Re: learning and teaching a subject

From: Esther Goody (
Date: Thu Apr 01 2004 - 04:56:10 PST

Dear David Preiss et al,

Some thoughts on maths teachers/teaching in Ghana. (Sorry about time lag,
but I found xmca somewhat overwhelming at first!

Because my current work involves teaching children to read in their mother
tongue in nine government primary schools in northern Ghana, I have been
sitting in these classrooms over several years. This is the 'Local languages
initial literacy project'. The LLIL project sort of happened when what I
expected to be a fairly streightforward study of factors involved in
effective school learning turned out to be impossible because these kids
weren't really learning anything. These Class 4 children just sat there,
mostly not paying attention. When called on by the teacher, replies were
either silence, monosylables, or rote repetition of a text. Children seemed
just as happy to give a wrong answer as a correct one - apparently because
this showed they could answer at all. Or perhaps because the teachers'
response to wrong answers is usually to ignore it and ask another child -
continuing this until there is a correct answer - or until finally the
teacher gets angry and states the correct answer (usually with no

I gradually realised that this whole dynamic was about the fact that the
children didn't understand much of what the lesson was about. What I was
observing were defense mechanisms for handling incomprehension - by both
children and by the teachers. To an outsider (academic anthropologist
innocent of any training as a teacher) the cause of this problem seemed
simple. Lessons are all in English - which village children never even hear
until they start school. They are 'taught to read' in English beginning in
Grade 1. Hardly any children learn to read. So as they continue through
primary school where all texts and teaching are in English, they understand
less and less. Their skills are memorising; some get very good at guessing
which passage they should repeat in answer to a teacher's question. Some are
even able to 'read' passages aloud in English. However when asked what the
passage was about they are in difficulties - and tend to answer by repeating
verbatum. (When I did some formal testing of English reading comprehension
with Class
3 children, one girl read the two paragraphs quite fluently, but said they
talked about the little black cat - which was the subject of a different,
earlier lesson.)

Since I had just finished working on informal learning in these same
communities, I knew these were clever children who learned many things - and
learned with imagination and often intense concentration. But now I needed
to compare informal and 'school' learning. How to get classrooms in which I
could observe effective learning was the problem. Teaching/learning in the
child's own language was clearly the key. And their main handicap was that
they couldn't read - in any language. They had no idea at all about the
possibility of ideas in written form, let alone of the world of books.
So rather than abandon the school research, I set up the LLIL project in
which we teach children to read in L1. These classrooms are a rough
laboratory for observation - and recently for some interventions.

Sorry about this long preamble/ramble to comments on maths teaching. But
this is the situation 'on the ground' in which maths is taught and ?learned.

In order to get into a teachers training college in Ghana everyone must have
high pass marks in basic maths, algebra and calculus. I have looked at the
Senior Secondary texts for these and would myself fail utterly. (I had to
take calculus twice in college - and just scraped through.) I haven't looked
TTC texts, but from talking to trained teachers suspect that these pretty
much repeat the secondary school syllabus - in hopes that trainee teachers
will themsleves come to understand them. The core curriculum in training
college is the same for all teachers. Those intending to teach in secondary
school take
further courses.

Comment - this requirement that in order to train as a teacher everyone has
to have good passes in higher mathematics elimates many who would be good
teachers, particularly for literacy.
Certainly higher maths is not necessary to teach in primary school!

At the national curriculum-planning level there is an anxious determination
to (obsession with) make sure that standards for training teachers in Ghana
are identical with those of England and America. Indeed it has seemed to me
that throughout, curriculum planning moves from the top down, as it were.
They begin with what skills students should demonstrate in order to do well
at university. This determines the curriculum for secondary schools. And
requirements for entry to secondary schools determine the curriculum for
junior secondary schools (grades 7-9). Not surprisingly, in primary school
the curriculum is designed in relation to what children must master in
junior secondary.

There is no 'space' to ask what maths might mean and be meaningful for
primary school children.

Back to my primary classroom observations.
Grades 5 and 6 (all in English - L2) from a Birifor village school I know
The teacher is excellent (i.e. the issue is not bad teaching). He is
teaching a unit about 'profit and loss'. Although he explains what 'profit'
and 'loss' are, and gives examples about a shopkeeper, the children do not
understand at all. They cannot solve profit/loss problems; they do not ask
any questions when invited to do so; they cannot give their own examples.
Yet these children can do basic maths operations - addition, subtraction,
mulitplication - division is a problem. But they cannot seem to see any
connection between such operations and the profit and loss problems the
teacher poses for them.

