Wednesday, December 14, 2011

Transformations Matching Cards

In my Advanced Algebra 2 class, we discussed the rules for transforming equations (shifts, compressing/stretching and reflections). Tomorrow is our last day before Winter Break (staff still has to go Friday), so rather than give practice problems that won't get done, I put together matching cards. I wrote 6 equations that are transformed from a base function, graphed them on the TI-84 and screen captured them, and wrote the description of how the new graph was transformed from the original. I did 5 sets. Then I put codes in the corner of each card (F#, G#, D#).

Students will work in pairs to match up the triples. I am going to provide them with a worksheet to record their information. Students will need to work through all 5 sets during the class period. I did make some sets easier than others. Cards are 3 1/2" wide by 3" tall and were originally done in Word. Enjoy!

Edit - I updated the file on December 15th - found a typo when doing it in class.

My students got through 2 of the 5 sets in class today (over about 35 minutes or so). We will do the 3 sets they didn't get to the day they return from break. Actually, this will work out nicely, for it will get them back into the swing of things with what we left off with.

Tuesday, December 13, 2011

Students Hate Word Problems

Today, I quizzed my Advanced Algebra 2 students and part of the quiz included Linear Programming problems. They did poorly. Part of it may be that we did it before Thanksgiving, and part of it may be they just don't care about word problems. As they came into class today, several of them commented something along the lines of "I hate word problems. Why do we have to do word problems?" My answer was that word problems are the application of the mathematics, and it shows you where in the "real-world" that the mathematics is used. They weren't thrilled.

Over the last few years, I have taught word problems less and less. Mainly, this has been because we have so much material to cover in Algebra 2 and I have to make sure they are prepared for state tests as well. But I also realize I am doing them a disservice. Word problems are the application. How are they going to be able to apply the mathematics?

So how do you get students to not hate word problems? I know part of the answer is along the lines of what Dan Meyer is doing, but, let's face it, it's kind of hard to do that with Algebra 2 topics. So, what's the answer? How do you get students (particularly ones who have not done much with word problems for many reasons), to not hate word problems?

Thursday, December 08, 2011

Drive Introduction and Chapter 1

Drive by @DanielPink - chat on Introduction and Chapter 1 Thu 12/8

lmhenry9                   I guess let's start with the introduction. What caught your attention? #drivebook

druinok                      @lmhenry9 the idea of the “puzzle” mindset caught me…and when rewarded, they made more errors. #drivebook

cheesemonkeysf   @lmhenry9 Well, naturally, the *1st* thing that caught my eye was that he started by talking about motivation with monkeys. :) #drivebook

lmhenry9                   @druinok The last line about the Soma experiment: "Nobody was expecting rewards would have a negative effect." caught my attn. #drivebook

crstn85                       @lmhenry9 I'm here now!  Just read it today and I'm trying to think what this means for the classroom #drivebook

cheesemonkeysf   But the 2nd thing that I noticed was the multiplier effect of flow/intrinsic motivation. As a t & as a learner, I find flow key. #drivebook

druinok                      @crstn85 @lmhenry9 I kept thinking about rich problems while reading it... the puzzle mindset, the intrinsic curiosity #drivebook

crstn85                       @lmhenry9   Yea, that was surprising to me at first, but it makes sense to stop working if the reward is removed #drivebook

lmhenry9                   It's funny - I'm really struggling w/the motivation piece right now. My Alg2 students aren't giving effort 2 anything not graded. #drivebook

cheesemonkeysf   As a math learner, I find that no amt of #wcydwt or #anyqs holds my attn until I'm in flow w/the basic mathematics. #drivebook #justme?

crstn85                       @lmhenry9  I spent my afternoon coming up with a reward system for my autistic students. Might skip to section on when it works. #drivebook

johnberray               @druinok A sense of guilt came over me for some of the trivial rewards I've given out in the past. #drivebook

lmhenry9                   But my Math 1 students (lower ability 9th) actually do all the test probs - graded or not. #drivebook

cheesemonkeysf   @lmhenry9 I can understand yr frustration. I find that extrinsic motiv. doesn't get me ANY LONG-TERM YARDAGE w/middle-schoolers  #drivebook

crstn85                       @cheesemonkeysf So what does have long term success? #drivebook

druinok                      @crstn85 that section (on when it works) is in 2A... it's not often :( #drivebook

lmhenry9                   @johnberray I had that thought too. Glad that I am doing SBG now where I'm only grading each concept - no HW,no extra credit,etc. #drivebook

cheesemonkeysf   I find rewards simply DON'T work. What DOES seem to work is when I cultivate curiosity/engagement. This seems to be Pink's msg #drivebook

druinok                      @johnberray me too... made me really sit back and think about papers being awarded points and what the kids get from that #drivebook

cheesemonkeysf   @johnberray @druinok Don't feel guilty--it's just what YOU find works. As Henri Picciotto says, n.t. works for e.o. all the time. #drivebook

johnberray               @cheesemonkeysf @lmhenry9 There's always a duality of teaching content & why learning is important in general. #drivebook

druinok                      @lmhenry9 @johnberray I agree - it definitely ties in with #sbar... #drivebook

cheesemonkeysf   I find a couple things yield long-term success. 1st is cultivating a positive disposition twd math. #drivebook

