Mother Tongue Policies and Mathematical
Terminology in the Teaching of Mathematics

Mercy Kazima

University of Malawi
mkazima@chanco.unima.mw

Many countries in Africa have mother tongue policies which require learners to be taught in
their mother tongue for at least some of the years of primary education. This paper
discusses the implementation of such policies in relation to mathematical terminology in the
teaching and learning of mathematics. I present and discuss two strategies of dealing with
mathematical terminology when teaching in the mother tongue: the strategy of developing
mathematics registers in the local languages and the strategy of borrowing from
mathematical English. I discuss the cases of Nigeria and Tanzania as examples of the former
and the case of Malawi as an example of the latter. The discussion illustrates the strengths of
each strategy as well as potential problems. I conclude with a discussion of implications for
Malawi specifically and for any African country in general.

Mother tongue policies require that learners be
taught in their mother tongue for some or all of the
years of schooling. This is fairly manageable when
the subject concerned is one that does not have its
own highly specialised terminology. However, the
picture becomes rather complicated when the
subject is mathematics. The problem arises
because the mathematical information comes in a
register of the so called ‘language of wider
communication’ such as English. It therefore
becomes necessary to render this information into
the language of the learners. In Malawi this has
hitherto meant rendering it into Chichewa, among
other local languages. However, it has been shown
that Chichewa is currently inadequate as a vehicle
for conveying scientific information in general,
and mathematical information in particular because
the language lacks suitable terminology for
expressing scientific and mathematical concepts
and ideas (Kishindo, 1987; Kishindo & Chiotha,
1995; Kishindo & Kazima, 2004). This finding is
important because it shows that using Chichewa as
the language of instruction for mathematics needs
consideration of how to handle mathematical
terminology to help Chichewa overcome its
present limitations.

Mother tongue policies and issues of language of
teaching and learning are often thought of as a
dichotomy between the mother tongue and English
(Setati et al., 2008). Many, including policy

makers, take it to mean making a choice between
teaching and learning in English or teaching and
learning in the mother tongue. As Setati et al.
(2008) explain,

Debates around language and learning … create
an impression that the use of the learners’ home
languages for teaching and learning must
necessarily exclude and be in opposition to
English, and the use of English must necessarily
exclude the learners’ home languages. (p. 3)

Setati et al. (2008) argue, however, that using
home languages in the classroom does not have to
be in opposition to English.

The role of language in mathematics
teaching and learning
Use of English in teaching and learning
mathematics involves ordinary English (as in
everyday use) and mathematical English (where
words and phrases have specific meanings in
mathematics) (Pimm, 1987). The latter is what has
been referred to as the mathematics register
(Halliday, 1974). The mathematics register
includes words from ordinary English but having a
specialised mathematics meaning, for example,
‘set’, ‘power’, ‘similar’ and ‘difference’, and also
includes words like ‘polygon’, ‘isosceles’ and
‘quadrilateral’ which are borrowed from other
languages (Orton, 1992; Pimm, 1987).

Pythagoras, 67, 56-63 (June 2008) 56

Mercy Kazima

Studies that have investigated learners’
understanding of a variety of mathematics words,
have demonstrated that some learners do not
understand many of the words that are commonly
used in mathematics classrooms (for example,
Berenson & Vidakovic, 1996; Kazima, 2006;
Otterburn & Nicholson, 1976; Williams, 1995). In
particular, learners have problems with words that
have one meaning in mathematics and another in
ordinary English. The word ‘similar’ for instance,
means ‘proportional’ in mathematics yet in
ordinary English it means ‘alike’. This causes
confusion because what is similar in ordinary
English is not necessarily similar in mathematics,
and vice versa (Orton, 1992). Pimm (1987) and
Orton (1992) have given some interesting
anecdotes about learners experiencing difficulties
in mathematics because they do not understand the
mathematical meanings of the words involved. For
example, in response to the question “what is the
difference between 47 and 23” one learner
responded “one of the numbers is bigger than the
other”. When this was not accepted, he tried “one
number contains a 4 and a 7 but the other number
doesn’t” (Orton, 1992, p. 128). Another example is
that of a 13-year-old learner who counted the
number of diagonals in a given figure as the
number of sloping sides the figure had relative to
the orientation of the page (Pimm, 1987). The
learner’s response to the question “if you knew the
number of sides of a polygon, could you work out
the number of diagonals?” was “it depends on what
the shape is and which way you place it” (p. 84).
The two examples show clearly that the learners
did not understand the mathematical meanings of
the words ‘difference’ and ‘diagonal’ and were
employing the ordinary English meanings which
landed them in difficulties. This is an illustration of
the problems learners experience when they make
errors of interpretation based on common everyday
use of the words. This problem exists even for
older learners as was demonstrated by Monaghan
(1991). He studied A-level learners in England and
observed that the word ‘converges’, for example,
which is commonly used in calculus courses to
mean ‘approaches’ or ‘limit’, was confusing for
many learners. The learners could not see how
sequences of numbers could converge because
ordinary use of the word is strongly linked with at
least two lines ‘converging’ and eventually
meeting.

