I have added two new "pages" at the top of my blog - the first is a link to my Common Core Mathematics Links page at school. I am assembling what web resources I am finding for our staff there and like Kristen Fouss did, I thought you all may find what I've got to be helpful.
Also, I have added a link to my Common Core Resources I have assembled on Diigo. I haven't been through all of them, but once again, you may find them helpful. Enjoy!
Saturday, March 31, 2012
Thursday, March 29, 2012
Closing the Gap
I was "voluntold" to be a part of a committee working on a grant that is supposed to close the gaps between high school and higher education. Our first meeting was this week. I believe the percent of students entering college in Ohio requiring either remedial English or Mathematics (or both) is 41% (this was for the 2009-2010 school year). For my district, that number was 62%. It didn't used to be that bad. The data that I saw from 2003-2007 was not that bad. However, there were several things that happened to our class of 2009 (and earlier). We had significant staff cuts. Our number of students needing free and reduced lunch increased. Some of our stronger students went to other districts due to the cuts. I'm not making excuses - these are the facts that I can think of that might have affected that number.
How am I supposed to help reduce the number of students who need remediation in college if they won't help themselves? How do I get across to them that by 2018, 62% of jobs will require some sort of post-secondary education? These kids can barely focus on stuff happening that week, as evidenced by the influx of re-assessments this week since it's the last week of the grading period, let alone next month, next year, etc. How do you instill in students the perseverance they need to be successful? How do you convince students that they will need to go to some sort of post-secondary education?
As we are delving into the information, I know I am going to find that we are not teaching all of what needs to be taught for students to be college-ready. We did a gap analysis this week between what we have been teaching (or are supposed to be teaching) and the Common Core. I had two realizations as I did my gap analysis for Algebra 2:
- Even though Ohio never specified what was to be taught in Algebra 2 (they did our old indicators by grade level), my students probably weren't taught as much of what would be considered Algebra 2 as they should have. It has gotten worse each year. The first year I taught Algebra 2, I taught a lot more Algebra 2 content than I did this year. In fact, I think I have taught less each year for about the last 5-6 years I have taught it.
- Even if I did teach what I was supposed to in Algebra 2, this is a huge step up. Common Core should close the gap between what colleges expect our students to have learned and what we have taught. This is, assuming of course, that we teach everything that we are asked to in Common Core.
What both of these items is going to mean for me is that I have a lot of catching up of my students to do. At least I know that next year's students are coming in with a little bit more mathematical knowledge than this year's group did.
With what has happened in my classroom this week, I can't help but wonder how we work on closing the gap when our students don't seem to retain what is taught. My Algebra 2 students couldn't remember factoring, which I spent like 3 weeks on and finished about 6 weeks ago. I did not have to spend a lot of time reteaching it, but students who seemed to have had a good grasp on how to factor have forgotten it. Do they really forget it, are they too lazy to recall it, or do they not have the skills to know how to go back and refresh their own memories? I think what bothers me even more about their lack of remembering factoring today is that they just reviewed it on Monday (when I was out) and several were able to successfully complete the worksheet. What's the deal? Have students become so focus on the immediacy of the present that they don't know how to recall information? I even have seen this the last few years on my midterm and final exams. How do I alleviate this problem? Is it a problem in how I teach or is it more of a systemic problem - that students have the same problem everywhere and/or in other courses?
I was conversing with the chair of the mathematics department of one of our local universities. He has the same issues with his class - lack of outside practice, tests are very similar to homework and students don't do well, etc. - and this is a class of juniors who are majoring in math and computer science. I found it interesting that this college professor was complaining of some of the exact issues we complain about as high school teachers. It makes me wonder if it really is a widespread problem or just in this area of the country.
I'm sure that some of this goes back to being less helpful (which I'm not doing anywhere near as much as I think I should be) and I'm sure I'm not doing anywhere near the amount of application problems I should be. I know I have improvements to make. My class this year doesn't look like it did last year, and I am certain that next year's version will be different from now. I know I am going to put forth the effort to make the improvements. How do I instill the same in my students?
I can't figure it out
I just spent 3 out of 4 classroom days out of my classroom. Between taking sophomore girls on a field trip to learn about careers that use math and science, doing a gap analysis between our old curriculum and Common Core, and attending the first meeting of a committee working to close the gap between High School and Higher Education, I have been one busy puppy as of late. I was out two days, back in for one, and then out again.
We only got through the expressions with monomials. I just didn't have enough time to get to the ones with factoring in them. So, with being out the classroom again on Wednesday, this is what I left them:
I also left them a note on the board letting them know two things - that I intentionally did not cross out the common factors in numerator and denominator and that they would have to do that, and that I had made a mistake (which is corrected in this) and the first person in each class to correctly identify it to the sub would get a treat when I came back on Thursday. (I baked cookies!)
My first class had no one identify the mistake (I had typed in x - 2 instead of 3x - 2 in the answer). The other three classes all had students identify the mistake. When I got back today, I did the same activity as Tuesday - sign up for a problem, work it out on the whiteboard, put it up. Most of my students struggled with the problems. Now, granted, a couple of the factorings may have been a little bit of a challenge, but most of them didn't even remember to factor in the first step. Again, I didn't really see anyone referring to their notes that I had given them.
We did go through the rest of the lesson that I had started on Tuesday. Most students left feeling more confident in the process than they came in. I have an in class practice activity tomorrow since it is a shortened staff development day and I won't see all of them tomorrow due to an assembly. (I borrowed what Mimi did here) I suspect they are going to struggle with it - they didn't remember factoring very well (even though we did it in January) and if they can't factor it, it will be hard to reduce.