cheesemonkeysf   Th means a discouraged st must stand a chance of experiencing SOME kind of success -- even if only by participating/being engaged #drivebook

cheesemonkeysf   The #1 thing I see among my discouraged s's is how strong & entrenched their defense mechanisms are, psychologically. #drivebook

crstn85                       @cheesemonkeysf Good point, the examples in the book were of easy access, non-threatening puzzles. Need to start simple #drivebook

cheesemonkeysf   Many s's come in hunched over in a defensive crouch that doesn't let them open up to the possibility of doing any math/thinking #drivebook

druinok                      I found it fascinating that after getting "paid", the 3rd day w/ no pay, the people weren't curious at all #drivebook

crstn85                       @druinok I think that's the most important message.  It's not just not motivating, it's de-motivating. #drivebook

lmhenry9                   For many of my lower-level stdts, they come 2 class thinking they can't do math b/c they've not done well due to HW being graded. #drivebook

cheesemonkeysf   That's why I believe low-stakes  activities w/a slightly familiar UI that are immediately engaging are important #drivebook

johnberray               @druinok I've heard it said that the surest way to kill a joy is to get paid for that experience. #drivebook

druinok                      @johnberray they actually talk about that later... paying people for donating blood #drivebook

crstn85                       @lmhenry9 I'm not sure I see the correlation here. Just because HW is graded they don't do well? #drivebook

cheesemonkeysf   If s's come in shut down & defended against engagement, I have to start w/building trust & a kind of a "therapeutic alliance" #drivebook

druinok                      @crstn85 I think it's a good point too w #sbar... after a kid comes from a class where they are "paid", hard to transition #drivebook

cheesemonkeysf   What I got from the introduction was that without engagement/intrinsic motivation, there can BE no motivation. #drivebook

lmhenry9                   @crstn85 Teachers in the past put points on just "doing" hw (I was guilty of that). Students choose not to do HW and barely pass. #drivebook

johnberray               @druinok I see. I haven't read the whole book yet. I'm finding it a little difficult to only draw on the 1st 2 sections. #drivebook

cheesemonkeysf   @lmhenry9 They also come 2 class believing they can't do math b/c they have been
 publicly shamed before their peers & that sucks. #drivebook

druinok                      @cheesemonkeysf there is still bio and extrinsic motivation... I got from the intro that they had no idea that intrinsic existed #drivebook

cheesemonkeysf   @johnberray @druinok I think this is so true. Some of my s's LOVE the knitted dodecahedron on my desk & are amazed that I made it #drivebook

druinok                      @johnberray I think the intro really shows a lot of insight into classrooms though #drivebook

johnberray               @lmhenry9 @crstn85 And many SBG models have to be hybrid models in which homework is counted. I count "Homefun". Guilty. #drivebook

cheesemonkeysf   @johnberray @druinok *THEN* then offer to pay me, like, $50 if I'll make one for them. I tell them, NO WAY! #drivebook

crstn85                       @druinok Definitely. I'm not doing #sbar but it's still hard to get kids engaged when they're used to being given the rules #drivebook

cheesemonkeysf   BTW, all knitting has screeched to a halt until Winter Break #explainstheknittingsilence #drivebook #dontdespair

druinok                      @cheesemonkeysf @johnberray similar to reading for pleasure & reading for a grade.  I love to read, but was horrible in LangArts #drivebook

cheesemonkeysf   @druinok It struck me as a typical business bestseller at 1st in that the biz BS/hype is laid on thick at the beginning. #drivebook

lmhenry9                   I found the discussion about open-source fascinating in Chapter 1. #drivebook

crstn85                       @johnberray @lmhenry9 I count it too. But even pure SBG is about learning until you get the grade for some #drivebook

cheesemonkeysf   @druinok I don't think of bio motiv as true "motivation" in that it is biologically programmed in. I found that less convincing #drivebook

johnberray               @crstn85 @druinok In some ways I wish I could shadow my s's through all 4 years of math. Like the Freedom Writers teacher did. #drivebook

crstn85                       @lmhenry9 The analogy to wikipedia was eye-opening. Never thought of that! #drivebook

druinok                      @cheesemonkeysf I've not read many biz books - I was thinking about it more from an #sbar /grading perspective #drivebook

lmhenry9                   @johnberray That would be an interesting concept. #drivebook

crstn85                       @johnberray @druinok We would need to start in Kindergarten for it to be really effective! #drivebook

druinok                      @johnberray as in "looping"? #drivebook

cheesemonkeysf   @lmhenry9 The open-source discussion fascinated me too! Evolution of Wikipedia articles is like this. Ppl take it v. seriously! #drivebook

cheesemonkeysf   @druinok @johnberray And that's the EXACT problem I face w/my reluctant readers/writers in ELA classes-same as in math. I use SBG #drivebook

johnberray               @crstn85 @druinok Kinde? Yeah. Too many students in my day to really know how they're learning. But SBG is a good step. #drivebook

cheesemonkeysf   @druinok Sorry- spent too long in high-tech business world before coming back to teaching. #drivebook

johnberray               @druinok Yes. Although certain students would be a labor of love for 4 years. #drivebook

