English for Specific Purposes: A Math Preparation Course

Kevin Munson

placement exam. There is a distinct lack of

The most recently released numbers
from the United States Department of

preparation in most intensive English

Homeland Security (2012) records the total

programs in preparing international students

number of F1 visas at 1,514,783 in 2012.

for the challenge of taking placement exams

Most of these students choose to complete an

in English. Furthermore, the international

intensive English program and thenstudent sometimes is not aware of how

matriculate on to an institution of higher

different these placement exams can be. For

learning in the United States when they are

an intensive English program that wishes tofinished with their English studies. Although

aid students’ future success at a university

the requirements for admittance arethat operates in English, there is a need for a

institution specific, there are some common

course that develops the ability of a student

areas that students have to demonstrate at

to express what they already know about

least a basic proficiency before they aremath in their native language in English.

admitted. In addition to English, some areas

While the area of content and language

include math, and science. Higher education

integrated instruction (CLIL) is already wellinstitutions test prospective students for aestablished in the European context

demonstration of their abilities or rely on a

(Dalton-Puffer, Nikula, Smit, 2010), there isthird party to do so by using tests that are

a great need for CLIL curriculum design andrecognized as legitimate, such as the SAT,

implementation in these specific areas at

TOEFL, GRE, GMAT, and the ACT.

intensive English programs at AmericanThe

students that do not pass these exams or canuniversities. This paper will present the

not get their credits to transfer are required

research and development of such a CLIL

to take placement exams at the university

course for the MPE at a large research based

where they seek admission. One of the first

university.
Settingrequirements that a recently admitted
university student has to fulfill is to take a

The setting for this project is at an Intensive

mathematics placement exam (MPE) in order

Language Center run by a public-private

to see what classes s/he needs to take to fulfill

partnership at a large research oriented

the prerequisites for taking math courses. Alluniversity in the United States. The

students must either take this mathpartnership offers an academic program thatplacement test or demonstrate, through“is accredited by the Commission on English

official transcripts, that they already have

Language Program Accreditation (CEA) andtaken the prerequisites courses for the upper

prepares international students forlevel math courses. While it is fairly easy foruniversity study in the US. Thisan American student to demonstrate this,academically rigorous program provides

international students often can not get theirinternational students with high–quality

credits to transfer and have to take a math

English language instruction and academic㻌㻌㻌－ 31 －

skills” (INTO CSU, 2014). There are threewere triangulated by conducting interviews

programs to choose from at this institution:with a current calculus teacher, the Director

Academic English (AE), General Englishof the Pathways program and English(GE), and the Pathways program. The AE

language programs, the Assistant Director ofprogram is intended for students who wish to

Advising, a math professor, and several

matriculate, but do not have the language

students. An informal questionnaire (seeskills yet to do so. The GE program is forAppendix A) was administered verbally to

students that wish to have an American

most of the informants and their responses

cultural experience, or at the very least do

were recorded on paper. See table 1 for a

not have an academic goal in mind for theircomplete listing of all responses to thelanguage learning.

questionnaire.

The Pathways program is a track that

The director of the Pathways

students can take which allows them to start

program and English programs was ourconcurrently taking classes at the university

initial contact and she outlined the general

while continuing the finish their language

areas of concern that the students in theprerequisites. These classes are mixed with

Pathways program have after they leave thestudents from the university and English

program. The Director of the Pathways

language learners (ELLs) and are taught byprogram and English language programs

professors with a specialization in Teaching(personal communication, October 1st, 2012)English as a Second/Foreign Language

indicated that the students’ areas of concern(TESL/TEFL).

were the math placement exam (MPE) and
Needs Analysis

expressing and understanding general and

The impetus for this MPA class, conceived

specific mathematics lexical items. She also

within an English for Specific Purposes (ESP)

gave a list of expert informants from theframework, originated from a conversation

mathematics department whom should bewith the director of Pathways and English

contacted. The Assistant Director of Advisinglanguage programs and the Assistant(personal communication, October 1st, 2012)

Director of Advising at a large research

confirmed what the information given by theuniversity. Both informants identified a need

Director of the Pathways program andfor a preparatory course in mathematics forEnglish language programs. After gatheringinternational students who intend to study at

information from informants at thethe university in the fields of engineering,administrative level, an expert informant

science, and business once they have finished

was contacted to understand the content

their intensive English program. In order tospecific areas of concerns.

