ERIC Identifier: ED334310
Publication Date: 1991-03-00
Author: Schwartz, Wendy
Source: ERIC Clearinghouse on Urban Education New York NY.
Teaching Limited English Proficient Students To Understand
and Use Mathematics. ERIC/CUE Digest No. 70.
Understanding and using mathematics are increasingly crucial to an individual's
ability to function in society and succeed in the job market. Nevertheless,
students lacking proficiency in English often have been denied access to
an adequate mathematics education because educators believed that it was
necessary to significantly improve their English language skills before
even attempting to teach them more than basic computational skills.
Recent research and experience suggest, conversely, that some of the
techniques developed by the reform movement in mathematics are effective
with Limited English Proficient (LEP) students, whether instruction is
provided in the students' native language or in English. Math instruction
can even help promote students' fluency in English when used in concert
with other bilingual instructional methodologies.
This digest presents some basic techniques for teaching mathematics
with understanding to LEP students and briefly describes two instructional
programs that have demonstrated effectiveness.
ASSUMPTIONS THAT LEAD TO GOOD PRACTICE
Students are capable of learning advanced mathematics whether or not
they are fluent in English and whether or not their teacher can speak their
native language. Students who are taught math in their native languages
will transfer that knowledge to English as their language skills improve.
Only a small part of mathematics knowledge consists of the ability to
compute. Far more important is an understanding of math that allows students
to link what they are learning to previous knowledge and to explain why
they believe something is true in a way that is sensible to someone else.
Such math understanding also enables students to apply what they have learned
in new settings.
While students should learn number facts, they can memorize them more
quickly and easily within the context of learning to understand math than
through drilling in a vacuum.
In general, students should be exposed to more content than has been
done traditionally. The practice of going over the same content repeatedly
year after year (via what is known as a "spiralling curriculum"), instead
of moving on to cover more challenging content that incorporates what has
been covered before, limits students' opportunities to learn.
Students' everyday lives provide sources of math knowledge, regardless
of their cultural backgrounds. Drawing on this naturally developed knowledge
both facilitates teaching math and demonstrates its practical usefulness.
DEVELOPING A MEANINGFUL CURRICULUM
Since LEP students can learn mathematics by solving problems (Secada,
in press; Carpenter & Moser, 1983), their learning tasks should be
adjusted in terms of linguistic complexity, but the mathematics should
not be simpler than it is for other students. LEP heterogeneous cooperative
groups have been shown to be particularly effective learning settings for
LEP students (De Avila, Duncan, & Navarrete, 1987).
Teaching students "mathematics language"--unique terms, symbols, and
expressions that occur in math discourse--enables them to communicate on
the subject and to clarify their math thinking as it develops language
skills (Cuevas, 1984). On the other hand, using "key words" or rules to
teach math can limit students' ability to solve problems that are presented
in ways that use the key words differently or confound the rules.
It can be both efficient and effective to combine math and language
development in a single activity, but one goal should be chosen as primary
when planning the lesson.
Asking students to devise math problems from their own experiences increases
their interest, concretizes the subject, and demonstrates math's usefulness.
It also promotes multiculturalism.
The Curriculum and Evaluation Standards (National Council of Teachers
of Mathematics, NCTM, 1989) provide specific recommendations for math course
content that will help students meet future workforce and personal needs.
New content should include number theory, discrete mathematics, probability
and statistics, geometry, and measurement. Teaching students complex computations
(such as adding long columns of figures or doing long division, where use
of pencil and paper is required) should be deemphasized, since more efficient
tools like calculators are easily available.
Students can best master the content proposed by NCTM if it is presented
in meaningful contexts that call for students to reason and conjecture
when solving problems. Math, thus, becomes a social task--something that
students do, alone or together--rather than something they absorb. While
bilingual settings are most appropriate for teaching this kind of math
to LEP students, all-English classrooms can be adapted to allow all students
to participate in the social interactions necessary for learning. Fostering
communication among students develops language as well as thinking skills.
Math curriculum should dictate assessment, not the reverse. Too often,
and particularly in compensatory education programs, achievement testing
leads to teaching to the test, and this results in emphasis on students'
ability to memorize number facts rather than to use reason for problem-solving.
