Educare 3-1.indb

EDUCARE:
International Journal for Educational Studies, 3(1) 2010

Limited English Proficiency Students

and Misconceptions in Mathematics:

A Case Study

Norlia T. Goolamally & Jamil Ahmad

ABSTRACT: When Mathematics is taught in English, students not only have to learn English but
they must also learn English words used in Mathematical context. This can lead to misconception
again due to the lack of understanding of English. So, Mathematics can be particularly challenging
for Limited English Proficiency (LEP) students. However, despite these challenges, the Malaysian
government’s policy to teach Mathematics and Science in English started eight years ago in 2002
with the intent to provide the citizens of the country with the scientific and technological competence
to face the globalize world. Thus, this study aimed to identify the approaches and strategies teachers
integrate in their lessons to overcome the challenges faced by LEP students. This qualitative case
study was conducted in a rural primary school in Pahang which has an enrolment of 1,800 students.
The school’s excellent achievement in the UPSR Mathematics grade has been ranked among the
top five schools in the state of Pahang. Other findings through classroom observations, interviews
with teachers and students and document analyses proved that teacher’s strength, enthusiasm,
and proficiency in English and creativity in their teaching strategies enable them to teach LEP
students, the subject most feared that is Mathematics, in the English language. In addition to that,
teachers teaching techniques encourage students to build confidence in learning Mathematics and
become less anxious to this fearful subject.
KEY WORDS: Bilingual learners, homework assignment, limited English proficiency students,
Mathematics, and misconception.

Introduction

Mathematics has its own specialized language, grammatical patterns and rules,
and it involves formulas, relationship, application, and explanation (Short &
Spanos, 1989). Due to this complexity, students create a certain kind of attitude
and thinking about Mathematics.

As mentioned by M. MacGregor and R. Moore (1991) that language plays an
important part in organizing knowledge, thinking logically, giving explanations, and
presenting results. But how do you account for teaching Mathematics in the students’
weaker language? These students are the group of Limited English Proficiency (LEP)
students who are learners of the English language. They learn English as a second
language but now have to be in a Mathematics class is taught in English.

Norlia T. Goolamally is a Lecturer at the Faculty of Science and Technology OUM (Open University
of Malaysia), Jalan Tun Ismail, 50480 Kuala Lumpur, Malaysia; and Jamil Ahmad, Ph.D. is a
Lecturer at the Faculty of Education UKM (National University of Malaysia), Bangi, Selangor Darul
Ehsan, Malaysia. They can be reached at: nolee@oum.edu.my and jamil3191@yahoo.co.uk

NORLIA T. GOOLAMALLY & JAMIL AHMAD,
Limited English Proficiency Students and Misconceptions in Mathematics

Teachers should not expect miracles to happen when teaching Mathematics to
LEP students in a language other than their mother tongue. Since Mathematics
has a language of its own, the nature of Mathematics is itself a burden to students
regardless of the language of instruction. Teachers have to teach students to develop
academic Mathematics skill as well as learning English. As a matter of fact teachers
should understand that learning a second language is as difficult for a child in
their class as it is for the teachers as adults. It may be more difficult for a child,
since they do not have the access to the memory techniques and other strategies
that more experienced learners can use in acquiring vocabulary and learning the
grammatical rules of the language.

Together with learning English as a second language, these LEP students must
also learn the unique meanings that some English words have in Mathematical
context. LEP students need to pick up and learn many content-specific vocabulary
words (e.g. quotient, equivalent, divisor, numerator, and denominator). Besides that, they
have to know the meaning of many complex phrases (e.g. least common factor and
greatest common factor). Many complex phrases are not found in bilingual dictionaries.
What most LEP students will do is that they will break apart the phrase (e.g. least
common multiple) and look up each individual word in a bilingual dictionary to try
to understand the meaning of the phrase. However, this strategy does not ensure
accurate translation. They need to understand that many common English words
have unique meanings in Mathematics (i.e. bring down, face, plane, cone, net,
positive, and negative). LEP students have to understand that prepositions (i.e. by,
with, to, into, from, etc.) are used in a variety of ways in word problems to highlight
operations. They need to know the meaning of prefixes and suffixes (i.e. hept-, tri-,
bi-, poly, -gon, and -lateral). There are other examples such as sentence constructions
and statements that they have to understand and acquire before starting to think
of solving the problem. Table 1 shows some common English words that can be
assigned to a single Mathematical operation.