So, I'm sitting here tonight trying to figure out what I did wrong here. I put together the worksheet rather hastily Tuesday when I realized that my original plan wasn't going to work. In retrospect, I probably should have picked different problems that factored easier for their practice worksheet (which wasn't posted). But as far as my worksheet that I left for them in my absence to help guide them as to what to do, I'm not totally sure where I went wrong. I am glad that the rest of the lesson seemed to go well. I think the guided notes are helping them.
The day I was back in the classroom, I did try what @druinok suggested in our chat last weekend. It did not go well. The directions on the board told them to sign up for a problem from the previous assignment, work it out on the whiteboard, and put the whiteboard on the chalk tray when they were finished. My Algebra 2 students actually did a little better with it once they were reminded to read the board and get started. My Advanced Algebra 2 students struggled. In debriefing a bit with them, they did admit that they had done at least half of the assigned problems, but I did not see any of them actually look at their work from before. I will probably have to add to the directions to get out the problems first.
What frustrates me with being gone is that things that I take for granted they should do or know to do (like look at the homework they did if they are working on a homework problem the next day in class) they have seem to have no clue. It's as if they can't, or won't, help themselves. On Tuesday, both my Algebra 2 and Advanced Algebra 2 students started simplify rational expressions with multiplication and division. We started these notes on Tuesday.
We only got through the expressions with monomials. I just didn't have enough time to get to the ones with factoring in them. So, with being out the classroom again on Wednesday, this is what I left them:
I also left them a note on the board letting them know two things - that I intentionally did not cross out the common factors in numerator and denominator and that they would have to do that, and that I had made a mistake (which is corrected in this) and the first person in each class to correctly identify it to the sub would get a treat when I came back on Thursday. (I baked cookies!)
My first class had no one identify the mistake (I had typed in x - 2 instead of 3x - 2 in the answer). The other three classes all had students identify the mistake. When I got back today, I did the same activity as Tuesday - sign up for a problem, work it out on the whiteboard, put it up. Most of my students struggled with the problems. Now, granted, a couple of the factorings may have been a little bit of a challenge, but most of them didn't even remember to factor in the first step. Again, I didn't really see anyone referring to their notes that I had given them.
We did go through the rest of the lesson that I had started on Tuesday. Most students left feeling more confident in the process than they came in. I have an in class practice activity tomorrow since it is a shortened staff development day and I won't see all of them tomorrow due to an assembly. (I borrowed what Mimi did here) I suspect they are going to struggle with it - they didn't remember factoring very well (even though we did it in January) and if they can't factor it, it will be hard to reduce.
So, I'm sitting here tonight trying to figure out what I did wrong here. I put together the worksheet rather hastily Tuesday when I realized that my original plan wasn't going to work. In retrospect, I probably should have picked different problems that factored easier for their practice worksheet (which wasn't posted). But as far as my worksheet that I left for them in my absence to help guide them as to what to do, I'm not totally sure where I went wrong. I am glad that the rest of the lesson seemed to go well. I think the guided notes are helping them.
Thursday, March 22, 2012
Revelations?
I am so fed up at this point. I don't know if it's just my lack of snow days/break, but I'm just fed up. I need Spring Break soon.
So, as a follow up to yesterday's questions/ponderings about how to get students to practice more, here are some excerpts of a conversation that @druinok and I had:
S: But part of the problem is on a practice day, how to make them do the practice
S: I pretty much stopped giving worksheets like that and do it other ways instead
me: ..But I don't know all those things. Where do I find them?
S: Speed dating is from Kate's blog
me: However, it still doesn't address the other issue - if you weren't planning on having a "practice day," how do you make sure they practice?
me: I know speed dating. I can't remember what other ideas I've seen.
S: You don't... the way I see it, the only way to ensure the practice is do it in class.
S: And I can say my kids were more willing to do a worksheet if it was a puzzle worksheet.
me: So you're saying I should build practice into my lesson? Maybe along the lines of what Jackie did? Her stuff looks to be discovery-based. Intriguing idea.
S: Yes... I build practice into the lesson... if I work them hard every day, the need for outside time should reduce.
S:And in order for them to practice more, I had/have to learn to talk less.
me: So how do you do that? How do you know how much direct explanation with examples to give before letting them try one? I usually give 2-3 examples of each "type" - easiest to hardest. Maybe I give too much. Maybe do one with the notes and have them try one on their own?
S: I've done that...
me: And then I assume you walk around the room as they are doing the one on their own. But then how do you avoid getting stuck with 2-3 students, each asking the same question as you walk around? I feel like I should know how to do this. I've taught for 20 years, for cryin' out loud!
S: I do walk around... when they raise their hand, I might say a word or two, but I don't linger.
S: I tell them to just try out... same as the other problem, just different numbers.
S: ok, so for practice...sometimes I will do a PPT with one problem per slide, put it up, walk around watch kids do it
problems are from worksheet then put up the answer or have kids go put an answer up for me
me: Is this after you've shown them how to do it?Same day or different day?
S: different day - as an alternate to giving a worksheet for them to practice
me: oh okay
S: part of the reason kids dont do a worksheet is proximity I think.. and being overwhelmed... one problem at a time and me walking around seems to curb both of those
me:: : makes sense
me: but, as i sit here on march 22nd feeling time pressured - i am still sitting here looking at, how do you teach something and ensure practice within a class day?
