39
votes
How do I convince students to use Boolean algebra?
Well, for one, computing a truth table doesn't scale: generating one takes exponential time, with respect to the number of variables you're using.
You can perhaps "subtly" drive this idea home by ...
- 4,005
9
votes
How do I convince students to use Boolean algebra?
I am mostly with @Buffy, A student should be praised for finding their own way of solving a problem. However I also think it is often good to have more than one way of doing things.
Therefore:
If ...
- 10.8k
7
votes
Differentiating Inclusive from Exclusive Or
Play the “if you have brown hair stand up” game.
For the introductory lesson. We use this to introduce selection (if statements), and a little bit of boolean logic.
“Stand up if you have got brown ...
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7
votes
Active learning for boolean algebra
The activity that occurred to me was categorical logic puzzles where you're given a list of hints and have to figure out a set of facts using a grid.
These puzzles are solved by breaking the hints ...
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7
votes
Active learning for boolean algebra
Build logic gates out of dominoes.
Start off by showing this video from Numberphile in whole or in part. In it is a demonstration of how to use dominoes to model logical operations of a computer. It ...
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5
votes
How do I convince students to use Boolean algebra?
I've never encountered this particular problem (possibly because I mention that truth tables are great, but we need both sets of skills?) Looking through the examples that I teach, though, a few of ...
- 34.3k
5
votes
Active learning for boolean algebra
I used a card game activity to review Boolean expressions in a CS1 context. You may be able to adapt to involve more abstract propositions and more complex operators.
tl;dr Students play a card game ...
- 1,995
5
votes
Differentiating Inclusive from Exclusive Or
You might go about explaining it by using the words "either" and "or".
"Either" means that any option out of two available would be enough:
perfect indifference of the two (or more) things.
But ...
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4
votes
How do I convince students to use Boolean algebra?
Well, you won't do it by simply insisting. In fact, if your student has an alternate way to demonstrate the truth of the statement, he/she should be praised, not censured, even implicitly. Your ...
- 36.8k
4
votes
Differentiating Inclusive from Exclusive Or
I enjoy using cartoons in my teaching, such as this one:
You can also teach students the XOR trick for swapping two values without using intermediate storage:
...
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4
votes
What Notation for Teaching Boolean Logic?
As per ctrl-alt-delor's response, I use different systems with different groups. It has been my experience that most of my students use no formal system of Boolean Algebra prior to beginning studies ...
- 34.3k
4
votes
How do I convince students to use Boolean algebra?
You haven't given them any practical applications for it, so the merit of doing so is lost on them. Why should anyone care about things like De Morgan's Law, etc, if they can just use a truth table to ...
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4
votes
Accepted
What Notation for Teaching Boolean Logic?
If your students were a bit older, I'd be more comfortable with the following, but suggest it anyway.
There is an advantage for a student to know that the concepts exist independent of any notation ...
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4
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A beginner example of xor, that is functional (does not switch to procedural)
I can't tell whether I've missed something in the other answers or comments, but the natural language equivalent of XOR is to ask "is there any difference?"
Used in a sentence which follows the ...
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3
votes
Accepted
Boolean Logic: How to Explain + as OR?
Since your students are getting the beginning of Boolean from you, you have the advantage of being able to lay the proper groundwork to work within. To begin with, hopefully, you will be stressing the ...
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3
votes
What Notation for Teaching Boolean Logic?
The two systems have different value.
For $\land$, $\lor$, $\lnot$
It is good in that you can see its relationship with set theory.
∧, ∨,<,> vs ∩, ∪, ⊂, ⊃
The not symbol is easier to type that ...
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3
votes
A beginner example of xor, that is functional (does not switch to procedural)
Say I’ve got two coins. They can each take on two states (heads or tails). Flip em both; xor can tell you if they are different (not-equal).
The name has exclusive ...
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3
votes
Differentiating Inclusive from Exclusive Or
Think pizza shop. You order a one-topping pie. Would you like pepperoni or sausage? In common parlance, that's an exclusive or.
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3
votes
Accepted
Unit Review for boolean algebra
I don't know if I have a solid answer to the main thrust of your question, but I do have some one-off suggestions that may or may not be helpful.
First, something you could try integrating into your ...
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3
votes
Unit Review for boolean algebra
I've found a lot of success giving real world (often times very silly) examples of boolean algebra to give them a more intuitive understanding in addition to the pure algebraic laws. An example would ...
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3
votes
A beginner example of xor, that is functional (does not switch to procedural)
Let me give a not-answer that may be just about as valuable as an answer. Natural language is ambiguous. Many uses of or in natural language have an xor intent. Your intention, I expect, is to make ...
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3
votes
How do I apply 'A Logical Approach to Discrete Math' to programming?
I'd rephrase the question as Should I apply 'A Logical Approach to Discrete Math' to programming, and if so, how?
My answer to the rephrased question is No. Logic is a must but that approach doesn't ...
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2
votes
Unit Review for boolean algebra
A couple of ideas:
1st day
Start by getting everybody up and moving. Have people form sets - say, a set of colors, with everybody wearing a different color, or a set of ages - but remind them that ...
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2
votes
Active learning for boolean algebra
Peer Instruction materials exist for Discrete Math, for instance Cynthia Lee's Peer Instruction questions from Stanford. You may be able to adapt some of the questions to fit your needs for a HS ...
- 1,995
2
votes
Active learning for boolean algebra
For the introductory lesson. We use this to introduce selection (if statements), and a little bit of boolean logic.
“Stand up if you have got brown hair.”
“Sit down.” look around “Stand up if you ...
- 10.8k
2
votes
Differentiating Inclusive from Exclusive Or
I wouldn't bother trying to tie this in to English language. Exclusive or is a strange connective. For example:
$a \oplus (b \oplus c)$
means "An odd number of ($a$, $b$, $c$) is true" (you can see ...
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2
votes
A beginner example of xor, that is functional (does not switch to procedural)
This was fun! Here are three, and I will update as I think of more:
You may go on the symphony trip if you are in the music history class or if you are not enrolled in any arts class this semester.
...
- 34.3k
2
votes
Accepted
How do I convince students to use Boolean algebra?
Back to the question :
Since Boolean variables can only have 2 different values, proving a Boolean algebra equality can always be done exhaustively. Or am I wrong ?
Yes. ...
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2
votes
A beginner example of xor, that is functional (does not switch to procedural)
The more I think about this, the more that I'm convinced that the or doesn't independently carry the weight of exclusivity in any circumstance outside of choices, ...
- 34.3k
2
votes
A beginner example of xor, that is functional (does not switch to procedural)
Experimental Approach
This is based on the example given by candied_orange, which I found intriguing because of its simplicity. The example was (slightly edited here):
Say I’ve got two coins. They ...
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