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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

explanation).

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

passage

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

at

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

well:

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

understand.

[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: <david.preiss@yale.edu>

To: <xmca@weber.ucsd.edu>

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?

David

**Next message:**Phil Chappell: "Tzvetan Todorov lecture"**Next in thread:**Steve Gabosch: "Re: learning and teaching a subject"**Reply:**Steve Gabosch: "Re: learning and teaching a subject"**Reply:**david.preiss who-is-at yale.edu: "Re: learning and teaching a subject"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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