S: when teaching, I would do an example, then give another that was the same except for numbers.. they worked it, asked partner if stuck.. I walked around then we tried another that was a bit tougher
me: just to get through domain, vertical/horizontal asymptotes and holes of a rational function with my advanced alg 2 kids, it took me 2 days of class, and i could use another 10-15 minutes more. i did one example per part with fill-in-the-blank explanation and one addl example
S: now the downside of it was I focused too much on the "do" and not enough on the "why
me: which of course we have to focus more on the why now
... S: right
so assuming I teach alg2 next year, that is going to be one of my major things
S: my summer list is shaping up to be a major redo of alg2
but I would have the kids discover as much as I could...
me: i am starting to think that also
which would mean a major redo also
i've had crazy thoughts this week of not giving students textbooks next year and just giving note pages/problem pages
with common core changing things and our textbooks being 10 years old - maybe it makes more sense
S: I dont think that is crazy
me: i can't see buying new textbooks yet
i don't trust anything that says it's ccss yet - too quick to really be well thought out correlation to ccss
S: I tried to do discovery when I could - things like zeros, transformations, etc.. but I need to figure out how to do more
me: i need to figure out how to develop it in the first place - i've never done it before with my students
S: I want to do more activities like matching cards, etc... the kids respond very well to that
me: sometimes mine do, sometimes mine cop-out and don't really try with them
i really do like how the transformations ones turned out though
S: i want to work on engagment in general
me: with you on that
me: i may end up spending next year doing a major overhaul of how i do algebra 2 - i have taught it for 17 of the 20 years I've taught, so this will be major for me
S: we're gonna have a busy summer, huh?
here's the issue I see with common core though - we can't change alg2 until alg1 has been changed
bc quadratics are pretty much gone from alg2 based on what i've read... ?
me: yes
but i am certainly going to start. at least next year i'm not going to do much linear at all. i'm starting with quadratics i think.
S: we will still have our state tests that have systems on alg2, so I dont think we'll get to do that yetI hope I know soon if I'm teaching alg2..
me: it all depends on how much the alg1 teacher gets through where i'll startbut i am DEFINITELY not starting with solving linear equations in one variable.
S: agreed 100%
i would really like to get to a point where I start w/ an engaging problem and it sparks an exploration
me: maybe someday
... S: yup
but how to fix your issue right now is where we need to focus
tell me how a class day is structured
me: warm up - which they don't do until i get to the board
go over any questions from yesterday's problems, which are getting fewer since they aren't doing outside practice
new lesson
if time, start on practice problems. usually about 10-15 minutes if i'm lucky
very traditional
when i do something other than worksheets - speed dating, the thing i did yesterday, more tend to do it than not
giving them a worksheet and tell them to have at it doesn't work
although with being out 3 of the next 4 school days, they're getting worksheets. not much more of an option with a sub
S: I never liked the hw questions part.. always seemed like a waste of time don't know how to fix though
me: i am really becoming resentful of that
S: resentful of what?
me: i have a few kids who will ask question about a problem who have not done the assignment and then i watch them and they a) don't pay good attention and/or b) don't write a thing down as i do it
i am resentful of making that time daily and it being abused
but you want to provide question time for the students who honestly want their questions answered
S: okay, so let's break it down from start to finishwarmup time - what do you think? do you like it? does it work for you?
me: yes and no
S: could it be done differently?
me: it does give me something to focus on (themes) although some days are getting tough now
S: do your kids work in pairs or groups?
me: i like that they were practicing state test questions twice a week if they actually did them
they are seated in pairs
i may not do the themes next year - just rotate what they're warming up on
i like the concept of it, but my students don't follow through
they sit and talk while i'm getting attendance
at this point in the year, that's hard to correct. trying to think of how i would do it better next year so they are more engaged
S: remember you could try some new stuff after spring break - tell them you are testing out some ideas for next year
me: i am thinking if they are not doing outside of class practice, they could pick up a worksheet as they come into class
S: I have an idea, but not sure
me: start on it.
it would have a warm up at the top, then the "lesson"
S: do you have mini whiteboards?
me: hopefully somewhat discovery
yes
S: what if each pair came in, got a whiteboard and a problem (could have several problems)... worked it on the whiteboard w/ their partner
it would be a review of previous day's work
then had them switch slates and "grade" a different groups board?
might have the same effect as the HW check
OR - do the problems fom the HW - they worked on their whiteboard, lined them up at the chalk tray for kids that had HW questions?
then you kill two birds w/ one stone
me: if i did the problem with a partner - how many problems?
i don't want to create a ton of work for me in set up
(i know that sounds really selfish right now, but i don't want to be creating 12 problems and have them blow off the doing/checking of the problems)
i feel so darn stretched right now.
i really need that spring break
S: maybe use the problems from Kuta?
I honestly would figure out a way to do the homework problems.. if they did the HW, they can copy it on the whiteboard.. if not, they can work it
how many HW problems do you assign?
me: varies
S: more than 10?
how big are your classes?
me: after teaching 20 years, i am still struggling with what the "right" amount is. i feel they really need to practice, but if i assign 20ish problems, they won't do it
i have been trying to keep to 10ish
don't kill me... my largest class is 22
18-22
S: so, 9-11 groups
me: generally
S: lets say you pick 5 of the HW problems - assign each one to 2 groups (so they have a built in "check").. they work on the whiteboard, put on the chalk tray
could even ask each group to briefly explain the problem?
gives them some public speking practice too
then can move on to the new lesson
me: totally skip warm up? go straight to this?
S: then you aren't creating warmups
this would be both
me: may be worth a try
S: review of last night and warmup in one
now as for assigning.. could do randomly as they walk in... could post the 5 problems and they sign up?
me: so... what if i want to keep them doing the state test problems?
