ERIC Identifier: ED317086
Publication Date: 1989-11-00
Author: Short, Deborah J. - Spanos, George
Clearinghouse on Languages and Linguistics Washington DC.
Teaching Mathematics to Limited English Proficient Students.
At an in-service workshop on content-based instruction, the facilitator
presents an exercise designed to increase awareness of the difficulties
encountered in learning mathematics in a second language. The participants are
instructed to solve the following word problem in a language with which they
have little or no familiarity (French), and to think about some questions that
focus on factors involved in problem solving.
"Jean et Andre sont freres. Jean est l'aine. Les deux vont au lycee qui se
trouve a moins de cinq kilometres de leur maison a Paris. Bien qu'il y ait une
difference d'age de trois ans entre les deux freres, leurs niveaux scolaires ne
sont separes que par deux annees. Jean est en quatrieme. En quelle classe est
1) What are the language difficulties in this problem?
2) What are some math difficulties in this problem?
3) What are some extra-linguistic features that could cause difficulty in
solving this problem?
The participants study the problem and try to answer the questions. They
begin to realize the difficulties word problems may pose for nonnative-speaking
students. The facilitator lists some possible language difficulties:
difficult lexical items, such as "aine," "niveaux," "ait"; comparative terms
or structures, such as "aine," and "moins de"; grammar structures with relative
and subordinate clauses, such as "qui se trouve a, bien qu'il y ait."
Before announcing the solution, the facilitator distributes an English
version of the problem that simulates a student's word-for-word attempt at
"Jean and Andre are brothers. Jean is older. The two go to a school which is
found less than five kilometers from their home in Paris. Although there is a
difference in age of three years between the two brothers, their grade levels
are only two years apart. Jean is in the fourth. What class is Andre in?"
The group discovers some potential math pitfalls in the wording of the
problem. There is extraneous information--unnecessary numbers (five kilometers,
three years)--and a mixture of cardinal (two, three) and ordinal (fourth)
The facilitator then gives the answer: Andre is in the 6th grade at school.
You are surprised. You had concluded that Andre was in second grade. After all,
4 - 2 = 2. In response to challenges by participants, the facilitator directs
attention to question number 3 on the worksheet.
The facilitator explains that simply knowing the language of instruction and
the required math skills may not be sufficient for solving problems. Cultural
issues may be present as well. In this problem, one needs to know that the
French educational system counts the grade levels in secondary school from 6th
(youngest) to 1st (oldest). A teacher must be careful not to assume that all
students have the same background knowledge.
THE NEED FOR LANGUAGE-SENSITIVE CONTENT INSTRUCTION
preceding example suggests the desirability of instruction that is sensitive to
the linguistic and cultural needs of language minority students. From the
language educator's point of view, it is obvious that a lack of proficiency in
the language of instruction has harmful effects on a student's ability to deal
with content-area texts, word problems, and lectures. Many language educators
(e.g., Spanos, Rhodes, Dale and Crandall, 1988) and a growing number of
mathematics and science educators (e.g., Cuevas, 1984, and Mestre, 1981) are
providing arguments suggesting that the nature of math and science language
imposes a heavy burden on all students regardless of the language of
instruction. Furthermore, national organizations, such as the National Council
of Teachers of Mathematics (NCTM), the Mathematical Sciences Education Board
(MSEB), and the American Association for the Advancement of Science (AAAS) are
calling for an approach to education that emphasizes communication for all
students, at all school levels.
The recently-published NCTM Curriculum and Evaluation Standards for School
Mathematics (1989) lists learning to communicate mathematically (p. 8) as one of
its five major goals. The NCTM authors maintain that all students can benefit
from listening, reading, writing, speaking, and demonstration activities (pp.
26-28, 78-80, 140-142). For nonnative speakers of English, the NCTM states:
Students whose primary language is not the language of instruction have unique
needs. Specially designed activities and teaching strategies (developed with the
assistance of language specialists) should be incorporated into the high school
mathematics program in order for all students to have the opportunity to develop
their mathematics potential regardless of a lack of proficiency in the language
of instruction (p. 142).
The MSEB (1989) supports this call for more communication, recommending that
teachers engage students in the construction of mathematical understanding
through the use of group work, open discussions, presentations, and
verbalization of mathematical ideas (p. 58). The MSEB advocates the use of
non-traditional teaching models, such as paired classes, that have one teacher
for language arts and one for mathematics and science (p. 65). Such statements
challenge language and content-area educators to begin working together to
educate students for whom basic English skills or academic language skills are
an obstacle to success.
FOCUSING ON THE LANGUAGE OF MATHEMATICS
Some research on
content-based instruction has focused on the language of mathematics. In 1984,
researchers from the Center for Applied Linguistics (CAL) (Crandall, Dale,
Rhodes, and Spanos, 1984) initiated a project funded by the Fund for the
Improvement of Postsecondary Education (FIPSE). This study involved
collaborative research with mathematics educators at several two-year colleges
with high language minority enrollments, and led to the development of a set of
materials that could be used as a language-focused supplement to beginning
algebra classes. The research phase of the project involved group
problem-solving activities with language minority and majority students. The
researchers produced evidence that the performance of both types of students was
severely impeded by a lack of proficiency in the language of mathematics.
