Something Based Grading

We changed up our grading structure this year. Our admin wants to move towards standards based grading, so we’re sort of supposed to be transitioning towards it a little bit this year. Sorry for all the qualifiers, but that’s how it actually is.

I’ve read enough blogs on SBG to feel like I have a vague grasp of what it should look like. Choose standards, assess & reassess on those standards, then final grades are based on the scores on those standards. Its definitely a huge change from how I’ve taught and assessed before, but I would be up for the challenge.

Except we have to use Gradebook, and we have to enter grades at least weekly and Gradebook is very much not designed for this sort of thing. Gradebook will give you a max of 9 categories, and those categories are the only way to have any weights to things.

So we have this crazy system where we have nine topics/standards and then all the assignments under that standard are coded under that standard but weighted differently according to their type (so that the whole grade doesn’t come from homework, for example). And if you feel a little fuzzy about what that looks like, my math teacher friend, consider how my freshman feel. Or their parents. Or, actually, me. I’m pretty sure that despite the weighting homework is getting way too much value. Progress reports are nearly unreadeable because the multipliers muck it up.

And about that homework…I do think some kind of practice is really helpful in math class and although I don’t care about how they do it (and have only ever graded homework for completion), they probably care that I give them credit for that. So how do I balance that with not really wanting that credit to count?

I can make some minor changes this semester, but I do get a clean slate 2nd semester. Any ideas to help me out? What are your favorite SBG [lite] resources?

Making an Effort

Oh, hi.

I have so many things I want to say, but its been so long that I’ve said anything at all that I feel like I have to come back with something brilliant. Or at least good. And then I get stuck picking what to talk about and so I say…nothing.

Which is silly. So, hi. I’m teaching Algebra 1 to students a few grade levels below this year, which means I haven’t actually taught any algebra at all to date. I don’t have any residents this year. I got a real classroom. Oh, and I did indeed get married this summer and we bought a house and moved. And my sister moved cross country and I helped. So we’re basically all caught up.

CHP_MikeMaryFavorites-127

Caili Helsper Photography

My students this year already think they’re bad at math, and one girl in particular tries so hard to give up. She won’t try anything (and by anything, I even mean writing down a practice problem in her notebook–not doing it, just writing it.) Today I told my students they  needed the first section of their grid (just a bunch of rounding problems) filled out for an exit slip. She did nothing. It’s her M.O. To wait. And I guess it’s always worked. And it isn’t with me and it’s making her so mad. So she couldn’t leave. And we talked. And she cried. She’s a cheerleader who really doesn’t want to miss practice, but she went to the first half of practice and she’s here now. I want her to stay, and so I stay too, even though I’ve finally started to get caught up and I finished grading everything I have right now during lunch (don’t worry, I give an Algebra test and collect Stats homework tomorrow).

And, as if this post isn’t lame enough, here’s what I hope to be writing about soon:

  • Our foray into some mess of pseudo-standards-based-grading (Spoiler: It isn’t pretty.)
  • Maybe more fractions
  • Favorite lessons and practice structures

I missed you internet. It’s good to be back.

Fraction Success

Today is the last day of finals. I gave my regular-level Algebra class the final section of their final exam today, a “Choose 3 of 7” component.

Question 2 asked students to “Order the numbers 3/7, 0.75, 1/7 and 3/5 in ascending order, and explain how you arrived at your answer.”

I forgot to remind them that they can’t use decimals. When we spent so much time teaching fractions earlier in the year, we emphasized that our students needed to be able to work with fractions as fractions. That was the only way to get credit and we worked really hard on it. We felt like it worked, but that was ages ago.

The first question I graded was, “I switched them all to decimals to make it easier, then I ordered them.” Oh, NO. I forgot to say something, they’re all going to do it wrong, I can’t give them credit for that.

And then I kept reading.

This was a CHOICE exam. No one HAD to do fractions. And a third of them did (Ok, to be fair, the kid with a 90.03 chose all 7–better safe than sorry I guess.)

