Mastery of Objectives

So during a discussion on twitter today, @misscalcul8 and I were discussing the number of objectives taught per week. On average, in Algebra 2, I would say I cover 3-4 objectives. Her question, and a very valid one was this:

So how do you teach to mastery in one day of experience with a LT? I don't meant that critically.

Now that response is way over 140 characters, so I told her I would blog my answer :)

In short, the answer is "You don't." Mastery is not a one-day process - it is a long term process that differs for every child. You have to continue spiraling the curriculum so that over time, mastery is obtaining. Some of you may have seen the "forgetting curve"...

Here's how the forgetting curve works for me...
On the first day of an objective, I teach, they take notes, do problems, etc like normal. Then the next day, I give a "Checkpoint" - this is an ungraded formative assessment so I can provide written feedback and correct errors. On day 3, they get the checkpoint back, look over it, read my notes. (Note: during days 2 and 3, I am teaching new, but related objectives that I try to continue tying into each other). A few days later, there is some kind of cumulative activity to see how objectives work together, review multiple objectives, etc. There are also Jing videos that I have created and put on the class website that they are supposed to refer to if they need additional instruction. About once a week, there is a SBG quiz that covers that week's objectives. Again, lots of written feedback if needed. Over the next few weeks they are working on those objectives using self-check materials, the Jing videos, tutoring, etc so they can reassess. (In order to reassess, they must provide evidence that they have worked on mastering the objective)

In a nutshell -
From start to finish, the student has seen and worked with the objective many many many times, so that they are constantly bringing it to the forefront of their mind, spiraling the material so that they will achieve mastery.

Definitely longer than 140 characters :)

Spring Break :)

I have been meaning to post for a few days, but I'm struggling with forming coherent thoughts right now... This post will be somewhat of a rambling one, so bear with me...

At school, some of the teachers have decided to get together for lunch once a week in order to discuss vertical alignment. This has caused me to pull out old Pre-AP materials from workshops, do some research online, and even do a few calculus problems. What I have learned is that at the time I took calculus in high school and college, I really was clueless about what was going on. It makes so much more sense now that I've taught geometry and algebra 2 and have the conceptual maturity to get it!

As an extension of that, I've really been feeling a need to do a better job in Algebra 2, specifically with making connections. So I am going to steal borrow from the wisdom of my amazing blogger and twitter friends to rework the exponential/logarithm chapter with more active learning techniques. That was part of my goal today and I have 1 lesson done out of 8.. woot! :)

While I definitely enjoy having a break and being able to sleep in, I really am not a fan of this time of the school year. For some reason, each year in March and April, I look back over the year and thing, gosh, I did a cruddy job :( Then I start my to-do list of things to do better next year and the cycle repeats itself....

I need a nap...

Gallery Walk - Stat Style

Remember that blizzard that hit the midwest two weeks ago today? Yeah, well, yesterday (Feb 14th) was the first day I had seen my students since Jan 31st. In AP, time is a very precious thing because we have a lot to cover and every day is really special to us. Thankfully I was a bit ahead before the storm AND the AP exam was moved to the 2nd week of testing this year, so I'm not frantic - yet! I was in the middle of teaching confidence intervals for proportions when the storm hit and I really feared that the cobwebs would take awhile to clear in order to get us back on track. Yesterday I did the half sheet review and it went very smoothly. The kiddos settled back into the routine like no time had passed at all! Since for each halfsheet, they have to come up for me to check it, I was able to clarify thinking and remind them of details quickly and more effectively than I could have through lecture. However, I knew I needed more practice on confidence intervals before the chapter quiz, and then a brainstorm hit - GALLERY WALK! :)

The idea behind a Gallery Walk is pretty simple and I had used it before in workshops, but never with my students. I didn't know how well it would work at all, but I really liked it! Last night, I took a worksheet with 7 confidence interval problems and printed it. Today, I cut those problems apart and posted the problem and a piece of chart paper around my room. When the students got to class, they worked on their warmup in their groups while I went around and gave each group a different colored marker. Then we got started. Each group went to a piece of chart paper and read the prompt. Then as a group, they decided what the parameter of interest was and wrote that down. When all of the groups were done, we rotated clockwise to the next chart paper station. The group then read the new prompt and the previous group's work. With a new group member as the writer, they corrected the previous group's work and then continued the problem by checking the conditions needed for a confidence interval. Again, when all groups were done, we rotated clockwise again. Repeat with a new group member as the writer, read the prompt, check the two previous groups' work, then continue the problem with the name of the procedure and the calculations of the interval. Again, when done, rotate to new station, marker goes to a new writer, read the prompt, correct the previous groups' work, and write a conclusion for the problem. Finally, the writing is all done. They rotate once more to read and check the previous work. Now comes the self-checking part. Each group rotates back through the posters they had written on to see what errors had been caught by someone else. Here is a completed poster:

So how did it go? I think today's activity was a success. For the most part, the kids did really well working together and moving about. When I read over their work, rarely was there an error, so I was glad to see that. I have pretty much taught this chapter with no direct instruction, so I am eager to see how they do on Thursday's quiz. Overall, I would deem this a success and will try it again when we do hypothesis testing... which reminds me, I need more chart paper :)

Til next time.... :)

Snowmaggedon

Yeah, so tomorrow is the 9th straight snow day we've had. The last time I saw my students was January 31st. Crazy, huh?

So during my second Winter Break, I wasn't nearly as productive as I should have been. Seems like each day was in limbo, waiting on the phone call that decided my fate for another day. However, since I've not seen my students in 2 weeks, that does create some issues when deciding what the heck to do with them after an unexpected and record-breaking blizzard and it's aftermath.

In AP Statistics, I had just introduced confidence intervals for proportions a few days prior to us being out. Based on an idea that I got a few years ago from an AP workshop, I created a lab where my students got the "big picture idea" of a confidence interval based on tossing around inexpensive inflatable globes with the task of predicting the true proportion of water on the Earth's surface. I love lab activities that require the kids to read, question, and discuss the big ideas without any direct instruction from me. At the end of the day, they had a pretty decent idea of the purpose of a confidence interval and the basic idea of how it is related to the Normal model. The next day (Friday) I did some direct instruction over the Margin of Error (MoE) and the more nitty-gritty details of the process required for a confidence interval. However during the weekend, the forecast started getting gloomy and I knew direct instruction would not work for Monday. Instead, I created another lab where the students were rolling Pass the Pigs pig dice to create confidence intervals for Razorback, Trotter, Sider, etc. This time, the lab was more detail oriented than the globe lab, walking them through a complete write-up of a Confidence Interval for Proportions. At the end of the hour, we quickly reviewed and that was the last time I saw them.

So now, here I am, thinking of the 2 weeks that I lost and trying to figure out how to get them back on track. Last weekend, I created a "half-sheet" activity to review what we had already covered about Confidence Intervals as well as introduce the idea of finding a sample size for a given MoE. I have done the "half-sheets" before and my students *LOVE* them. When they come to class, they sit with their collaborative groups and each group gets a copy of Card #1. As a group, they work through it, discuss it, make sure everyone is on board, then they bring it up to me to check. If it's correct, I OK it, then hand them Card #2. If it's not correct, I point out errors in thinking, etc and they go back to the group to find their errors. This continues until the end of class. Pretty much, any worksheet can be done as "half-sheets", but for some reason, they ASK to do half-sheets! Anyway, here's the confidence interval for proportions half-sheets in case you want them :)

For Algebra 2, Partner Teacher and I decided to review and quiz them on Monday/Tuesday over function operations, compositions, and inverses before moving on to the Radicals unit. I had found this neat "Ghosts in the Graveyard" activity a while back but hadn't had a chance to use it yet. Well, of course Monday is Valentine's Day AND we're going to review, so why not do Math Conversation Hearts? :) I created 8 heart-shaped cards with review problems that I will copy onto red and pink cardstock and laminate. Instead of Graveyards, I'm leaning toward possibly letting them choose some of the big Conversation Heart candies (or maybe just cutouts?) when they get their problem set correct, then at the end of the hour, determine which color is worth how many points. The prize will (of course) be yummy Valentine's candies!

