Hand Holding vs Solid Examples

I feel like a flippy-floppy fish on this whole topic, but I guess I could "spin it" as I'm readjusting my attitude as I gather more data. For the last few days, I've been studying statistics for the N.B. exams I had to take today. I went right to the source and bought a prep book for AP Statistics. Since it's a prep book, they don't TEACH every topic in depth, they just review it and do SOME examples and then give practice tests. ... Maybe not the best way for me to review something I haven't seen in ... oh my ... 16+ years.

I found that as I was learning one of the topics, they kept describing each piece/terminology of it in many ways and then building on and then redescribing each piece/terminology, and I found myself saying: JUST SHOW ME A SOLID EXAMPLE FOR THE LOVE OF GOD. And then I had to laugh and say, "oh what, you want them to HAND HOLD YOU through the stuff? can't you piece it together yourself for the joy of learning?"

"Gripe 2": there were SO many new vocabulary words that I'd understand in the context while I was learning it, and then when the book refered back to such a word, oh say 50 pages later, I was thinking, "yesssssss, that SOUNDS familiar, but holy cow, don't ask me to use it in a sentence other than: _____ is a word related to statistics.

All this to keep circling back to the topic of how my (any) students learn and retain math. I guess mostly I write this, so I can get over my uppity self and keep in mind that learning anything new and hard for students is, well, hard, and students should be provided with scaffolding and good-humored reminders that they're doing something hard and should pat themselves on the back between note-taking and problem doing and such. AND teachers should keep this in mind and keep spiraling back to old topics and bla bla bla.

WooHoo! The School Year is Over

The students' last finals were on Wednesday 6/4/08. We had to come in on Thursday to check out, and our graduation was held in the early afternoon. I went in on Friday to finally clean up the rest of the clutter in my classroom. And now ... I'm at home completely done. Whew. As usual, it sneaks up on you and is over before you know it. (unless you're still in school, and then it NEVER seems to be over)

I had a bit of drama (still ongoing) with a parent EXTREMELY upset because of my grading policy for the last 6 weeks. Ultimately her child got an 87% for the semester, but that's not acceptable to her, and I've ruined her child's life, and she'll be speaking to my administrator to make sure I don't have this opportunity EVER again to do this to another student. Deep breaths. I've talked with various other teachers and friends and have calmed down a bit, but obviously I'm still bitter.

In brighter news: I've started "playing" the guitar (and by playing, I mean random strumming and posing and trying to look cool while screechy sounds eminate from the instrument as my tongue sticks out of my mouth to aid in better concentration) and am self-teaching myself (that sounds redundant) via books and cds and dvds. It is so fun.

I'm also planning on making a simple big-square quilt for our guest room this week, so that when my friend visits, I won't have to subject her to the 80's style black-neon-pink-&-green-&-purple syntheticy cover.

Calculus project news. I liked how my volumes of revolution foam projects turned out. BUT. I have an idea I want to play around with for a teaching tool for next year. I'm thinking of getting card stock or laminated color paper and cutting the same shape out many times. Then I'll either cut a hole in each one or a slit in order to string all these shapes onto a circular thin wire or stiff cardstock that is curved into a circle. Then I can "fan out" the shapes or clump them together, and the students can get a better visualization of a "volume of revolution". I'll have to experiment this summer.

Note Taking

My precalculus students have recently taken a test on sequences, series, & the binomial theorem. The students run the gamut from they-could-teach-themselves-out-of-a-book to please-take-my-hand-and-do-the-problems-with/for-me-over-and-over-again. It dawned on me while I was helping this latter type of student to study that she had no concept of what might have been some good things to study and review before taking the test: formulas for explicit terms, partial sums, pascal's triangle ...

I thought over the notes they took, and I'm wondering if it ALL was so foreign and important sounding to her that she saw it as:

sdlkfoe sdoowieur sdeoe 5 = sdlfoein sdifuoeen
oeiwonewio sdf e3dof soieen sdeid nli lskejoi i9 dflk

so maybe she couldn't parse through it all and figure out what was important to know. I know when I was presenting the stuff, I had them do examples, and I had them write down the formulas and I discussed why they work and how to think about them .... but apparently, for some students, I have to stress what's important before, during, and after. And then maybe I should make them get out their red pens and BOX all the key things.