Other mathematics words, especially those
borrowed from other languages, like ‘isosceles’
and ‘quadrilateral’ do not seem to occur elsewhere

outside mathematics (Orton & Frobisher, 1996).
Since the words have only one meaning, learners
might be able to learn the meanings without
confusion with other everyday usage in ordinary
English. However, some researchers have found
that although some of the words can be explained
in terms of their roots and origins, the words still
cause problems because often learners do not
remember the meanings (Berenson & Vidakovic,
1996; Otterburn & Nicholson, 1976; Williams,
1995).

Comprehension of mathematical word problems is
another area that highlights the role of language in
learning mathematics. Researchers such as Fasi
(1999) and Woo-Hyung Whang (1996) explored
how learners understand word problems in
mathematics. A common finding was that the more
competent the learners were in English the better
they were at comprehending word problems. In
addition, many learners with low competence in
English performed better on non-verbal
mathematics tasks than on mathematically
equivalent word problems (Fasi, 1999), which
suggests that language difficulties interfere with
learners’ ability to solve mathematics word
problems. As Fasi concludes, the English in the
word problems confuses and misleads many
learners even when the mathematics involved is
simple.

Other researchers (e.g. Adetula, 1990; Beecham,
2000; Jones, 1982; Berry, 1985; Bunyi, 1997) also
had similar results and drew the same conclusion
that language presents difficulties in learners’s
understanding of word problems. Furthermore,
many observed that when learners do not
understand the word problems they often resort to
‘cue word strategy’ (Adetula, 1990; Jones, 1982)
that is, searching for a word that will give them a
hint of which arithmetic operation to carry out. For
example, it has been found that the words ‘more’,
‘less’ and ‘share’ prompt learners to add, subtract,
and divide, respectively, regardless of what the
question is asking (Adetula, 1990; Jones, 1982).

It is important to realise that language difficulties
with word problems are not unique to second
language speakers of English. Research has shown
that even first language speakers face difficulties
with word problems (De Corte & Verschaffel,
1991; Gibbs & Orton, 1994; Orton, 1992).
However, one would expect that first language
speakers have difficulties mainly with the
mathematical English while second language

Mother tongue policies and mathematical terminology in the teaching of mathematics

speakers have difficulties in coping with the
ordinary English, which they are not competent in,
as well as the mathematical English.

Setati et. al.’s (2008) study which aims at helping
learners with this problem of comprehension of
word problems by using the learners’ home
languages as resources in the classroom offers
versions of word problems in the learners’ home
languages. They conclude that this strategy
improves learners’ comprehension of the word
problems and so makes the mathematics accessible
to all the learners because they focus on the
mathematics and not the language as is the case
when comprehension is a problem. An interesting
observation in Setati et. al.’s study is that, where
one teacher translated mathematics word problems
including mathematical terms into the learners’
local languages, the learners found the terms
harder to understand than when presented in
English. Although it can be argued that it might
have been the teacher’s translation that was
problematic, the point is that it was not easy to
provide a translation that learners could
understand. As Setati et al. (2008) explain the
problem for learners when working with English
word problems is not only with terminology but
comprehension of the entire problem. This can be
extended to the whole lesson to say the problem is
in comprehension and communication of
mathematics in the classroom, so focusing on
terminology alone might not be helpful in our
objectives of making mathematics accessible to
learners.