druinok                      @johnberray some are a labor of love for one year :) #drivebook

lmhenry9                   @johnberray @druinok Some are a labor of love for 1 period. #oneclassatatime #drivebook

cheesemonkeysf   @johnberray @lmhenry9 @crstn85 Can't remember what @samjshah calls HW, but he has some hilarious reframing like "Home Enjoyment" #drivebook

lmhenry9                   @cheesemonkeysf @johnberray @crstn85 @samjshah I believe that's correct. #drivebook

cheesemonkeysf   It's hard doing #sbar when you come face to face w/the hypocrisy of the system about stuff like HW. I find I can't grade HW #drivebook

druinok                      So how do you promote engagement and intrinsic motivation in the classroom? #drivebook

crstn85                       @cheesemonkeysf I'm still struggling with what I'm teaching- habits vs. content. Plus what grades really represent #drivebook

johnberray               @lmhenry9 @cheesemonkeysf @crstn85 Have you all read Stephen Covey's 7 Habits of Highly Effective People? #drivebook I sense a parallel.

crstn85                       @johnberray No, is it a worthwhile read? #drivebook

johnberray               @crstn85 Yes, indeed. #drivebook

lmhenry9                   @johnberray @cheesemonkeysf @crstn85 I have it- my dad gave it to me when it came out in paperback. Have started it several time. #drivebook

crstn85                       @druinok I try to do a lot of discovery- students experiment, conjecture and prove results rather then getting them from textbook #drivebook

cheesemonkeysf   @druinok My 1st rule of engagement is to design so that s's HAVE to be able to get a personal "win" out of an activity #drivebook

johnberray               @druinok Creative hook+well planned activities that run on s's dev intrinsic motivation. #drivebook

johnberray               @lmhenry9 @cheesemonkeysf @crstn85 7 Habits: opens with Personality Ethic vs. Character Ethic. Extrinsic vs. Intrinsic. #drivebook

cheesemonkeysf   @druinok Intrinsic motiv requires that I surprise & delight s's so they'll be willing to renegotiate their relationship w/math #drivebook

cheesemonkeysf   @johnberray @lmhenry9 @crstn85 It's funny-I read Covey & it never spoke to me #drivebook #bornarebelisuppose

crstn85                       @johnberray Well planned is key. Sadly few books have this all already set up. I'm experimenting on them while they experiment! #drivebook

johnberray               @cheesemonkeysf @druinok Bingo! But the system needs me to be something it can replicate. And it can't. #drivebook

cheesemonkeysf   @johnberray @druinok @crstn85 But with creative hooks/discovery activities, aren't we trying to create on-ramps to flow? #drivebook

cheesemonkeysf   @johnberray @druinok Wait, what did I/we say that sounded good? #drivebook

johnberray               @crstn85 That hook is the bridge to invite them in. My high school has a masterful history teacher who does this. @burgessdave. #drivebook

cheesemonkeysf   @crstn85 @johnberray The difficulty is that if a hook isn't authentically hook-ish for *me* individually, I can't force it 4 kids #drivebook

cheesemonkeysf   @crstn85 @johnberray I agree completely. And "well-planned" is different than "written by a control freak." #drivebook

johnberray               @cheesemonkeysf @druinok I fancied the "surprise and delight" part. #drivebook

crstn85                       @cheesemonkeysf Yes. If I'm not interested in a topic I have a hard time teaching it, have to find a cool problem worthy of time #drivebook

cheesemonkeysf   @johnberray @crstn85 Exactly! Getting them to (a) accept the invitation & (b) relax re using the on-ramp is a giant behav. change #drivebook

burgessdave            @johnberray @crstn85 Thanks, John! Sorry to be late to the party! #drivebook

johnberray               @cheesemonkeysf @crstn85 "well planned" sometimes means "able to go off script" because teacher knows intimately the content. #drivebook

cheesemonkeysf   @johnberray @druinok Glad that resonated. Surprising & delighting them is the only on-ramp to engagement I've found that works. #drivebook

cheesemonkeysf   @crstn85 That was my problem w/the "reform" curricula I tried working with last yr. Most of the prob's didn't speak to me. #drivebook

johnberray               @cheesemonkeysf @druinok Can we call a hook an intrinsic motivator? It seems like both in a way. #drivebook

cheesemonkeysf   @johnberray @crstn85 *And* also can "read" his or her class/audience #drivebook #somedaysmathteachingislikedoingstandupcomedy

lmhenry9                   (1/2) When Pink was talking about the idea Motivation 2.0, I kept thinking about how some people in union prominent areas (here) #drivebook

cheesemonkeysf   @johnberray @crstn85 Some reform curricula present lessons too rigidly structured for one type of understanding #drivebook #mightjustbeme

crstn85                       I think teachers absolutely must be flexible. Someone said we have to make the most decisions per min, bar air traffic control. #drivebook

johnberray               @cheesemonkeysf @crstn85 Being able to read" udience is the nemesis of a green teacher. Super important. #drivebook

burgessdave            #drivebook agree with you @johnberray about ability to go off script. Must be able to take advantage of teachable moment

lmhenry9                   (2/2) seem to be chasing the $ but everyone loses. People aren't as productive (u can't do that - contract) & neither is the co. #drivebook

cheesemonkeysf   @johnberray @druinok I think a hook is only an **on-ramp** to intrinsic motiv. The motivation need to come from w/in #drivebook #literalist?

