Slug Behavior

Yeesh! Okay, so I'm sick, and my favorite activities involve sitting a lot, but holy cow, one reason I'll be glad school is starting again is that it prevents me from lounging around and expanding in front of the gas fireplace and doing puzzles ... or walking a few steps to the cushy couch to do puzzles ... or walking to the computer to do online puzzles ... or using my husband's iPad to play Arctopia or Sudoku. Honestly, I burned 1 calorie yesterday, and that was just from the exertion of blowing my nose repeatedly.

I did get this great new puzzle book, "The Monster Book of Logic Puzzles & Sudoku", and that made me search on line to see if nikoli had a website. YES!. My new favorites are Heyawake, and Yajilin.

I think I'd be in danger of becoming like those chair people in Wall-E if I don't watch it. On a positive note, we're going to Alamo Drafthouse for a movie and dinner tonight (True Grit) - a great way to end vacation. Dinner WHILE you're watching a movie ... does it get any better?

1/1/11

Okay, I just had to write that somewhere before it was too late, and I'm probably not going out today and writing a check. Last night was nice and relaxed. Had drinks with my friend, then went to dinner with my husband and another couple, Macaroni Grill. Oooh, high life. I was shocked, SHOCKED I tell you that this other couple had never been there. She started getting worried when I was drawing all over the "table cloth" with the provided crayons.

Got home around 10:15pm and looked on the Internet at the live stream from Times Square. I never did that when we were in NJ, but it's still fun to see it from afar. I think I'd get too claustrophobic being there. That and cold and worried that I wouldn't be able to find a bathroom and stressing about all the trash that would have to be cleaned up. But other than that, I'm sure it would be great :). I also like to go online on 1/1/11 (or 1/1/**) and see New Year's Eve pictures from around the world.

I think I lasted until about 11:30pm until I hit the sack after reading a bit in my new great book, "The Sweetness at the Bottom of the Pie".

I have one resolution for me, and I thoughtfully made one for my husband.
Mine: Try one new recipe a month. Need to get out of my cooking-the-same-thing rut.
His: Take wife out on a date once a month.

See, what a nice wife I am. Now he doesn't have to worry about coming up with a resolution AND he gets a date consistently. You're welcome.

Tests Tests and More Tests

I know and have lived (like everyone else) the variety of stresses surrounding testing (assessing) students. I also know I hate when others claim that THEIR method beats all and you should, need to, must try it and if you don't then you're failing your kids and bla bla bla and what are you waiting for? Superman? ar ar ar ar.

I also know I've lived the horrors of even the word "retest". I'd never heard of it when I started teaching in New Jersey. My first year in Texas, one of my first math tests I gave, AS I HANDED IT OUT, a students asked me, "when is the retest?" I scrunched up my confused face and said there was no retest. That was the start of my journey. Then I got indoctrinated (or desensitized or whatever) and started giving retests in various forms:

* one retest only and you could keep your highest grade of the two tests
* only retesting if you've done all your homework
* averaging of the test and retest grades

None of it ever sat well with me. Then as I've mentioned before, this past summer I did various types of reading (blogs, books, ASCD magazines...) and something clicked for me.

My results are not globally stunning (I calculated the average final exam grade of my 3 geometry classes ... without curving what-so-ever), and they were roughly: 71%, 80%, and 76% (stem and leaf plot, I love you). But this was the FIRST time this happened for me with my "regular" classes. I'm guessing before I used to have final exam grade averages of 60% or lower.

Two commenters asked about details, so I thought I'd combine my responses here.

First of all, I make up all my own tests. I've been fortunate enough to work in schools and with people where this is the norm and/or this is okay. I'd hate to be forced to administer someone else's test. Every class is different, and you focus on different things when you teach. I comb through what they've learned and what types of problems we had done for homework and through the bazillion of math texts I've amassed from the years of teaching and through the Internet, etc. Then I make up my tests. I make up new tests every year, and sometimes if I've taught a topic before I cut and paste old test problems. We hand back all our tests and the students can keep them.

Here's what I've been doing this year in my regular geometry class (though it's called preAP).

I give about 2 tests every 6 weeks (that's our grading period, and I teach on block schedule). I made it so that the 1st test is in about week one or two of the 6 weeks, and the 2nd test is about the 4th week. This gives them time to come in and study with me and reassess. They have until the end of the 6 weeks to finish any retests of that marking period. Here is a rough outline of my last geometry test:

Section A: I had one problem with a "complicated" triangle/parallel lines type picture with some angles written in, and they had to find the measures of various missing angles.