But I read answers like these, with no reminders about decimals:

I arrived at my answer by looking at the fractions and seeing the amount of shares they needed to accomplish a whole and I took the one fraction who the most shares…

I turned .75 into 75 and put it over 100 it gave 3/4, which is bigger than the other fractions. 1/7 & 3/7 have the same size but different shares and 3/5 is bigger than 1/7 and 3/7

For a topic dating back to October, I am so pleased with these answers. I think we managed to change at least some of our students attitudes towards fractions, and lead them to actual understanding of what they’re doing.

I hope to be able to do even more with this next year. Anyone interested in collaborating? My sister is teaching fractions to adults again this summer….

Telephone

This has become one of our favorite quick activities in my Algebra 1 classes this year–and credit for this one goes out to my resident once again.

Remember at birthday parties, where you would whisper something to the person next to you, and then they would whisper it, and so on? And it changed from “Lesley has a cute shirt with rainbows” into something totally inappropriate.

Kinda like that.

The materials are super simple–get a bunch of paper (maybe from your enormous stack of leftover mental math?) and cut it into fourths. Then get problems, cut on to slips of paper.

You could cycle one problem through the whole group (I’ve done similar before with one whiteboard and called it a drill), but we prefer to have all the students working, so one problem per student will do.

  1. 1. Students in groups of 4
  2. Each student gets 4 blank slips of paper and labels them ABCD
  3. Each group gets four slips of paper, numbered 1-4.
  4. Each student picks up a problem, does it [distributes 2(3x-5)] and then passes it to the next person. They hold on to the original problem.
  5.  Pass once to the right, factor out the common factor (or a different step), put the piece you were given on the bottom and pass it on with a new top.
  6. Repeat a total of four times, until you get your original problem back.
  7. Have the group check how well they did keeping their problem the same.

We’ll be doing it with multiplying binomials/factoring quadratics, and we also tried it with translating between words and algebra. It fits a lot of places and can be a quick single round activity or something a little longer–lots of fun and a new favorite. I highly recommend you try it out!

What’s your favorite quick practice structure?

Final Answers

Last week, my AP Statistics class took their final exam: 20 multiple choice questions and 4 free response, basically a half-AP.

I wanted to review the answers with them, especially noting some common mistakes, and also give them a chance to reflect on how it went. I’m really excited with how it went down.

Students went into their (new!) groups of 4 (new seating chart today) with a copy of each question, distributed one per person. My second class had half groups of 3 and half 4, which didn’t matter here (the ghost just got the fourth question and they passed through the ghost).

They got 2 minutes to silently answer as much as they could on the question in front of them, then passed and had two more minutes, and so on. Then they had 10 minutes as a group to come up with their best answers to all four questions. There were a ton of good discussions, both in writing before they were allowed to talk (“I got that too!” “I think its center not spread because…”) and verbally.

Once that wrapped up, I reviewed solutions and they scored their group solution. It also gave me a chance to remind them how rigorous the AP exam is–for students who are used to getting perfect scores fairly easily, the difficulty of the AP exam comes as a shock, and they have a hard time wrapping their heads around 75% correct on multiple choice being GOOD.

It was one of those periods in which I kind of felt like I wasn’t doing much, but I think it was so valuable for my students. This would even work well for a word problem (each person does one step) or explaining several different kinds of problems for a review. By the time they were allowed to talk, several students were really invested in justifying their perspective.

Have you ever tried a write-around strategy like this? Any tips for how it could go even better next time?

The Twelve Days of Statistics

A little late about this, but bookmark this one for next year!

Last year, I posted the Twelve Days of Algebra, which I got from ICTM several years ago. But my Stats students were a little hurt when I had to sing them the 12 Days of Algebra in Stats. So we fixed that right up.

My awesome resident took lyrics that some former students had worked on and refined them and now we have:

Behold, happy 10th day of Stats class!

[Lyrics by Miranda De Young, 2013]

Probability for Babies

Ok, not babies, but not AP Stats students, which is what I’m usually rambling about.

