2/3, 2÷3. No matter what way you slice it, it means 2 divided by 3, which means the 2 is going inside the division box and the 3 is going on the outside. I told my students the numerator of a fraction is always on the inside, the denominator always on the outside of the division box. And if it is written out like the second one, the number to the left always goes inside and the number to the right of the sign always goes outside.
It is a pretty hard and fast rule. But I have that one person who loves to challenge me. And he isn’t asking ‘why,’ but rather he is challenging me by saying that it isn’t true. No. It is ALWAYS true. But for whatever reason, he and most of my students have a tendency to due the exact opposite, especially when the dividend is smaller than the divisor.
In developmental math we deal with positive numbers only, so my students know they always put the larger number first when subtracting. They apply this logic with division as well, which makes no sense. Sometimes you are going to get things that are less than one. Fractions and percents are technically less than one. Heaven forbid. I give them 7÷12 and ask them which number goes inside our division box. Their answer: 12. They don’t like to have numbers less than one apparently. No. You have to deal with parts of wholes and not always wholes, which make them less than enthusiastic.
A whole semester has now passed, finals are looming and one of my fears (besides people royally screwing up area, perimeter, circumference, and radii/diameters) is that they’ll go back to dividing wrong. We shall see, I suppose.
I have another student who challenges me, not with division, but saying that I have not told him how to do something properly. I spend an entire half hour instructing these students on how to work things out step by agonizing step. Granted, that is not a lot of time, given the amount of questions they have some days, but I go over formulas and setups, stressing each and every one. When he said that the other day, I was like I just went over and over how to do these for an entire half hour. And what, praytell, was he doing during that time? Either listening to his MP3 player or messing around on his laptop. So how is it ME not telling him what to do?
One day he got so fed up with me. There was a breakdown of communication regarding finding the area and circumference of a circle and he was getting snotty with me telling me I was not explaining it right, that he was only doing it exactly the way I told him to. And I must admit, my patience has run out with him (and with one or two others as well). I got a little testy with him. Not a solution, but by that time after explaining and re-explaining and doing more examples, I was just a little peeved. What to do?
Thank god the end of the semester is here. There are students I’ll miss and students that I can’t wait to never see again.