Losing (My) Marbles

My AP Statistics class starts Probability sometime next week (I’ve scheduled a couple days of how-to-answer-multiple-choice in there, so I’m not precisely sure when). I’m dreading it.

I think I’m less-than-great at teaching it, but I also think I come up against a lot of baggage when we hit probability. No one thinks they know z-scores. Students readily accept that I will teach them new things about scatterplots. But probability? I’ve got that down.

Probability is easy, right? We started those problems in third grade, and for whatever reason it shows up every.single.year. Marbles? Jelly beans? Candy? Socks? Shoes? Elvis’ jumpsuits? Done ’em all.

And so I take a bunch of students who “know” probability and…it all falls apart.

I suspect the breakdown happens in between the students feeling like they’ve totally got probability (marbles) and getting at the idea of a long-run frequency of something occuring. Instead of probability as “over many tosses, about half will be heads”, it becomes “you get heads half the time, because that’s just the way it is. And since I just got tails, heads is next.”

So how do I undo that? How do I help them see probability as long-run chance, and never ever a sure thing (well, unless its 0 or 1)?

Part of me thinks I should try to teach as much probability as possible without using the word “probability”. Or maybe do some exploration of different probabilities before I start formally teaching the actual content.

Part 2 is how tricky vocabulary is around probability (especially since English isn’t my students first language). Last year I did a foldable with vocab but I’m not sure how helpful that was (if at all).

Should I have the students model the same situation several ways? Generate our own data and use that?

How do you teach probability? Any ideas of where the disconnect might be? Help!!


Fun with Fractions: Day 1

My students don’t understand fractions. They hate them, they don’t get them, etc. They know plenty of the “rules” but they don’t why they’re doing anything or how it actually works. We’re currently in the midst of Number Sense, and this is how we’re doing fractions. A huge thanks to my sister for her work on this individually and with WISME and CCLM in Wisconsin (for, um, fourth grade math). I’m not comfortable posting the powerpoints here, but am willing to share them.

Day 0:

Fraction Screener. 20 minutes to mostly model fractions in various models, representing things like sharing items equally, sharing items with a remainder, equivalence and partitioning.

Start fraction strips. We cut a rainbow of paper strips (9 colors), as well as spare “practice” strips from scrap paper (yay! Another use for all that blank-on-one-side mental math!) My sister said to cut waaaaaay more than you need, and it still wouldn’t be enough. True. I did and it wasn’t. I asked the students if they could work on folding for homework, and they gamely said yes. [If you do something like this: no writing on the strips, with the exception of blacking in the fold lines to make them easier to see/count. That’s how you find which one is which–counting, not looking at a number.]

Day 1:

While some students made a lot of progress over the weekend, many of the students came in Tuesday with several still-flat strips. We walked around and helped (and so did some of the already-finished students) and I had some very eye-opening conversations. “I need help with ninths.” “Ok. …any ideas which strip ninths might have a relationship with?” “….eighths? tenths?” and the like. Same thing with tenths. This is an on level ninth grade math class, and if anything my students have impressed me so far both with their ability and their willingness to try things. I don’t think this is unique. My students aren’t the only ones dying to blindly multiply by the other denominator ad nauseum because someone told them to.

We took a couple quick pauses in here for:

  • How many numbers is a fraction? (Consensus: probably two. Bizarre: the two kids who said “something else”)
  • How many folds did you make on each strip?

After that, we had the students fold each strip so that one unit was showing. We used the phrasing, “One share of size one-half” and so on, first with single shares, then moving into fractions like 3/4 (way harder to say–try it! Its tongue-twisty!). I tried to stay away from the technical language of numerator and denominator because I felt like students would be more likely to approach this in a new and different way (as opposed to multiply-all-the-things) if they were using different language.

Then we moved through some practice problems having students fold the strips and use them to represent and then talk about different comparisons. Some other discussion worked its way in there nicely, such as when one student said that more shares is bigger and was paused to develop some counterexamples.

I had already done this in my Honors class, and the show in Honors went something like this:

Do three comparisons using fraction strips. resist models. get annoyed. everyone’s frustrated.

