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This booklet is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike
4.0 International License.
3. 3
Why a facilitators’ guide?
This handbook is intended to equip facilitators with the
knowledge they need to model and facilitate correct
language use, in order to enable learners to improve
their Mathematics and language proficiencies
simultaneously.
Many learners attending township schools do not have
exposure to good models of English use. Depending on
the context, some learners are not exposed to English
at all outside of their school. In order for learners to
become good at English, they need good examples of
spoken and written English on which they can model
their own language use. This is why it is important that
facilitators, teachers and tutors (henceforth referred to
as facilitators) take care to use correct English.
Please note that this is a work in progress. We
welcome you to use this handbook for non-commercial
purposes, and would greatly appreciate your feedback
on its use.
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How can I introduce new words?
1.Balancing old and new words:
One of the key elements of language proficiency is the
size of one’s vocabulary. As such, it is also the
facilitator’s responsibility to expose the learners to as
wide a variety of vocabulary items as naturally
possible. This is a bit of a balancing act, as one should
not be using so many new big words that the learners
do not understand anything, and at the same time, one
should not stick to only using simple words in an
attempt to ensure the learners understand. A good
way to navigate this is the following:
When explaining a difficult or brand new concept, try
to stick to words that you know the learners already
know. When talking about something the learners are
already familiar with, try using new words. We learn
language by placing words in context and so, for
example, if I did very well in a test and my teacher said,
“Well done! Your marks are terrific!” I will be able to
figure out that terrific means really good.
2.CCQs
A concept checking question (CCQ) is used to check
whether the learners have understood or not. It is easy
to stick to questions like “does everyone understand?”,
but for these questions the expected answer is obvious
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to the learners and so they may often answer “yes”
without actually having understood.
CCQs should be short questions where the answer is
not obvious, for example, “so are these vertically
opposite or co-interior angles?” or “how many angles
are there in a pentagon?” If you are teaching more
than one learner at a time, make sure you also
nominate some learners to answer your questions
instead of getting the class to chant answers. (It’s a
good idea to first nominate a stronger learner to break
the ice, and then nominate a weaker learner to check
that the work has been understood, or get the learners
to discuss it amongst themselves before nominating
learners.)
3.Morphemes (different pieces of meaning inside
words)
English is confusing because of all the strange words
and how things are spelt, but these words and spellings
often help us understand what the word means. For
example, we know that triangle means a shape with
three angles, because we know that tri means three.
Learners are more likely to remember difficult words if
they know what the different parts of the words mean,
and also if they say the words themselves. Taking the
time to explain morphemes and getting the learners to
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say it themselves will save time in the future and help
them to remember it!
Here are some examples of useful morphemes to
explain. You can also add your own
Morpheme Meaning Example of
meaning
Example of
word
bi- two bicycle bisect
tri- three tricycle triangle
quad- four quad bike quadrilateral
oct- eight octopus octagon
deca ten decagon decade
4.Mathematical words with English friends
There are lots of words in Mathematics that we also
use in everyday English, but have different meanings in
mathematical English. Many English first-language
speakers are at an advantage because they already
know the everyday meaning of the word that they can
build on and adjust their existing understanding. For
example, we know that “arrange in descending order”
means “arrange from biggest to smallest” because we
know that descend means to move downwards.
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It is useful to explain these words in an everyday
context (for example, illustrating ascending and
descending stairs). Once the learners understand the
word in everyday English, explain what it means in
mathematical English, and then ask the learners to use
the word in a mathematical context (for example, are
2, 4, 6, 8 arranged in ascending or descending order?).
Note: Some words have very different meanings in
mathematical English and everyday English. Make sure
the learners not only understand the definitions of the
words, but also the difference between the everyday
and mathematical use of the words. Use CCQs and ask
learners to give you examples to check that they have
understood this correctly.
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Here are some examples of useful words to explain.
You can also add your own
Word Everyday example Mathematical example
Ascending I ascend the stairs
when I go from
the lowest floor to
the highest floor.
2, 4, 6, 8 are arranged in
ascending order
Descending I descend the
stairs when I go
from the highest
floor to the lowest
floor.
8, 6, 4, 2 are arranged in
descending order
Equal Men and women
have equal rights;
their rights are the
same.
2 x 6 is equal to 4 x 3
Multiply When they heard
there would be
refreshments, the
number of people
at the event
multiplied.
2 multiplied by 6 = 12
5.Pictures
A picture often can paint a thousand words – and save
you time! Try to use pictures that are relevant to the
learner’s everyday context. If a learner does not know
what you are talking about, you can draw it, look it up
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on Google, or even point to it if you can see an
example nearby. For example, if you are explaining the
crocodile story1
of the < and > signs and the learner has
never seen a crocodile, just Google it! The same goes
for octopuses, quad bikes, or anything else you may be
talking about. Wherever possible, encourage the
learner to keep the picture somewhere (e.g. in their
file or book) or, if it is useful for the whole class, keep
the picture up in class for extended exposure.