But this doesn't sit well with me. It seems that I'm doing the thinking for the students that way, and they'll never learn to sit back and reflect on what may be important to know without someone spelling it out for them all the time.

Stress City

Good riddance to a bad week. I had 3 bad run-ins with kids that left me so angry.

Run 1: I've had issues in the past with students conveniently not showing up on exam day. Then they'd take weeks to make up the test. Two tests ago I started the new policy of, "you miss the test, you make it up during class the next day". This helped. Then this past test, I had 2 students mysteriously absent on test day, last period of the day. I checked ClassXP, and, gee, mine was the only class they were absent for. I decided to use technology to my advantage and pop a quick e-mail home to mom: "is there a reason your child is absent from my class today?". This got results, and it alerted the parents without sounding accusatory (they could have had a dentist appointment). Well, it turns out one kid lied to his mom about where he was, and I found out, and thus he got a zero for that test. So, here we are Friday, and he's in my class just sitting there fuming all period. One and a half hours. Yay. So, not really a "run-in", more like a long, drawn out sit-in with teenage angst of getting caught and having to sit and take it.

Run 2: One child is in NHS, and has been slacking off on the homework department and just general character department all year (okay, all 4 years). After a bunch of stuff had happened, the NHS sponsor would only let him wear the "stole" at graduation if he got letters from his 4 core teachers that he deserved it. So he comes in to my class and tries to good-naturedly try to bully me and guilt me into writing his letter. He still didn't get that it's his actions that brought this on. He still thought/thinks that "we" are doing this to him. That left a bad taste in my mouth.

Run 3: Oh my. We're doing projects during calculus class, so it's a wee bit more unstructured as a class period than I like or am used to. Some kids are doing videos, and one kid in particular doesn't have any of his equipment at school, so just basically sits in class and says he'll work on it during the weekend. That's all a side issue for this run-in. He comes into class on Friday and does not look physically well, so I basically don't bother him much. Towards the end of the period, one student had turned to him and asked what he was doing. Apparently, he had unbuttoned his pants and unzipped them a ways because he was uncomfortable and didn't want to put pressure on his stomach. Well, okay. So I catch this interaction, and say to him, "well just put your shirt over your pants, so we don't have to see your unbottoned pants." Then he starts arguing with me. I keep asking him to just pull his shirt over and that it's just not socially acceptable to sit there like that. This goes on for about 3 rounds as he's refusing. Then he suddenly turns all creepy and lowers his voice menacingly and leans forward to me and says, "I'll decide what is socially acceptable and I'm NOT going to button my pants so you can be on your power trip and .....". Oh my god. I was livid. I told him to stop talking to me and that he was being completely inappropriate and he just needed to either leave the room or button up his pants. Holy Cow. Jerk. Excuse me while I jump off my teacherly manner and just fume about the brat. Okay, deep breath and the knowledge that I only have to see him for 2 more days.

Anyhow. WooHoo for weekends, especially 3 day ones. And only 7 more school days.

End-o-Year Calculus Project(s)

I ended up deciding to give the students a choice of 3 projects to do for the remainder of our time in class:
1. a volume of cross section project using colored cut foam that I've done before
2. a volume of revolution project again with foam (never done and I'm doing it with the kids)
3. a video or power point (never done before, and thanks, Sam, for your tips which I've incorporated).

I'm happy that 7 students picked the video project, and 2 picked the power point project. From talking with the kids, they mostly had great ideas and are working hard. One student is resisting everything and being really derisive and dismissive and coming up with every argument in the book as to why he shouldn't be doing this. Or talking about doing something sarcastic and such (because, you know, math just isn't that exciting). I'm working on setting him straight using my teacher voice as I'm simultaneously resisting the urge to vigorously shake some manners/sense/attitude-adjustment into him.

I'm excited about the volumes of revolution project. There are 6 (?) of us doing it. I picked the same region for all of us (y = 4 - x^2 , y = 0 , x = 0) and we're each revolving it around different lines. That way we can put them all together and see what's what.

One video pair is working on a video about someone getting ready for a "math party" and they have to cut eggplant and for some reason need to know about the volume (details will emerge). They wanted to know how to get a function that looked like an eggplant. One girl was really excited and happy to learn something new when I showed her how to plot the shape on paper, pick some points on the "graph", put them in L1 and L2 on the calculator and then do a Quartic Regression. Cool. It DID look like an eggplant when she showed me.