Table 1
Multiple Meanings of English Words to Single Operation in Mathematics

Operation Common English Words
Addition add, plus, and, combine, sum, total of, more than, increased by, greater than.

Subtraction subtract, minus, less, less than, fewer than, decreased by, difference, lower, take
away, from, shorter.

Multiplication multiply, times, product, as a factor, twice, double, triple, groups of.

Division divide, divided by, quotient, separated into equal groups, shared equally, over,
into, how many groups.

Equal is, are, result, make.

Teachers’ ability to provide an environment where the integration of the English
language and academic skills development can be enhanced is necessary (Tikunoff,
1985). However, one major problem that leads to serious learning in Mathematics
is the occurrence of misconceptions which results if students do not have proper or

EDUCARE:
International Journal for Educational Studies, 3(1) 2010

adequate teaching, informal thinking process or poor remembrance. Misconception
is defined as a mistaken idea or view resulting from a misunderstanding of
something. Misconceptions are strongly held beliefs that students constructed based
on limited understanding of a certain phenomena. An example of a misconception
is a teacher might just describes the operation of multiplying by 10 as adding a 0.
These misunderstanding will cause students unlimited trouble in grasping with
Mathematics from the most elementary concepts until they do Calculus.

Students’ misconceptions cause teachers a lot of stress and frustration on why
students cannot follow their teaching (Resnick, 1983). Misconception needs to
be repaired and remedied and it can only be done by changing the conceptual
framework of students (Resnick, 1983). It is not enough to just merely inform or
advise the student on the misconception that they have. Neither does repeating a
lesson or making it clearer help students who have already formed strong reasons
for their misconceptions (Champagne, Gunstone & Klopfer, 1983; Resnick, 1983;
and McDermott, 1984). Teachers have to explore and understand why these
misconceptions arise and then plan a strategy on how to remedy the problem.
Teachers must help students to reconstruct correct conceptions (Mestre, 1987).
Misconception results from students belief systems and also their thinking
process and the only effective way to correct misconception is to change these
misconceptions from the inside, which is from the students’ systems.

Statement of the Problem

In 2003, the Malaysian government had implemented a national policy for the
teaching of Mathematics and Science in English. This is in line with the increased
importance of Mathematics and Science in the development of knowledge-based
economies. Mathematics and Science teachers are required to use the English
language for their instructional delivery. The MOE (Ministry of Education) is very
much dependent on the capability and the expertise of teachers to bring change to
any policy brought about especially with regards to reform in education. Teachers are
direct agents of change for the mission and goals set by the MOE. Have the spirit and
enthusiasm of our Mathematics teachers declined ever since they started this mission?
Are they capable to overcome students’ problems in learning Mathematics?

Mathematics is not an easy subject to teach. Mathematics teachers have a growing
concern about students’ misconceptions in Mathematics (Mestre, 1987). Teachers
understand that when students have misconceptions, students can become slow
learners in Mathematics and may even develop fear or anxiety toward Mathematics.
These problems if not solved early will interfere with students’ future learning of
Mathematics. Teachers can easily make an easy explanation or excuse by saying that
these students are not capable of understanding and should not take Mathematics or
class them as low intelligence students. But what teachers are most concerned with
is, every child is not left behind and have the right to learn in class.