S: are the state test problems general review or do they go w/ the lesson?
me: i like the sign up idea but have to make sure they stick to only 2 pairs to a problem/can't switch out someone involuntarily
S: on the state test problems, I would probably put a timer on the board too - that sems to light a fire under some
me: i have a few jokers who might try that
me: state probs are generally review - not usually correlated to lesson (although sometimes I try to put something we recently did when i see it). usually i just start picking problems from a certain year's test. this year started with 2009 released questions and then moved to 2008 when i finished '09
S: are they pretty good about doing them?
me: no
a few are, but most of them don't do anything about them until i am ready to survey them on their answers
when i force them to do it on a 1/4 sheet, they do them, but again, slow starting
S: is your HW from the book or on a worksheet?
me: depends
both
boy do i really feel like i suck as a teacher right now
S: if its part of your HW, then it could be one of the warmup problems?
gosh no! if you sucked, we wouldn't be talking about this
me: it's not usually part of the hw, however, if i go to no textbook next year, could be part of hw
S: when is the state test?
me: it was last week
(yes, i know that makes no sense... test them 8th-10th grade at mid-march of 10th grade year)
S: that's right
then it would be okay to try something different for now w/ warmups
me: yes
S: and next year put them on the HW
me: i've been bringing in act practice problems on testing tue/thu
S: I think after spring break is a great time to try something new though - let you see if you like it before committing to it next year
S: okay, so moving on to the new lesson part... how active are the kids during that?
me: not very
S: so they fill in the notes and copy down the problems you work?
me: i am way too laid back - i don't tend to make them raise their hands.
i know i should. but i like the conversational bit as opposed to having to call on them. less formal.
some do. some just watch
S: i dont make them raise hands either
me: depends on which class. my classes with the "better" students tend to fill in notes/copy what's on the board. the ones with "weaker" students have a larger group that just watch
nice to know i'm not the only one
my advanced alg 2's tend to ask more questions. i have a couple of pretty ditzy freshmen girls who ask a ton of questions - but they do get it
sometimes it gets really annoying because i just answered the question and they just slightly change the question for the same result
S: so during this time do they try any problems on their own?
me: i haven't been having them do that
it goes back to the question i asked you earlier - how many do you show them before having them try?
i guess if i only showed them one and had them try it, they would have to work on figuring it out more on their own
S: one
me: but i am also afraid that if i did that my lower students wouldn't even try - if they didn't understand the first example, how could they try it on their own type thing
even in alg 2? i can see that ap stat would have a different caliber kids
S: yes in alg2
stat is a whole different ball game
me: i don't mean to be a pain. i am just trying to work through what my reality is
S: i'm thinking alg2/geometry here
me: i see how these kids have been so dependent/clueless
some of them are FINALLY coming around and making good progress but the lowest ones are still stuck
S: i tell them to try it - work w/ their partner.. and all i've done is change the numbers
me: not a lot of parent involvement here - this year i had my lowest number of parent conferences in 20 years
also got the poverty issues going on here too
me: so glad you "get" me
can't just have this conversation with anyone - or twitter at large
S: i understand some things are not for public consumption
me: although it could be an interesting twitter at large convo
not sure i want to go there tonight though
S: probably not since its still a work day for you tomorrow
me: geom lends itself to discovery so much easier than alg
S: yes
but I was trying to find a copy of guided notes and show you how I did indepedent practice within a class
me: i understandwhat did you have on the board then? the filled in parts for the defs/thms?
S: yes, I had a PPT that matched it
I am on my netbook, but I can send you a typical lesson tomorrow
I never did guided notes in alg2
me: i'm just starting them
i do like them - i think it makes a difference, even though it goes against the "they need to take responsibility so they can do all right in college" part of me
S: I liked the guided notes in geometry
and they used their notes
but in order to do them, I had to be very organized and prepared w/ the copies
no putting together PPTs the night before
Now, I will be honest, this is a little difficult to put out in the blogosphere. I feel as if I am at a very exposed moment here. I do a good job of explaining the mathematics to my students (or at least I'd like to think so), but my class is very traditional. And I know it's not working well. I need to make changes and I'm not sure where to start or how to change things. It's like there there is so much to change - where do I start? It's very overwhelming. I think that @druinok has some good suggestions and I will probably incorporate them.
So why am I putting this out there? I think there are other teachers who are in the same place I am and feel as I do. Maybe it will help them. Maybe some of you have some of the same thoughts (or have been there) and have some practical suggestions for me. But I think that there are some good nuggets here and it's worth having it out there for others to read and possibly add to. Feel free to add to the comments. I'm sure this is to be continued...
So, as a follow up to yesterday's questions/ponderings about how to get students to practice more, here are some excerpts of a conversation that @druinok and I had:
S: But part of the problem is on a practice day, how to make them do the practice
S: I pretty much stopped giving worksheets like that and do it other ways instead
me: ..But I don't know all those things. Where do I find them?
S: Speed dating is from Kate's blog
me: However, it still doesn't address the other issue - if you weren't planning on having a "practice day," how do you make sure they practice?
me: I know speed dating. I can't remember what other ideas I've seen.
S: You don't... the way I see it, the only way to ensure the practice is do it in class.
S: And I can say my kids were more willing to do a worksheet if it was a puzzle worksheet.
me: So you're saying I should build practice into my lesson? Maybe along the lines of what Jackie did? Her stuff looks to be discovery-based. Intriguing idea.
S: Yes... I build practice into the lesson... if I work them hard every day, the need for outside time should reduce.
S:And in order for them to practice more, I had/have to learn to talk less.
me: So how do you do that? How do you know how much direct explanation with examples to give before letting them try one? I usually give 2-3 examples of each "type" - easiest to hardest. Maybe I give too much. Maybe do one with the notes and have them try one on their own?
S: I've done that...
me: And then I assume you walk around the room as they are doing the one on their own. But then how do you avoid getting stuck with 2-3 students, each asking the same question as you walk around? I feel like I should know how to do this. I've taught for 20 years, for cryin' out loud!
S: I do walk around... when they raise their hand, I might say a word or two, but I don't linger.
S: I tell them to just try out... same as the other problem, just different numbers.