lmhenry9                   Where I live is very pro-union (not just for teaching) & it just seems like so many things come down to the contract. #drivebook

cheesemonkeysf   @johnberray @crstn85 Being able to "read yr audience" is 1 of the keys to success in life generally, IMHO! #drivebook

crstn85                       @cheesemonkeysf That's why I like CME- good combination of traditional and reform. #drivebook

cheesemonkeysf   @lmhenry9 Didn't they try the giant salaries/bonuses as extrinsic motiv for t's...only to find it doesn't work? #drivebook #ohthosepeskydata

lmhenry9                   What happened to people doing things or doing them until they were "right" or "best" rather than worrying about the contract? #drivebook

cheesemonkeysf   @lmhenry9 I understand what you mean re things coming dn to the contract. Does this affect how you teach in classrm? #drivebook

johnberray               @lmhenry9 Contract IS a problem. And so is however many thousands of minutes we say a s has to have for credit. #drivebook

crstn85                       @lmhenry9 We're in our 2nd year without a contract here. It's an issue whenever someone wants to try something new! #drivebook

lmhenry9                   @cheesemonkeysf I don't let it affect me in the classroom. But I have watched people doing/not doing things b/c of the contract #drivebook

cheesemonkeysf   @lmhenry9 That's where I think getting s's into a state of flow comes in -- #drivebook

johnberray               @cheesemonkeysf @lmhenry9 I think it plays out in others saying no to doing/being more as a team.  #drivebook

cheesemonkeysf   -- Students have to TASTE that exper of losing themselves in the quest to figure something out. Then it builds on itself #drivebook

cheesemonkeysf   @lmhenry9 That's been my sense of you from reading yr blog. I admire your courage to experiment & see what unfolds. #drivebook

johnberray               @cheesemonkeysf @lmhenry9 I think the best teachers today are the mavericks who will not settle if others won't help. #drivebook

crstn85                       @johnberray The intrinsically motivated ones! #drivebook

lmhenry9                   @cheesemonkeysf I'm just so tired of hearing about "contract" says... Sometimes you just need to do what's best for students/team #drivebook

cheesemonkeysf   @johnberray @lmhenry9 I'm DEFINITELY with you there. Willingness to be a maverick is key to improving, in my view. #drivebook #imweirdthough

maxmathforum      This #drivebook chat is such a neat conversation. Mind if I join even if I haven't read the book?

lmhenry9                   @cheesemonkeysf @johnberray I'd be inclined to agree with you. #drivebook

lmhenry9                   @maxmathforum By all means. #drivebook

cheesemonkeysf   1 reason I like designing activities around SBG-type skills is that I can use them regardless of what curriculum/fad is mandated #drivebook

cheesemonkeysf   @maxmathforum Definitely! I say, never let a lack of doing the reading stifle your creativity. ;-) #drivebook

cheesemonkeysf   @maxmathforum Come on in -- the water's fine! :) #drivebook

crstn85                       @cheesemonkeysf I was very happy I'd done that when I moved schools & all my materials still applied. A good problem always works #drivebook

lmhenry9                   @crstn85 That's a wonderful bonus! #drivebook

maxmathforum      #drivebook I was intrigued by the question of if a "hook" can lead to intrinsic motivation.

johnberray               @crstn85 @cheesemonkeysf @lmhenry9 @druinok @burgessdave Gotta run! Dinner awaits. Pleasure hanging out with you all. #drivebook

maxmathforum      #drivebook I was just writing a stats lesson around the question "is my nose freakishly large" -- is that intrinsically motivating?

crstn85                       @maxmathforum perhaps we can only hope students will be intrinsically motivated if we offer them a hook? #drivebook

cheesemonkeysf   There's a great quote re how, if you can't find the culture you need & if you build it yourself -- #drivebook

cheesemonkeysf   -- others will magically appear and declare that they've been looking for this very same culture! #drivebook

maxmathforum      @crstn85 so a hook is necessary but not sufficient? #drivebook

cheesemonkeysf   @crstn85 @maxmathforum I truly believe a great "hook" can only be an inviting "on-ramp" for s's. You can lead a horse to water... #drivebook

crstn85                       @maxmathforum I feel like we're talking about the "you can lead the horse to water.." issue here.  Ha! You typed it faster.  #drivebook

lmhenry9                   @cheesemonkeysf @crstn85 @maxmathforum This is a great thought. Just have to find the right "hook" for some things. #drivebook

crstn85                       @maxmathforum Been struggling with this lately- progress reports due today so considering how much I should chase kids down etc. #drivebook

maxmathforum      @lmhenry9 @cheesemonkeysf @crstn85 my best criteria for hooks is what the heck made someone come up with this in the first place?#drivebook

cheesemonkeysf   @crstn85 @maxmathforum Great minds are all on the same wavelength! #drivebook

maxmathforum      @crstn85 Guess it depends too on what else is going on... what s's are used to, outside stresses, their interests #drivebook

maxmathforum      @crstn85 was observing a good math class today but 6 kids in the back were totally distracted by a burning, non-math issue #drivebook