This was a lot better. Students are still uncertain, but are trying their fraction strips, willing to trust us and hopefully ready to summarize comparison rules tomorrow (we’re calling it the Big 4).

A few notes on this and the posts that will follow: I’m not going for how-to-compare-every-last-fraction you can make up. I want my students to understand that thirds are larger than fifths because a unit is being split into equal pieces. I realize sometimes, you do need to multiply. But a lot of the time you don’t, and a basic comprehension of a number as being closer to 1 or 0 would go a long ways.

Do you teach fractions? Do you get annoyed when your students resist what you want them to do? Have you ever folded fraction strips?

Sounds like my school…

(See below for a full explanation behind this). We’re training teachers to work in some of the toughest schools in Chicago (the nation?),  so its helpful to have a shared vocabulary. And part of that shared vocabulary comes from this guy:



We roll out strategies throughout the year, and mentor teachers model them for their residents. Full disclosure: This was HARD for me. I have excellent classroom management, but a lot of it is fully my personality, and you can’t reproduce that.

Mentor: Then get them quiet.

Resident: But how?

Mentor: Stare at them.

Resident: I do stare. Nothing happens.

Mentor: Funny, works for me.

Not helpful. But its tough to retrain yourself to be more transparent, even if it does help me grow professionally–discomfort is not fun! Some of these can be cheesy or overdone, and I definitely don’t think teachers should be robots, but being able to say “strong voice” and have both parties know what that means and looks like is really helpful.

My favorite of these strategies, and one that makes my school distinct from other schools I’ve taught at is narration.

Narration is exactly what it sounds like: narrating what’s going on. It’s always positive, and can be either behavioral or academic in focus. It’s immediate, and does wonders to help guide class in the right direction.

Here’s an example:

Pass across your papers, one per pair, and work with your partner at a voice level one. You have three minutes. Go.

[slightly softer] the first row is all ready to work, I hear Samantha discussing problem one with Jose, Evelyn is writing while Samuel tells her what to do, the left side is at a voice level one.

It’s even better when students might be confused about what to do–instead of repeating the directions over and over, students can catch on to what should be happening by the narration.

Elizabeth has her notebook out, Amy is writing down the first problem. Alan is checking his work on number one.

Sometimes my students don’t do what I want them to do because they aren’t sure what that is. So confusion looks like noncompliance. But its such a little thing, they don’t want to ask, and sometimes you get yelled at for not knowing what you should be doing, so I’ll just sit here and hopefully I’ll figure it out… Students hearing the narration above get everything they’re supposed to do. I should get out my notebook and write down the first problem, and then I should check my work.

It works like magic on volume too. Ten minutes into your Around the Room and its getting a little loud? “Eli is working silenty. Esme and Diana are at voice level one”. And like magic, the volume just drops. No one got yelled at. No one did anything wrong. Just a quick reminder about what RIGHT looks like (never wrong) and we get back on track.

Try it out–if you feel awkward doing it in class, narrate your spouse or kids or roommate. Dave is clearing his plate and putting it in the dishwasher…Think of it as I spy. Narrate all of the good you see, and see how many students try to match it!

Have you ever narrated before? Are you going to try it?

Full Backstory:

My school is part of Chicago Public Schools, but also part of a network of schools within that. (That is not code for charter. We are not a charter school, the key difference is in our governance structure–we follow all CPS requirements AND all of our network requirements.)

Our mission is twofold, both training teachers and turning around failing schools. This is a teaching blog, not politics, so my whole point here is that I teach in one of our training academies and am in fact one of the trainers. Trainers–mentor teachers–are assigned resident teachers for the year. Typically each mentor teacher is assigned two residents, but this year I have only one (this is lovely, but I feel bad for her. I am a lot to take alone.) Our residents are selected by June, spend the summer in training and remain with us Monday-Thursday (Friday they have grad classes) for the school year.

Looking for…

I mentioned a couple of times that I was a “Mentor teacher” this past year, and I got my official letter last week that I will be again this year. The definition is a little different than what you’re thinking of–basically a cooperating teacher for an alternative certification program that lasts for a full school year.

