Teaching a Rule or Teaching for Understanding

[rexboggs5]

I have downloaded quite a few maths flipcharts over the years from the Promethean website. Generally they are presented at an appropriate pace, with engaging backgrounds and great graphics. And the mathematics is usually correct. However ... many of them teach mathematics "by rule".

For example "To divide fractions, flip over the second fraction and multiply."

Now there might be some arrows to suggest the flipping, or maybe if you click on the second fraction the division is changed to the multiplication of the reciprocal. But rarely is there an investigative approach so students can discover this themselves, or even a teacher-directed discussion that shows "why" this rule makes sense. Just the rule - "Yours is not to reason why, just invert and multiply".

Now, in my opinion, this is bad teaching. Teaching "by rule" works great on Monday - students just follow the rule and get the worksheet questions correct. And it works great on Tuesday with the next rule - students just follow that rule and get the worksheet questions correct. But on Wednesday, when the students have a mix of questions, or some word problems that require them to know which rule to apply, things start to unravel ...:confused:

And by Friday, with 3 or 4 rules under their belts, well .... :confused:

What do others that read and write to this forum think? Is this a problem worth addressing, or is it only me?

Once holidays start next week, I will submit my recent attempts at teaching this topic, for discussion.

But prior to that I would be interested in any comments on this topic.

Cheers

Rex

[slohse]

Hello Rex,
I agree with you.. although it is important to teach the "rule", students do need the opportunity to discover the "reason". I think with the Activclassroom, now more than ever, teachers have such an advantage to allow them to investigate, have a discussion around "why" their approach is a certain way.

I think too many people get stuck in teaching only the "rules" because this may be the way they were taught.... The ability to give control to the student to create the learning process is a crucial step in educating these visual, digital students.

I'd be interested to see what you develop or how your discussion goes as you approach this topic.
Thank you for posting...
Shannon

[srchlc]

I wouldn't assume that what is in the flipchart is the whole lesson. Maybe the investigative part happened before we jumped in? :) I'd be interested to see what kind of investigative things you would suggest that would make a student of elementary age come up with a method on their own.

Very intrigued!:D

Holli

[Westlake]

Not Maths, but I have similar concerns with an equivalent 'rule-based' process in Chemistry - using 'drop and swap' for writing chemical formulae.
Easy enough to plug in the values and get a 'right' answer, but no thinking involved and little understanding of the underlying electron transfers. :eek:
Hilary

[saha]

I think in Chemistry, teaching with "Rule driven " versus "process/logic driven" has to have a very delicate balance.

For example, a teacher should never introduce the process of writing the correct chemical formula using the simple "criss cross rule method of oxidation numbers". The teacher should teach that the process is logic driven and show the reason(s) how oxidation numbers are generated, tie that to valence electrons, atomic structure and the need for neutral charge. Once student master this, then the easier "rule based" approach can be shown to students merely for them to be able to check their answer.