Mathematics and the ESL Student
Halpern N., Patkowski, M., Brooks, E.
Brooklyn College of the City University of New York
Abstract
We describe a pilot program pairing an English as a Second Language
reading and writing class with a Calculus I class. Theoretical and
practical pedagogical issues are discussed.
Rationale for Linking Language and Content Instruction
Recent surveys show that almost half of all City University of New York (CUNY) students
come from homes where a language other than English is spoken, and that 15 to 20% of entering
freshmen register for English-as-a-second-language (ESL) courses. This phenomenon is by no means
particular to CUNY; indeed, the number of second language students is rising dramatically across
the United States.
Generally, there have been two broad approaches to attempt to meet these students' needs.
The first approach has consisted of requiring the students to complete an ESL-only program before
being allowed to matriculate as regular college students, while the second approach has sought to
integrate language and content instruction.
While the first approach ("take care of the problem in ESL before the students are allowed
into the mainstream") holds a strong intuitive appeal for many, the research in second language
acquisition over the past two or more decades suggests (a) that reaching grade-level norms in the
schools can take from four to eight years and (b) that second language acquisition often proceeds
more successfully when the instruction is focused on academic content rather than linguistic form,
when the instructional language is made accessible to the students, and when the instructional
atmosphere is relatively stress-free. Thus, in order not to delay the academic progress of second
language students while simultaneously providing them with the opportunity to develop their
academic language skills, there has been a growing recognition of the need to link ESL and content
courses.
In practice, the attempt to link content and language instruction has taken many forms
including the following:
- bridge courses: these are theme-based ESL courses designed to prepare students for specific
content courses. Such courses typically employ readings and vocabulary which will be covered in
the content area course.
- sheltered courses: these courses are focused on academic content but designed specifically
for ESL students. The
curriculum is adapted to meet students' language needs and the course may be taught either by an
ESL teacher with an additional specialization in a content area, or by a content area teacher with
training in ESL techniques. Unlike a bridge course, the sheltered course does not act as a pre-
requisite for a content area course but rather as a substitute.
- paired courses: the same group of students attends both a specific ESL course and the
content course with which it is paired or linked. The ESL course will focus on the students' language
development but make use of themes, readings and vocabulary from the content area course. The
ESL teacher needs to learn the material of the content course and develop teaching materials based
on it. The content area course will focus on traditional academic concepts, but the instructor will
seek to incorporate instructional techniques such as:
- selection of well-written and clear texts
- presentation of adequate visual reinforcement
- use of study guides, outlines and glosses
- assignment of appropriate reading and writing tasks
- willingness to allow rewriting of papers
This model requires thorough coordination before and during the term particularly between the
language and content teachers but also with the administrative staff (and tutors, if any are involved).
- blocked courses: this approach is similar to the paired approach but involves more than two
courses. For example, the same group of students might take an ESL writing/reading course, an ESL
speech course and two content area courses. The instructors involved will then decide which content
materials to adapt for the ESL classroom, but otherwise the process is essentially similar to the
paired approach.
When effectively carried out, the paired or blocked course approaches a promising avenue
for providing ESL students with the opportunity to make effective progress both in their academic
development and in their second language proficiency.
Block Programming at Brooklyn College
For a number of years, Brooklyn College's Office of the Dean of Undergraduate Studies has
created blocks as part of CUNY's freshman experience programs. Although blocks were originally
created for incoming students who failed one or more of CUNY's Skills Assessment Tests (reading,
writing, or mathematics), they are now scheduled for all freshman and even extended to the first two
semesters rather than only the first to ensure greater success for first year students.
Students are placed into a block of courses (for example, an integrated ESL reading and
writing course and a section of a mainstream college course such as art history, classics, or computer
science). Usually the same students are in all sections of a block, thus increasing their sense of
community. Since students who report speaking a language other than English at home are expected
to soon represent 50% of CUNY's entering freshman, such blocks were initiated by the college to
address their needs and have evidenced higher retention rates. The Freshman Year Program course
pairings offer enriched, intensive instructional team models and meet the curricular requirements of
this population. ESL students have programmatic and financial needs for credit-bearing courses.
Students barred from college courses perceive ESL programs as barriers rather than aids. ESL
students in CUNY have been found to do well in academic courses despite their lack of native
proficiency in English. Thus, a mathematics/ESL pair would address students' skills needs, credit
needs, and provide an integrated base for their future goals: to succeed in core curriculum and
advanced academic courses.