cheesemonkeysf   @maxmathforum @lmhenry9 @crstn85 I like that criterion. I also like looking at where, developmentally, a concept is coming from #drivebook

maxmathforum      @crstn85 specifically, why there are so few racist jokes about white people compared to jokes about people of color. It's a gd ? #drivebook

cheesemonkeysf   @maxmathforum @crstn85 Also on how shut down (or whether) the s's are. To me a hook is necessary but not sufficient #drivebook

crstn85                       @maxmathforum I've had a couple issues lately stemming from dating/breaking up. You have to be really interesting to beat that! #drivebook

cheesemonkeysf   I hate to leave this conversation, but I just got a text that my burrito is ready! My burrito calls -- literally! 'Night for now! #drivebook

maxmathforum      @crstn85 In my dream school/class it's ok to take a mental health day when that kinda stuff is going on #drivebook.

crstn85                       @cheesemonkeysf Yes, sometimes you need a hook that doesn't look like math.  #drivebook

maxmathforum      @crstn85 maybe part of understanding motivation is understanding when life is more important than math class! #drivebook

crstn85                       @crstn85 And that has to be the case.  Back to teachers being flexible. #drivebook

lmhenry9                   I will archive #drivebook later tonight or tomorrow. Any thoughts on when you want to do Chapter 2?

maxmathforum      @crstn85 and the need for flexible systems to support them #drivebook

crstn85                       @lmhenry9 This time slot was good for me. Any day but Wednesday is okay. #drivebook

lmhenry9                   Should we look at next Thursday (12/15) 8p est for next #drivebook? Then take a break for the rest of December?

maxmathforum      @lmhenry9 I'll try to read the 2 chapters of #drivebook by then. Or just absorb y'all's wisdom!

cheesemonkeysf   @lmhenry9 Next Thurs 12/15 8 pm ET/5pm PT sounds good to me for next #drivebook! And a break! woo-hoo!

cheesemonkeysf   @maxmathforum @crstn85 AMEN TO THAT. #drivebook #mentalheathdaysaregood

Time to change?

Yes, it was another quiz day in Algebra 2 today. Yesterday, I had them work on review problems over all the learning targets (not just the ones being tested). Still had quite a few students not make much of an attempt on the feedback only problems. If you haven't been following the saga - here is my last post and it has the previous ones linked to it in the second paragraph.

So, as I was grading today, this was the thought I had:
(For those of you seeing this for the first time, I teach, quiz 5-6 learning targets - 3 that were previously quizzed and students only got feedback, 3 that have not been previously quizzed and were the most recently taught and give feedback only.)

Starting with the next quiz (which for my classes will be the last one before Christmas Break), I will still grade the older 2-3 learning targets. On the "newer" learning targets, if a student shows they totally understand it and would earn a 5/5 on it, I will record that 5. On the next quiz, when everyone else is doing those learning targets for the grade book, those students who earned the 5 on the previous quiz will not have to do those problems. I will still write feedback for those students who didn't earn 5/5 so they know what they need to work on, but I won't record a score.

My hope is that students will take all the learning targets seriously, not just the graded ones. I have a growing group of students who are not even attempting the feedback problems.

Thoughts??? Please comment below on what you think. I hate to change mid-stream, but I'm not sure what else to do here. Thanks!

Tuesday, December 06, 2011

Early Merry Christmas to me

Last week, our principal offered a day of training along with a (school) i-Pad to two of our staff members. We had to submit how we would use the i-Pad in our classroom. Here's what I submitted:

If I were to receive the training and I-Pad, the first way I would use it would be to put together screencasts to upload to the internet for my students. A screencast is when you write on the screen and audio is recorded along with whatever you are writing so that it would be similar to being in the classroom (although they wouldn't see my smiling face). My intent would be to have screencasts for each concept and to use some examples that we went over in class and possibly additional examples as well. Students would be able to view these outside of class to help their understanding of the material. Although there are programs to do this with a computer and our SMARTBoards, it is very difficult to do between having a microphone close enough as you are writing on the board as well as getting the software to work with it. I have read several accounts of teachers doing screencasts and have noted which apps they have used to do it. My understanding is that it is much easier process to record the screencasts on the I-Pad since the microphone is built-in to the I-Pad.
There are also a couple of apps that will allow the I-Pad to control the mouse. It would allow me to write on the SMARTBoard while walking around with the I-Pad, similar to an airliner.
With only having one I-Pad in the classroom, I think for Math it would be challenging to use some of the math apps that are available for students in the classroom. There is a VGA to I-Pad cable available that would hook the I-Pad to the projector and would allow students to see what is happening on the I-Pad screen. I have a couple of thoughts of how this could be used in the classroom. There is an app called Wolfram Alpha that does a lot of mathematics. Although it is available on the internet, having the I-Pad in a student's hand manipulating the mathematics while others are seeing it could be one use of it. Also, in Algebra 2 we study the graphing of parabolas and bringing in Angry Birds could be interesting. When the birds are launched, they have a parabolic path and the path is left up on the screen. Students could find the equation of the parabola and use that to determine what to do next. I know of a teacher who has spoken with the developers of Angry Birds and he indicated that it is to scale, so students could find the equation accurately and go from there. This application does intrigue me a little, but I'd have to do a lot more research before launching it in the classroom (pun intended).
Those are the main thoughts going through my head at the moment. If I am one of the recipients, I would continue to research other viable options to try in the classroom.  Thanks for giving us the opportunity!