The discussion above clearly illustrates that
language plays an important role in the teaching
and learning of mathematics. We see that
mathematical terms with precise meanings in
mathematics but also with everyday English
meanings cause confusion for many learners. On
the other hand, completely new words that do not
occur elsewhere in everyday English might not be
confusing for learners but they do have their own
potential problems. The inference can be drawn

here that mathematical terms in any language
which have also everyday meanings in the
everyday usage of the language would cause
confusion among learners. Similarly completely
new words that are not part of the language would
have potential problems. What is a country to do
when implementing mother tongue policy? How
can a country deal with mathematical terminology
when teaching in the mother tongue? I will discuss
two different strategies; (a) developing a
mathematics register and (b) borrowing from
English. I will discuss three African countries:
Tanzania and Nigeria as examples of developing a
mathematics register and Malawi as an example of
borrowing from English

The Nigerian case
The use of an African language as a medium of
instruction has gone a long way in Nigeria. Meta-
language has been developed in the vernaculars for
language, literature and teaching methods
(Emenanjo, 1990; Muhammed, 1990; Bamgbose,
2004). The development of meta-languages for
Nigerian languages is in keeping with the
Government’s National Policy on Education,
which states that the medium of instruction in the
first three years of primary education should be in
the learner’s mother tongue. Furthermore the
government recognises any two of the three main
languages (Hausa, Igbo and Yoruba) as core
subjects for secondary school learners (Adesina,
1990). It is therefore believed that if teachers are to
be produced for the use of these languages as
mediums of instruction at both primary and
secondary school, the teaching will extend to
colleges of education and universities where
teachers will be trained on how to handle the
language effectively. For these reasons, the
devising of mathematical terminology is
considered as an important aspect of language
planning. A glossary of primary mathematics has
been developed in some of the languages. Table 1
shows a sample of some mathematical terms in six
languages: Edo, Efik, Hausa, Igbo, Izon, and
Yoruba (Bamgbose, 1986).

Table 1: Sample of mathematical terminology in six Nigerian languages
Set Zero Base Sum Factor Point Angle
Edo Usun Ihoi Ezi Esomu Evbayagha Ihe Ukoko
Efik Ebok Ikpikpu Besi Iboroedidian Fakto Ntoi Itun
Hausa Tari Sifili Turke Jumla Ciduka Digo Kusurwa
Igbo Ikpo Efu Nkweongu Mgbakota Facto Kpom Mgba
Izon Ituu Yefaa Kientibi Oseee Diediebo Tein lelei Ikoki
Yoruba Seeto Ofo Ipile Aropo Fato Oju Angu

Mercy Kazima

In addition to the terms, it is recognised that the
process of teaching the various topics involves
expression in the general vocabulary of
description, explication and argumentation. On the
whole, these already exist in the general
vocabulary of the languages, but in some cases
such processes may involve technical vocabulary
which has also been devised. Interesting to note
here is that some of the terms for example ‘besi’
(base in Efik), ‘facto’ (factor in Igbo) and ‘angu’
(angle in Yoruba) seem to have been borrowed
from mathematical English.

According to Bamgbose (2004) teaching and
learning in these languages has so far been
successful. Bamgbose (2004) reports on a study
that used experimental design to evaluate the
effects of teaching in Yoruba. The study had two
main groups of learners. An experimental group
which was taught in Yoruba for all six years of
primary education, and a control group which was
taught in Yoruba for the first three years and
followed by English the last three years. Both
groups were evaluated in five subjects including
mathematics. The results showed that the
experimental group consistently performed better
than the control group. Bamgbose (2004)
concludes that teaching in the learners’ language is
more effective than teaching in English. By
implication this claims that teaching in Yoruba and
the other Nigerian languages, which involves use
of the terms in table 1, has been successful.

The Tanzanian case
In Tanzania, issues of language were given priority
in the process of nationalisation. Nationalisation in
education meant ‘Swahilisation’ of the content as
well as medium of instruction. The political and
social vision underlying it was education for self-
reliance. Swahilization meant in practical terms,
creating terminology for subjects where such did
not exist. Mathematical terminology has thus been
developed for primary schools. This terminology
has been developed on the understanding that the
problem rested on ensuring that the learners
understood the concepts and not the technical
vocabulary, since this could be translated from
English into Kiswahili (Abdulaziz, 1980). As a
result a practical approach to the teaching of
mathematics was followed. In teaching about the
circle for example, learners would be involved in
practical constructions; for example they would
peg a piece of wood into the ground, tie a rope
around it, and by using this rope draw a circle on
the ground. In the process, concepts of centre,

radius, diameter and circumference would be
practically introduced and followed subsequently
by the naming of the concepts (Abdulaziz, 1980).
Radius for instance is called ‘nusu kipenyo’ which
can be literally rendered into English as ‘half an
opening’, and circle is called ‘duara’ literally
meaning ‘wheel’. Other mathematical terms
developed in Kiswahili include the ones shown in
Table 2.