In less than a month, I will be assigned two Residents, who will be paired with me for the school year, to learn to be a teacher, run a classroom, deliver instruction and more. Every Monday through Thursday, they go where I go (Fridays they take their grad school classes).

Last year I had two residents, one of whom was awesome–I’ve shared some of his great  work on here and the other…had some struggles. She ultimately left the program (and had anyone involved had more experience, myself included, the whole thing would likely have been much smoother). My load last year was hard. Really hard actually, although it took me months to realize that I wasn’t struggling only because I was adjusting to the whole “having two people with you every second” thing but also because teaching three completely different preps is just HARD.

For me, the part where they were different was the tough part, but my content itself was no picnic. I taught one section of AP Statistics (and primarily reserved that one for myself) and three sections of Honors Advanced Algebra–tough content, fast pace. When my resident struggled, the coaches kept asking how much of it was my (difficult) content.


Does it matter? I get where they need to know if she can’t teach or if she just can’t teach _____. But that’s what I had to teach; I couldn’t very well have her try something totally different instead of what my students should be learning.

All this is to say, this year I have TWO sections of AP, and while we are never allowed to choose our residents, I’ve been asked for my feedback about what the coaches should look for when I’m matched. And I’m CLUELESS.

I need someone who can admit that they don’t know or understand something (instead of teaching Stats wrong)

…but not someone who already knows Stats (awesome, but not likely to happen)

I need someone who can…work hard? Teach three preps?

I don’t think smart is nearly as big of a deal as willing to figure it out and be able to explain it to the students, but how do you vet that? I will still teach the really tricky stuff, like hypothesis testing, myself–so they don’t need to be able to pick up on everything.

See? Lost 😦

Any ideas? What are some qualities that make someone likely to be able to handle my AP classes? What kind of background should I look for? Please help me!

Bored to Tears

The ACT is next Tuesday.

The AP is in three and a half weeks.

I teach juniors.

I think I’ve spent at least five hours at the copier this week. And I feel like all I’m doing is watching people silently do the things I copy.

This sucks. And its painfully boring. Clearly, I could never be the kind of teacher that hands out a worksheet every day. My remedial class has been taking their interim exam (60 questions) for the past two days. The other classes aren’t spending ALL of their time doing things silently (actually, less than 14 minutes) but it sure feels like it.

Part of me wants to try to make it more exciting/interesting/interactive/DO SOMETHING , but they’re about to take these tests on their own. I’m out. And they’ve got to get on it themselves. So many of my students want to wait around for me to tell them how to do it (or what to do, or ideally, just do it for them) and that won’t fly on these tests.

I think I have a good mix of instruction and exploration and practice planned, but man is the practice part getting to me. I do believe it’s whats best for my students, I just wish it was a little better for me.

How do you structure practice for high stakes test? Have you ever spent five hours at the copier in the less than 3 days? How many trees have I killed this week?!?

First Day Reflections

First and foremost, ohmigod do my feet HURT. I counted three other teachers on walk back from the water fountain after school also walking around barefoot. So professional of us.

Today was crazy. The bells were all wrong, and even the right-ish ones didn’t match the clocks, so I was kind of guessing when my classes would each end (Hint: never quite when I thought).

But it was good. The residents introduced themselves in each class and tried going over part of the Do Now. It really took me back–it’s not hard for me now, or intimidating, but this was their first time in front of a class. It’s a little terrifying. This year I teach three Honors classes and one AP. Oh, and the lowest level course for juniors, which is almost half students with IEPs and no inclusion teacher. Everyone who has seen my seating chart (which was impossible to put together) has been shocked. It’s a really really tough group.

Luckily, I taught a lot of them two years ago and so they already like me/respect me. Which helps, although apparently not enough to prevent my mentee from walking out seven minutes into class. Figures.

In other news, my computer hates me, so I couldn’t project anything I planned on doing. A little stressful but I made it. And now I’m (super lame) off to bed. It’s rough, working full time.