better understand the contextual needs, aMathematics Placement Exams (MPE)

needs analysis was then conducted according

The MPE is a computer adaptive test thatto a synthesis of methodologies (West, 1984;

measures the ability of the test taker in three

Courtney, 1988; Benesch, 1996; Chambers,

areas of mathematical knowledge. The three

1980; Giménez, 1996). The areas of concern

areas that are randomly selected from a test㻌㻌㻌－ 32 －

bank are logarithms and exponential

classes. This student also indicated that it

functions, trigonometry, and algebra.

took a while to get used to having to explain

Data Collection

the problem solving process instead of justA professor of mathematics was consulted as

giving the answer, which is the expected way

an expert, in both the field of mathematics

in his culture.
Results

and as a current teacher of ELLs. The
professor (personal communication, October

As a result of the informant interviews, it was

3rd, 2012) was asked questions to assess areas

determined that vocabulary should be thethat students struggled with (see Appendix

largest portion of the ESP course as it was

A). The professor’s responses were recorded

biggest obstacle to the student's success. For

by the interviewer.

instance, it was apparent that students could
understand what the lab report was asking

A student who intended to take theMPE was also interviewed. This student

him to do, but this was only after some(personal communication, October 10th, 2012)clarifications with the native speaking

was interviewed to determine the areas ofinterlocutor.
The professor pointed out that she

concern from his/her perspective. This
interview was conducted informally and a

had observed that international students

questionnaire was not used with thislacked in several areas: interacting withinformant in writing. Instead the student,

classmates during in class and out of class

who was studying to take the MPE at thegroup work, interacting with the teacher

time of the interview, was asked to list theduring office hours, understanding technicalareas that he was concerned about in regards

and sub-technical vocabulary, general

to the MPE and generally taking mathcomprehension for math word problems, andcourses. After the student listed some ofbeing able to explain how the students

her/his concerns, the student was also given

arrived at an answer. Table 1 has a

the first lab report, which is assigned tosummation of all the information garnered

students taking calculus 160, received fromfrom informants.
Proposed Solution: Course Design

the math professor, and asked to read the
instructions. The student was also instructed

The nature of this project would be classified

to underline any lexical items that he/she did

as English for Specific Academic Purposes as

not understand. The informant was

defined by Jordan (1997) because it isinformally tested on his/her reading

concerned with a specific set of academic

comprehension of the introduction.

skills that are content specific, in this case,A student who had taken the MPE

the field of mathematics. However, this class

was also interviewed as the final part of the

can also be classified under a larger umbrella

needs analysis. This student also indicatedterm of CLIL which is defined as “anthat vocabulary was an issue, but that he was

educational approach where subjects such as

under prepared for using the calculator, thegeography or biology are taught through the

TI 83, that was required on the MPE and in

medium of a foreign language” (Dalton-Puffer,㻌㻌㻌－ 33 －

Nikula, & Smit, 2010, p. 11). The mostconcepts shown to them once they were given

important part of this kind of classroom isthe vocabulary needed to do so. In otherthat it is “neither exclusively language

words, the students are operating in Version

learning nor subject learning” (Dalton-Puffer,

B of the TOPRA model where they are

Nikula, & Smit, 2010, p. 12). In other words,“processing for word meaning, word form, andthe course would not focus on solely math orform-meaning mapping”(Barcroft, 2012, p.

solely language. It would be an even28) and the processing power dedicated to

distribution of the two. Since the focus of theeach area is constantly shifting based on thecourse is the MPE, the sequence moves fromindividual students. This made vocabularysimpler to more complex mathematics topics

the most important part of the course to bethat are covered on the MPE. In other words,

integrated into the in class tasks. However,algebra first and logarithms and exponential

as Barcroft (2012) noted, it is important not tofunctions last. Furthermore, the order is therequire the production of target words tosame as they are presented when thequickly for maximal retention. As a result,students are taking the MPE.

math sections are often presented by the

A task-based syllabus was chosenteacher to expose target words to the students.

because of the nature course, which is to take

Then the students would work on solving thea test which is comprised of a series of tasks

math problem, which does not require thatto solve. A task is defined as “an activity

the students use the word for the idea they

which requires learners to use language, withare working with, to help solidify theemphasis on meaning, to attain an objective”

understanding the word in context. For(Nation & Macalister, 2009, p. 80). Solving a

example, students often have done the mathmath problem in English constitutes a task

they are review, like polynomialthat focuses on meaning and that can be

manipulation, so the concept is not new so

divided into different skills and sub-skills.

