ByB. Yushau, M. R. Alaimia & M. H. Omar

Mathematical Sciences DepartmentKFUPM, Dhahran, Saudi Arabia

for Students acquiring English as Second Language

Contents

Background

Literature review

Methodology

Conclusion and Recommendation

Results and Discussion

Why word problems

The Questions of the study

Aim of the study

Introduction and Background

In many classrooms around the world, in both developed and developing countries, many students are learning mathematics in their second or third language (Austin & Howson 1979; Ellerton & Clarkson 1996).

Communicating mathematically in these classes is by means of managing the interaction between the following:

1. Ordinary English (OE) and mathematical English (ME).

2. Formal and informal mathematics language.3. Procedural and conceptual discourses.4. Learners’ main language and the LoLT. (Setati,

2003)

Introduction and Background

Most of the empirical studies on bilingual attempted to find the relationship and interaction between L1 (first language) and

L2 (second language) from both social and cognitive domain.

Most of the findings indicated that students achievement in mathematics are higher if taught in their native language.

Similarly, Conceptual understand of mathematics seems higher in students that learn in their native language

Studies have shown that the task of acquiring language of instruction, and at the same time struggling to learn mathematics in the new language is not an easy task.

In terms of Classroom Discourse, both students and teachers discuss more freely in their native language than in a different Language of instruction

L2 students are not facing much difficulty in general English. However, they face greater difficulties with technicalmathematical Discourse (Barton & Barton, 2003)

L2 students unjustifiably rely on symbolic modes to make up for textual disadvantages (Barton & Barton, 2003)

Compared to natives, L2 students experience a 10% disadvantage in overall performance through lack of understanding mathematical text (Barton & Barton, 2003)

Why Study Word Problems?

.

Now that English is gradually becoming the language of instruction at university level in Middle East

Then it became imperative to investigate how these student are coping with the language issue particularly in Word Problems

Word Problems is language laden

most of the students are bilingual

having minimal English proficiency.

Why Study Word Problems?

.

Word Problems are commonly used by teacher for one of the following reason:

Sharpening of students problem solving skills to new situations.Bridging the gap between mathematics in the classroom and mathematics for the real world.

Word Problems are known for their difficulty.

Students generally find them difficult regardless of their language proficiency.

Application of mathematics in common real world settings.

Literature Review

“Word Problems” have different meaning to different people.

.

For a review of different definition and framework of Word Problems, see Craig (2001)

In this study, we define word problem in contrast to other algebra problems

That is: a problem presented fully or partially in English language, and some command of English language is required for understand the problem.

Literature Review

.

A review of literature revealed that intensive studies have been done on Word Problems

Classification of Word Problems

Strategies students used in solving Word Problems

Complexity of Word Problems

Difficulties students face in solving Word Problems. etc

This include issues related to the:

Literature Review

.

1) All these studies were largely carried out in primary and secondary schools level.

2) Not much is known with regards to the university students

3) In particular, not much is documented with regards tothe bilingual Arab university students.

However,

Aims of the Study

The study aims at investigating the difficulty bilingual Arab students, who are acquiring English as a second language at the same time learning mathematics in English, faced while solving Word Problems.

Specifically, we intend to know:

What are the problem solving strategies of bilingual Arabstudents in solving Word Problems?

What language related problems bilingual Arab students face in solving Word Problems?

Aims of the Study

How are these problems if any hindering them in understanding mathematics?

How are the performance of the student in comparison to other symbolic problems?

How do these affect their achievement on assessments in mathematics?

Are the findings different from what is available in the literature?

Methodology

Two set of students were involved in this study

1. Math 001, consisting of 48/251 students (20%) First Preparatory Year Mathematics

2. Math 002, consisting of 251/828 students (30%) Second Preparatory Year Mathematics.

Four questions were selected from each exam

The questions were not premeditatedThe Exams are all multiple choice

Two set of Exams were used for data collection, and

Methodology

1) The dichotomous (right vs wrong) grading were done by computer

2) While a hand grading was done to the sample polychotomously (wrong, partially correct to fully correct).

The grading was done carefully with the aim of answering the research question stated earlier.

Our areas of concentration include: Students attempt of the question Putting the appropriate graph or equation The algebraic processes followed, and Interpretation of the obtained results.