S: ok, so for practice...sometimes I will do a PPT with one problem per slide, put it up, walk around watch kids do it
problems are from worksheet then put up the answer or have kids go put an answer up for me
me: Is this after you've shown them how to do it?Same day or different day?
S: different day - as an alternate to giving a worksheet for them to practice
me: oh okay
S: part of the reason kids dont do a worksheet is proximity I think.. and being overwhelmed... one problem at a time and me walking around seems to curb both of those
me:: : makes sense
me: but, as i sit here on march 22nd feeling time pressured - i am still sitting here looking at, how do you teach something and ensure practice within a class day?
S: when teaching, I would do an example, then give another that was the same except for numbers.. they worked it, asked partner if stuck.. I walked around then we tried another that was a bit tougher
me: just to get through domain, vertical/horizontal asymptotes and holes of a rational function with my advanced alg 2 kids, it took me 2 days of class, and i could use another 10-15 minutes more. i did one example per part with fill-in-the-blank explanation and one addl example
S: now the downside of it was I focused too much on the "do" and not enough on the "why
me: which of course we have to focus more on the why now
... S: right
so assuming I teach alg2 next year, that is going to be one of my major things
S: my summer list is shaping up to be a major redo of alg2
but I would have the kids discover as much as I could...
me: i am starting to think that also
which would mean a major redo also
i've had crazy thoughts this week of not giving students textbooks next year and just giving note pages/problem pages
with common core changing things and our textbooks being 10 years old - maybe it makes more sense
S: I dont think that is crazy
me: i can't see buying new textbooks yet
i don't trust anything that says it's ccss yet - too quick to really be well thought out correlation to ccss
S: I tried to do discovery when I could - things like zeros, transformations, etc.. but I need to figure out how to do more
me: i need to figure out how to develop it in the first place - i've never done it before with my students
S: I want to do more activities like matching cards, etc... the kids respond very well to that
me: sometimes mine do, sometimes mine cop-out and don't really try with them
i really do like how the transformations ones turned out though
S: i want to work on engagment in general
me: with you on that
me: i may end up spending next year doing a major overhaul of how i do algebra 2 - i have taught it for 17 of the 20 years I've taught, so this will be major for me
S: we're gonna have a busy summer, huh?
here's the issue I see with common core though - we can't change alg2 until alg1 has been changed
bc quadratics are pretty much gone from alg2 based on what i've read... ?
me: yes
but i am certainly going to start. at least next year i'm not going to do much linear at all. i'm starting with quadratics i think.
S: we will still have our state tests that have systems on alg2, so I dont think we'll get to do that yetI hope I know soon if I'm teaching alg2..
me: it all depends on how much the alg1 teacher gets through where i'll startbut i am DEFINITELY not starting with solving linear equations in one variable.
S: agreed 100%
i would really like to get to a point where I start w/ an engaging problem and it sparks an exploration
me: maybe someday
... S: yup
but how to fix your issue right now is where we need to focus
tell me how a class day is structured
me: warm up - which they don't do until i get to the board
go over any questions from yesterday's problems, which are getting fewer since they aren't doing outside practice
new lesson
if time, start on practice problems. usually about 10-15 minutes if i'm lucky
very traditional
when i do something other than worksheets - speed dating, the thing i did yesterday, more tend to do it than not
giving them a worksheet and tell them to have at it doesn't work
although with being out 3 of the next 4 school days, they're getting worksheets. not much more of an option with a sub
S: I never liked the hw questions part.. always seemed like a waste of time
don't know how to fix though me: i am really becoming resentful of that
S: resentful of what?
me: i have a few kids who will ask question about a problem who have not done the assignment and then i watch them and they a) don't pay good attention and/or b) don't write a thing down as i do it
i am resentful of making that time daily and it being abused
but you want to provide question time for the students who honestly want their questions answered
S: okay, so let's break it down from start to finishwarmup time - what do you think? do you like it? does it work for you?
me: yes and no
S: could it be done differently?
me: it does give me something to focus on (themes) although some days are getting tough now
S: do your kids work in pairs or groups?
me: i like that they were practicing state test questions twice a week if they actually did them
they are seated in pairs
i may not do the themes next year - just rotate what they're warming up on
i like the concept of it, but my students don't follow through
they sit and talk while i'm getting attendance
at this point in the year, that's hard to correct. trying to think of how i would do it better next year so they are more engaged
S: remember you could try some new stuff after spring break - tell them you are testing out some ideas for next year
me: i am thinking if they are not doing outside of class practice, they could pick up a worksheet as they come into class
S: I have an idea, but not sure
me: start on it.
it would have a warm up at the top, then the "lesson"
S: do you have mini whiteboards?
me: hopefully somewhat discovery
yes
S: what if each pair came in, got a whiteboard and a problem (could have several problems)... worked it on the whiteboard w/ their partner
it would be a review of previous day's work
then had them switch slates and "grade" a different groups board?
might have the same effect as the HW check
OR - do the problems fom the HW - they worked on their whiteboard, lined them up at the chalk tray for kids that had HW questions?
then you kill two birds w/ one stone
me: if i did the problem with a partner - how many problems?
i don't want to create a ton of work for me in set up
(i know that sounds really selfish right now, but i don't want to be creating 12 problems and have them blow off the doing/checking of the problems)
i feel so darn stretched right now.
i really need that spring break
S: maybe use the problems from Kuta?
I honestly would figure out a way to do the homework problems.. if they did the HW, they can copy it on the whiteboard.. if not, they can work it
how many HW problems do you assign?
me: varies
S: more than 10?
how big are your classes?
me: after teaching 20 years, i am still struggling with what the "right" amount is. i feel they really need to practice, but if i assign 20ish problems, they won't do it
i have been trying to keep to 10ish
don't kill me... my largest class is 22
18-22
S: so, 9-11 groups
me: generally
S: lets say you pick 5 of the HW problems - assign each one to 2 groups (so they have a built in "check").. they work on the whiteboard, put on the chalk tray
could even ask each group to briefly explain the problem?
gives them some public speking practice too
then can move on to the new lesson
me: totally skip warm up? go straight to this?