Section B: I had a diagram with 4 intersecting lines with angles labeled (think tic-tac-toe), and 4 questions:
1. name 2 sets of corresponding angles
2. name 2 sets of alternate interior angles
3. .... alt ext
4. same side int
oh, and by the way, make sure you use each of the 16 angles at least once.


Section C: I had portions of proofs with statements labeled, and they had to give me the reason/theorem/postulate/definition we could conclude various things.

Section D: I had 2 questions that they needed to use algebra with to find the values of various angles.

Section E: a question about lines (review) .... given an equation, find 4 points on the line .... or something like that. P.S. this is another reason I'm loving this retesting thing, because I don't feel guilty reviewing algebra, and it's forcing them to get it to stick in their heads.

Each section was worth 10 points regardless of the number of questions in the section. I graded roughly as follows:

They have no clue what they're doing: 0
They started out right but tanked early: 3-5
They started out right but tanked late in the problem: 5-7
They knew what they were doing but made a careless error: 8-9
They nailed it: 10

Those are just rough guides. I just asked myself as I penned in the grade, "do they know it or not and to what degree?".

Then the students had the opportunity to come in and retest for each section as many times as they wanted to get an ultimate final grade of 8 out of 10 on a section. I made up little 1/2 sheets of tests for each of the sections and made various versions and kept a store of them near me. With geometry (and maybe just so far), since I've taught it for so long, it was not too bad for me to make up the retests. And usually I could grade it that night or on the spot and quickly update GradeSpeed (that had 5 different columns for the tests). I kept the retests, so that I could reuse the problems for different kids on different days.

I'm guessing my success with it so far is that this forces the kids to go over and over something until they get it. And again, I'm lucky I only do this with roughly 50 total kids, AND some of them do great the 1st test and don't come in for retests. Again, this is what is working for me and my style and my kids and my situation.

I mentioned that I'm learning JAVA with that "Head First" book. This has also gotten me thinking about this retesting/relearning/learning situation. I'm guilty of being on the teaching treadmill: "learn" a topic one class, practice it for homework, move on to another topic the next class. Repeat until the test. Ackh! I know I've vowed to change my ways, and here I am vowing again ... slow learner. BUT.

First of all, I don't consider myself stupid or a slow learner, and yet when I'm going through that JAVA book (18 chapters, currently on chapter 9, doing about a chapter a day, roughly) .... I find myself scrunching my face in the "what was that????" action on things they've mentioned way back in a previous chapter that made perfect sense, and then they're just using it as a given currently and I'm wide-eyed with the deer/headlight thing going on as I flip back a few pages to refresh my memory on what's what. Then the, "oh yea, THAT", expression, and I move on.

That got me thinking about my kids. We'll go over something, practice, do homework, move on, and then when I mention or expect them to have instant recall on something later, they do what I just described above. AND I don't do it out loud or with any facial expressions, but I've been guilty of thinking in the past, "ackh! we did that, you know that, I taught that, get ON with it". Or I'm on my internal high horse thinking, "welllllll, they just need to see it several times, bless their hearts." Ew! I obviously have been served a lesson. If you happen to be human and are learning something new, you need to see it over and over and over again in various forms and that'll give it more chances to stick.

So all this to say, that maybe my new-found "success" is because this mechanism of my retesting is allowing the kids to spend more time with the topics than they have in the past.

Christmas in Toronto

I'm spending a week in Toronto for Christmas with the in-laws. My body is wondering at the sudden change in temperatures and units. We went from a balmy 75ish degrees F to a super chilly -3 degrees C. Though I've heard that Texas now has a cold front with temperatures in the 50's F. Oooooh, discussion about the weather ... Well, there's some math in there, right?

I'm also having fun learning JAVA with the "Head First" book. It's also giving me teaching ideas ... Since they devote a whole first few pages on how people learn. I like their fireside chats with various new concepts and pictures to explain concepts and such.

Okay, off to downtown.

Who'd a Thunk

I'm freeeeeeee. The last finals have been graded and entered. All the grades are done. No more school for 2 weeks. AND I got an early Christmas present in terms of final exam grades.

This year, for the 1st time in, oh say the last 8 years, I have not had to "curve" the living daylights out of their final exam grades to make them come out of the great dark cavern that would be their grade. Now I'm talking about my "average, grade level" students, my 10th grade geometry kids. Their grades went in as they stood, and everything was fine. Their final exam grades averaged in with their 6 weeks grades reflected how they did all semester. What happened? What was different?