I found out today that I am one of the two lucky recipients! Yay me! Now for the somewhat scary part.... 

I know I have seen on Twitter that some of you have done screencasts on i-Pads and I did find some blogs that discussed this (Screencasting Apps for the i-Pad from, ScreenChomp from Teaching Math with Technology are the two I tagged in Diigo), but I'd love to hear from math teachers who have done this and what works well (or doesn't work well).

Does anyone else have any other suggestions of what I could with the i-Pad? I only have one for my classroom and I teach Algebra 2 and Math 1 (think Algebra 1 at a slower pace). Thanks for the help in advance!

Meanwhile, I'm trying to patiently wait until December 20th...

Wednesday, November 30, 2011

My (underwhelming?) 100th Post

Since I posted last and saw on Blogger that it was my 99th post, I wondered what my 100th post should be. After all, 100 seems like a rather momentous number. There is a part of me that is somewhat in awe that I am writing my 100th post after starting this blog in June 2010. I don't really consider myself a writer and I really don't blog for anyone  or any purpose other than reflection on what I've encountered as a math teacher. Most of the time, taking the time to blog about something helps me sort it out in my head and if that doesn't happen, one of my readers offers a comment that is helpful to me (or in many cases affirms whatever it is that I'm going through is not something I alone am facing). But as I sit here on the last day of November, I still have a nagging issue in my head.

I've blogged about this before (first here, then here, and most recently here). It's the whole quizzing/reviewing thing. You guessed it, today was another quiz day in my Algebra 2 classes and tomorrow is quiz day in Advanced Algebra 2. I'm not through grading the Algebra 2 quizzes. The one class I have graded actually wasn't too bad. However, today I am frustrated with time. You see, I ended up spending most of the class period with my Advanced Algebra 2 students going over questions from the review I gave them (with answers, I should add!) instead of answering a few questions and starting into the next learning target as I had planned. Yesterday I had spent significant class time going over review problems with my Algebra 2 students, but I had pretty much anticipated having several questions from them given how things are going, plus quite a few were out on Monday since it was the start of deer hunting season with guns. I expected that my Advanced Algebra 2 students would remember things better and have a better grasp on it and I was disappointed with that today.

Now, granted, I think part of the reason going over the review took a little longer was the way I did it. Instead of my explaining the problem, I pretty much just wrote what students told me was the next step. After each step, I prompted them with "what's next" or something along those lines. I actually liked this - students had to articulate what to do which helps them to review it and there was some good discourse going on while we were working the problems. One student would ask how another student got something and the students answered it instead of me. I think that helped. I think I'll do that again and bring that more into my teaching and other classes. I liked that the students who knew or mostly knew what they were doing were engaged and reinforcing what they knew as students who had questions were getting them answered.

What I am really disliking this point is that I am spending so much time reviewing. I teach 3 concepts and as we are coming up on the next quiz (which has up to 6 concepts - 3 that were previously assessed, they got some written feedback, and now are being given a score for, and 3 that are the most recently taught concepts where they only receive feedback), I give them a review sheet with answers on the 2-3 concepts that are going to be graded. Students like having the review sheets because it gives them a good idea of what to expect. I get that. But since I am quizzing every 5-7 class days, I lose pretty much 2 days every 5-7 days. Not good. I'm already behind because these students didn't cover as much ground as they should have in Algebra 1 (I've talked about that a lot here) and now I am losing more time reviewing. In my last post about this issue, Damion really hit the nail on the head - like his students, my students don't seem to be retaining well.

In addition, we are coming up on Christmas Break here. Now, mind you, we just had Thanksgiving Break (we were off Wednesday - Friday last week). We have 2 full weeks (this week and next) and the third week, the students have 4 days while the staff has a waiver day on Friday (December 16th). So when students leave on Thursday, December 15th, the next time I see them in class will be Tuesday, January 3rd. Almost three whole weeks! Now, I will be honest, I am totally looking forward to being off school that long. However, being off that long will most likely mean that anything that I teach that last week before break (or earlier) will be mostly forgotten by the time I see them again on January 3rd. I am pretty certain that I am going to need to assess everything before break, which would mean that I would not have a feedback opportunity for them.

So, at this point, I am trying to figure out what to do. I am already contemplating going back to how I used to assess - teach the concepts that form a "unit," actually follow through on quizzing for feedback only every 2-3 concepts and at the end of the unit, have a day or possibly two of review and assess. Just as I typed that, my mind was mentally calculating and maybe I'm not losing as many days as I think... I'll have to ponder that a little later on. (ooooh - squirrel!) Or, I could continue in the same manner - teach 3, assess with most recent 3 concepts getting feedback and the 3 concepts before that earning grades in the gradebook. I'm not sure what other options I have at this point without dramatically changing things and I don't want to go down that road right now. Another option I had contemplated during the summer was to give each concept 2 grades and combine them - that's definitely not something I want to change to mid-year. I'll have to think about that come Summer 2012.