I teach two sections of Algebra 1, and I like to use that last-day-before-Christmas for some fun with probability.

Once students end up in my AP Stats class, there’s a lot of fixing to do. They’re pretty sure they know probability. Its simple stuff really. Six blue marbles? 8 red? Done. Except that the “probability” they’ve had beaten into then (for how many years!) isn’t all that useful. Probability is not, be definition, neat and tidy. Its LONG-RUN. It’s THEORETICAL. It doesn’t tell you what “will” or “won’t” happen, it tells you what might happen.

I still remember talking to the nurse in college, and saying I wanted to stop taking the pill because it made me gain weight. I’d started it in March of my freshman year to help with my cramps and a few months later the improvement was minimal but I’d promptly gained 10 pounds. The nurse’s reply?

“This is a time in a lot of young women’s life when they gain weight.”

“What, March? I don’t think so.”

“Gaining weight on the pill is a myth. Only 2% of women actually do.”

Subtext: 2%= Impossible. I couldn’t actually gain weight because of the pill, because only 2% do, and 2% is close to 0, so no one does for real. She was totally serious. It did not occur to her that I could be in that 2% (I was. I ignored her, stopped taking, and the weight promptly disappeared.)

I want my students to explore situations like that, even if we can’t “answer” them.

Sure, I know some more sophisticated ways to calculate probability. But that doesn’t make simulating some halfway-there situations doesn’t have value too.

Here are some of the ways I’ve played with my kids, and awesome ones I’ve seen from others around the MTBoS.

  • Jackpot
  • Fire!
  • Roulette (get an iPad app, project it, and let them make bets, then simulate on the calculator)
  • Bumpy Flight: an excellent set up from Mathalicious. I’d have my students make a prediction, then simulate it using slips of paper, technology or whatever else they can come up with. Pooling our results is informative enough, and we can even make a recommendation at the end.
  • Greed: Everyone stand up. 5 loses, everything else gets points. Roll (let’s say…a 3) and tell they can keep their 3 points and sit down or they can risk it and keep standing–but as soon as you roll a 5 you lose it all. Play a couple rounds. See who won the most overall and what their strategy is.

Last year, we did Greed, Roulette and Jackpot, but I definitely want to throw Fire! in my rotation too. I love that these are fun, get kids thinking, and starting getting across the idea that the same probability doesn’t mean the same result.

Jackpot

I’ve talked some about Probability and I’m sharing a couple of simple ways to explore probability with your students. While you not be able to get exact answers, these are great ways to test out how probability really works, and whether what is “supposed” to happen actually does.

So you know Jackpot. It’s a Holiday classic on the Country station here, and super easy to simulate.

Listeners call in and the nth caller gets to guess how much is in the Jackpot. If you guess the exact amount, you win. Otherwise they tell you if you’re too high or low. There’s several times a day you can call in, and the idea is that listeners are keeping track at home.

Here’s how I run it in my class:

  • Everyone write down a number between 0 and 1000.
  • Choose someone to make a guess.
  • Say, “Sorry ____, thats too low/high” in your best cheesy gameshowhostvoice.
  • Get your Vanna White up to the board. All you actually need to know is how many guesses have been made, but its more fun to have them write the amount too (someone may even catch that it would be helpful to record if its too high or low, but I never point that one out).
  • Continue calling students for guesses.
  • Once you finally get it, have Vanna record the # guesses and winning total. Even the winner if you want.
  • Tell them all to write down a new guess, then repeat the above.
  • Hopefully by the next round they realize its totally pointless to write down an initial guess; they should be revising as they go.
  • Then split them into groups of 3-4, and show them how to use randint on their calculators.

There are a couple places you could go with this:

  • Have them go from 1000 to 10000 and see how many more guesses it will take
  • Make a class dotplot or other representation of how many guesses it took
  • Tell them you plan on doing this in an upcoming assembly but they can pay you off to get to guess at a certain time. Think about it on your own first, then talk it over with your partner. Discuss as a class why they picked that number of guesses. (Some kids will want to guess 5th to make sure they ALWAYS get a guess, others will want to go 10th because if it does get to them they feel they’re likely to get it.)
  • See if any groups can figure out how to make an optimal number of guesses.