Knowing the fact that students have misconception in Mathematics (students do
not come to class as “blank slates” – L. Resnick, 1983) and coupled with a few more

NORLIA T. GOOLAMALLY & JAMIL AHMAD,
Limited English Proficiency Students and Misconceptions in Mathematics

issues from the new policy, teachers are more stressed than ever. Certain issues such
as teachers inadequate proficiency in English and it has been observed that some
Mathematics teachers failed to plan effective measures to help students in overcome
difficulties in learning Mathematics in English (Noraini Idris et al., 2007).

Therefore, this study is conducted basically to look into the practices of the
Mathematics teachers on students’ misconceptions and also teaching Mathematics
in English. This study aimed to investigate teachers’ best practices in handling and
overcoming misconceptions in the teaching of Mathematics. In addition, this study
also aimed to further explore the delivery methods teachers incorporate in their
class in order to deliver Mathematics instruction in English.

Objective of the Study, Research Questions,

and Scope of the Study

The main objective of the study is to uncover the best practices of successful teachers
in this school in their delivery method in order to minimize misconception among
students in Mathematics as well as to maintain the culture of teaching the subject
in English.

The main research questions investigated in this study were: (1) How do
teachers manage to teach Mathematics in English while at the same time trying
to overcome students’ difficulty in learning Mathematics?; and (2) What are the
common misconceptions that teachers observed among their LEP students?

The scope of the study was limited to a Primary School situated in the outskirt of
Kuantan, Pahang. Primarily, this school was selected because it has been ranked among
the top five of all the Primary Schools in Pahang according the UPSR (Ujian Penilaian
Sekolah Rendah or Primary School Assessment Test) 2007 examination results.

Research Methodology and

Data Collection and Management

The methodology used mainly consisted that of a qualitative case study. Data
was collected mainly using interviews, class observation, and document analysis.
Context and background information of the school was collected through
observation and document analysis. A case study design was conducted since it
seems that it is the most appropriate method to look into the nature of how the
teaching and learning of mathematics takes place in class.

The school selected for the study was one of the top five schools in the state
despite being located in the outskirts of Kuantan, Pahang, Malaysia. The classes
observed were from the Year Three and Year Five classes. The researchers also
managed to gather data from the homework exercises done by students in their
exercise books. These exercises were identified and collected according to the
research questions.

Various procedures were followed before data were collected from the sample
school. The principal provided the proper resources for the data collection. On the

EDUCARE:
International Journal for Educational Studies, 3(1) 2010

first day of the research, the principal gathered some of the Mathematics teachers
for a short meeting. The Mathematics teachers were explained of the purpose of
the research and the welcome the objective of the research. They showed their
support and were willing to be interviewed and also to be observed in class while
they are teaching (Crandall et al., 1985). The principal, the assistant principal, the
Mathematics expert teacher (guru pakar Matematik), and the rest of the Mathematics
teachers were involved in the semi-structured interviews. Interview questions were
focused on the issues and challenges of teaching Mathematics based on the new
policy: the common misconceptions teachers observed among their students and
also their teaching strategies to guide and help students in learning Mathematics
in the English language. The Mathematics expert teacher collected students’
exercise books from various classes in different years for further analysis of the
misconceptions that can be traced from the Mathematics questions answered
by students. Focus group interviews explained the activities carried out by the
Mathematics panel in improving their teaching methods to ensure that students
continue to learn even if they have to learn in English.

Presentation of Results:

Results were discussed and presented in two sections. The first section presents
findings of the study, whereas the second section will cover discussion, conclusions
and implications of the study.

A. Findings of the Study

The overall findings reflect the research question which focuses on the issues related
to the misconception due to language and the subject matter. Findings will also
reflect on the variation in teaching approaches to meet students’ requirements in
understanding the concepts.

There were altogether 17 Mathematics teachers and all of them have more than
five years teaching experience. The school has a male Mathematics expert teacher
who has more than 12 years teaching experience.