I asked myself - What is going on here?
These children are 10 through 13 years old. In village life they use
arithmetic every day. The girls do petty trading for their mothers - and I
cannot keep up with their L1 calculations. They regularly help their
mothers/sisters to brew beer and help to sell it on market days. I have
heard their mothers complaining that this is risky because family members
drink and don't pay, while other villagers come, drink, and promiss to pay
later but 'forget'.
There seems no connection between such very real 'profit/loss' problems and
what is taught in school. The boys play a gambling game with older brothers
and fathers which involves calculating odds and paying in cowries - again
they are quick and accurate. One boy makes sling shot catepults from sticks
and rubber cut from inner tubes to sell to other boys. Surely he must make
some kind of calculation as to whether he makes a profit or not.

[Drawing on Mike Cole's work, I started a math club with these children.
This was based on their individual out-of-school activities. For two weeks
each one was to keep track of one activity they did for money: frying peanut
paste to sell as snacks; brewing and selling beer; raising yam mounds;
making sling shot catepults, etc. Then in class, as an activity was
described we turned it into a profit and loss maths problem. It was
difficult to pull out 'profit' and 'loss' - (for interesting reasons
discussed in a working paper). But the kids spontaneously used simple maths
operations. And there were several who suddenly grasped what this topic was
all about (Ahaa!). ]

Back to the national teaching and curriculum situation.
Teachers are expllicitly trained to surpress any use of local mathematics in
the classroom. It is 'a known fact' that using local ways of counting and
calculating will interfere with learning 'real mathematics'. Thus the
teacher feels s/he has little alternative to presenting the same lesson in
formal maths again and again, hoping that with repetition children will
[The worst aspect of this is that teachers feel it is their poor teaching
which is responsible for failure to learn. And the Ministry of Education and
Aid Agencies wonder why teacher motivation is so low.....]

Am I wrong to see a parallel between failure to learn literacy skills and
failure to learn maths skills here?
In most Ghanaian primary schools children are not learning to read. They are
taught to read in Engliish (L2). When they are taught to read in their own
language, they do learn to read - and transfer reading skills (teachers are
astonished at how quickly) to reading in English.

In most Ghanaian primary schools children are not learning simple maths.
(National scores are slightly worse than for reading - barely 10%). They
learn maths in English ('school maths' = M2 as well as L2). When set
problems relating to
familiar activities in local maths (M1) they do these quite well [admittedly
on the basis of a single experiment].*

However - thinking about the Brizilian work, and Saxe's work, and reading
one study on teaching maths in US primary schools it seems that perhaps
there is the equivalent of 'local maths' even where only a single language
(L1) is involved. All children use 'local maths' (M1) in everyday
situations. The formal maths they encounter in school seems to bear no
relationship to the simple skills they have already mastered. It is like a
foreign language - M2.

How does this relate to what teachers need to know in order to teach maths
well at primary school level?
Logically it almost seems as if it would be better if teachers of maths in
primary school did not know too much higher maths.
Expertise in higher maths can only reinforce the existing bias towards
orienting maths teaching 'upwards' rather than seeking ways of linking it
with children's existing 'local maths' skills.

Indeed - should there not be courses specifically addressing the
co-existence of 'local' and 'school/formal' mathematics, and
ways teachers can enter the children's world of local maths and help them
build bridges between this and formal maths?

[*I use 'local maths' rather than 'street maths' as these are village
children, not working in urban street settings. Sorry - have forgotten the
name of brilliant Brazilian who did the lovely work on 'street maths'.]

                I would be grateful for any feed back. Also for
references - especially obvious ones, as am a stranger in this field.
Are ther journals that focus on this sort of issue?

                    Cheers, Esther Goody

----- Original Message -----
From: <>
To: <>
Sent: Tuesday, March 16, 2004 8:23 PM
Subject: learning and teaching a subject

Dear friends of XMCA,

IŽd like to take advantage of the international nature of this list to
get help with the following. I need to know how different countries
decide the level of math teachers need to know in order to be
accreditted as such as elementary, middle, and high school teachers.
The question of concern here is how the subject matter is incorporated
within their professional curriculum and whether there is a formal
standard decided by the government.

My goal is to move from there to some most particular questions such
as, does a Math elementary teacher need to know advanced maths? Is a
high knowledge of the subject matter a prerequisite to be a great
teacher? Beyond maths, are there similar standars in other domains?


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