Limits

I was teaching algebraically finding limits today in precalculus. We got to the part where x --> infinity. I've tried various ways of explaining it in the past about how you only need to look at the highest power term on the numerator and denominator and make your decision that way.

I've likened it to "when you're plugging in REALLY LARGE NUMBERS, the largest power term is like the ocean and the smaller powered terms become like spit. They don't make much of a difference to the ocean volume." This stuck with some kids, but I don't know that all were convinced.

Well. I had one problem: (8x^3 + 2x - 7) / (-4x^3 + 5x + 100) or some such thing. On the graphing calculator, we entered 1,000,000,000 and stored it in x. Then we calculated 8x^3. Enter. Then we calculated 2x. Enter and compare. That semi-convinced them. THEN we calculated 8x^3 + 2x, and that really convinced them because it "was" the same output as 8x^3 by itself. And we all know that if the calculator says something, then it must be true.

If I was thinking (because what I did was on the fly and then I moved on), I should have also then (in the main window) plugged in the whole expression using the stored value of x .... or then putting in larger values of x and then "2nd entering" to recalculate the expression. Next time.

The Quiet Ones

For various reasons I thought it would be best for my calculus students to practice more than class would allow, so to entice them to come after school for 6 straight days before the AP exam, I called them "power sessions" and said I'd bring food every night, and we could meet from 4:30 -6:30 and just do and discuss old released exams. I had anywhere from 10 to 28 kids show up (out of my total of 40) each night. I think it helped. We were all relieved once the AP exam was over, and I think it payed off for the ones that put out more effort.

During these sessions I'd call out a couple of problems at a time, and they'd work them, and then we'd discuss them. As usual I mentioned that people should just ask questions when they had them. I always have people asking questions. This gives me a false sense of things-are-okay-for-everyone. Or maybe I'm just gauging my time and trying to get through a lot and just moving on once the questions die down. Or something else.

I know there are a couple of girls that work hard but struggle. They asked NO questions. I'd even look them in the eye and ask if they had questions. Nope. I know I should know better than that, but apparently I don't (even after 11 years of teaching). So finally I started going over to them while the class was working the problems and would say, "you're fine? or do you have questions?" and invariably they'd have some question that I could quickly answer for them to set them on their way.

It seems like each class gets a culture, and there are the talkers and jokers and more vocal participators and then after a while we all settle into a routine and maybe it's hard to rock the boat and make your voice heard if you are not used to it and the other kids are the "cool kids (?)" or the "class representatives (?)" or something. Here's to being reminded to remember the quiet ones.

Filler Classes

This past week was our TAKS week, and therefore I only saw some of my precalculus classes, and so I could not move on, and I did NOT want to have "free days". One day, I taught them about binary and counting and adding and subtracting and multiplying in different bases.

I made the connection to base 10 where you can think of each position as a bin where you drop marbles. You start filling them up from right to left. The capacity of each bin is 9, and once you try to put one more in a bin, it would overflow, and so you have to scoop the 10 you want to put in there out and place one marble in the next bin over to the left to designate a higher power of 10.

So we started counting in base 4. Each bin has capacity 3. We did the "scooping" thing. We counted to 20.

1, 2, 3,10,11,12,13,20,21,22,23,30, ..., 103, 110.

We made the connection that each bin represents (from right to left: 4^0, 4^1, 4^2, 4^3, ...). We did other bases. We then converted between base 4 (say) and base 10. And between base 10 and another base.

I also recalled a version of a game I played in 8th grade, that I still play when I need to occupy my mind and have time to kill.

Pick any 4 single-digit numbers. Then number your page from 1 - 10 (as one example), and you have to use every one of your chosen numbers once and any math operation to get all 10 numbers listed. I had them play and the first one done would get candy. Boy were they quiet and working. I'm SURE it was the math and not the candy.

For example: 5,2,8,9

1. 9 - 8/2 - 5 = 1
2. 2 + 5 * (9-8) = 2

Attitude

I think I've learned to perfect the, "what do you MEAN you're not going to do the thing I've asked you to do?" look/attitude.
The, "of course you'll do it" look.
The, "there's no other option" look.
The, "I'm amazed you'd even think to ask such a question" look.
The, "don't be silly" look.