So, here's where you, wonderful readers, come in. I need some help. I can't shake this issue in my head. I'm on my 4th blog post about this issue and I can't work it out in my head. Please offer thoughts, experiences, advice, etc. - Do I keep my assessment system the same (teach 3 - assess 6, 3 graded, 3 feedback), revert back to what I've done before (teach the unit, quiz for feedback a few times, and give a "unit test" with however many concepts are on it), or something else? I look forward to interacting with you in the comments!

Thursday, November 17, 2011

Open Question Attempt #2

This was the open question I posed to my Advanced Algebra 2 students today:

Write a system of inequalities that has (4, 3) as a part of its solution. It should have 2 or 3 inequalities. (I had thought about leaving the last sentence off, but I was trying not to overwhelm them.)

When I asked for their answers, I got crickets again. (Recall, I had tried this with them a couple of weeks ago and pretty much got no response from them.) So, I asked them for one inequality that would work. Crickets. More crickets. That, and a "I don't know how to work backward." After a few moments, someone gave me one inequality. So we graphed it and checked (4, 3) and it didn't work - (4, 3) was on the line. I asked him how to change it and he thought about it and came back with a different inequality. This time (4, 3) wasn't on the line, but he had the wrong inequality symbol. We flipped the inequality and had a working inequality. Yay! How about a second one? Crickets.... but for a shorter time. Same student, new inequality. Worked - success!

Can we come up with 2 different ones? Just try... Different student, new inequality. Got a working one and the student came up with a second one.

By the time we were done, we came up with 5 systems (look at the first 3 pages of the pdf below - first 5 slides). The first time we did an open question, I primarily had 3 students contributing. This time I had 6 or so contributing - 4 of them who had not last time. I'll take the improvement. Maybe next time, I'll have more.

Tomorrow I'm trying this question with Algebra 2 (similar to what I did with my Advanced Algebra 2's a couple of weeks ago):
I know that (2, 3) is the solution to a system of equations. Find two equations (in x and y) that have (2, 3) as their solution. How do you know that (2, 3) is the solution?
(I think that's how I phrased it.

Wednesday, November 16, 2011

Quiz Time Blues Again

I just gave another round of quizzes over the last few days. I am not pleased with how it's going. This is nothing new. I can't decide if it's because I'm not happy with doing teach 3 - quiz (3 for feedback/3 for grade) - teach 3 or because I have a lower-ability/less-motivated/less-knowledge-of-Algebra-1 group of students this year.

As we continue with the quizzes - grading the three concepts that were given feedback only the last quiz and giving feedback only on the three most recently taught (details on my SBG system this year is here and reflections on why I wanted to make changes from last year is here), I am seeing that several students are not trying or making little effort on the feedback only questions. It is not a majority of students, but with each new quiz, I am noticing there are more students each time who are not attempting the feedback questions. This worries me and I feel it defeats the purpose of giving the questions for feedback only the first time. The students are cheating themselves of the opportunity to seeing what they know about the problem in a practice situation.

I have been giving them review sheets for the concepts that are being graded since in some cases it has been 2 weeks or so since they had the original instruction on the topic. I suspect what that is doing is focusing the students on preparing for only those problems and they are not doing much preparation on the newer concepts. I am afraid that if I give review sheets with all 6 concepts, we will be spending one day reviewing and another day quizzing every 7-8 class days. As much as I don't want to dwell on what content I am covering over the course of the year, I am already concerned that I will not get to many concepts that I should be for Algebra 2.  Last year I ended with exponentials and logarithms and I am deeply concerned that I'm not going to get there this year with their lack of Algebra 1 skills and the time I've had to spend remediating those skills - and that's not factoring in the additional number of testing days (and some review days).

In two of my three Algebra 2 classes, students expressed that they weren't ready for today's quiz. Now, I know it's not due to lack of time and energy we I've devoted to it in class. They weren't ready because they weren't prepared. Students aren't preparing well - they aren't taking the time to work through problems as they should be. I have watched as I have helped students who have wanted the help and seen several students not using the time well. They choose to talk instead of starting the problems. I'm not sure if it's due to lack of confidence in doing the problems or if they don't want to after spending class time listening and (maybe) taking notes. The last few sections I have given students a note sheet to fill in. I did this partially because we were doing graphing systems of equations and inequalities and I thought it would be helpful to have the problems with graphing spaces ready to go for them. I also did this because I thought if they had the examples in front of them, they would actually take notes. I'm not sure how well that worked.

I'm at a bit of a loss tonight. I cannot continue to go backwards. Students have to learn they have to pick up the slack at some point. I feel like I am wasting time quizzing every 5-7-10 class days if they aren't preparing for all of the concepts. Part of the reason I changed to the quizzing concepts twice system was that I thought they would do better on the concepts since they had a chance to get some written feedback from me as a part of the process. If students aren't even going to attempt the feedback-only problems, then the purpose of quizzing this way is moot. I could go back to the way I assessed last year (at the end of a "unit" with a couple of days of review in front of the assessment) and end up with the same results with hopefully less wasted time, not to mention less stress since I would only have to prepare an assessment every 2-3 weeks. Part of what also appealed to me about the teach 3 - quiz 6 - teach 3 - quiz 6 system was that it would be smaller chunks for students to focus on and hopefully they would find that to be more manageable.