most of the students' processing power can go

Each section of the math review materials

towards form processing and mapping. Thisthat the math department gives out to study

method was employed more frequently later

for the MPE is a slightly different kind of task

in the course as the content became lessthat the students need to learn to solve.

familiar to the students, i.e., logarithms andFurthermore, some sections even have word

functions are not as fresh in students’ minds

problems that must be decoded before theif they even learned them at all in theirmath task can be completed. After deciding

country.

the form of the course, objectives for the

Furthermore, students also need thecourse can be set.

ability to read word problems and extract theFirst, the main objective of themath information from it to create

course is to increase the mathematical lexicon

expressions or equations. It is one aspect toof the students. Based on our interviews withknow the technical vocabulary of math, but it

student informants, they would understandis incomplete without the semi-technical andand be able to explain the mathematics

general vocabulary that is commonly used in㻌㻌㻌－ 34 －

math problems. It is very common inwhether or not their answers make sense in

American math classes to have to read or

the given context. For example, if a problem

hear word problems and extract the proper

is about time to complete a small gardening

information to create an equation to solve.

task and the units are given in minutes andThis task is generally difficult for native

hours, it should cause some concern if the

English speakers, but especially for ELLs.

answer that the student ends with an answer

Compounding this area is the use ofin years. By dissecting and solving math word

non-technical words that are very low

problems, the two goals were accomplishedfrequency. The classic example of thissimultaneously.

category of word is buoy. If a math problem

The secondary focus of the tasks in

has a context of the ocean, then there is anclass was to foster academic study skills inassumption on the part of the creator of thethe students. Math does not rely on higher

problem that the student will already have anorder thinking skills for the most part andawareness of ocean related lexical items. It

many times, there is a problem and a student

was therefore also necessary to work on theeither understands it and can solve it or not.

ability to guess the meaning of a word from

While this is not new for many students,

the context of the math problem.

having to explain how they arrived at theanswer is. As a result, most classes involve

The secondary objective was toincrease the academic skills required togroup work that reinforces the need tocomplete the mathematics courses at CSU.

practice doing the problems and thenAn adjunct professor teaching calculus 160 in

explaining the problem solving process. Whenthe math department indicated that theya student teaches something, it reinforces thenoticed many of the ELLs in their classroom

learning process and it is acquired faster by

had a hard time working in groups to solve inthat student. Part of the needs analysis

depth problems and that they often would

informed the need for international students

only give the solution to the problem, which is

to work in groups. By working in groups anda problem in American universities because

explaining how a problem was solved, thethey often require that a student show theirstudents are being prepared to enter mathwork to get full credit for solving the problem.

courses at the university which is the goal of

These two goals formed the largest threads

completing the MPE successfully. This is anthat would run throughout the entire course.

example of a thread (Nation & Macalister,In order to achieve the course2010) that runs throughout the whole course

objectives, foci were set from classroom tasks.

in order to develop the abilities and skills

A primary focus of in-class tasks is tothey will need during the MPE and inunderstand what the problem is that needs tosubsequent classes.

be solved, which includes understanding theMaterials

context. It is important to understand the

The use of corpora and concordancers hascontext of the math problem because it will

been established as a useful tool whenhelp guide the intuition of the students as tocreating activities and even courses㻌㻌㻌－ 35 －

(Flowerdew, 1993a; Allison & Tauroza, 1995;

calculus, algebra, trigonometry, logarithms,

Stevens, 1991; Thurstin & Candlin, 1998).

and geometry. When all of the sub categories

For this project, the needs analysis showed aof math were combined, a unified corpus ofneed for creating a corpus of technical andapproximately 1.4 million words was created.

semi-technical words for international

For reasons of materials development andmathematics students. There are a variety ofease of use by the students, the corpora weredifferent ways in which a corpus can be

kept as the separate files to allow students toutilized to aid in the development of many

look at specific topics of interest. For instance,

aspects of a course, from the overall design

if a student is confused about a term thatand flow of the course to giving authenticity

they encounter in a future trigonometry class,to the content of the classroom tasks. The

they can look only at the trigonometry corpus

design of the general corpus included texts

and not be burdened by too much irrelevantfrom various sources that relate todata. This allowed the course to target

mathematics and the academic environment

specific areas of mathematics for lexicalof which the students are expected to be

development.