Table 2: Sample of mathematical terminology
in Kishwahili

Mathematical
English Kiswahili

Literal
meaning

Fraction Sehemu Portion
Decimal Sehenu za kumi Portion of ten
Percent Sehenu za mia Portion of hundred
Positive Hakika Certainty
Negative Kukana To say ‘no’
Multiply Nyongeza An increase
Remainder Mabaki What remains
Angle Pembe Angle
Triangle Pembe tatu Three angles
Quadrilateral Pembenne Four angles
Rhombus Msambamba sawa Parallel and equal

The Swahili method has aimed at transferring the
concept rather than mere translation. It is a faithful
transfer from the source language into the target
language of the concept conveying the term. Thus
a literal translation of the term has been avoided
because in most cases it does not convey meaning
of the term. In some cases a descriptive coinage
such as ‘sehemu za mia’ has been preferred. The
Swahili examples illustrate how internal resources
can be exploited to creatively develop a viable
mathematical terminology. As can be seen, the
vocabulary is already available in the language
only that now the meanings have been extended to
the realm of mathematics. The strength of the
Tanzanian strategy is that it focuses on the
mathematical concept of a term and not the literal
translation of the term into Kiswahili. However,
there is a potential problem because the literal
meanings might become a source of confusion for
learners. For instance the term for ‘multiply’ is
‘nyongeza’ literally meaning ‘an increase’. This
could be confusing for some learners since a
number can be increased by adding to it.
Furthermore, multiplying by zero, a negative
number or a proper fraction does not increase a
whole number but rather decreases it. Therefore
here the problem of everyday meanings interfering
with mathematical meanings, as discussed earlier,
might also occur.

Mother tongue policies and mathematical terminology in the teaching of mathematics

The Malawian case
Malawi’s mother tongue policy states that all
public schools should teach in the learners’ mother
tongue from standard 1 to 4 – the first four years of
primary education (Ministry of Education, 1996).
There are at least two factors which led to this
policy. Firstly, the Malawi government signed the
United Nations convention of learners’ rights in
education which emphasised the rights of learners
to be taught in their mother tongue. Secondly, the
Malawi government also signed a memorandum at
the African Unity which encouraged use of African
languages as mediums of instruction (Chienda,
2002). Local languages in Malawi include
Chichewa, Chitumbuka, Chiyawo, Chisena,
Chilomwe and others. In this paper I focus on
Chichewa because of its dominance as Malawi’s
national language.

Malawi’s strategy of dealing with mathematical
terminology when teaching in Chichewa was
introduced by the Malawi Institute of Education.
This was done through textbooks written in
Chichewa which were introduced in Malawi
primary schools in 1991. Before this all textbooks
were in English and so mathematical terms were
presented in English. Important to note here is that
the Malawi Institute of Education is a government
body and is the sole provider of textbooks for
primary schools in Malawi. The strategy is that of
borrowing from English, that is, they take terms as
they are in mathematical English and spell them in
Chichewa. Table 3 gives some examples.

Table 3: Sample of mathematical terminology
in Chichewa

Mathematical English Chichewa
Circle Seko
Decimal Desimo
Factor Fakitala
Fraction Fulakishoni
Multiple Matipo
Number Nambala
Percent Pelesenti
Quadrilateral Kwadilatelo
Quotient Koshenti
Rectangle Rekitango
Square Sikweya
Set Seti
Triangle Thirayango

Comparing the Chichewa mathematics terms with
the local language mathematical terms in the
Nigerian and Tanzanian cases presented in table 1
and table 2 respectively, where the terms have

meanings in the various languages, the Chichewa
terms in table 3 do not have meanings in Chichewa
although they are spelled in Chichewa. For
example, ‘triangle’ in Kiswahili is ‘pembe tatu’
literally meaning ‘three angles’, and ‘set’ in
Yoruba is ‘seeto’ literally meaning ‘to put
together’. On the other hand, the Chichewa terms
‘thirayango’ and ‘seti’ for ‘triangle’ and ‘set’
respectively, do not mean anything in Chichewa.