First, Data collected from classroom observation. In all the classes observed,
the teachers were organized and efficient in their delivery of the subject content.
Teachers communicate clearly and slowly to ensure students followed their
instructions. In some of the classes observed, teachers explained the concepts in
Malay before introducing the English term. In one of the classes observed almost
95 percent of the lesson was conducted in the Malay language. This class is one
of the end classes in Year Three.

Overall, classroom management in all the classes observed was good. This is
so because students are actively involved over half the time of the lesson observed.
Students followed through the instruction conscientiously, paying attention, and
looking at the teachers explaining in front of the class. Students participated actively
especially during the 5 minutes questioning session at the beginning of the class.

NORLIA T. GOOLAMALLY & JAMIL AHMAD,
Limited English Proficiency Students and Misconceptions in Mathematics

Students were motivated and appear to be more interested when their teachers bring
in some teaching aids for them. They appear to enjoy listening and look earnestly
at their teacher’s explanation using the teaching aids.

In almost all the classes observed, the teachers speak slowly and they came into
class with their manipulative to increase students’ attention toward the subject.
Teachers continuously explain in detail although students responded in groups
when answering questions. The Mathematics teachers accepted students’ remark
or students’ responses in Malay. They do not penalize students who communicate
with them other than the English language.

However, in summary, what have been observed is that at the end of the class,
almost all the teachers’ ask simple questions for example class: do you understand
this example?; and/or do you think you can do some questions at home?. They tend to
limit themselves to Yes or No questions; or low level questions which is sentence
completion type and almost invited chorused answers. Throughout the classes
observed, there were hardly questions to probe students’ ability to analyze the
content discussed in the lesson.

The results of the study indicate that the classroom interaction in the classes
observed were total class instruction. Teachers’ instruction made up about 70
percent of the time and approximately about 30 percent of the time students
worked independently. Almost 90 percent of the time students were observed
doing seatwork.

The following is an observation of one of the classes:

Teacher enters class and distributes questions for the day.

Students were given five minutes to do the questions.

After five minutes teacher gives the answer and students mark their own paper. Teacher then ask for
the number of students who got all correct answers. Students raised their hands to show the correct
answers they have got.

Then students put away the paper and formal class teaching begins.

Teacher begins by saying, “Hari ni Cikgu akan mengajar pecahan. Ingat, kita dah pernah belajar pecahan
pada tahun lepas?” (Today, I am going to teach you fractions. Remember, we have done something
on fractions last year?).

And teacher explained the whole topic of “improper fraction” using the Malay language. To start
introducing the topic, she called two students (one being smaller than the other) to the front and
showed the possibility of a smaller classmate carrying a bigger classmate and compared it if it is
vice versa. And in Malay, she explained that a smaller child cannot carry a bigger child, thus it is
not proper.

Then only she introduced the term “improper fraction” to tell the class of some numbers which
is bigger than the number at the bottom of a fraction and she uses the Malay term “pecahan tak
wajar”. She then used the teaching aid that she brought in and showed the class further examples
of improper fractions.

EDUCARE:
International Journal for Educational Studies, 3(1) 2010

Second, Data collected from interview session. From the interview sessions, the
Mathematics teachers worked collaboratively in a team to teach the examination
classes. The Mathematics panel prepared questions that can be used during the first
5 minutes of class time. These questions were kept and sequenced according to the
dates proposed by the panel. Teachers used these questions as a drill before teaching
starts. Teachers admitted that they have very serious problems when teaching in
English. They explained that almost 98% of the students are from families who do
not use the English language at home. The other difficulty that they complained
is that of their own deficiency in delivering the subject in English. Although they
have attended the ETeMS (English Teaching for Mathematics and Science) course
conducted by the MOE (Ministry of Education), yet they still feel that they have
not acquired the skill to successfully deliver confidently in English.