6.Pronunciation
Pronunciation is a lot more important than it seems.
The vowel sounds in English often differ from the
vowel sounds in African languages. In order to be able
to read and write in a language, you need to know
which sounds match up to which letter (or cluster of
letters). If you are pronouncing the word incorrectly, it
is likely that you will struggle to spell the word
correctly. For example, a speaker of a Nguni language
(e.g. isiZulu, isiXhosa, isiNdebele) might want to spell
the word third. Because the ir sound is not common in
Nguni languages the learner is likely to pronounce it
with a different vowel sound, for example thed. And so
when the learner wants to communicate third but
1
The crocodile story tells of a hungry crocodile who only wants to eat the
biggest numbers. < and > represent the crocodile’s mouth, and the open side
represents the crocodile opening his mouth to eat. That is why the open side is
always facing the bigger number, e.g. 8 > 6.
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writes thed the learner’s meaning is lost in their
writing.
You can draw learners’ attention to pronunciation by
getting them to listen to you say it and asking them to
repeat it. If they are saying the vowels differently, draw
attention to how you shape your mouth when you say
it (are you smiling wide, making an O shape, pushing
your lips forward, etc). If they are putting the emphasis
on the wrong syllable, you can write the word on the
board and underline the emphasised syllable(s), or you
can ask them to clap, stomp, or beat out the syllables
and clap/stomp/beat the emphasised syllable more
loudly.
7.Translate
It is possible for learners to transfer things that they
have learnt in their first language into their second
language, and this is especially true for conceptual
knowledge. If you are able to speak the learner’s first
language, remind them of what the term is in their first
language. When you are comfortable that the learner
understands the concept, check that they can also
express it in English (as this is the language they will be
expected to do maths in). You could do this by asking –
in English – “What did you just do?” and getting the
learner to explain it to you in English. This is explained
in more detail in the beginning section.
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How can I use learners’ home language effectively?
Many teachers feel conflicted because they feel a
responsibility to use as much English as possible
(especially in cases where learners are not exposed to
English outside of the classroom environment), but
also a need to use the learners’ home language in
order to ensure they understand the content. It is
recommended that you allow learners to use their
home language in cases where they are struggling with
a concept, and encourage them to use English in
contexts where they are comfortable with the content.
The aim of this is to make learners comfortable with all
mathematical concepts so that they can then focus on
expressing these concepts in English.
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I can speak their home language. How do I use it?
The following method of “language scaffolding” is
suggested when introducing a new concept or
explaining a concept learners do not understand:
1.Introduce the lesson in English
e.g. “Today we’re going to talk about fractions”
2.Give an example of an everyday situation that
illustrates the concept in the learners’ home
language.
e.g. an example of how big the pieces of bread
would be if you shared the bread between three
people
Encourage the learners to participate in this
conversation either by talking to you or each
other. Using their home language means that they
can grapple with the concepts without being
distracted by trying to get the language right.
3.Still using their home language, show the learners
how to write it and explain how what you have
written corresponds to what you have just
explained.
e.g. 1
/3 represents one piece of the bread you cut
into three pieces
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4.Ask the learners how they would explain the
concept and/or the written work in English. Bring
them back to the everyday example and ask them
to explain that in English before moving to the
more abstract explanations.
e.g. now how would you explain this to me in
English?
If you are doing this with a group of learners (as
opposed to one-on-one), encourage learners to
collaborate in doing this. Make sure weaker
learners are given an opportunity to contribute,
and that the other learners support them in doing
so.
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I can’t speak their home language. How do I use it?
The following method of “language scaffolding” is
suggested when introducing a new concept or
explaining a concept learners do not understand:
1.Introduce the lesson in English
e.g. “Today we’re going to talk about fractions”
2.Give an example of an everyday situation that
illustrates the concept in English. Then ask a
learner to translate the example into the learners’
home language.
e.g. an example of how big the pieces of bread
would be if you shared the bread between three
people
3.Encourage the learners to discuss this example
with each other in their home language. This
means that they can grapple with the concepts
without being distracted by trying to get the
language right.
4.Ask the learners to explain their conversation to
you in English.
5.In English, show the learners how to write it and
explain how what you have written corresponds to
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what you have just explained. Then ask a learner
to translate the example into the learners’ home
language.
e.g. 1
/3 represents one piece of the bread you cut
into three pieces
6.Ask the learners how they would explain the
written work in English. You may want to bring
them back to the everyday example and ask them
to explain that in English before moving to the
more abstract explanations.
e.g. now how would you explain all of this to me in
English?
If you are doing this with a group of learners (as
opposed to one-on-one), encourage learners to
collaborate in doing this. Make sure weaker
learners are given an opportunity to contribute,
and that the other learners support them in doing
so.
Notes:
Try to separate language clearly when possible by
distinguishing between when you are initially
discussing the concept in the learners’ home
language and when the learners are explaining it in
English.