Thankfully, it looks like we will be going back on Monday. Next week's highs are near 70, which will be sandal weather compared to this morning's -12!! To help make up the days that we missed, it definitely looks like I will be working on "flipping" my classes earlier than I originally expected! I'm ready to be back into my routine, although I'm pretty sure I have forgotten how to set my alarm.... :)

I *heart* my iPhone

About a year and a half ago, our phone contracts were up for renewal and hubby had been wanting an iPhone. A lot of my students had them, but I was not impressed, I couldn't figure out why anyone would want to spend that much money on a phone, plus an outrageous monthly fee for the data plan. So hubs ended up getting one while I got a "texting" phone that I thought totally fit my needs. About 6 months later, I finally saw the need for one as my students were studying for final exams and asked to take a picture of the review answer key so they would have it at home. *Shrug*, sure why not! One student offered to post the pictures on his facebook page and the kids were happily reviewing, but it got me to thinking about the uses of an iPhone in the classroom. A few days later, after stalking Craigslist for an affordable iPhone, I found a good deal and bought myself one. Now, less than a year later, I can't imagine what I would do without it!

For example, in Algebra 2, I use it as a scanner, to take pictures of files that I want to post on the class website (answer keys, etc), or when I want to point out specific instructions on a paper. When we were solving polynomial functions, I did a matching jigsaw like puzzle, but I knew if I just verbally told them that most of the expressions were repeated as equations, they would be clueless, so I snapped a picture, hooked up phone to my computer and projected the following onto the Promethean to show the kids what I was referring to.



I've also used it as a scanner in AP Stat, but I also like it for snapping pictures of students doing class activities or to embed into a Jing video later on as a remediation tool. I took pictures as we explored what happens when we flip a penny 10 times, recording the proportion of heads versus flipping the penny 20 times. Now these pictures will be put into a screencast for review of sampling distributions of proportions. (Note: I'm also fond of Post-It pad paper and Dollar Tree smiley face stickers when I need to make graphs in Stat). I didn't take a picture of all of the writing I did afterwards - we talked about the difference between p and p-hat, and talked about the overall Normal model pattern that would emerge if we were to continue flipping the penny and recording p-hats



(Sorry for the sideways graph....)

In addition to using my iPhone for about every avenue of my life, I sent my AVID kids on a snow day scavenger hunt to find cool education apps that they could use to help them study and/or get organized. Since I haven't seen them since I gave them the assignment, I'll have to update you next week on what they found :)

I know there has to be more awesome ways to harness the power of my little mobile computer, how do you use it in the classroom?

Snow Week....

So, in case you didn't hear, the nation got pounded by a massive storm system this week. In my neck of the woods, where a 3-4" snow is considered pretty big and closes us down for a couple of days, we got a whooping 21 inches! Needless to say, that set a few records, then we got another 3.5 inches today, with more forecast for Sunday *sigh*. The system came in overnight on Monday and hours before any snowflake even hit the ground, the schools were cancelling Tuesday's classes. Ultimately, we ended up cancelling the entire week due to the horrible road conditions. Tomorrow is the first day it is supposed to get above freezing, so I'm hoping for some melt as I go out to clear my driveway.

Anyway, so how did I use my snow days you ask? The first day or two was a total waste of course, spent the day gawking at the snow drifts and watching the news coverage while lounging under a warm blanket. But by the end of day 2, I started getting antsy, so I combed through blog after blog after blog stealing all of the good Algebra 2 ideas that I could find and organizing them by chapter of my textbook. I read through all of the Math Teachers at Play blog carnivals and brainstorming the various review ideas/structures and how I could increase student engagement in Algebra 2. There are some really awesome ideas out there, but it takes hours to comb through all of those sites and find the good ones.

A few weeks ago, I stumbled upon a new math teacher blog (because she was awesome enough to post a comment here, or I would have never found her!) and totally stole this neat Math Stations activity. (Click HERE to read her instructions). We happened to have a short day a few days after I found her blog, in which I would only see one of my Algebra 2 classes, so I whipped up a quick review of the material we had been learning. I printed it double sided, but I did do the answers by hand because I didn't want to type that much :) I gave the kids 4 minutes per card and overall I think it worked REALLY well. Here is the file:



Now to watch the news again... they are forecasting more snow in my future :(

Function Dice

Today was a snow day (yay!), but we were supposed to teach function operations in Algebra 2. I had given a quiz yesterday and while they were quizzing, I had a brainstorm - function dice!!!

So today during my snow day, I found some foam dice in my closet (thanks @Fouss!) and using tiny post-its from Walgreen's Back to School sale, I made an f(x) and a g(x) dice set :)

By rolling the two dice, we have a large set of practice problems and example problems for tomorrow's lesson :)

Now I need to figure out an tetrahedral die for the four functions :)

(Although I wouldn't be opposed to another snow day either!)