I got to use it Monday when I prepped my AP Calculus kids on the fact that they had homework that was due Tuesday even though I wouldn't see them due to the state test, and they'd better walk their butts over to school from whatever vacation they think they're getting and hand in the no-lates-accepted AP-exam--multiple-choice corrections to me.

Of course I'm semi-bluffing and know I'm asking a lot of them, but I think the "look" gets them to get off their duffs, and maybe I'll have a higher turning-in rate because of "the look". I also reminded them of the fact that the AP exam is coming up next week, and don't give up now, and you can do it, and it would be a shame to work so hard all year and flake out now and miss the opportunity to pass, and rah-rah-rah ...

Plus I get to practice being a bad-a** when I think I'm a softy inside ... but maybe I'm fooling myself, and I've become mean and cranky with high expectations. Oh well, they usually rise to the challenge - and I guess it's our job to push them to do their best, even though it's their job to resist and try to get away with what they can. Our little teaching tug-o-war.

Idea for post AP exam calculus

The last 2 years I've done different things after the AP exams in my calculus classes. One year we did a rubber foam volumes of cross sections project. One year we discussed "multiple" integrals and (non calculus) counting and adding and multiplying in different-than-10 bases.

I just had a thought I haven't fleshed out for what to do this year. I'm thinking of getting a list of topics that span the calculus year, and having the students make short videos that teach or showcase the topic. That way I can post the useful ones on my website for the next year's students to have a different perspective on things they may struggle with. Also, the students are creative, and I think they may come up with good stuff.

Grading? I'm thinking there has to be a time limit (less than 4 or so minutes), effective (to be judged by other students), creative (again judged by students), done on time, ....

One issue may be various student access to video equipment. Another issue is size of groups working on one video. We'll see ...

Shhhhh

I was at an AP Calculus prep session for the students most of the day today. There were 3 sessions running in parallel, and 4 different time slots throughout the day. I sat in on the sessions and worked along with the students. One teacher had great problems, and he'd keep talking and talking and say, "okay now you work the problems", and then he'd only give us 1 second (or so it seemed) before he started talking again - either about something else, or to start working the problem.

It made me reflect and wonder if I do this more than I should. I know I try to shush up with enough time for the kids to work, but at the same time I'm clock watching and stressing about finishing in time and getting everything in and then maybe rushing the kids.

I also tried something different in BC calculus on Friday. I handed them my notes from "math camp" on parametrics, and then also handed them a separate packet of problems with answers provided in the back. On each of my "camp" notes, after each problem that had been worked out, I had written on their copies, "now work problem so-and-so". I barely talked to them at all, and only monitored to see if there was any clarification needed. They worked like champs all period, and were doing all the problems. Hopefully, they'll continue over the weekend, as I told them there'd be a "free response" quiz the next time they came to class.

Testing Testing

Okay. It finally got to me. All year when I've announced tests and given tests, there's ALWAYS some students absent. Then it becomes a game of, "when are you going to make up the test". Then days and literally weeks would go by before some students made up the test. They all eventually do, but really! It usually didn't annoy me TOO much, but now during this last test about 1/5 of my class was gone from each period during the test.

In the past I was diligent about mentioning and then checking up on whether the students were cutting or not, and then they had zero chance of making up the test. This year, I had other things on my plate.

I'm giving a test this week on Wednesday and Thursday (block scheduling). I mentioned ahead of time, "if you are absent the day of the test, the next time you are in class, I will put you out in the hall, and you will make up the test during class time and miss the current lesson." Hopefully, this will make it less appealing to the students to all of a sudden feel really ill on the day of the test and use that as an excuse to drag it out.

I heard another teacher at the beginning of the year announces: every time everyone is here for a test, everyone gets a bonus point(s). She found that then the students were policing each other to make sure they were there.

I guess my method will work (I hope), because either way, the students will finish the test within a week (unless they're super skipping class).

Getting In Trouble

We recently had an incident in our school regarding relations between a teacher and a student. Phew! The repercussions of that. Part of me thinks: WHAT was the teacher thinking. There goes the career, the chance to earn a living, the student's psyche, ...

We had to all go to "harrassment" training for 1.5 hours. All the way up to the meeting I was grumbling to myself: I didn't do anything wrong. I have classes to prep for during my prep periods. I know right from wrong. Grumble. Grumble. Then as these things sometimes go, I learned some things.