The only thing I did drastically different this year was my form of retesting, or as I now like to think about it: benchmarking or "seeing-if-you-know-it-yetting". The fact that the kids HAD to come in multiple times to grasp a concept in order to be checked off on that concept made them really dig down deeper than they normally would and had them work through the repetition of practicing so that things had a better chance of sticking in their heads. With the old way, if they didn't know it by my set test time, well then oh well, too bad, we're moving on and won't visit this topic again until finals and good luck with that. With the new method, it's, oh? you don't know it yet? well keep trying and keep trying again and come on you can do it.

I think I've gotten over my: ackh! now they can slack off and not study for the FIRST test and just see what's on it way of thinking. Sure, they can do that, and for some maybe they do do that. The way I have it structured is that the MOST they can eventually make on a retest is 80% on a portion. That made it palatable for me in that they couldn't get 100%, and it wasn't as "bad" as an eventual 70% ... it was an extra carrot (but not TOO big of a carrot) for putting in the extra brain power to finish strong. AND now my final exam grades have cemented it for me.

Now. I only did this with 3 classes of size 19, 13, and 21. Ooh, I realize how lucky I am with small class sizes (from the days when I had sizes of 38, 44, 35,...). And I only did it with my "grade level" students. My advanced students did test corrections, and were good at it, and it served them well, and they were the population that got 96%, 98%, 90%, etc. on the final anyway. I don't know how I'd manage this or if it would be TOO unmanageable if I did it with more classes and had more kids. I guess maybe I'll find out next year depending on the type of classes I teach. But for now, I'm extremely happy with the whole process.

Perceptions of Our Kids

Today in tap dancing we had a substitute teacher. I'm always pleasantly surprised when we do for 2 reasons. One, the person teaches slightly differently than our awesome regular teacher. Even though I enjoy class on a regular basis, it's nice to have a variety sometimes. Second, the substitute invariably comes in without knowing anything about us, and that usually leads to them teaching us "harder" stuff. We don't always get it, but it's nice to be presented with it just to test it out ... knowing we'll go back to our normal routine next time and there's no anxiety if we "get it or not" because it's "not our routine".

Then on my drive home, I started thinking about me being the "regular teacher" in my math classes. I basically do the same thing every day. Yes, there are variations ... about once a month or so (?), but hmmm, maybe it's time to spice it up more often. Second, I know my kids. Especially since I've had more than half of them for the 2nd year now. I guess I have certain expectations of what they can and can't do. But now I'm thinking I need to again, sometimes spice it up.

Maybe I can toss in a "hard" day or a "hard" problem every week or couple of weeks. Well scaffolded, and with the very clear disclaimer that it's not business as usual, but they should just dip their toes in the water. Maybe not everyone would "get it", but the variety would be good, and the "faster" kids would get their cookie crumb every now and then.

They're Just Teenagers

I had an epiphany the other day. Now maybe it's obvious to others, but it's my epiphany, so allow me to be thrilled. Background: I don't have children. And as such, I'm sure I'm an expert on rearing children (cough cough).

Anyway, in the back of my head, or sometimes out of my mouth are phrases like, "well, in college .... or in your upper level classes ... you'll be expected to ______." or "you need to learn to do ________ by yourself." or "it's up to you to review, you have all the materials; systematically go through them from scratch; you don't need new review material." or "I don't want to baby them and hand hold them through things." With the thought that if I did things for them, and "enabled" them, then they'd never learn to do on their own. Or, I'll do such things for them but have a bad taste in my mouth because I feel I'm doing them a disservice by doing the "heavy lifting".

Then I thought about parenting. Your children don't automatically clean their rooms or cook dinner because "when you're on your own in your apartment, you'll need to be able to do this." They don't notice they have no clothes and then immediately wash a load because "that's what they're expected to do as adults" and parents "won't baby them by reminding them and showing them how and giving consequences if they don't". Parents have to teach such behaviors and tasks.

This makes me feel better about "babying them sometimes" by guiding them on how to do things and "hand holding them", that should just be a given later on WHEN THEY'RE OLDER ... but not now. So if I teach them how to review, and provide them with a guideline or extra practice, or if I discuss strategies of studying without expecting them to be born with the knowledge, or a ton of other things that are learning-related, then that's just a part of growing up.

Finals Time...

As probably everyone else in the world, I can't believe fall finals are here already. It'll be great to be off and be able to get enough sleep. I think I'll also spend the holiday studying. Maybe I'll have some time for fun tasks.

