Sets Discussion

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Contents 1 About Sets 1.1 Writing of Laws 1.2 Adsorption Law 1.2.1 Definition of Sets 1.2.2 Starting From Both Sides 2 To Do 3 Problems Observed 4 Exercises

About Sets

Writing of Laws

I have reliable source that says that writing of the laws aren't necessary for STPM, just using it correctly

--Senghong79 12:21, 15 August 2009 (MYT)

Adsorption Law

Should we teach or not teach adsorption law?

We can, on one hand, take the easy way out and don't include it, and face the risk that it will suddenly come out in STPM. And also explaining to students that certain questions are not in the syllabus if they ask us a question that requires adsorption law.

Or, we can include it like now, but risk students using it when they should be using associative and commutative instead, and having their answers rejected by marking scheme.

I am standing by the decision to include it for now, but to reduce the above problem, we can add more emphasize on not using it unless necessary. The main reasons are

• For the sake of completeness. It feels weird to tell students that certain identities, even though perfectly valid, cannot be proved.
• Even if it has never come out in STPM, I am less inclined nowadays to say "It's not in the syllabus and will not come out in STPM". The truth is, I am starting to wonder whether those who set the question really understand the STPM syllabus.

--Senghong79 17:36, 19 August 2009 (MYT)

Definition of Sets

First of, I admit I was rather pissed off that after being rather successful in teaching the students to use set algebra, they have to come out with a "Using definition of Set" last year.

But beyond personal reason, there is a reason why I disagree that definition of sets should come out in STPM.

• Definition of Sets DO NOT prove the set algebra laws, it is very much THE OTHER WAY ROUND
• Proving using definition of sets REQUIRE knowledge of set algebra law, not the other way round

How else do we expect students to know that if if not by knowing distributive law?

We CAN say using Venn Diagram, but if we need them to use Venn Diagram, why not just ask them prove the whole identity using Venn Diagram? Proving an identity using definition of sets in the way required, is just an unnecessarily more difficult way to prove as compared to set algebra.

In fact, the approach I am going to take (when I do find time to write the part of definition of sets) will be probably asking the students to write it out in set algebra first, and THEN translate it to definition of sets.

--Senghong79 17:41, 19 August 2009 (MYT)

Starting From Both Sides

This was another reason that made me question the marking scheme. I was told that the question , one mark will be deducted if the student did it from both sides and then say that

But why? Did the person setting the marking scheme think that smart students must be able to think from one side all the way to the other? The truth is, weak students are NOT able to think from both sides, and thus, will not be able to solve it. Doing from both sides is a smart way of thinking, NOT a less smart way as many people tend to believe. And in complicated questions such as this, we should always encourage students to do from both sides.

Yes, I know the students can then just cut away one side and copy it to the other side, but still, the marking scheme is punishing students for something that is conceptually correct.

To Do

• Guidance for every exercise
• Definition of Sets
• Some Venn Diagrams to illustrate some laws
• Better emphasize on NOT using adsorption law unless absolutely necessary
• Complete Past Year Questions

--Senghong79 16:33, 12 August 2009 (MYT)

Problems Observed

• Some students still face problem with combining commutative and associative. Detailed guidance is to be added for Exercise 4.
• Some students use adsorption law when it wasn't necessary in the proving part. It will be noted in the guidance for Exercise 7 and Exercise 9.
• Some students still face problem with the past year question (7 marks). Further explanation is needed for the crucial step.

--Senghong79 16:33, 12 August 2009 (MYT)

Exercises

• Exercise 1
  • A lot of composite sets thrown in, arrangement of laws needed is varied
• Exercise 2
  • Complements are varied, number of sets involved increased
• Exercise 3
  • Expand type -> Position of brackets varied
  • Factor type -> Position of common sets varied
• Exercise 4
  • Position of operations are varied, as with the sets needed to be paired
• Exercise 5
  • Random rearrangement of questions from exercise 1 to 4
• Exercise 6
  • Method used after dealing with De Morgan's law is varied.
• Exercise 7
  • Composite sets included
• Exercise 8
  • Includes those with multiple minus
• Exercise 9
  • Includes long questions where it is necessary to work from both sides