involved in. The resources for this corpus

As for the corpora analysis, two

included syllabi from relevant courses, lab

programs were used: lextutor.ca and AntConc.

reports, tests samples, and transcripts ofFirst, each content area was looked at using

relevant lectures, academic assignments, andboth Antconc and www.Lextutor.ca toonline math tutorials.

analyze the frequency data. The technical

The majority of the math corpus cameand semi-technical words were collected andfrom the Khan Academy website

they populated the vocabulary list to be(https://www.khanacademy.org/), which is ataught during that section of the course. Any

website that seeks to provide a college

words that appeared in the corpora that wereeducation for free on the Internet through thealso part of the K2000 word list were removed.

use of video presentations. Using the Khan

Since the intended audience of this course isacademy, students can start learning theeither a Pathways or conditionally admitted

basics of math, simple arithmetic, andCSU student, it was expected that they

continue to the most complex concepts ofshould all already be familiar with the K2000

math, like differential equations and linear

word list and to some extent the academic

algebra. This website was chosen because it

word list. The remaining words were sorted

simulates a lecture setting that students will

according to how they were used. The focus

encounter in American universities, and it

quickly became the nouns and verbs, some ofprovided more data than could be gathered

which are common but used in a way that thefrom observing and transcribing lectures by

students were not accustomed to. For

hand. Using the transcript function on the

instance, verbs commonly indicate operators

website, about thirty three separate corpora

in math problems and therefore need to bewere created based on the different content

taught in a math context. For example, aareas in math. The subject areas include

math problem where people are leaving a㻌㻌㻌－ 36 －

restaurant represents subtraction or a large

activities that are commonly used in moregroup that breaks into smaller groups

normal ESL settings. However, the typicalindicates division. Nouns comprised thevocabulary exercises quickly proved to be notlargest portion of the vocabulary list, bothvery effective because of how different thetechnical and general, such as tenant, buoy,

subject-matter is. Using the vocabulary lists

nurses, and ripple.

and the concordancer, the students were able
to look at how the words on the list are used

Other materials for the course camefrom different sources including the Maththroughout the lectures which was more

Department, math related websites, and abeneficial for building their intuition about

GRE prep book.

the vocabulary, as well as show them the

The math department materials were useddifferent ways that they are used, which arebecause they represent precisely what is

not always uniform.

expected of the students to know before theStudent Assessment

test. These materials were the most useful in

Gimenez (1996) notes that process oriented

setting benchmarks and syllabus design forassessment and EAP courses are perfect forwhat should be included in the course.

each other for a couple of reasons. Generally,

However, they are lacking in that they do notthere are greater time constraints placed on

properly prepare the students for the

ESP courses and therefore require a

multiple choice nature of the MPE and theytightening of what is normally accomplishedcontain very little in the way of word

in a classroom. Oftentimes, it is the

problems. Generally, the study materials

assessment that is subject to the mostcontain section explanations and sometrimming. Since the objective of this course issample problems and solutions to those kinds

a workshop in nature, the decision was madeof problems. The student is presented withto not have formal assessments be part of thean equation to solve and the solution iscourse, at least when dealing with theprovided. Another reason for not using thesestudents' grades. This decision was madematerials in the classroom is that the

because the focus on the class is process

language that is used in these materials

oriented and how well each student does on

makes them inaccessible to ELLs. They were

the MPE is the real grade for the class. In

distributed to the students to use as study

other words, the goal of the class is to better

materials while at home because theequip the students to undertake and explain

students, for the most part, are able to solve

the process involved with interpreting andthe equations presented to them. What theysolving math problems. It is for this reason

are lacking is the ability to explain what theythat course contained many informal

have done in English. Therefore, the PDFs

assessment measures used on a daily basis.

were a better tool for homework and used as

Informal assessments that were used include

such.

creating their own math problem within
The corpora were also used tocertain parameters, drawing a dictatedgenerate a variety of different vocabulary

picture, and giving mini presentations about㻌㻌㻌－ 37 －

topics that were discussed. Watching thetest scores will be used by the teacher as one

presentation of the groups will give thedata point to determine the grade for theteacher the information needed to makeclass; and the test taker will use the scores toon-line adjustments to the course. This

determine if they are ready to take the Mathmeans that any time the students are

Placement Exam at CSU.
The test is syllabus based andproducing in class; it is an informal

criterion referenced test, which is defined asassessment of their progress.

