> GSC - I want to suggest a more focused (to math) open
> pedagogical question related to your posting:
>
> Given that there are always a heterogenous
> arrangement of students in any math classroom (with
> n>1), what are the most effectiveness ways to teach
> them?
>
> Richard
Thanks very much for that well-reasoned response, Richard - and you are correct in suggesting a question better focused on real math issues. The situation you describe is very real and teachers surely have to deal with it almost every day - thus any improvement or enhancements on existing and well-known methods could be useful. My claim is that the OPMS process could help, very significantly indeed, in many ways.
Using the OPMS process, one might articulate an appropriate Mission for this situation as follows:
M: "To reach our math knowledge, more effectively than is possible conventionally, to the heterogeneous mix of students comprising most math classes".
(As opposed to those special classes for students who may be gifted or more advanced in their math abilities). [Feel free to rephrase that Mission as you feel fit: YOUR ideas about the Mission are what's important].
There should be adequate discussion about the articulation of the Mission, to ensure it satisfies the needs and interests of participants. (Participants might be: math teachers; students who wish to do better in their math; parents; others who have a genuine interest in the issue)
[I shall here on assume that you know something about the OPMS process that I recommend (needed information available at the attachments provided with my message posted on Jul 14, 2008 8:42 PM:
http://mathforum.org/kb/thread.jspa?threadID=1770721&tstart=50 . Below my signature, I list the documents available at that posting, with brief notes on some of them. Anyone requiring more information or clarifications is most welcome to write to me direct at gs (underscore) chandy (at) yahoo (dot) com].
Every OPMS session starts with one 'startup trigger question' (followed by a small sequence of trigger questions to cover various aspects and dimensions of the issue). The starter question in this case would be:
"What, in your opinion, are the THINGS TO DO to reach our math knowledge to the heterogeneous mix of students comprising most math classes, more effectively than is possible in the conventional way(s)?"
[Other relevant trigger questions relate to BARRIERS/ DIFFICULTUES/ WEAKNESSES / THREATS hindering or preventing accomplishment of the Mission; STRENGTHS (available/ required) that may help accomplish the Mission; and so on. List of trigger questions is available at the document OPMS - Major Steps to Create].
People interested in this Mission (the teachers and others involved and interested) would respond to that question, in appropriate format. Three example elements are illustrated below (only to show the appropriate format!):
1. To capture the interest of students who are normally 'turned off' by math (A)
2. To ensure, if possible, that we do not lose the interest of the 'proficient students' while we try to tackle the issues of those with lesser gifts in math (B)
3. To ensure that the math class actually promotes the math learning of the various students in it (C)
As an adequate number of elements becomes available, we can start with the important work of constructing one or more representations of the mental model(s) held by the members of the group of interested participants: we are seeking a process by which they can arrive at a reasoned consensus that enables and ensures progress towards accomplishment of the Mission. The first representations to be made would graphically show just how, in the opinion of the participants, the various elements may "contribute to" the other element(s) and to the Mission. (In a follow-up message, I shall provide illustrations with brief explanation of how such models may appear and how they are to be read, interpreted, acted upon, etc. I am NOT providing these illustrations right here as I have observed that messages with attachments are invariably delayed - and sometimes they do not show up at all!)
As those representations are developed and understood, the understanding gained of the educational and related system(s) that today exist - and of the systems that are required/needed (per the perceptions of those involved) - would enable participants to work out all the design aspects of systems (including all needed subsystems) that could be developed into something FAR more effective than what today exist.
Some doubts that will surely be raised: how to carry the process over, with reasonable effectiveness and efficiency, to the great many who have interest in the Mission? If there are 100,000 people interested, can we get ALL of the contributions of ideas into the Action Plan model? Indeed we can. However, it is difficult (perhaps impossible) to demonstrate this claim in the pure prose mode in which we are now debating. It would not be difficult to develop a reasoned justification of this claim if we were actually working on the Mission, actually using the OPMS!
NO CLAIM IS BEING MADE THAT this (the OPMS process) is some kind of magic wand which when waved about will bring about our hearts' desires in math education right there and then. However it is, I have found, a truly effective means to discuss complex issues effectively and productively so that all involved would at the end of the process feel satisfied that their good ideas have been properly taken into consideration in the total design of the system. Where people with genuine intent and desire to tackle complex problems effectively get together to do just that, using an appropriate and effective language and process, much that is highly productive can often be accomplished.
As often stated previously, there is a (little) learning required - along with a fair bit of 'unlearning'. Unlearning is considerably more difficult than learning - but it is essential and MUST go hand in hand with the learning (or the learning will not 'take'). By and large, children are the best learners (of ways to think and act productively and unlearners (of wrong thinking habits). [Check out document "How a child learns"].
More in due course (particularly if this thread gets going properly!)
Best wishes,
GSC
Some OPMS background (provided in posting linked above):
========================
The list below is in slightly different order from how the documents were uploaded at the referred message. Now, the ordering brings to the head of the list the documents that should be read earlier than the documents that should be read later.
A: PowerPoint presentation:
========
1. . GSC___OPMS for getting a great job2.ppt (2.4 MB) [I now have a PowerPoint presentation illustrated with a model that is more apt to the issues of our interest than the above of "getting a great job". I've worked out a presentation for the issue: "Designing effective educational systems for India's real needs". Those interested may please write to me direct at:
gs (underscore) chandy (at) yahoo (dot) com
and I shall be happy to send them this presentation as an attachment to an email message. (Its about 3-odd MB in size).
B: Word documents:
=======
0. 7. 09 Background note: What Is Modeling.doc (32.0 K)
[Explaining just where 'OPMS modeling' comes from and how it is different from conventional modeling processes].
1. 01_OPMS___in_Outline.doc (154.5 K)
2. 07 How To Accomplish a Mission.doc (132.0 K)
[Quite useful]
3. 06 OPMS Major steps to create.doc (62.0 K)
[All OPMS 'trigger questions' briefly articulated]
4. 05 OPMS Technology behind.doc (54.0 K)
[The logic behind the modeling tool at the heart of the OPMS process].
5. 04 OPMS Deep Logic.doc (59.5 K)
['Deep' logic - explains how and why this processes can take us deeper than the superficialities of the kind of analysis that Haim has faith in]
5. 03 How a child learns2.doc (39.0 K)
[GSC's view of just how a child learns - part of the philosophical underpinning of the OPMS]
6. 02 The power of the word.doc (142.5 K)
[A simple - but VERY important document, useful for those who are already interested in the process].
7. 07_10_07___GSC___On__Systems.doc (55.5 K)
8. 08 OPMS Hierarchy of OPMS in Organisation.doc(37. K)
9. Partitioning - outline 09-03-05 .xls (181.5 K)
[A useful document for those who would like to learn to do this modeling without aid of computer, software, etc]
10. OPMS - Innovative Culture in organisations.ppt (2.1 MB)
11. 06-26-07 - Potential OPMS projects, ideas.doc (29.2 K)
+++