S: then you aren't creating warmups
this would be both
me: may be worth a try
S: review of last night and warmup in one
now as for assigning.. could do randomly as they walk in... could post the 5 problems and they sign up?
me: so... what if i want to keep them doing the state test problems?
S: are the state test problems general review or do they go w/ the lesson?
me: i like the sign up idea but have to make sure they stick to only 2 pairs to a problem/can't switch out someone involuntarily
S: on the state test problems, I would probably put a timer on the board too - that sems to light a fire under some
me: i have a few jokers who might try that
me: state probs are generally review - not usually correlated to lesson (although sometimes I try to put something we recently did when i see it). usually i just start picking problems from a certain year's test. this year started with 2009 released questions and then moved to 2008 when i finished '09
S: are they pretty good about doing them?
me: no
a few are, but most of them don't do anything about them until i am ready to survey them on their answers
when i force them to do it on a 1/4 sheet, they do them, but again, slow starting
S: is your HW from the book or on a worksheet?
me: depends
both
boy do i really feel like i suck as a teacher right now
S: if its part of your HW, then it could be one of the warmup problems?
gosh no! if you sucked, we wouldn't be talking about this
me: it's not usually part of the hw, however, if i go to no textbook next year, could be part of hw
S: when is the state test?
me: it was last week
(yes, i know that makes no sense... test them 8th-10th grade at mid-march of 10th grade year)
S: that's right
then it would be okay to try something different for now w/ warmups
me: yes
S: and next year put them on the HW
me: i've been bringing in act practice problems on testing tue/thu
S: I think after spring break is a great time to try something new though - let you see if you like it before committing to it next year
S: okay, so moving on to the new lesson part... how active are the kids during that?
me: not very
S: so they fill in the notes and copy down the problems you work?
me: i am way too laid back - i don't tend to make them raise their hands.
i know i should. but i like the conversational bit as opposed to having to call on them. less formal.
some do. some just watch
S: i dont make them raise hands either
me: depends on which class. my classes with the "better" students tend to fill in notes/copy what's on the board. the ones with "weaker" students have a larger group that just watch
nice to know i'm not the only one
my advanced alg 2's tend to ask more questions. i have a couple of pretty ditzy freshmen girls who ask a ton of questions - but they do get it
sometimes it gets really annoying because i just answered the question and they just slightly change the question for the same result
S: so during this time do they try any problems on their own?
me: i haven't been having them do that
it goes back to the question i asked you earlier - how many do you show them before having them try?
i guess if i only showed them one and had them try it, they would have to work on figuring it out more on their own
S: one
me: but i am also afraid that if i did that my lower students wouldn't even try - if they didn't understand the first example, how could they try it on their own type thing
even in alg 2? i can see that ap stat would have a different caliber kids
S: yes in alg2
stat is a whole different ball game
me: i don't mean to be a pain. i am just trying to work through what my reality is
S: i'm thinking alg2/geometry here
me: i see how these kids have been so dependent/clueless
some of them are FINALLY coming around and making good progress but the lowest ones are still stuck
S: i tell them to try it - work w/ their partner.. and all i've done is change the numbers
me: not a lot of parent involvement here - this year i had my lowest number of parent conferences in 20 years
also got the poverty issues going on here too
me: so glad you "get" me
can't just have this conversation with anyone - or twitter at large
S: i understand
some things are not for public consumption me: although it could be an interesting twitter at large convo
not sure i want to go there tonight though
S: probably not since its still a work day for you tomorrow
me: geom lends itself to discovery so much easier than alg
S: yes
but I was trying to find a copy of guided notes and show you how I did indepedent practice within a class
me: i understandwhat did you have on the board then? the filled in parts for the defs/thms?
S: yes, I had a PPT that matched it
I am on my netbook, but I can send you a typical lesson tomorrow
I never did guided notes in alg2
me: i'm just starting them
i do like them - i think it makes a difference, even though it goes against the "they need to take responsibility so they can do all right in college" part of me
S: I liked the guided notes in geometry
and they used their notes
but in order to do them, I had to be very organized and prepared w/ the copies
no putting together PPTs the night before
Now, I will be honest, this is a little difficult to put out in the blogosphere. I feel as if I am at a very exposed moment here. I do a good job of explaining the mathematics to my students (or at least I'd like to think so), but my class is very traditional. And I know it's not working well. I need to make changes and I'm not sure where to start or how to change things. It's like there there is so much to change - where do I start? It's very overwhelming. I think that @druinok has some good suggestions and I will probably incorporate them.
So why am I putting this out there? I think there are other teachers who are in the same place I am and feel as I do. Maybe it will help them. Maybe some of you have some of the same thoughts (or have been there) and have some practical suggestions for me. But I think that there are some good nuggets here and it's worth having it out there for others to read and possibly add to. Feel free to add to the comments. I'm sure this is to be continued...
Wednesday, March 21, 2012
Spring HW Blues
Spring fever has hit here and it is only the second day of spring. Our weather warmed up considerably last week and it felt more like May 15th than March 15th here. Of course, since the weather has warmed up, the students' focus has gone down. Yesterday, I had taught my Algebra 2s the last part of graphing quadratic equations, using the axis of symmetry to find the vertex. It certainly wasn't my most spectacular lesson. As I was getting ready this morning, I just had the sense that my students didn't do the 5 problems I assigned for practice. On the drive in, I had thought about doing a matching activity similar to what I had done with my Advanced Algebra 2 students when we did transformations back around Christmas. As I thought about it, if I gave them the equations and the graphs, I felt that enough of my students would just try to substitute the points from the graph into the equation rather than figuring it out as they would have to on their quiz Friday. I guess I just feel like my students are at the point right now they are looking for the easiest way to get through class rather than trying to do their best. I hate that feeling.