The strength of this borrowing strategy is that there
is no confusion with Chichewa everyday use since
these are not Chichewa words. Furthermore, the
precision of meanings of the terms is not lost in
interpretation. However, there are potential
problems as has been observed in classrooms
where English was the language of teaching and
learning that learners do not always remember the
meaning of English borrowed terms. Similarly the
Malawi learners might experience the same
problem with the Chichewa borrowed
mathematical terms.

There is as yet no thorough research that has
evaluated the effectiveness of this strategy for
teaching and learning mathematics in Malawi
primary schools. However, according to a small
study that explored the views of teachers and
learners in the effectiveness of using these terms in
teaching and learning mathematics, it was found
that all the teachers in the sample said it is
effective to teach mathematics using the Chichewa
borrowed terminology. Reasons that the teachers
gave for viewing this strategy as effective were
mostly that their learners could easily read and
write the Chichewa borrowed mathematical terms
(Kazima, forthcoming).

Discussion of the three cases
Looking across the three cases, Malawi’s strategy
has the advantage of easiness. First, it is easier for
the developers at Malawi Institute of Education,
since they only had to spell all the mathematics
terms used in Malawi schools in Chichewa to
present the Chichewa terminologies for schools.
This saved time and made the terms available for
use in schools in a short time which would not be
possible where a mathematics register in the
language is sought. Second, it is easier for teachers
as they implement teaching in Chichewa. The
teachers do not have to learn new words for
Chichewa mathematical terms, since they are used
to using the English words. Third, it is easier for
the learners. When they proceed from standard 4 to
standard 5 and onwards where the language of

Mercy Kazima

teaching is English, the learners do not learn new
words for the mathematical terms that they have
already encountered since the terms are the same.
The learners only have to learn the English
spellings and pronunciations of the terms

In contrast to the Malawi case, the Nigerian and
Tanzanian cases of developing a mathematics
register in their local languages took some time.
Educators had consultations with many people and
discussions among themselves as they developed
the mathematics registers. In Tanzania for example
they focused on transferring the mathematics
concepts and not providing literal translations. To
do this they explored their culture to find ways of
presenting the mathematical concepts. This
therefore demonstrated the link between
mathematics in the classroom and mathematics in
their culture. Consequently the strategy made the
mathematical concepts relevant to the learners’
everyday life. This opportunity of illustrating
relevance was lost in the Malawi case. However,
the challenge for Tanzania and Nigeria is to
capture precise mathematical meanings in the local
language terms and for teachers to avoid everyday
meanings interfering with learners’ understandings
of the local language mathematical terms.
Malawi’s case avoids this confusion with everyday
meanings but brings in its own problems of
learners not remembering what the terms mean.

The Nigerian case is similar to Malawi’s case in
that the mathematical terms are one word only
unlike the Tanzanian case where sometimes a
description in more than one word is used, for
example ‘msambani sawa’ for rhombus. While
single word terms might be desirable for
convenience, it might not be easy to get equivalent
terms in the local languages which capture the
mathematical meanings. However, using a
description might not necessarily capture the
precise meaning of the mathematical term. For
example the ‘msambani sawa’ for rhombus
literally means ‘parallel and equal’ which is not a
precise enough description of a rhombus since a
rectangle or parallelogram can also fit the
description. These are some of the dilemmas that
policy makers would face in making decisions
about how to deal with mathematical terminology.

What does this mean for Malawi?
The strategy of borrowing from mathematical
English has stirred discussion among mathematics
educators and linguists in Malawi. Many have
argued against the use of borrowed terminology in

the Malawi textbooks and in teaching. For example
Kishindo and Kazima (2000) have argued that
although the terms might have the phonological
structure of Chichewa, such as ‘fulakishoni’
(fraction) or ‘sikweya’ (square), they do not mean
anything in Chichewa. They argue further that the
underlying assumption seems to be that the
learners understand the English in the first place
hence the free use of ‘Chichewalised’ English.
Kishindo and Kazima (2000) argue for the need to
devise a mathematics register for Chichewa as has
been done for Kiswahili in Tanzania. They suggest
for example that the term ‘fraction’ which is called
‘sehemu’ in Kiswahili meaning ‘portion’, could be
called ‘gawo’ in Chichewa also meaning ‘portion’.
This argument might seem reasonable but there is
also an assumption made that if terms are in
Chichewa then learners will easily understand their
meanings. This assumption might not be true
because the meanings that learners should
understand are the mathematical meanings and not
everyday meanings of the words, and sometimes
these two meanings are different. Mathematical
meanings are often more precise than everyday
meanings. In English language it has been shown
that learners find mathematical terms such as
‘similar’, ‘difference’, or ‘converge’ that have
mathematical meanings different from everyday
meanings difficult (Monaghan, 1991; Orton, 1992).
Therefore it can be argued that although the
Chichewa borrowed terms do not mean anything in
Chichewa, learners could learn their meanings
without confusion with everyday use.