Here's a sheet I made and the kids did for part of their geometry review.

Inspiring Words of Study Wisdom

It's time for finals, and I'm trying to think of a variety of ways to say, "study". Since different combinations of words work for different kids, I figure if I say it in many ways, one or more may filter through to more kids. Here's what I've said so far:

* Don't let your grades just happen to you. Take charge of your grades.

* You can't expect to play a great game of soccer just by reading about soccer and watching others play; you actually have to practice. Similarly, you can't do well on a math test by just reading over what you or someone else did before on a problem; you actually have to do/practice problems from scratch.

* Study time won't just magically appear out of thin air, you have to allot time and find pockets of time and manage your time.

* Try your best, and that's all you can do. But don't just pay lip service to this phrase, if you dig down deep enough and are honest enough with yourself, did you really put out your best effort?

Hopefully, I can think of a few more to be "rah rah queen" for the next (last) class before they take their finals next week. Eek.

College Visits...

Just got back from visiting colleges with some of our students. Things I learned:

* "Are there opportunities for foreign students to obtain scholarships and work study?" is a safe way of inquiring for undocumented students.

* High school students need to be taught hotel behavior for late night arrivals (and hotel patrons need to bend your ear several times that evening and the next morning about such incidents).

* With each subsequent visit, students have more confidence asking a variety of questions about the college programs/resources.

* Young children are not the only age group that will watch the same movie over and over (and over) again ("White Chicks" anyone?).

* Long bus rides are an opportunity to see how you'd fare in a sardine can situation with other stinky sardines with whom you're not necessarily swimming buddies.

* Ear plugs are a must have for sane travel (la la la la la, I can't HEAR you).

* What does not kill you, either drives you to drink (immediately upon return of said field trip) or makes you stronger (or both).

* Hearing about study habits (and perils of having a lack of them) from a college student pulls more weight than hearing it from a teacher/adult. (What? We have to actually study in college? Who knew?)

* Student ideas about emergencies (as in don't knock on our door unless there is one) are vastly different from adult ideas of emergencies. Cases in point: I left my cell phone charger on the bus vs. my roommate got run over by a bus. Or .... The tap water tastes funny vs. my room is flooding from a tap water tragedy.

* Interacting with students for an extended period of time outside of your class setting allows you to have fun with them in a more relaxed setting without the get-your-work-done pressure.

Puzzle Sheet

I'm proud of this puzzle sheet I just made, and I like the self correcting aspect of these things. I think that if I had 20 more hours each day, I could spend my time making these types of things up. Notice that it basically has the exact same pictures from the previous sheet, but now the students have to place the vertices in order and determine what type of triangle congruence it is.

After we had our day of constructing triangles in geometry to see if they were all congruent or not, and after we discussed how to read information, then I had the kids learn about the various postulates and theorems (SAS, SSS, ...). THEN they're ready for this puzzle just to see if they can piece things together. If they complete the congruence statement with the triangle vertices in the right order, and if they correctly place them on the blanks at the bottom, then an interesting fact appears. (UPDATE: yeesh! There was a typo on the picture in #10, but it's fixed now in the download.)

Proving Triangles Congruent

We just started talking about congruent triangles in geometry. After a day of notation and vocabulary and such, I start up the class with asking them how many pieces of information a triangle has (6). Then I ask a series of questions: what if I asked everyone in here to draw a triangle. Is there a 100% probability that everyone would draw the same triangle? What if I told you one side had to be 5 cm? What if I told you that one side had to be 6 cm and one angle 40 degrees? And so on. Then they conjecture what would be the minimum amount I'd need to tell them. I get a range of answers, which is great.

Then we went through a series of carefully thought out constructions on my part of the 6 possibilities (AAA, SSS, ASS, SAS, ASA, AAS in order). I like that it gives them practice with protractors and compasses. There's also time for them to process (through the drawing), why some information doesn't give a unique triangle. We discuss how we know I gave them all the possibilities.

Then we barely had time (in a block class) for this side of the sheet:



In the past, students have had a hard time "reading the triangle information" in the right order. I think I found a fix. I have them lightly circle the sides or angles without information. Then I tell them that when they read the given information in order, they can't pass by 2 or more pieces of non-information. This seemed to help.

I assigned this side for homework:

Reaction Reality Check

Today was our last day of school before the Thanksgiving break. Woo Hoo for 2 day work weeks! As I'm scurrying along in my flustered crabbiness from my November funk and getting ready for the day, a geometry student stops by to inform me that she won't be in class today and to drop off her homework because her family is leaving early for their long drive to visit family for the holidays.