This is pretty informal, but my kids love it and it gets them thinking about how the same situation doesn’t mean every detail is identical.

What are some fun ways you have to get kids thinking about probability?

Sharing is Caring: MTBoS

I’ve participated in a couple of the Missions put together by the fine folks running this fall’s Explore the MathTwitterBlogosphere.

And I’m cheating a bit, but thats ok, because its well within the spirit.

My school is four years old (or at least, will be once our seniors graduate in June), which means the majority of our staff is pretty young and inexperienced. At nine years, I have far more experience than many of my colleagues. I love sharing (its why I have a blog), and while I think it would be awesome if my colleagues all subscribed to a bunch of blogs…probably not happening.

So I started a distribution list. It began as emailing my residents cool things I saw that I thought we could use in the classes we taught together. Initially I just thought other residents might be interested, but it felt rude to only ask them, so I opened it up to the department–and a whole bunch of people were interested. (Again, almost all of the teachers in my department have less than five years experience and most are in their first or second year).

Google Readers passing this summer messed up my list for awhile, but I’m back on track with Feedly. If you’re interested in doing something similar, here’s my method:

  • Set up a googlegroup (Ok, get your more-technically-proficient-colleague to set up a googlegroup for you because you’re lame)
  • Email your department and see who wants to sign up. I explained that I usually send out a couple things a week, the text is included in the email so its very easy to read, and you don’t have to read it (I’ll never know). I aim to make it as low stress as possible because I think that encourages people to sign up. I’m also pretty open that I look for blogs that fit me, so I don’t send out a ton of geometry (I don’t teach it, so if thats all a teacher posts on I wouldn’t subscribe)
  • Subscribe to a whole bunch of blogs in Feedly.
  • Read them on your computer or your iPad. If you read it on your computer and want to share it, save it as unread because you don’t bother to set up a mail client.
  • Read something cool. Think others might be interested. Hit email on your Feedly app on your iPad and share it. Never write more than two sentences intro, and sometimes write nothing.
  • Share.

I have gotten SO MUCH positive feedback about this. I hear colleagues refer to things I sent out, people have tried these things–its awesome. And it takes very little effort on my part, a win all around.

Do you have a distribution list? How do you share?

If you’re interested in joining my list, let me know and I would be happy to sign you up. 

Back to Basics

There are so.many.things out there on math blogs. I share my own, I forward others to my department, I try them in my class.

And I love it.

After this post, a comment sent me to Math With Bad Drawing’s Probability stories, and Ben Orlin graciously gave me permission to repost them on my (private) class blog. One of my students even asked when their next bedtime story was!

I love coming up with really interesting ways to teach things, and engage my students, and do inquiry.

But sometimes I need to take a step back and remind myself that isn’t always the answer. (I think.) As I mentioned, my AP classes have just started Probability. I’m not that great at teaching it. It’s my students weakest area, so its a safe bet its mine too (and my fault). Most of my class had to retake that test last year.

So I spent a lot of time and agony on this years schedule. I added a couple of days. I tried to come up with great things to do.

But you know what I think we need right now? Some practice. We need to do some problems. We need the time and the space and the permission to draw 20 Venn diagrams and fill them in correctly, til it isn’t at all scary anymore. We need to find conditional probability of six different situations, one at a time. And we need to make sure we have our vocab and probability rules down.

Ironically, this is so, so easy to plan. I wrote 5 problems. I’m done teaching for two days. It feels lazy, but that doesn’t mean it is–and it doesn’t mean that’s bad for my students.

I wish I was better at really teaching this so they got it…but until I am, giving them to time and space to really practice (and review each problem, one by one) is the most beneficial thing I can think of.

Do you feel guilty when you do “boring” things in class? Any more ideas on how to help my kids with probability?