Logic… OH BOY. Teaching logic is like introducing an entire new language to my students. The language of math. I started out this unit with a lesson on inductive and deductive reason that was created by Julie Reulbach. This lesson consisted of a SMART notebook and a foldable handout.
I had students discover the difference between inductive and deductive reasoning by using slips of paper with the following statements, pictures, and numbers on it. I told them to separate the slips into two piles. How are the piles the same? How are they different? Why did you group certain ones together? A common response I heard was “one pile is words and the other is shapes and numbers”. It wasn’t until i had them finish each statement that they started to see the pattern. At the end of the lesson we watched this clip from the Princess Bride. It was great to show them logic in a round about way and good wrap up for the lesson.
Next time I would give students inductive reasoning examples that did not have numbers or shapes. When they did their homework they had a difficult time deciding which type of reasoning was which. My students were also over thinking almost every statement.
So now day two…. Conditional Statements.
So first off… I am OBSESSED with Don’t Panic, The Answer is 42. I’ve found amazing things for my geometry class from her blog.
I used her lesson on Conditional Statements and decided to recreate it by adding my own little touch. I turned the note section of her lesson into a foldable and a SMART Notebook. I started the lesson out with students reading misleading newspaper article headlines to make them see that words can be misleading. We talked about how in math we need to come up with a universal way to get across what we want to say. Before even introducing Conditional statements I had my students write 3 if-then rules that they live by. I then had 3 students to come to the board to write their rules. When I finally did introduce conditional statements we used my students rules to point out the hypothesis and conclusion of each statement. This was good because the students felt by looking at their own rules. I also had students come up to the board and underline and label the hypothesis and conclusion. This got my students up and moving around the room. During a class that is mostly lecture it can be hard to keep students engaged. I tried my best to keep students moving and involved in the notes.
After students became comfortable with labeling conditional statements we moved on to using p and q to represent statements. I told students that mathematicians are “lazy” and wanted a quick way to write conditional statements that made sense to everyone. We worked through a few statements, making them conditional and then writing it in p q form.
Next we moved onto truth values and negations. I introduced truth values the day before but now they were being applied to conditional statements. Students seemed to understand negations pretty quickly. Although taking it one step at a time seemed a little show students seemed to truly understand what was going.
Students were finally introduced to truth tables by given a p and q and then multiple case scenarios. Students were able to see and figure out themselves that the only time the conditional statement was negative was when the hypothesis was false. I thought that this lesson went pretty well even though “math felt like an english class today”. The intro into logic can be tough and confusing, so I hope that my students continue to go into it with a solid foundation!