What's going through my mind: Great! She's going to miss our important activity of constructing various triangles to see if AAA, SSS, ASA, AAS, SAS, ASS can give unique triangles or not! She'll not be able to make it up! She won't know how to do the homework!

What comes out of my mouth: Aye! You're going to miss a vital activity that you can't do by yourself. Well, you'll have to look through the book and figure things out. Look through the index for "triangle congruence". Good luck. Here's the homework. .... and honestly, I don't remember what else I said.

She leaves. Hopefully, I wished her a happy holiday, but I don't remember in my rush to have myself a pity party.

Time passes, and then I realize what a jerk I was. I send her the following e-mail:

----------------------------------------
Hi ***,

I feel like this is how I sounded on Tuesday morning when you came by to mention you'd not be in class:

"What?! How DARE you miss math? Family?!?! What's more important - Math or Family? Think carefully! Your WHOLE school career depends on what you do next!"

What I really meant to say was:

"How fun you get to spend quality time with your family on this family vacation. Have fun. Thank you for coming by to let me know. How responsible of you. I know you will have no trouble making up the work because you're THAT good."

Oh and by the way:

We did an activity in class that you'll have to hear about, but you can get the gist of the importance of it by reading sections 4-4 and 4-5 in your geometry book.

See you after break,

Ms. ***
-------------------------------

Seriously, what goes through my mind sometimes? I teach math robots who live and breathe math?

Spherical Geometry

This past week I spent part of a class period on a spherical geometry activity, and it went well. Beforehand, I went to the store and bought some 4"-5" diameter soft/squishy balls (tennis balls will do, but not really large 12" diameter ones, I think, because of the rubber bands). I bought enough for one per table (4 kids). I also had 3 rubber bands per table.

As always we had a quick discussion about these things being "math tools" and not annoying distractions that you throw or bounce or snap people with, etc. MATH TOOLS. Then I had a brief introduction on how we've been studying Euclidean geometry where everything happens on a plane and everything is defined on a plane, and what if we defined things on a sphere where our objects had to all live on the surface of the sphere? With that I handed out this worksheet:



and told them to do the bold questions, 1,5,7,9,11,14. We discussed the answers, then I walked them through 2,3,4. Then I set them on their own to explore the remaining questions, one at a time, and making sure that everyone had a chance with the ball. And we discussed the answers after each problem.

There are a ton of resources on the web that have answers, and I love the surprising results. They're brain hurters. For their homework, they had to find at least 2 more cool facts about spherical geometry, and then they had to find 1 new fact about a geometry on another type of surface.

This all took about 45-50 minutes with my advanced class. They came back with some interesting facts, and it was a nice addition to our normal routine of "every day geometry".

Synopsis of the Day

This should sum up how my school day went ... that started with a faculty meeting wherein we:

* were informed about how our school district is thinking about cutting various things to meet their budget shortfall (which may include teachers giving up a prep period)
* were chastised for not willingly giving up class time for students for extra curricular things (because we were greedy with instructional time)
* were told of upcoming events that would further alter the schedule to allow less class time
* had 1 hour less of prep time in the morning because of said meeting ....

SO....... one of the highlights of my day (aside from numerous other student interactions), was a student who informed me at the start of geometry class that they had a new joke to share (which as a bonus sums up what's expected of teachers):

Q: How do you fit an elephant in a Safeway Bag?
A: Take away the "f" in "safe" and the "f" in way.

Google Genius

Am I the last person to know this? Today we were calculating all sorts of values related to polygons and regular polygons and interior and exterior angles of regular polygons and such. As I'm sending the kiddies off with their homework, I thought to mention that if they didn't have a calculator at home, they could just "google" free calculator, and they could use one of the options that showed up.

Then a students said, "well, you could just type in your math equation right into the google search bar". What? So I tried it:

1080/3. Yup.
sin(pi/4). Yup.
log(5.234). Yup.
arctan(1). Yup.
e^(-1). Yup. Yup.

Holy Moly! Genius-ness.

Blogging Topics....

Maybe every "anonymous" blogger reaches this point. I've been blogging for about 6 years (I had to just go check the first month shown on the front page), and to this date, I've never directly mentioned to anyone I know, husband, friends, teachers, that I blog. At first it was because I didn't know where I was going with it. Then later it was because .... who knows. Maybe it was a "once it's out, I can't take it back" type of thing, or a "if no one I know knows I blog, then I don't have to self edit" type of thing.