Teachers also explained that they were unable to build the necessary conceptual
foundation of Mathematics due to the language barrier of the students. Now
that teaching is in English, they are worried that students will have double their
misconceptions: misconception due to Mathematics and misconception due the
language. Their concern is that this will cause serious problems later because
students are taught only the lower Mathematical skills and the reasoning skills are
not focus in class. They explained that reasoning skills requires the ability to explain
Mathematical concepts and how students’ thinking is progressing. Students find
difficulty in expressing their reasoning power because they are not proficient in the
language. Some comments from the teachers in the interview are as follows:

Teacher A: “Mathematics is not an easy subject to teach. Even when we teach in Malay, they are
having problem what more if they have to learn in English”.

Teacher B: “All of us here, help each other in class. Teachers who are not teaching the exam classes
will teach Math if they have to go in for relief […]”.

Teacher C: “Students do not understand the question – many don’t understand the English terms
teachers use in class. One operation, for example, to find the total, a question can be phrase as
find the sum or how many altogether?

Head of the Mathematics Panel: “[…] Students mark their own books and do the corrections
themselves according to teachers’ example. We teachers are so busy, we simply don’t have time
to check every book”.

Teacher D: “[…] misconception […] we don’t have time to trace students misconception”.

Teacher E: “Sometimes I can see wrong answers repeated. But I cannot do much, I have to finish
the syllabus and other school activities, and teaching in English makes us slower”.

Teacher F: “[…] sometimes I feel guilty because I cannot speak well in English, especially the end
classes, students need more explanation”.

However, despite these problems and constraints, the teachers from this school
are always prepared with teaching aids and tried their very best to make the lessons

NORLIA T. GOOLAMALLY & JAMIL AHMAD,
Limited English Proficiency Students and Misconceptions in Mathematics

beneficial for the students. They attended to students weaknesses in the Malay
language, especially when introducing new concepts for the first time.

Third, Data collected from students’ exercise books. Two sets of students’
exercise books were taken from each of the classes in Year Three to Year Six.
Students maintain 2 Mathematics exercise books. All exercises were either marked by
themselves or by their partners in class. Errors were corrected beside the appropriate
question and the corrected answers were noted down. Further analysis of the
exercises showed that some common errors in a number of questions were repeated
observed. A few examples from their exercises are attached as in Appendix A.

B. Discussion

Findings from this research were specifically representative for this school that has
been observed only. However, some aspects of this study can be used as a guide to
help teachers to reflect on their own practice in their school.

This research has shown that teachers played an active role during class
instruction. Teachers delivery of content and use of manipulative in their classroom
helped to increase students attention and teachers keep students alert by calling out
their names to answer teachers’ questions. Although the language of instruction
has to be in English, teachers continue to teach classes at the lower end using the
Malay. Teachers feel more confident and comfortable to teach using the Malay
language to these students who are not proficient with the English language. It is
not easy to explain Mathematical ideas when students cannot follow or understand
the language of instruction.

This finding is in line with J. Echevarria, M. Vogt and D. Short (2004), who
placed great importance in communicating Mathematical ideas as it is not a straight
forward process since Mathematics involve concepts, processes and applications,
and the development of the English language should be done in a naturally.

Although teaching Mathematics in Malay is not recommended in the curriculum
policy, teachers in this school felt that they were left with no choice. This is their
last resort to ensure students come into class and learn Mathematics. Teachers pay
less concern on the language skills but encourage students to be engaged in the
Mathematics content but in Malay. Looking back into literature, it seems that this
method is similar to the instructional models for teaching LEP students which is
the sheltered instructional model. According to J. Crandall et al. (1985), this method
can be effective for LEP students because they can learn Mathematics better in
their first language and also learn a second language successfully. In this study,
teachers use of visual aids and hands-on activities helped to keep students focused
to teachers’ instruction. As S.D. Krashen (1982) asserted that language acquisition
occurs when input is meaningful and understandable when lessons use concrete
objects, graphics, manipulative, and hands-on activities to clarify and reinforce
new concepts. It has also been reported that a child progresses if teacher explains
and clarifies concepts in the child’s primary language which is their mother tongue
(Cummins, 1981; Tikunoff, 1985; and Wong & Valadez, 1986).