The more I think about it, the more I don't like how I am doing homework or practice problems, or whatever you want to call it. I don't grade it - I stopped grading it a couple of years ago when I switched to doing my version of Standards-Based Grading. I want students' grades to reflect what they know, not what (busy) work they've done. Even though their grades reflect what they know, I don't think they take the practice portion as serious as they should. When we do stuff in class, sometimes they practice well, sometimes they don't. For instance, today, students were fairly engaged. I had them get into pairs and work through 4 problems. I left it up to them whether they divided them so they each did 2 or whatever worked for them. The only answer I gave them was the vertex so students would have a mid-way check point. I walked around as they were working and checked their five points and let them know they were correct. I gave them a worksheet with additional problems to practice for homework after they were done.
The original plan for today was to have them work on the aforementioned worksheet in class and I would walk around and help students as needed. That's what I've done in the past when I know students would need additional practice - teach it one day, give a worksheet or other additional practice problems in class the next. That doesn't work anymore. Some students will do it in class no matter what - just like many of us did when we were in school. However, I am seeing more and more students not taking advantage of the class time to work or to get help. I know I need to make changes to what I do, but I just don't know what. I cannot keep coming up with these activities - I am stretched pretty thin right now and if I want to maintain what little sanity I have left, I need to make sure I have time that is not work/mommy related.
I know some people seem to think that the flipped classroom may be the answer - let the students watch the instruction piece at home on their own time and use the classroom time for practice/homework. I just don't see that being the answer. If that is the direction to head, classroom activities have to be more dynamic and engaging for students than here are x problems - do them in class. Plus with what is coming down the pike with Common Core, I just don't see that working.
So what do you do in class to ensure/motivate/encourage students to practice? It is hard to be successful in mathematics without practice. About the only thing I am certain of is to not make the amount of practice too long. Even though 4 problems may have been too short (time-wise) for some students, overall, today, it seemed like the right amount. Most of my students did complete at least 2 problems and some did do all four themselves. At least I know they actually did practice and talked with their partner and/or me to figure out what was going on, and I think that was a good thing. For some students, 2-4 problems was enough practice, but I suspect that for most of my students, they probably needed a little more practice. How do you get them enough practice?
The more I think about it, the more I don't like how I am doing homework or practice problems, or whatever you want to call it. I don't grade it - I stopped grading it a couple of years ago when I switched to doing my version of Standards-Based Grading. I want students' grades to reflect what they know, not what (busy) work they've done. Even though their grades reflect what they know, I don't think they take the practice portion as serious as they should. When we do stuff in class, sometimes they practice well, sometimes they don't. For instance, today, students were fairly engaged. I had them get into pairs and work through 4 problems. I left it up to them whether they divided them so they each did 2 or whatever worked for them. The only answer I gave them was the vertex so students would have a mid-way check point. I walked around as they were working and checked their five points and let them know they were correct. I gave them a worksheet with additional problems to practice for homework after they were done.
The original plan for today was to have them work on the aforementioned worksheet in class and I would walk around and help students as needed. That's what I've done in the past when I know students would need additional practice - teach it one day, give a worksheet or other additional practice problems in class the next. That doesn't work anymore. Some students will do it in class no matter what - just like many of us did when we were in school. However, I am seeing more and more students not taking advantage of the class time to work or to get help. I know I need to make changes to what I do, but I just don't know what. I cannot keep coming up with these activities - I am stretched pretty thin right now and if I want to maintain what little sanity I have left, I need to make sure I have time that is not work/mommy related.
I know some people seem to think that the flipped classroom may be the answer - let the students watch the instruction piece at home on their own time and use the classroom time for practice/homework. I just don't see that being the answer. If that is the direction to head, classroom activities have to be more dynamic and engaging for students than here are x problems - do them in class. Plus with what is coming down the pike with Common Core, I just don't see that working.
So what do you do in class to ensure/motivate/encourage students to practice? It is hard to be successful in mathematics without practice. About the only thing I am certain of is to not make the amount of practice too long. Even though 4 problems may have been too short (time-wise) for some students, overall, today, it seemed like the right amount. Most of my students did complete at least 2 problems and some did do all four themselves. At least I know they actually did practice and talked with their partner and/or me to figure out what was going on, and I think that was a good thing. For some students, 2-4 problems was enough practice, but I suspect that for most of my students, they probably needed a little more practice. How do you get them enough practice?
Saturday, March 17, 2012
A Small Success
Recently, I taught completing the square to my Algebra 2 classes. This has traditionally been something that they have struggled with over the years. I have always felt like I have explained it well, but it didn't tend to stick with them. Not long before I was about to teach it, Glenn Waddell had blogged about guided notes that he was implementing in his classes. I took his idea and modified it a little. I really want my students to be doing some of the writing of the notes. So, this is what I gave my students:
For the first example of each type of problem, I set up notes for them to fill in that explained each step. The pdfs below shows what my notebook slides looked like after the two class periods I taught completing the square. (If you look at the actual documents, things line up much better)
When I tested both my Advanced Algebra 2 students and my Algebra 2 students (who I did x^2 quadratics, not 2x^2, etc.), they actually did fairly well with it. I think that's the first time that's happened in my 20 years of teaching. In addition, when I got to rewriting quadratic equations into vertex form (using completing the square), they remembered how to do completing the square without too much cajoling. Yay!