Further, there were few language-based materials or activities in mathematics
classrooms, and fewer opportunities for language arts teachers to become
involved in educating these students. In sum, there was little articulation
between language arts programs and mathematics programs, despite the obvious
language deficiencies faced by large numbers of students enrolled in
MEETING THE COMMUNICATION NEED
Language minority students
are often quick to develop the social language skills that enable them to
communicate with their peers outside of the classroom. Within an academic
context, however, this basic proficiency is inadequate because language minority
students are inexperienced with or lack an understanding of the terminology and
writing styles particular to a content area. These students may not be prepared
to perform the higher order language and cognitive tasks required in rigorous
academic content courses. This latter point also applies to native speakers of
English who are often not skilled in analysis, argumentation, and evaluation.
Instruction that emphasizes language activities should be incorporated into
content area lessons and curricula. This requires development in teacher
training, curricula and materials, assessment, and cooperation between content
and language educators.
"Teacher Training." Training workshops and seminars can provide content
teachers with an opportunity to consider language objectives and increased
communication in their classes. An important aspect of these training seminars
is the joint participation of content and language educators, providing
opportunities for cooperative activities that draw on the expertise of both
disciplines. Training seminars present teachers with the theoretical background
for integrating language and content and provide opportunities for application
through analyses of curricula, suggested instructional strategies and
techniques, and assessment tools. Techniques include discovery learning,
hands-on and problem-solving activities, cooperative learning and group work,
and peer tutoring.
Teacher training can also be provided through the use of video. Several
videos, currently under production (see Resources), demonstrate the
content/language approach and materials, and have accompanying manuals, for use
by teachers for self-instruction when direct training is unavailable.
"Curricula and Materials." Once teachers have been trained to increase
communication in class, they need appropriate materials for developing their
lessons and activities. Teachers can attend workshops on material adaptation
where they can learn to modify existing materials for their particular needs. In
such workshops, strategy sheets (see Cuevas, Dale, Richardson, Tokar, &
Willets, 1986) are used as developmental models. These strategy sheets focus on
content and language objectives in lesson plans designed with communicative
activities. Teachers might consider using prepared supplemental materials (e.g.,
English Skills for Algebra, Crandall, Dale, Rhodes, and Spanos, 1989) that help
students become more proficient in the academic language through interactive
listening, speaking, reading, and writing activities.
"Assessment." Although assessment tools for determining concept mastery of
mathematics, science, and social studies are numerous, instruments for measuring
content area language proficiency are scarce. Assessment tools, such as the
Pre-Algebra Lexicon (see References), are currently being developed and field
tested. The diagnostic techniques in the Pre-Algebra Lexicon are organized
according to four math categories (concepts, operations, word problems, and
problem solving) and the four language skills (listening, speaking, reading, and
writing). The techniques allow teachers to assess growth in language skills
within the context of daily mathematics instruction.
"Cooperation Between Language Educators and Content Educators." Content
teachers need to implement strategies for increasing teacher-student and
student-student interaction in the classroom and to emphasize communication of
the concepts. Language teachers need to address content language in their
classes. Collaboration between content and language teachers can be beneficial
and essential to both, as language teachers can provide insights into linguistic
and cultural problems and offer communicative activities for overcoming these
problems, and content teachers can suggest topics for the language courses that
reinforce the content the students face. These collaborative efforts can help
students develop greater language proficiency and concept mastery.
American Association for the Advancement of
Science. (1989). "Science for all Americans." Washington, DC: American Association for the Advancement of Science.
Center for Applied Linguistics (in progress). "Improving articulation between language arts classes and mathematics and science classes." Project funded by the Carnegie Corporation of New York, Grant No. B 5003.
Crandall, J., Dale, T.C., Rhodes, N.C., & Spanos, G. (1984). "The
language of mathematics: the English barrier." Project funded by the U.S. Department of Education, Fund for the Improvement of Postsecondary Education, Grant No.G00B440473.
Crandall, J., Dale, T.C., Rhodes, N.C., & Spanos, G. (1989). "English
skills for algebra." Englewood Cliffs, NJ: Prentice-Hall.
Cuevas, G. (1984). Mathematics learning in English as a second language. In "Journal for Research in Mathematics Education," 15, 134-144. (ERIC Document Reproduction Service No. EJ 295 800)
Cuevas, G. , Dale, T.C., Richardson, G., Tokar, R., & Willets, K. (1986). "Strategy sheet for integrating mathematics and language instruction." Los Angeles: UCLA, Center for Language Education and Research.
Cuevas, G. & Hayden, D. (in progress)."The pre-algebra lexicon." D. Short
& G. Spanos (Eds.). Center for Applied Linguistics project funded by the Carnegie Corporation of New York, Grant No. B 5003.
Mathematical Sciences Education Board. (1989). "Everybody counts: A report to the nation on the future of mathematics education." Washington, D.C.: National Academy Press.
Mestre, J.P. (1981). Predicting academic achievement among bilingual Hispanic college technical students. In "Educational and Psychological Measurement," 41, 1255-1264.
National Council of Teachers of Mathematics. (1989). "Curriculum and evaluation standards for school mathematics." Reston VA: National Council of Teachers of Mathematics, Inc.
Spanos, G., Rhodes, N.C., Dale, T.C., & Crandall, J. (1988). Linguistic features of mathematical problem solving. In R. Cocking and J.P. Mestre (Eds.), "Linguistic and cultural influences on learning mathematics." Hillsdale, NJ: Lawrence Erlbaum.
Center for Applied Linguistics (in progress). "Integrating mathematics and Science education (tentative title)." Video project funded by the Carnegie Corporation of New York, Grant No. B 5003 and by the Xerox Corporation, Grant No. HE90788.
Miami-Dade Community College. (1989). Preparing teachers to integrate math and language instruction. Video project funded by the U.S. Dept. of Education.