SAMPLE INSTRUCTIONAL PROGRAMS
Two types of math instruction programs are promising for use with LEP
students in both bilingual and all-English classrooms. Each program can
be adapted for teaching elementary and higher level math:
Active Mathematics Teaching (ATM). ATM is a form of "direct instruction"
whose function is to convey large amounts of highly structured information
to students just beginning to learn a subject (Good & Grouws, 1979;
Good, Grouws, & Ebmeier, 1983). It prescribes a sequence of teaching
behaviors organized around a math lesson that consists of 8-10 minutes
on review, 20-25 minutes on developing new content, and 10-15 minutes on
seatwork, which can be supplemented by homework. Each lesson in the sequence
builds on the last. The teacher provides process explanations, illustrations,
and demonstrations, while frequently checking students for comprehension.
Teachers using ATM in classes with LEP students can facilitate their
learning by providing the definitions of math language in ways that students
are sure to understand. Frequent monitoring of students' understanding
prevents misconceptions from taking hold and allows teachers to match the
pace of the lesson to the students' ability to master each component.
Cognitively Guided Instruction (CGI). CGI requires that teachers focus
on students' thought processes while they solve math problems and that
they use this information to guide their instructional decisions (Carpenter,
Fennema, Peterson, Chiang, & Loef, 1990). Ongoing assessment of what
students understand is critical to this instructional technique. Students
develop both basic skills and higher ordering thinking through problem-solving
activities. Moreover, experience has shown that students in CGI programs
have better number fact recall than do students who practice number facts
outside a problem-solving context. Students should be encouraged to engage
in math problem-solving at any time during the day that a question arises,
regardless of the course content being taught at the time; this not only
increases students' opportunities to learn math but demonstrates math's
usefulness in all aspects of life.
To use CGI effectively with LEP students, it is often productive to
invite them to express themselves in the language they can use most comfortably.
While extra time may be needed for translation so all students can understand
each other, the benefit is that students are learning to communicate using
math language that can be transferred as students' English fluency increases.
The translation process itself can foster greater English fluency. Homework
that takes the form of problem-solving not only promotes students' English
language and thinking skills, but can help parents better understand the
value of learning mathematics.
Teaching mathematics with understanding to LEP students provides them
with a tool for successful living that native English speakers have traditionally
been given. It also offers them an opportunity to increase their English
fluency at the same time as they acquire other skills. More important is
development of their ability to communicate their answers and the reasons
for them. Students transfer math knowledge learned in their native language
to English. Advanced math courses should be made available to LEP students,
either as part of a bilingual program or in all-English classes. Finally,
teachers should encourage students to take advanced courses, and should
expect that all students will master the material.
Carpenter, T.P., Fennema, E., Peterson, P.L., Chiang, C.P., and Loef,
M. (1990). Using knowledge of children's mathematical thinking in classroom
teaching: An experimental study. American Educational Research Journal,
Carpenter, T.P., & Moser, J.M. (1983). The acquisition of addition
and subtraction concepts. In R. Lesh & M. Landau (Eds.),The acquisition
of mathematics concepts and processes (pp. 7-44). Orlando, FL: Academic
Cuevas, G. (1984). Mathematical learning in English as a second language.
Journal for Research in Mathematics Education, 15, 134-144.
De Avila, E.A., Duncan, S.E., & Navarrete, C.J. (1987). Finding
out/Descubrimiento (Teacher's Resource Guide). Northvale, NJ: Santillana.
Good, T.L., & Grouws, D.A. (1979). The Missouri mathematics effectiveness
project in fourth-grade classrooms. Journal of Educational Psychology,
Good, T.L., Grouws, D.A., & Ebmeier, H. (1983). Active mathematics
teaching. New York: Longman.
National Council of Teachers of Mathematics. (1989). Curriculum and
evaluation standards for school mathematics. Reston, VA: Author.
Secada, W.G. (in press). Degree of bilingualism and arithmetic problem
solving in Hispanic first graders. Elementary School Journal.
This digest is based on a monograph, "Teaching Mathematics with Understanding
to Limited English Proficient Students," by Walter G. Secada and Deborah
A. Carey. In addition to providing an in-depth discussion of the principles
of teaching mathematics, the monograph demonstrates the use of Active Mathematics
Teaching and Cognitively Guided Principles in teaching basic math.