1. Even if the student is 18 or over, it's still cause for dismissal.
2. If you hear any rumors about other teacher/student goings-on, and you don't say anything to the authorities, and it's later found out that you knew/suspected, you are in the wrong and could face .... whatever.
3. Even if your relationship is innocent (and later proven so) with a student, if others perceive it as fishy and the rumors start to fly, you could lose your job because the public has "lost faith" in your ability to be effective in the classroom (hmmmmm)
4. If students get too friendly with you and develop a crush, and you don't nip it in the bud or make sure you're never alone with one student, etc. one of them could become jealous and start spreading rumors about you (creepy) that may cause you to lose your job.

There's probably more, but that's depressing enough as it is.

Parents

Two weeks ago I was scrambling and rushed for time, so I did not complete the official "progress report" sending via the school (every student who is failing or within 3% of failing receives a progress report). So. Within the next couple of days, I printed up IGPro grades, 4 to a page, chopped them up, attached them to a 1/2 sheet stating that parents should discuss this with their child and write me a note and sign it that they've done so. I made it a SMALL quiz grade to guarantee I'd get them back, docking off 10% per day late.

I have one awesome kid that is always in for tutoring, asks questions in class, does all his homework, scores very well on tests, takes "retests" (bane of my existence) every time if he does not get a perfect score, has a 99.63% average at the time of the reports. His mom writes back: I know he can do better. I will make sure he comes in for tutoring so he can improve.

Compare this with another student who has a 93% with the parent comment of: my son is so great!

Compare this with another student who has a 3% and who scratched out his mom's comment to call her.

Fun vs. Effective

Last year from a workshop I learned of a fun activity with which to introduce volumes of revolution to my class. It involved candy, the kids seemed to get it. They loved it. We all walked away with smiles on our faces. But then they got home and couldn't do homework involving revolving regions about various axes. Granted in class, we only went through 3 examples, I talked them through it all the while giving them a chance to process it. But still, no.

This year, I was looking through my files and came across another way to introduce volumes of revolution. It's (free) from www.mastermathmentor.com . And there are TONS of calculus AB and BC (did I mention free) worksheets there. I'd hesitated using it before because it looked TOO LONG to get through in class. Then the homework was TOO LONG. Hey genius :), just because all the problems are there, it doesn't mean you have to use them all.

I used this sheet this time. I slowly walked them through the 6 parts of example 1. I kept stressing the questions to ask yourself, and I weaned them off my help so that by the 6th problem they could do it by themselves. Then for homework I assigned them examples 2 and examples 3 (12 problems) from the class work worksheet. Wouldn't you know it. They all got it right. AND they could then go on and do more challenging problems. Success.

I keep having to teach myself that not every student can get by on just one to two examples to teach a concept. Some students need 5 or more examples. But then there's always the time factor and the other kids in class that can get it with just one example. Anyhow. I'm now excited because I've found a new effective way of teaching this topic.

Seeing Pink

Well honestly, seeing Red, but since I'm not doing anything about it other than losing sleep last night, it's been downgraded.

Apparently, our algebra, geometry, and algebra 2 teachers have been told to stop teaching the curriculum and start teaching to THE TEST. The state-mandated, must-pass in junior year to graduate, must-pass in sophomore year to make our school "acceptable", must pass in freshman year or else the uppy-ups start to panic and worry you won't pass in 10th or 11th grade ... TEST. And for how long are they to teach to this test? FOR 3 MONTHS. That's 3 months of math knowledge they won't have the next year, and the next and the next. Oh my god that is so short-sighted.

Honestly, if I was teaching one of those classes, I don't know what I'd do. Would I refuse? Would I teach part of my class to the canned activities that they all must follow and then teach the curriculum? Would I raise a big stink and even go so far as to quit in protest? And why am I not doing something now? Just because it doesn't directly affect me (it will when they're in precal and calculus)? If you know something is wrong, and you keep letting it continue, aren't you just as guilty for it perpetuating? Argh.

People Watching

I was out with my friend this weekend, and we went to a tea house in an upscale, outdoor mall. It was fun to people watch, and there were all types - pregnant moms with little kids in tow, glamour teens with their high-price accessories, vogue 20-somethings, everyday people in shorts, lots of girls in sundresses. I started thinking about the things that go through your head when you watch people.

