Illogical Logic Units

Last year when I introduced the unit on logic I quickly realized that students were experiencing a ton of vocabulary with no context, and there was no way they would be able to "mind their p's and q's" just working with the textbook definitions.  I tried to backpedal but we'd already reached the "we're never going to need to know this" and "this isn't math" frustration level so it was only marginally successful.

This year I did things differently.  As students walked in I asked them to write a couple true sentences that fit the form "If ______, then _______."  Then we got started with this worksheet:

Conditional
It went much better than last year's introduction, but I need to rewrite the questions on the second page since I ended up doing most of those with the class (there were too many questions to answer individually).  Even so, they realized that a) and d) were always true, which translates to "if a conditional statement is true, so is the contrapositive."  And most quickly saw the repeated structure once I explained exactly what I was talking about.  Best of all, only one student asked why we were studying sentences in math; she asked it genuinely and was happy with the answer I gave about precise definitions and careful explanations.  When reading the journal entries about this class period there were students who said this was fun!  Such a difference from last year!

After we went over the general form for a) through d) I gave them the names (conditional, converse, inverse, contrapositive).  Vocabulary goes over so much better when they already have a context to apply it to.  The next class we talked about biconditional statements and I used some of the examples that students had made up, which is always more fun than creating my own.

On a slightly less successful note, we're still struggling with counterexamples.  At the beginning of the year we did an activity I call "True, False, Fix" (a simplification of Prove or Disprove and Salvage if Possible from PROMYS) where students read a statement, decide if it's true or false and fix the false ones.  They keep wanting to fix when I ask for a counterexample.  We've quizzed on it twice and I hand it back with "counterexample?" and re-explain, but they still keep fixing and explaining without providing examples.  I hate to mark off for accurate statements, but they aren't answering the question I asked.

So, advice on re-wording the 2nd page of the activity?  And/or how to convince my students that counterexamples are actually examples that prove the statement is false?  Thanks!

Organization System

It's Sunday evening and I don't feel like grading, so instead I'll tell you about how all of my piles of work are neatly organized.  Since it's systemized, when I do get some motivation I can get right to work without spending time figuring out where everything is.  That means I have extra procrastination time, great right?

In my classroom I have a magazine holder (cheap plastic thing from target that google can't find a photo of) with a bunch of folders.  It lives on a table filled with other supplies kids might need (extra paper, pencils, stapler, hole punch and sharpener) and the goal is to have students become self sufficient.  Not only do I expect them to think (and use logic! what??), but I want them to get their own supplies rather than ask me "Can I borrow ___?" or "Do you have any more ___?" every day.

First folders: Extra Copies.  I have two levels of geometry and each one has a labeled manila folder filled with extra copies of anything I hand out.  If kids were absent or lose a paper, they are learning to head to the folder to get one.  When students come in and ask what they missed, I send them to the folder.  If they lost the homework, I send them to the folder.  If they totally destroyed something, I send them to the folder.  I don't like to waste paper so I don't make many extra copies, but I know my Fundamentals class has plenty of kids who can't hold on to a single piece of paper for an entire chapter (I photocopy the review page and they do a section each night for homework- books stay in school).  

Next folders: Papers to Hand In.  This is a set of manila folders with the letter of the block (A Block is first period at my school) written on the tab.  Anything kids want to hand in must go into this folder.  I won't accept papers handed to me, but merely point at the folder.  For a class when I know I'm collecting something I will pick out the correct folder and lay it on the table ahead of time.  To reduce chaos of everyone up and crowding at the table at once we pass papers down and the kids sitting near the table put them into the folder.  If a student is handing in something late, or a correction, they find the correct folder and place the work inside.  

Last folders: Papers to Hand Back.  These are color coded pocket folders (one thing I kept from last year) with red for both fundamentals classes (matte for A and gloss for H) and blue/purple for CP classes.  Eventually I'd like to take this responsibility off of myself as well, but for now when there are papers to hand back I grab that folder and distribute them or ask for volunteers.  I like handing back papers while kids are working because it makes sure that I am moving all over the room in a rather random pattern, so I really do see what everyone is working on.  I also use it like Sarcasymptote's Ukelele Time- I tell everyone I won't answer questions about what I'm returning or the work they're doing until I'm done, so they'll have to ask their partner or look up the answer.  It's not much time, but it's a start of forcing them to talk to each other rather than come running to me.  Maybe next quarter I'll at least assign someone to look in the folders and remind me if they're full of stuff to return.

On my desk I have boxes of things everyone needs- journals, test corrections, quiz corrections and quarter sheets of scrap paper for quizzes (and every random thing I want to remind myself of).

Last year I had everything on my desk, which meant kids were in that area all the time.  When students wanted to hand work in I had them put it on my chair because I didn't trust that it would land in the right spot otherwise.  It was definitely chaotic and messy.  Now when I feel motivated to grade I just grab the manila folder of the class coming up (or really, the one filled with something easy to grade), grade and transfer to the corresponding color pocket folder.  Then I reset and I'm ready to go!  Now if only I could get started...

Reflection and Self Assessment

This year's school-wide focus is writing.  Many math teachers groan or cringe or opt out of the reading/writing initiatives, but I've always had kids do a minimum of daily journaling; sometimes up to entire stories or paragraphs explaining projects.  Last year's school-wide focus was rubrics.  It was our NEASC evaluation and so we were supposed to all use the same rubrics so kids had continuity.  I would argue that students are more intelligent than we give them credit for and don't need that much continuity, but the idea behind the rubrics was okay and I was able to reformat them into something I find kid-friendly.  The result of these two foci is an ellipse (math joke!), okay, actually it's a double sided weekly reflection sheet.

Journal and CW Rubric

We operate on a block schedule, so if I collect these every Friday that's 5 days (barring schedule changes, which happen approximately daily, okay not really, but I do plan to count how many of the two week periods I get all 5 days filled in).  I used to carry around a clipboard all class and mark down any time a student was off task.  This, combined with attendance/tardies made up their classwork grade.  I'm still making occasional notes on my clipboard, and of course still taking attendance, but most kids are pretty honest when they fill in the rubric.  The original plan was to have them out on desks all class so every time a student was off task or doing a good job at one of the sections I (or my co-teacher) would mark that down on the rubric.  This turned out to be totally unrealistic.  If a kid is off task I don't want them to find their rubric for me to write on, I want them to get to work!  And several of them relate to behaviors when I am standing at the board.  Instead, I'm trying to use the language on the rubric when I reprimand or congratulate students on the behavior, and making a few notes so if my memory completely fails me for some reason they won't get an unreasonable grade.

The journal side looks boring now, but that's because the questions will be on the board.  Every day they will be asked "How did you meet the objective(s)?" and if they didn't to explain why.  There's also a second question that varies.  Some examples: to make a connection, to predict, to reflect (what are your goals for 2nd quarter? how should you study for the test?).  I expect a minimum of two sentences and they don't get credit otherwise.  The first week of past years I'd get quite a few "writing in math class?!?" exclamations, but this year there weren't so many.  It's a quiet way to close class and students will remind me that it's journal time if I get too caught up with a lesson.  The goal is to get students thinking about what they did in the hope that more of it will stick until next class (2-4 days away thanks to block scheduling).  The first question has changed year to year, sometimes asking what math they learned and other times about the objective.  I'm hoping that they will be more precise if they have to justify how they met the objective, although I'll miss the occasional comment about how someone did some really cool math in science class.