Doing the wrong thing in class
Me, not the kids.
Earlier this week I more or less ditched my lesson on adding integers. And the next day subtraction was on the calendar.
Once again, it was clear early that my algebra students knew ‘the rules’ for subtraction; quick quiz results were excellent. Once again, most of their knowledge was procedural (not a problem) we discussed some alternate ways to consider subtraction (they added the opposite. With prompting they remembered “take away,” one student mentioned increasing and decreasing a bank account, I offered finding the distance from one numbered street to another.
And then I pulled out a worksheet. My partner, our other algebra teacher, who has been mercifully carrying me as I worked on fixing student schedules, she had prepared a wonderful activity sheet.
Fun activity below ———>
We introduced closure, associativity, and commutativity earlier this week. The sheet asked if the integers were commutative, associative and closed for each of the following operations (room was provided for an explanation for the yes’s and for counter-examples for the no’s
+
*
–
÷
average (A average B) = (A+B)÷2
max (A max B) = the larger of A and B
min
exponentiation (iow, AB)
right (A right B) = B (always equals the right number, ignores the left)
I think these are really neat. Can you tell which are commutative? associative? closed for the integers?
The kiddies were well-engaged. I put them into groups so that they would pick each other up for this activity, and so that I could provide help 3 at a time rather than one on one (too slow) or whole class (I would spoil answers for many kids).
Working, thinking, engaging with math on a slightly more general level. I need to thank my partner for the activity sheet again.
JD2718 
This is super-important stuff! Not because we need kids to remember if some operations are commutative or whatever, but because we need them to be willing and able to take on tasks of generalization and categorization, even when the terminology is new. How do you decide who goes in a group together? Do you intentionally pair strong and weak or just let it be random?
This class is freshmen who I do not know well yet (3rd week of school), so the current grouping is rather random. And I am walking around giving plenty of help.
Most of my work is definitely not groupwork. But usually my students sit immediately next to each other, with the admonition that they must communicate with neighbors. I eventually will distribute the strongest or the weakest evenly throughout the class. Sometimes I will leave next to each other students who seem to work well with each other, no matter their strength.
In groups, I will group by mixed ability, usually. Sometimes I group weaker kids together, so that I can leave the others on their own and concentrate my help on three or four kids who are lagging. In combinatorics I’ve thrown math team kids together. But sometimes a group of friends works well together, why not keep them that way?
And the opposite, in geometry my groups of friends are way too chatty, 5 cliques are going to be divided into four groups, no one with friends. Eeks, they will hate me for a while.
what a loser, your wasting the childrens time and yours if you put them together cuz you know that one in every group will just get the answers and still not get it.