Re: learning and teaching a subject

Date: Thu Apr 01 2004 - 11:53:44 PST

Dear Esther,

Thanks for putting my question "in context". The narrative of your
experience in Ghana is quite enlightening. In Chile teaching of Maths
is in L1. But the situation may be quite similar for kids from
impoverished backgrounds. I think that teaching in Brazil is also in
the mother tongue (somebody from Brazil there?), although there
certainly may be differences between kids` home language and the
language of school, which replicate what you said in a less dramatic

I think the name of the guy that did the work on Brazil is Antonio
Roazzi. There is a nice summary of his work on:

Ceci, S. & Roazzi, A. The effects of context on cognition: postcards
from Brazil. In Sternberg, R.J. & Wagner, R.K. (Eds). (1994) Mind in
Context (pp. 74-101). Cambridge University Press.

Stephen Ceci has a bioecological theory of intelligence that may be of
your interest and a nice paper on reasoning at the racetrack (betting
for horses).

As for journals, I guess that MikeŽs one is the best one for this kind
of work. There may be research on the issue scattered in some
mainstream psych journals too.

Thanks, again for taking the time to answer.


Quoting Esther Goody <>:

> 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: <>
> 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?
> David

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