So what to do, what to do? At the moment, my plan is to put the How to Study Mathematics article that crstn85 referenced in her recent blog post in front of my Algebra 2 students tomorrow. I am going to do it a little differently. I gave the article to the Advanced Algebra 2 students today (since some of them were still finishing their quiz) and had them read the introduction (through the middle of page 3). Then I counted them off and had each pair read one section instead of one page. Each pair shared with the class what they thought was important. I did not have a chance to share the Cone of Learning with them - I am going to do that tomorrow. My hope is with my Algebra 2 students to get through all of that in class tomorrow. I also had my husband print out in color 11" x 17" Cone of Learning posters that I am going to put up around the room. I want a visual reminder to my students that they need to take an active part in mathematics.

I need to continue to reflect to see if this is how I want to continue to assess, or if I want to go back to what I was doing last year, or if there is a different way I want to try. If I am going to make changes, ideally, I would do it after the end of the 2nd 9 weeks in January. I just don't know what the "right" answer is. If anyone has some thoughts to share that would be helpful, I sure would appreciate it. I am having a hard time separating myself emotionally from this decision. There is a part of me that feels that I am failing my students here. I feel like I am teaching them (not intentionally) to prepare for the short term rather than learning the material thoroughly. Intellectually, I know that this group of students does not have good study skills and that is part of it, not to mention that there are several students who are not strong mathematically. Their experiences in Algebra 1 isn't helping the situation either. Regardless, I have to work with the students I have, where they are at, and make the best of it I can.

Thursday, November 10, 2011

Struggling & GReader Cleaning

I feel like I am struggling at the moment. I really wanted to make some changes in how I teach this year and I have made some changes. I have incorporated some different things into my teaching, but I am still at the forefront of my classroom. I struggle with this mentally at least weekly, if not more so. I wanted to be incorporating Reasoning and Sense Making into my classes. I'm not. I did bring in an open question last week into my Advanced Algebra 2 class and it didn't go as well as I hoped.

I did partially use this approach today that John Scammell blogged about last week. I think the next time I use it, I will follow the approach as it was blogged about - when I was thinking about it this morning on my way into work, all I could remember was showing which points made the inequality true. In my first class, I had students choose any point on our grid (both x and y values go from -6 to 6 on it) and they all chose points with two positive coordinates. None of those points worked, so I had them choose a coordinate that had at least one negative coordinate and we got some points that worked. Also with the first class, I didn't have them graph the points we came up with. We just graphed the shaded area that did work. For my second and third classes, I had them plot the points we found that worked on their grid before we graphed the inequality on the grid. They then graphed the line and we talked about testing a point to determine which half of the plane to shade. Below is the pdf of my SMARTNotebook file from my last class.

In that last class, one of my students who has struggled with math spoke out as we were working through the problem. We had graphed the individual points that we found that worked and had just finished graphing the boundary line and right as we finished drawing it in, he said "I get it now!" I hadn't even gotten to the point where we talk about testing a point in one of the half-planes - he already saw where the answer would be and "got" why that was going to be the answer. That was worth it. #win

Getting back to the opening... I know I have done things differently this year. Yes, things are mostly the same. However, due to the twitter-blogosphere and reading and conversing with other math teachers, I have incorporated some different approaches to instructing my students and I think that has made me a better teacher. However, as I look at my classes, I am frustrated because they are so dependent. It's almost as if they don't know how to think.

In my Advanced Algebra 2 class, where we're working on solving systems of inequalities by graphing, we had this discussion about the test point today. It started first by clarifying how to determine which half to shade based on testing (0,0), which is the point I use unless it's on the line. Then the conversation shifted - can I test (1,1)? What about (2,2)? After answering the same question but with a different point for the third time, I got a bit frustrated with them. It was as if they couldn't take the concept of checking a point to represent the region and shift it to a different point. And these are supposed to be my "better" and/or "brighter" students. Granted, I didn't use the same start as I did with my Algebra 2 classes today, and that may have made a difference, but it was very frustrating to me that they couldn't transfer the idea to different points. As I said earlier, it's almost as if they don't know how to think.

Last night I was trying to get caught up on my Google Reader, this post by crstn85 caught my attention about studying for math. Since I was at 130 or so when I started trying to clear it out, I really only skimmed the post and starred it to go back and read later. However, as I continue to reflect, I think I may go back and read it much more thoroughly to see if I can use what she did with my classes. Maybe it will be helpful to them.

So here I am at the beginning of the grading period of disruptions second grading period and I have not really done anything as far as my second and third goals on my list for this school year. I have not made any progress on incorporating Reasoning and Sense Making activities into any of my classes, and although I try to ask my students questions as I help them, for the most part, I pretty much help them through their questions instead of asking them questions. I'm not sure why I am struggling with that one. I think part of it is that my Algebra 2 students are lower in ability/prior knowledge compared to previous groups and I am afraid of losing them. I suppose if I really thought about it with my Advanced Algebra 2 students I could work at it more with them, but again, there are some students in there that I could lose. I'm at a point that I'm not sure what to do, so I continue to do what I have been doing and trying to bring in some new things as I catch them in the twitter-blogosphere. Right now, I'm not feeling that's good enough. So now what?