I'm wondering if a lot of the mind chatter is like - oh I wish I had abs/legs/arms/etc like that, or I wish my hair swung like that, or I wish I looked like that .... and I'm wondering about how much that affects how you live out your life or the choices you make.

What if the mind chatter went more like - oh I wish I was as generous as that, or I wish I could forgive like that, or I wish I could contribute to my community in that way like that, or I wish I was as good a person as that ... more inside stuff than outside appearances.

Counting To Ten

I know we hear that once you ask a question of a class, you should "count to 10" to wait for the students to think about it quietly before you proceed to ask for an answer. And I guess when we're tutoring students, and trying to walk them through a process, you "count to 10" after you prompt them for a piece, so again they can process the information.

I literally "count to 10" in my head, and sometimes twice. Now not 1,2,3, ...., 19, 20, but 1, 2, 3, ..., 10 then 1, 2, 3 ...., 10. I'm wondering if other people do the literal counting in their heads while they wait.

Then again, I count the stairs in my house when I'm going down or up them (5, 8, and 6). I count the "bumps" in one piece of the highway on my way to work (10).

I think the counting is good. I sometimes count to 10 after I am "giving them notes", after short bursts of speech, so that they have time to process what I just said before I burst some more (I'm sure they're on pins and needles waiting for the pearls to fall from my mouth instead of thinking about boys or girls or prom or music).

I'm thinking of this one reporter on NPR. He always sounds different from the others. He's the one in Florida, and he talks really fast (compared to the other reporters) and it just sounds different and noticeable and you just want him to slow down. I don't want to be that "reporter" teacher, but I know I talk fast, so hopefully I'll keep counting to remind myself to slow down.

Snacks

A while ago I got into the habit of keeping snacks in my classroom in a big plastic (dark, non see-through mouse resistant) tub. I like to keep, graham crackers, pretzels, cheddar bunnies, Newman cookies, CheezIts, cereal, etc. It seems to be an incentive for kids to come in for tutoring at the end of the day, or at least to have them stave off their hunger (or ruin their appetite for dinner) as they're getting extra math help. I found that baby wipes and extra napkins and maybe small paper cups for pouring treats into are helpful.

There have been some incidents. Once during first period, a student mentioned she hadn't had breakfast and wondered if she could have a snack. I said sure, and envisioned her quickly taking something, closing the tub, and getting back to work. After I continue with my lesson, I glance over at her, and there she is in all her glory, open tub next to her, and an array of snacks on her desk. We quickly fixed that, and I made a mental note: no "tub" during class time.

Another time a student asked (during class) to have a snack. I said, no, that it was only for after school. Then she tries on her pleading voice, "but I really like them, pleaaaaaaasssssse". Ew. No means no. I'm reminded of a TV talk show I once saw where the message was, just because someone asks for something nicely, it doesn't mean you should give it to them, their example was: "oh I LOVE your diamond necklace. It's so beautiful and elegant. Can I please have it?"

Then there are the "vacuum" kids after school - not many of them, but, sheesh. All snacks inhaled, and thank you very much.

But mostly it has been something I think I'll continue.

Spring Break

WooHoo! Nine days off to relax and catch up and stuff. I went to Portland, OR for a few days just to wander around, and the rain gods must have been busy elsewhere because it only rained on the night I came in and on the night I left. Note to self: red-eye flights bad, but made better due to the fact that I had a whole glorious row all to myself to "stretch" out in for 4 hours of interrupted sleep.

As I was wandering around and needing a caffeine fix, I started looking for either the *green* popular coffee shop circle/emblem or the *red* one. Then I got to thinking how that's so ingrained in our brains, and we now have instant recognition of logos and various signs even if they're too far away to read, we've memorized them. Then that got me to thinking about various things I want/need my calculus students to know: derivatives/integrals related to e^x, ln(x), trig functions, etc.

My thought before spring break was to have various posters around the room with "need to know" things on them. Maybe in different colors or styles, and just the fact that the kids have to stare at them every day may help them when the AP exam comes around, and they can close their eyes (maybe) and "see" what they need to know. Then I thought I'd force the issue and periodically (daily?) have us recite the posters. Then after my trip, I thought maybe we can design some sort of logos for these things. Anything to make facts stick in their heads when they have SO much to memorize.

Must think about this some more.