Last year, I got a rude wake up call. I had written about a student and her lack of class attendance and such. Then another student was joking with me and mentioned that this 1st student had seen that I'd blogged about her. What? First of all, how do you go searching for math teacher blogs as a student (why?), and 2nd of all, why this blog? So then that started me being more circumspect. Again, maybe everyone has to do this.

Then a month or so ago, a teacher in our district was let go because of her blog. She was revealing personal student information. Yeesh, more self editing. .... All this to say, there are a ton of funny things that happen at school, but I can't process in writing. So basically, now I feel limited to sharing teaching tips, which is not bad, but it sure would be nice to vent/laugh/process/write about various things.

Anyway, bla bla bla. Just "venting" (which apparently I can't do :)).

Here's one funny (safe) thing. For some reason, unbeknown to me, a student keeps associating me with llamas: "do you have a llama herd?", "llama lover", "llamas", "how are the llamas?". I just roll with it. It reached a pinnacle today, and I went online and did a "llama lovers" search.

Go on, I dare you to type that in. Apparently, there are full on societies of llama lovers. There are songs, pictures, blogs.... Then I got crazy and tried, "yak lovers". Sure enough. There's a "yak appreciation society", a "yakkin about yaks" site, .... platypus lovers? But of course! Oh my goodness.

Anyway, this student bought me a present today. Guess what it was. Yes, a small stuffed llama. Soft. Crazy. I think I can make it my evil twin and channel my evil teacher thoughts into it: "you! shut up!" What? That wasn't me, it was the llama speaking.

SAT questions

Great! New resource for problems. I bought an SAT math only workbook, and it's chock chock CHOCK full of geometry problems asked in all sorts of cool ways. There are a ton of triangle problems using "angles sum to 180" facts and parallel lines and transversal problems.

Here's an example: picture triangle ABC. Then picture point D on segment BC. So you have your larger triangle separated into 2 smaller triangles. Put variables representing 5 of the 6 triangle angles (a,b,c,x,y). Let the 6th angle be 50 degrees. The question asks find a+b+c+x+y.

Love it.

Angle Pair Nitty Gritty

As I was merrily going along teaching linear pairs and vertical angles and corresponding angles and such, it came to my attention that various students were not "there" yet with internalizing the pictures and definitions, so I came up with this activity:



I like the activities I've seen where sometimes the answer is "none" and sometimes there's more than one answer, and sometimes the answers are repeated in different questions. I've tried to incorporate that style into these problems. I think it worked pretty well.

I'm also giving them a quiz on 6 types of angle pairs for the next grading period. I told them they have to identify each angle pair correctly, and spelled correctly, and no abbreviations, and no doctor handwriting, and in a timed manner. If they miss ANY, they get a 0%, and they have as many tries in the next 6 weeks to get it 100% correct. I likened it to recognizing the letters of the alphabet. It sure would be a shame if they couldn't and/or it took them a long time to process the information. I restated the fact that geometry (math) is like a foreign language, and they have to have fluency with all the words.

In other funny news. A student whose grade is suffering and who came in for tutoring today and was actually grasping things said, "wow, I should really listen more in class because this makes so much sense."

More Memory Tools ...

My 10th grade geometry students keep trickling in to take their logic retests, and many of them still had a hard time remembering the laws of inference to use in logic proofs. They would confuse the following two:

p --> q
p
-------
therefore, q

(Law of Detachment)

p --> q
~q
-------
therefore, ~p

(Law of Contrapositive Inference)

I tried 2 or 3 or 1000 different ways of explaining it, and nothing stuck. I thought I hit gold with the following:

If the Dog is a Terrier, then the CHihuahua likes MENTos.
The Dog is a Terrier. (I thought this would help them connect it to detachment).

and

If the CON is a TRAitor, then I POSsibly like TV.
I hate TV. (for contrapositive inference).

So that helped some kids, but wasn't the raving success I thought it would be. Then just the other day, we were going over problems in tutoring, and I was circling things to make a point, and saw this:



Do you see it? The Detachment scribbles look like "D", and the Contrapositive scribbles look like "C". Well. They thought that was SO cool, and then they started accusing me, "why didn't you just show us this in the FIRST PLACE!". Like I was secretly storing away the "good stuff" and doing things the "hard way" until they finally wore me down to giving up the goods. Is this on ALL their minds: teachers always do things the hard way and hold back on us. Phwueey. I told them I just thought of it, and there was nothing to prevent them from figuring things out on their own and stop bothering me kid. .... They also passed their retests with flying colors.