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International Journal for Educational Studies, 3(1) 2010

Somehow or rather teachers delivering in Malay can also be seen as the
inadequate proficiency of themselves in the English language. This coordinates
with the data collected from the interview session with teachers who feel that
they themselves are not fully confident in delivering the content of Mathematics
to the students because of their limited proficiency in the language. Teachers feel
that facing students in the end classes requires more fluency of the language when
compared to students in the first few classes. Lower achievement students need more
explanation and guidance. As suggested by Noraini Idris et al. (2007), teachers who
believe that they do not have adequate professional development tends to teach
Mathematics in other languages interchangeably with English. These teachers
feel that they are not competent to face students who have learning disabilities
in Mathematics who needs much more explanation and examples in class when
compared to the students who are able to do mathematics.

For LEP students to succeed in the Mathematics classroom, it is essential that
teachers connect previous knowledge and experience to new concepts that are
being taught and integrate academic vocabulary to build Mathematical concepts.
It is critical that teachers are able to integrate language and content instruction.
The teacher is the heart of the lesson. The design and planning of the lesson to
the questions asked at the end of the class is all dependent on the expertise of the
teacher (Ellerton, 2004). But, what seems to be forgotten in these classrooms is
that the teachers failed to establish learning environments which nurture students’
Mathematical problem solving skills and creativity. What has been observed is that
students are called to answer only low level knowledge questions; teachers do not
allow time for students to answer questions on their own.

This is quite understandable since teachers still feel the dissatisfaction to teach
Mathematics in English. This is mainly due to their own personal reasons for not
being competent in the language to give challenging questions to students and also
probably understanding their own students’ ability to answer the questions. During
the three days observation, teachers did not reach out to students with questions
leading to higher order thinking skills even in the good classes.

However, in one of the Year Five classes observed, the teacher start with asking
a high level cognitive question but not allowing time for them to give their answers.
But rather the teacher guided and structured the students thinking about the problem
slowly by asking a sequence of low level questions. Finally, both parties were
satisfied on arriving at the answer but there is no guarantee that lessons has been
learned. According to G. Brousseau (1984), guided instructions to solve higher level
Mathematics tasks will only deny students the opportunity to formulate and apply
their own strategies. This is observed when the teacher planned the question as well
as the answering technique leading the students to the answer. This is a quick way to
teach problem solving but do not ensure students understanding of concepts since
we deny our students the opportunity to think creatively at their own pace.

Teachers also provided a substantial amount of work in Mathematics for the
students to do at home. Analysis of the Mathematics assignment clearly showed
that students have been further reinforced at home with exercises according to the

NORLIA T. GOOLAMALLY & JAMIL AHMAD,
Limited English Proficiency Students and Misconceptions in Mathematics

topics taught in class. However, some remarks should be highlighted and discussed.
Exercises were given to reinforce and strengthen whatever is being learned in class
but they were not checked by the teachers.

Research findings have shown that homework assignments are helpful to
students if they were planned and have direct meaning to students as well as teachers
(Paulu, 1995). But the common practice in this school is that the individual student
concern will mark their exercise book. So teachers are not actually aware of the
errors or corrections that the students have undergone. Unmarked exercises by
teachers will lead to uncorrected errors by students. If teachers do not checked for
errors in students’ assignment, these same errors will be repeated throughout the
year. Students will not understand why they make the same mistakes. Mistakes or
errors like this will become misconceptions unless corrected by teachers. According
to H. Cooper (1989), teachers have the responsibility to attend to the mistakes that
students do and he even emphasized that homework assignments should be graded
and given remarks either positive or negative in order to improve the child.

