B. Yushau, M. R. Alaimia

1
The problems of Word Problems in Mathematics
Classroom
for Students acquiring English as Second Language

• By
• B. Yushau, M. R. Alaimia M. H. Omar
• Mathematical Sciences Department
• KFUPM, Dhahran, Saudi Arabia

2
Contents

• Background

• Why word problems

• Literature review

• Aim of the study

• Methodology

• The Questions of the study

• Results and Discussion

• Conclusion and Recommendation

3
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
• Ordinary English (OE) and mathematical English
  (ME).
• Formal and informal mathematics language.
• Procedural and conceptual discourses.
• Learners main language and the LoLT. (Setati,
  2003)

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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.

• 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.

• 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

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• 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 technical
• mathematical Discourse (Barton Barton, 2003)

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

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

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Why Study Word Problems?
Word Problems is language laden
most of the students are bilingual
having minimal English proficiency.
.
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
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Why Study Word Problems?
Word Problems are commonly used by teacher for
one of the following reason

• Application of mathematics in common real world
  settings.

• 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.
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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.
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Literature Review
A review of literature revealed that intensive
studies have been done on Word Problems
This include issues related to the

• Complexity of Word Problems

.

• Classification of Word Problems

• Strategies students used in solving Word
• Problems

• Difficulties students face in solving Word
• Problems. etc

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Literature Review
However,
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 to the bilingual Arab university students.
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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
Arab students in solving Word Problems?
What language related problems bilingual Arab
students face in solving Word Problems?
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Aims of the Study
How are these problems if any hindering them in
understanding mathematics?
How do these affect their achievement on
assessments in mathematics?
How are the performance of the student in
comparison to other symbolic problems?
Are the findings different from what is available
in the literature?
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Methodology
Two set of Exams were used for data collection,
and
Two set of students were involved in this study

• 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 premeditated

• The Exams are all multiple choice

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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.

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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?
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The Questions Math 001
1. The coefficient of
in the product
is equal to
2. The sum of all solutions of the equation
is equal to
3. If the expression
is written in the form
then ab is equal to
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
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The Questions Math 002
1. The length of an arc that subtends a central
angle of
in a circle of radius 40 ft is
2. If the hypotenuse of a
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
. If the shorter building is 8 meters high,
then the taller building is
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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
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Results Table 2. Percent of Students with
different levels of Correct Solutions to problems
Subject MATH No Correct solution involves comp drawing Corr Model/ Equation Corr Process Interpretation Corr Written work Prop. Corr Diff in prop. Corr
001 1 Algebraic Process Interpretation 90 69 69 76 7
2 Algebraic Process Interpretation 73 63 63 69 6
3 Algebraic 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
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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.
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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.
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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
question are 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.
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Concluding Remarks

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

• 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.

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

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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.

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• Many Thanks for Listening