“a test or other type of assessment designed

The development of this test is basedon the Bachman & Palmer (1996) model

to provide a measure of performance that iswhich includes information about test takers,

interpretable in terms of a clearly defined andtask types, the TLU domain, and constructdelimited domain of learning tasks” (Miller,definition. There are two parts to theLinn, & Gronlund, 2008, p. 40). Since the goal

proposed test. The first part is a vocabularyof the ESP course is to prepare the students

section, which includes isolated vocabulary

to succeed in future math courses, this test is

terms and a vocabulary in context section.

an achievement based design. One of the

The second part of the test is a question

vocabulary sections is a fixed choice

formation and hedging section regarding

assessment, and the other is a restrictedinteracting with the teacher during office

response question. The question formation

hours.

and hedging section is also a restricted
response.

The impact of this test will occur at

There are two formal tests in the

two levels: micro and macro (Bachman &Palmer, 1996). The micro-level impact willclass, one in the middle and one and the end.

affect the students and what they need to

The one in the middle is a type of formative

focus on while attending the ESP course.

test to make sure that there is vocabulary

Since this course is designed as a supplement

retention on the part of the students. Thisto the students' Pathways courses, the test in

test is strictly multiple-choice because there

the course will serve as a formative tool foris a binary of knowing and recognizing thethe students to recognize what areas theymath lexicon or not. This format was also

should spend more time studying. The

chosen because it is hard to put technicalmacro-level wash back will have two levels ofmath lexical items into context without

impact: an immediate and a delayed

having them actually do a math problem,(Bachman & Palmer, 1996). The results of thewhich they get enough practice with intest will inform the teacher to the current

in-class activities.

needs of the students so that the course can

The final test at the end is there for

evolve accordingly, if there is an area that is

two reasons. First, it would help guide future

consistently weak for a majority of theversions of the class. How well or poorly thestudents. The delayed impact will manifest in

students did on the test will highlight areas

the form of curriculum and syllabus changethat need to be adjusted in the curriculum orfor future iterations of the course. Finally, thelesson plans. Second, it will boost the㻌㻌㻌－ 38 －

Initially there was a third task

students’ confidence in their ability tounderstand and therefore solve mathrelating to question formation and hedging,problems in English. Motivation can play a

but after six weeks working with the students,

big part in how well or poorly a student does,it became apparent that they would not need

especially for high stakes tests. If the student

extra attention in these areas. Although

is confident in their abilities, many affective

academic etiquette and norms of American

variables can be mitigated if not eliminated.

universities were discussed, there was no

The test is comprised of three tasks: twoneed to test this area and the task was

vocabulary sections and a question formation

removed.
Conclusion

and hedging section. The input for all of thesections is visual, in the target language, andThe process of developing a class has ain real time. The first vocabulary section is abeginning but should not have an end. After

set multiple choice items testing knowledge ofcompletion of the course, revisions should betechnical mathematics vocabulary. This

made so that the next iterations corrects

section is designed to check recognition andmistakes or adds improvements to the way

ability to define basic math related lexical

things are done. The only end that a course

items which were derived from the Khan

should ever experience is a lack of need for

Academy Corpus. The input for this section isthe course and therefore there are noa single word, a phrase, or a sentence. The

students to take the course. Even when aexpected response for this section is either

curriculum is excellent, there is still a need

the correct word for the given definition orfor constant readjustment to accommodate

the correct definition for the word or example.

the needs of every new cohort of students that

The relationship between the input and thetakes the course. Lesson plans should be

expected response is narrow, non-reciprocal,

guidelines for how to navigate through aand direct. The scoring for this section will belesson but should never be inflexible as too

binary 0-1.

not allow any modifications. As campuses

The second vocabulary section

become more international, there will be arequires the test taker to comprehend andgreater demand for ESP courses from aanalyze words in context from a shortvariety of different fields. This paper

mathematics reading passage. The input for

highlighted some of the important

this section is a short reading passage

dimensions to consider when developing ESP

followed by a set of items. The relationshipcourses which should be applied to otherbetween the input and the expected responsecontent areas. While it is not an easy task to

is narrow, non-reciprocal, and direct. The

understand and weight needs, design

scoring for this section allows for a total of

curriculum to match those needs, andone point for each question. The test takerunderstand all the constraints, it can be done

can receive partial credit if the answer is notwith time, consideration, and data.

completely accurate.

㻌㻌㻌－ 39 －

㻌
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