Blocks also appear promising in terms of the number of students progressing through and/or
exiting ESL programs. At Brooklyn, there has been a higher pass rate (one study found a 47.5 % rate
vs. 34.5%) on the Writing Assessment Test (WAT) than in traditional ESL courses. Such data were
used to design a one-year ESL model to meet new limits on ESL and remedial instruction within
senior colleges of CUNY because it is believed blocking will best support and increase students'
opportunities to develop and progress in English proficiency.
Block programming also benefits faculty who teach in such courses. It promotes faculty
exchange and development of pedagogical strategies. Instructors collaborate and coordinate materials
and/or activities, thus reinforcing each other's work with students. Although faculty coordination
remains problematic without release time for faculty (especially part-timers) in a block to meet, those
who do meet or at least speak by telephone share information about course goals, texts, student
assessment and performance.
Implementation of a Calculus I/ESL block and Student Assessment
In addition to the reasons for linking ESL courses to content courses in general there are a
number of reasons why the content course should be mathematics. Many ESL students gravitate
towards mathematics and towards fields where mathematics is essential - such as the physical
sciences, computer science, engineering, business and economics - because they assume that their
language deficiencies will not handicap them as much as they would in other fields. They believe
that the necessary level of English proficiency is lower in the study of mathematics because of the
symbolic nature of the subject. They anticipate few reading and writing assignments. Moreover many
of the ESL students have a strong mathematical foundation from their native country and wish to
expand their mathematical experience. College advisors tend to steer ESL students into mathematics
courses for the same reasons. Because of the large number of ESL students in mathematics classes,
it makes sense pedagogically and practically to provide special support for them.
The current mathematical reform movement provides another impetus for pairing ESL and
mathematics courses. A common thread in the movement is the communication of mathematics via
reading, writing and speaking. It is well documented that communicating mathematics promotes a
deeper and more lasting understanding of the subject. Incorporating mathematics into everyday
language and experiences motivates and facilitates students' learning. Thus direct pairing of ESL
reading, writing and speech courses would encourage and support an enhanced instructional
environment in the mathematics courses.
We are currently planning to add a calculus I - ESL block to our program at Brooklyn
College. The ESL part of such a block will be directed at students on the high intermediate or
advanced level of English. The course will be integrated (reading, writing, speaking and listening)
to eliminate artificial divisions and allow for more efficient development in all areas. It will meet
six hours per week. Students who register for it will have to have both the appropriate ESL
placement and mathematics pre-requisites. The calculus section may be half ESL and half native
speakers or be made up of two sections of an ESL course. In the ESL course, students can more
actively discuss mathematics information, explain problems in groups, share knowledge, check
understanding (a form of comprehension monitoring), maximize use of English, and lessen their
social isolation on the campus.
The language of mathematics is concise and precise. It is a hi-density language expressed
with few redundancies. These characteristics help attract ESL students to mathematics courses but
they also pose difficulties. The lack of redundancy requires students to understand the material the
first time. An exact understanding of the language is essential to the comprehension of the subject.
The definition of logical connectors (such as if/then, either/or, if and only if, and therefore) often
proves crucial. Moreover, a single concept IS often expressed in several different ways. For example
"« n" can be expressed as "n divided by 2", "1/2 of n", "n over 2", or "1/2 times n."
A glossary of English words commonly used in the mathematics course will be prepared.
They will include three categories of words:
- mathematical words that students learn during their elementary and high school years.
Examples of such words are "quotient", "ratio" and "area"
- English words which take on a more specific meaning in mathematics. Examples of such
words are "limit", "increasing and decreasing functions"
- non-mathematical words that frequently appear in verbal problems. Examples of such
words are "velocity" and "acceleration."
The glossary will be provided to the students and to the ESL instructors. Its content will be
integrated into the ESL courses. Readings containing words from the glossary will be used by the
ESL instructors. In linking their classes with mathematics, ESL instructors can use some general
introductions to topics and chapters from the mathematics texts as reading material. Some of the
students' writing assignments can be based on their math course as well. They can write an essay at
the beginning of the semester explaining why they are studying mathematics and what they expect
to learn. They can summarize certain topics - for example max-min and related rate problems. They
can read and reword verbal problems and make up new verbal problems of a given type.
In thinking, processing information, and formulating both spoken and written responses
together, students gain confidence and competency in English and mathematics. They are more likely
to participate in lecture courses and retention in both English and mathematics is increased. English
and mathematics are foundations for the rest of their work in college and often their professional
futures.
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