Conclusion and Recommendation

To summarize, perhaps the most effective lessons are when the teacher does the
work beforehand in the planning, based on what has happened before and not at
the time when teaching takes place. Teachers are confronted with lots of challenges
in teaching Mathematics. Having said that Mathematics teachers should not make
all these challenges as an escapist route for them just to satisfy themselves and put
all the blame of failures to the students. Teachers should have the enthusiasm and
spirit to transform every challenge into an opportunity to improve students’ ability
in Mathematics. In order to promote Mathematics learning in class, teachers need
to encourage an environment where it is OK to be wrong. As teachers, we are
expected to try to think together with our students, especially when new concepts
are being introduced in class and we have to probe and identify the misconceptions
that need to be corrected.

In this particular study, the best practices observed was that teachers’
understanding of students limitation in English, made them proceed with their
delivery in Malay and introducing Mathematical terms in English slowly to students.
Teachers kept class attention by using teaching aids and supporting students with
prepared written questions to sustain their focus from the beginning of the class until
lesson ends. They were flexible in the teaching approach and able to manipulate
students’ strength and weaknesses in the language of instruction by introducing
various teaching strategies according to students’ ability. There is not a doubt that
these are best practices in this respective school.

However, what is left to be of our concern is that when there is too much
emphasis focused on the development of the English language, there are some
aspects of the Mathematics curriculum not being addressed. Do we raise questions
to challenge the cognitive development of the child in our daily teaching? Are we
looking into issues concerned with misconceptions and errors in Mathematics,

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International Journal for Educational Studies, 3(1) 2010

either in our daily instruction or in homework assignments? To what extent do we
know that by drawing students’ attention, they have cleared all their misconceptions
and finally use the correct conceptual framework that is required for that particular
topic? Is it enough to prepare our next generation of youth who will have to face
challenges in a more competitive world just by asking low level Mathematics
question just because of the inadequate proficiency of the teachers in the English
language or the inability of our LEP students? These are some painful yet truthful
issues that we have to face.

According to G. Valdez, A. Svedkauskaite and M. McNabb (2002), when a
teacher conducts quality teaching there will always be checking for understanding
when new concepts are introduced and continuous checking for understanding
in homework assignment, vocabulary, and writing activities to ensure students
are engaged throughout the learning process. What seems to be the problem in
Mathematics classes now is that teachers work too hard, teachers solve all the
problems but despite of teachers working hard, and the implementation of the
discovery and inquiry teaching approach, students are still “cognitively” passive,
uninvolved and not working hard enough. As teachers, it is always wise to look
back and become reflective practitioners so that every action that we plan will not
damage our children’s future.

References

Brousseau, G. (1984). “The IREM’s role in Helping Elementary-School Teachers” in Robert Morris
[ed]. Studies in Mathematics Education : The Mathematical Education of Primary-School Teachers. Oxford:
Pergamon, pp.235-251.

Champagne, A.B., R.E. Gunstone & L.E. Klopfer. (1983). “Naive Knowledge and Science Learning”
in Research in Science and Technological Education, 1(2), pp.173-183.

Cooper, H. (1989). “Synthesis of Research on Homework” in Educational Leadership, 4, pp.85-91.
Crandall, J. et al. (1985). “The Language of Mathematics: The English Barrier” in A. Iabarca & L. Bailey

[eds]. Delaware Symposium on Language Studies. New York: The College Board, pp.129-150.
Cummins, J. (1981). “Age on Arrival and Immigrant Second Language Learning in Canada: A

Reassessment” in Applied Linguistics, 92, pp.132-149.
Echevarria, J., M. Vogt & D. Short. (2004). Making Content Comprehensible for English Language Learners:

The SIOP Model. New York: Center for Research on Education, Diversity and Excellence, second
edition

Ellerton, N.F. (2004). “Developing Higher Order Thinking Skills Through Problem Solving in the
Secondary Mathematics Classroom” in Proceedings of the Seminar on Best Practices and Innovations
in Teaching and Learning of Science and Mathematics at the Secondary School Level. Kuala
Lumpur, Malaysia: EPRD, MOE, pp.23-35.

