in mathematics. The point from which this growth is measured varies
greatly from one literacy student to another but is usually far below the math
and English levels of their ESL and native English speaking peers. Reliance on
paper-and-pencil tests is often inappropriate because decoding the language of a
test may hinder students rather than allow them to demonstrate what they
understand. The use of a wide variety of assessment methods will provide a more
complete picture of each literacy student's progress, patterns of development,
or areas of need. Instead of focusing on what students do not know, it is
important to focus on ways students can show what they do know. That information
can be used to guide instruction. While grades from tests and quizzes have a
legitimate place in assessment, they comprise only one part of the total picture
of a student's math knowledge.

### REFERENCES

National Council of Teachers of Mathematics.
(1989).

"Curriculum and evaluation standards for school mathematics." Reston, VA:
Author.

National Council of Teachers of Mathematics. (1991). "Professional standards
for teaching mathematics." Reston, VA: Author.

National Council of Teachers of Mathematics. (1994). "News Bulletin." Reston,
VA: Author.

This Digest is drawn from Reforming Mathematics Instruction for ESL Literacy
Students (1993), a National Clearinghouse for Bilingual Education (NCBE) Program
Information Guide. In addition to a more in-depth discussion of the information
highlighted here, the guide provides sample lessons for teaching mathematics to
ESL literacy students.