Methodology

How many students attempted the questions?How many students did not?

How many students among those attempted got them right?How many among these did not?

What are the strategies of the students who got it right?What are the mistakes of students who got it wrong?

Compared to the other symbolic questions, what are the students performance?

The Questions –Math 001

4. Three students decided to share the cost of a car. By bringing in an additional student, they can reduce the cost of each students by 400 Saudi Riyals. The total cost of the car is

1. The coefficient of 2x y in the product

4 5 2 3 4x y x y x y is equal to

2. The sum of all solutions of the equation 3 2 1 4 28x

is equal to

3. If the expression 23 5 2x x is written in the form 23( ) ,x a b then ab is equal to

The Questions –Math 002

1. The length of an arc that subtends a central angle of 0135 in a circle of radius 40 ft is

2. If the hypotenuse of a 0 0 030 , 60 , and 90 triangle is 10cm,

then the perimeter of the triangle is equal to

3. If a car with a wheel of radius 40cm is moving with a speed of 120 kilometers per hour, then the angular speed of the wheel of the car in radian per minutes is

4. Two buildings are 240 meters apart. The angle of elevation from the top of the shorter building to the top of the taller building is

030 . If the shorter building is 8 meters high, then the taller building is

Results

Table 1. Number Of Students Attempting Question or Showed Work

Subject MATH

No N n Showed work in Booklet

No work Shown

001 1 251 48 98% 2%

2 251 48 96% 2%

3 251 48 73% 13%

4 251 48 33% 67%

002 1 829 251 83% 17%

2 829 251 80% 20%

3 829 251 79% 16%

4 829 251 72% 22%

Results Table 2. Percent of Students with different levels of Correct

Solutions to problems

Subject MATH

No

Correct solution involves

comp

drawing

CorrModel/ Equatio

nCorr Process

Interpretatio

n

Corr Written work

Prop. Corr

Diff in prop. Corr

001 1Algebraic Process & Interpretation 90% 69%

69% 76% 7%

2Algebraic Process & Interpretation 73% 63%

63% 69% 6%

3Algebraic Process & Interpretation 19% 10%

10% 14% 4%

4 Model, algebraic process & Interpretation

6% 2% 2% 2% 45% 43%

002 1 Formula, Algebraic process & Interpretation

47% 49% 54% 54% 82% 28%

2 drawing, equation, algebraic solution,& Interpretation

38% 27% 27% 33% 33% 63% 30%

3 equation, algebraic process & Interpretation

27% 21% 6% 6% 29% 23%

4 drawing, equation, algebraic solution,& Interpretation

29% 32% 32% 27% 27% 54% 27%

Results

The following are the preliminary findings in this study:

1. Bilingual Arabs students do not seem to have much difficulty with mathematics problems that involves mathematical English such coefficient and sum

This is unlike monolingual, they also do not have much problem with “Words which occur in both OE and ME, but which have a different meaning in ME from that of their meaning in OE, e.g. the words “Revolution” and “Product”.

This is likely because they are not aware of the other meaning. Therefore, the mastery is on the ME.

Results

2. The performance of the students in Word Problems is Below average compared to the clear algebraic problems.

3. The Word Problems that students have difficulty is indeed difficult either due to linguistic or cognitive demands in the question.

4. The inclusion of a single unfamiliar word can destabilize the meaning of the question. Example “Reciprocal”, etc.

5. The variation between the dichotomous grading and the polychotomous grading is wider with pure Word Problems.

Results

6. The tendency of guessing is more in word problems compared to pure algebraic problems.

7. The number of students who did not attempt questionare more in worded problem compared to pure algebraic problems especially for MATH 001

8. Although students have problems with Word Problems, their Algebraic skills also need to be sharpen.

Concluding Remarks:

There are language factors that affect students understanding and achievement in mathematics.

There is a need to pay special attention to these language constraints of our students while teaching mathematics especially to bilingual students.

Findings are pointing to the fact that language factors have serious ramification for mathematics education

Although students have problems with word problems, their algebraic skills also need to be sharpened.

Concluding Remarks:

Deeper studies are required to investigate the language issues among bilingual Arab university students.

In particular, the problem of “Word Problems” need further investigation.

A premeditated investigation should be carried out with well prepared questions that will target specific research questions.

Many Thanks for Listening