Khisty, L.L. (2005). “A Naturalistic Look at Language Factors in Mathematics Teaching in Bilingual
Classroom”. Paper presented in the Third National Research Symposium on Limited English
Proficient Student Issues: Focus on Middle and High School Issues.

Krashen, S.D. (1982). Principles and Practices in Second Language Acquisition. Oxford: Pergamon.

NORLIA T. GOOLAMALLY & JAMIL AHMAD,
Limited English Proficiency Students and Misconceptions in Mathematics

MacGregor, M. & R. Moore. (1991). Teaching Mathematics in the Multicultural Classroom. Melbourne,
Australia: University of Melbourne.

McDermott, L. (1984). “Research on Conceptual Understanding of Physics” in Physics Today, 37,
pp.24-32.

Mestre, J. (1987). “Why Should Mathematics and Science Teachers be Interested in Cognitive Research
Findings?” in Academic Connections. New York: The College Board.

Moschkovich, J. (2000). Learning mathematics in two languages: Moving from obstacles to resources.
In W. G. Secada (Ed.), Changing the faces of mathematics: Perspectives on multicultural and gender equity.
Reston, VA: National Council of Teachers of Mathematics.

Noraini Idris et al. (2007). “The Professional Preparation of Malaysian Teachers in the Implementation
of Teaching and Learning of Mathematics and Science in English” in Eurasia Journal of Mathematics,
Science, and Technology Education, 3(2), pp.101-110.

Paulu, N. (1995). Helping Your Child with Homework. Washington DC: U.S. G.P.O. Also available online
at: http://www.ed.gov/pubs/parents/Homework/title.html [accessed in Kuala Lumpur, Malaysia:
21 April 2010].

Resnick, L. (1983). “Mathematics and Science Learning: A New Conception” in Science, 220, pp.477-
478.

Short, D.J. & G. Spanos. (1989). “Teaching Mathematics to Limited English Proficient Students” in
ERIC Digest. Washington DC: ERIC Clearinghouse on Language and Linguistics, ERIC Document
Reproduction Service No.ED317086, November. Also available online at: http://www.eric.ed.gov/
contentdelivery/servlet/ERICServlet?accno=ED317086 [accessed in Kuala Lumpur, Malaysia:
21 April 2010].

Tikunoff, W. (1985). Applying Significant Bilingual Instruction in the Classroom. Rosslyn: National
Clearinghouse for Bilingual Education.

Valdez, G., A. Svedkauskaite & M. McNabb. (2002). “Critical Issue: Mastering the Mosaic-Framing
Impact Factors to Aid Limited-English-Proficient Students in Mathematics and Science”. Also
available online at: http://www.ncrel.org/sdrs/areas/issues/content/ma700.htm [accessed in
Kuala Lumpur, Malaysia: 21 April 2010].

Wittrock, M. (1988). A Constructive Review of Research on Learning Strategies. San Diego: Academic
Press.

Wong, F.L. & C. Valadez. (1986). “Teaching Bilingual Learners” in M.C. Wittrock [ed]. Handbook of
Research on Teaching. New York: Macmillan Publishing Company, third edition.

EDUCARE:
International Journal for Educational Studies, 3(1) 2010

Appendix A
Examples of Repeated Errors in Student Exercise Book

STUDENT A:

STUDENT B:

NORLIA T. GOOLAMALLY & JAMIL AHMAD,
Limited English Proficiency Students and Misconceptions in Mathematics

STUDENT A:

EDUCARE:
International Journal for Educational Studies, 3(1) 2010

STUDENT B:

NORLIA T. GOOLAMALLY & JAMIL AHMAD,
Limited English Proficiency Students and Misconceptions in Mathematics

Learning a second language is a complex process that develops in sequential stages. During this
learning process, students may experience various stages from a “silent period” to a one- or two-
word responses, and later basic dialogue in simple sentences until finally into the advanced stage

where they finally attained a grade level when they can converse fluently and understand grade level
classroom activities.