This method can span an entire lesson, or a short
five-minute conversation
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If you are explaining a complicated concept with
many elements, try breaking it up and scaffolding
each element from home language to English, and
then consolidating all the elements in a similar way
at the end.
Other ideas for facilitators who are not fluent in the
learners’ home languages:
Ask them to teach you how to say things in their
home language
Let them ask the question in their home language
first (even if you don’t understand any of it!) and
then ask them to tell you again in English. This way
they can first formulate what it is that they want to
ask and then translate it, rather than try to formulate
the question and try find the correct language at the
same time.
Ask one of them to ‘teach’ the concept to the other
learners in their home language, and then ask the
learners to ‘teach’ it back to you in English.
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How do I correct learners’ errors?
We all have something called a language ego, and that
influences how we feel about using languages. Some
people are very confident, while others are very shy. It
is extremely important that learners always feel
positive about learning and using English, and that they
feel that their home language (which forms part of
their identity) is valued. Learners should always feel
like it is ok to make mistakes, and they should be
encouraged to use English in a welcoming and
supportive environment. Here are some suggestions
for how you can correct errors while still being
encouraging:
If you find many learners are making the same error
(e.g. “homeworks”) it is better to address the whole
class so that no learner feels picked on.
If you pick up on an error that a student makes
repeatedly, (for example interchanging she and he)
you can gently correct the student throughout
conversations.
Learners who have poor English proficiency will
make too many errors for you to correct them all,
and doing so will make the learner feel sad. In these
cases rather correct an error that you notice is more
prominent.
Do not correct language when the focus is on
understanding a concept. It is better to either note
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the error and correct it afterwards, or to limit error
correction to a time when the learner is not focusing
on getting the maths right. If a learner keeps getting
corrected while they are explaining something, they
may become reluctant to explain things in future.
Draw attention to good use of language. For
example, if a learner uses a difficult word correctly
you could tell the learner what a great word they just
used, and possibly ask the class if they know what
the word means and ask the learner to explain it.
You can repeat what the learner said using correct
English if they are not forming their sentences
correctly, for example by starting with “Do you mean
…?” or “Oh, so …” and correctly forming their
sentences for them. By doing this the learners will
perceive you as being part of the conversation,
rather than you just correcting them.
Some learners like to use big words but get the
meaning or context wrong. In these cases you can
acknowledge the word and talk about what it really
means and when to use it. In this way you encourage
learners to try new words and also ensure they have
correct understandings of these words.
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Note: being able to speak English well does not
necessarily mean the learner is also able to read, write,
or listen to it well. By the same token, being bad at
speaking English does not necessarily mean the learner
is also bad at reading, writing, or listening to English.
See if you can identify learners’ strengths and
weaknesses. Furthermore, having a good
understanding of a concept does not necessarily mean
a learner can express their understanding in English;
nor does having a good grasp of English mean the
learner has good understandings of all concepts.
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What errors should I look out for?
The following are common errors that have been
identified at OLICO Diepsloot. Some of them will be
common in other contexts, and you may also find other
errors that are common within your learners’ context.
Facilitators should look out for these errors, document
them, and try to correct them as early as possible.
While some are easy to fix, some of these errors can
easily become ingrained in the learners’ language use:
Punctuation
Especially when typing, learners often do not put
spaces between punctuation marks.
Borrow me
Rather than lend me. This is common in South African
English, but is incorrect. You can make sentences using
borrow and lend to illustrate the difference.
Plurals on non-count nouns
Different languages make different nouns countable,
for example while some words in English remain the
same whether singular or plural they may change in
other languages, or vice versa. It is important for
facilitators to point out such instances (common errors
include homeworks and a scissor).
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Affixing pronouns e.g. iwent
This is more common among learners who speak Nguni
languages as words are written joint together in these
languages. It is likely that these learners got used to
writing like this when they were writing in their home
language at school and transferred this to English when
they began writing in English.
Gender
Many learners confuse gender pronouns (e.g. he, she)
because this distinction is not made when speaking in
most South African languages.
Statements as questions
Learners often phrase their questions as statements
(e.g. We can go inside now?). This may be because the
difference between a question and a statement is
intonation rather than word order when speaking
conversationally in most South African languages. In
such cases one could ask, “Are you telling me or asking
me?” to make the learner aware that their sentence is
unclear, after which you could point out how to
arrange the word order to create a clearer question.
Nouns with pronouns
Nguni languages use a noun and a pronoun together
(e.g. umama uyakhuluma [lit. mother she is talking]). In
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English, a pronoun replaces a noun. Point out to the
learners that we don’t say “My mother, she is talking”
but that we use either one or the other.
Using –ing too much
Learners often overuse the –ing form of the verb (e.g. I
am living in Diepsloot, I am having a problem instead of
I live in Diepsloot, I have a problem). This is the direct
result of a very poor apartheid-era textbook.
Encourage the learners to rather use simple present
and past tense.
Please note: this handbook is simply a guide, and
different things are likely to work for different people
in different contexts. So feel free to add your own
ideas and use the methods that work for you in your
contexts