Other Malawian researchers in this area also
strongly recommend the development of a
mathematics register in Chichewa (for example, ;
Chienda, 2002; Kaphesi, 2000; Kaphesi, 2001;
Rambiki, 2004). Kaphesi (2001) in particular
argues that if no register is developed, then
teachers might use their own Chichewa
interpretations of mathematical terms which could
cause confusion and mathematical misconceptions
among learners. There is an assumption here as
well that if a term is presented in Chichewa then it
will not require further interpretations by the
teacher. This is not necessarily correct because a
Chichewa term could still require interpretation
and explanation by the teacher. For example
calling a fraction ‘gawo’ as suggested by Kishindo
and Kazima (2000) does not mean a teacher will
not have to explain its meaning, and like anything
else in teaching, the explanation is subject to the
teacher’s interpretation and is open to confusion or
misconceptions by the learners.

Mother tongue policies and mathematical terminology in the teaching of mathematics

It is interesting to see these arguments against the
strategy of borrowing mathematical terms when
according to the small survey mentioned earlier,
the teachers who are the implementers seem to be
happy with the strategy. The reasons the teachers
gave are quite convincing especially from the point
of view of the teacher whose main concern is for
the child to be able to learn. The teachers all said
that their learners are able to read the Chichewa
borrowed terms. This shows us that, for the
teachers, this ability to read the terms is important
for their teaching and hence a step towards
effectiveness. Indeed being able to read the terms
makes it possible for the child to engage with the
textbook. Whether they understand what they read
is a different matter but at least they can read the
terms and the teacher can take it from there.

In Setati et al.’s (2008) study, it is intriguing that in
some cases learners found the local language
mathematical terms (as translated by their teacher)
difficult to understand. Indeed mathematical terms
have precise meanings which are not easy to
capture in one word in many African languages;
often one needs a whole sentence to elaborate the
precise meaning of a term. This seems to suggest
that we should not try to present everything in the
local languages; some mathematical terms might
be best presented in their English form. This raises
the question of whether it is worthwhile to engage
in the huge task of trying to devise mathematics
registers in Chichewa and other local languages
that include all the mathematical terms used in
schools, as is being suggested by many interested
parties in Malawi. It is important to remember that
it is not the name of the term that is important but
the concept behind the term. For example, it is not
the name ‘fulakishoni’ or ‘gawo’ that is important
for learners to know but the concept of fraction.

What might be a way forward for Malawi is to
evaluate the strategy to establish its level of
effectiveness. Until there is evidence of lack of
effectiveness in teaching using the borrowed
terminology, it would not be wise to consider
alternatives. If and when there is a need to consider
developing a register for Malawi, again careful
examination of the proposed strategy will need to
be done other than copying what other countries
such as Tanzania or Nigeria have done because
what works for the other countries might not
necessarily work for Malawi.

Conclusion
This paper has discussed issues of mathematical
terminology in the context of implementing mother
tongue policies. I have discussed borrowing from
English and developing mathematics registers in
the local languages as two strategies for handling
mathematical terminology when teaching in the
mother tongue. I have presented the case of
Malawi as an African example of borrowing
strategy and have presented the cases of Nigeria
and Tanzania as African examples of developing
mathematics registers in the local languages.

The discussion has illustrated the dilemmas that
decision makers might face as they suggest ways
of handling mathematical terminology when
teaching in the local languages. Each of the
strategies discussed has strengths as well as
potential problems. It is therefore advisable that
whatever strategy a country decides to use for its
mathematical terminology, the teachers and other
implementers of the strategy be aware of the
strengths and potential problems so that efforts can
be made to exploit the strengths and minimise the
potential problems.

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/ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
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/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
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(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /ConvertToCMYK
/DestinationProfileName ()
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/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
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/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
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]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /UseDocumentProfile
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice