Teacher's corner: Who says mathematics is only about numbers and calculations???!

In one of my classes, hmmm not one but in all of the grade X I taught in this semester, I have a little funny struggle when we deal with the mathematical logic. It’s a new topic for the students in the grade X. I notice at least the following points in my classes. It took my time a little bit longer to prepare the materials for them.

In the first meeting we started to get in touch with the topic, my students said that, “oh come on, where are the numbers, Sir? It is not mathematics. We are not in a Bahasa class aren’t we?” They were complaining since I invited them to define the term “statement” and made up several examples of statement from each of them. And then I asked them to distinguish a statement and an open sentence.

When they shared the statement they made as the examples, most of the students just came up with the example in the daily life things such us,” I am hungry, the teacher is very handsome, the sun is shining, etc” only few of them related it with mathematics. Not mathematical sentence, but a sentence like “lingkaran itu bulat, jam itu bulat” things relate to geometry (a little bit). So it was not a surprise to see their reaction when I put “2+5=7” as one of the example. At least they got a new knowledge that that expression is also called a sentence in mathematics. J

Okay, that is only the beginning.

The struggled came when we started to explore the “majemuk” sentence about conjunction, disjunction, implication and bi-implication. There was no big issue in the conjunction part. We could find the truth table of it nicely. I used a story like what my high school teacher told me. For example “the mother asks her son to buy sugar and coffee”. With this example we could agree that the mother will only happy when the son gives her both sugar and coffee. It means that the truth value of the conjunction will be true only if the truth value of the both single statement on it are true. It will be false when it is not.

The discussion started when we continued to the truth table of disjunction. We used the same example but with the connector “or”. The confusing was if the first and the second single statement of it are true. The students said that it is not “fine” when the mother asked to buy sugar or coffee but the son gives her both. The students said that it against the mother will. The mother will be angry since the son uses money unwisely. It’s still not logic for some of the students that the truth value is true, some of them keep complaining. Hmm, its hard to be a teacher right J

To “shut them up”, I said that although the son have sugar and coffee in his hand, he will only gives one kind of it to the mother, he free to chose whether he will give sugar or coffee. And the mother will not angry. It is also not a big problem for the mother to accept both of it. in mathematical logic we only care about the information in the statement and the fact, we are not concerning about the other factor like “using money wisely or not”.

Okay, the disjunction is done.

But the next battle is about the implication. Fiuh, can you guess what was happening?

To be continued….