I have continued to do these kind of notes with my all my Algebra 2 classes for each topic. I think they are helping them to better understand what we're doing. Thanks Glenn for the suggestion! Yet another reason why I love the blogosphere and Twitter - I have learned so much from each of you. Thanks!
For the first example of each type of problem, I set up notes for them to fill in that explained each step. The pdfs below shows what my notebook slides looked like after the two class periods I taught completing the square. (If you look at the actual documents, things line up much better)
When I tested both my Advanced Algebra 2 students and my Algebra 2 students (who I did x^2 quadratics, not 2x^2, etc.), they actually did fairly well with it. I think that's the first time that's happened in my 20 years of teaching. In addition, when I got to rewriting quadratic equations into vertex form (using completing the square), they remembered how to do completing the square without too much cajoling. Yay!
I have continued to do these kind of notes with my all my Algebra 2 classes for each topic. I think they are helping them to better understand what we're doing. Thanks Glenn for the suggestion! Yet another reason why I love the blogosphere and Twitter - I have learned so much from each of you. Thanks!
Thursday, March 01, 2012
Assessment Questions
Something else I am going to be revisiting is how I'm doing assessments. For the first 19 years of my teaching career, I did unit tests, sometimes with quizzes in between. This year, I teach 2-3 Learning Targets and then quiz - the most recent Learning Targets for feedback, the preceding 2-3 Learning Targets for a grade. Right before Christmas Break, I revised the feedback problems to "feedback or 5" - if students could show me they knew it, they could earn their 5 and were exempt from the problems on the next quiz, otherwise, they got feedback.
I have to be honest, I'm not happy with this system. I feel like I've lost instruction time. I spend more time than I'd like between reviewing and assessing. About a third of my students don't try anything on the feedback problems. However, when I surveyed my students, they liked having less concepts on a test. I'm not sure what I'm going to do next year, but I'm pretty certain that it's not going to be the way I did this year.
Lately, I've also been thinking about how assessment needs to be in class. I have always been a "given them a test to see what they know" person. With the revisions in testing coming from the Common Core, I have started to wonder about giving my students a task instead of a test for assessment. For example, when we did transformations in December, I had my Advanced Algebra 2 students do a matching activity in pairs. Could I count that as their assessment? Granted, I would need to modify it a little so they would explain why they matched the way they did, but could that count? If I'm going to use that as their assessment, do I allow them to use their notes? Can they talk to other groups? Should they even be allowed to do it in pairs? Normally when I give a test, students are not allowed to use their notes, books, or talk to other students. Does that change now?
I'm curious what you all think - please, if you will, address my questions in the comments. Thanks.
I have to be honest, I'm not happy with this system. I feel like I've lost instruction time. I spend more time than I'd like between reviewing and assessing. About a third of my students don't try anything on the feedback problems. However, when I surveyed my students, they liked having less concepts on a test. I'm not sure what I'm going to do next year, but I'm pretty certain that it's not going to be the way I did this year.
Lately, I've also been thinking about how assessment needs to be in class. I have always been a "given them a test to see what they know" person. With the revisions in testing coming from the Common Core, I have started to wonder about giving my students a task instead of a test for assessment. For example, when we did transformations in December, I had my Advanced Algebra 2 students do a matching activity in pairs. Could I count that as their assessment? Granted, I would need to modify it a little so they would explain why they matched the way they did, but could that count? If I'm going to use that as their assessment, do I allow them to use their notes? Can they talk to other groups? Should they even be allowed to do it in pairs? Normally when I give a test, students are not allowed to use their notes, books, or talk to other students. Does that change now?
I'm curious what you all think - please, if you will, address my questions in the comments. Thanks.
Going and Coming
February is over. Even though it is the shortest month by number of days, it certainly almost always seems to take the longest to pass. February is also usually when the teaching doldrums set in for me. This year was no exception, and I think it hit me even harder because of this goofy weather. It is March 1st as I write this and the only weather-related change we have had was a 2-hour delay on our first day back from Christmas Break. Last year at this point we had missed either 6 or 7 days due to weather (we ended up missing 8 days).
In spite of being in school more days and not having lost instruction days due to semester exams, I am about 2 weeks behind where I was last year. Part of it is due to the amount of review I have had to do with this group of students. Part of it is due to having to teach factoring from scratch. But I also wonder if part of it is due to the additional quizzing I'm doing. I really wonder that last part with my Advanced Algebra 2 students. I am over 3 weeks behind with them once I factor in that I didn't do matrices with them. I have polynomials, rational expressions/functions, radical expressions/functions, and exponentials/logarithms to do with them and I don't think we'll have enough time. After talking to the Pre-Calc teacher, I think I'm going to postpone polynomials. Of the remaining topics, it is the one I am most certain that the Pre-Calc teacher will go into more depth with them.
As the year is headed towards the end, I am a little apprehensive about our switch to the Common Core. We have been told we are to be teaching Common Core next school year. Although I am certain that next year's Algebra 2 students will have a stronger Algebra 1 foundation, since this year's Algebra 1 students weren't taught under Common Core, it will be a bit of a challenge to make the full leap to Common Core. Having said that, I do think we'll be able to get a decent start into Common Core. I have to look at Algebra 2 more in depth, but at first glance, it appears that all linear and some quadratic material has been taken out of Algebra 2 and put into Algebra 1 (or in some cases, 8th grade). My present thought is that I will end up starting with quadratics and try to fill in the gaps along the way. We'll have to see how things develop....
In spite of being in school more days and not having lost instruction days due to semester exams, I am about 2 weeks behind where I was last year. Part of it is due to the amount of review I have had to do with this group of students. Part of it is due to having to teach factoring from scratch. But I also wonder if part of it is due to the additional quizzing I'm doing. I really wonder that last part with my Advanced Algebra 2 students. I am over 3 weeks behind with them once I factor in that I didn't do matrices with them. I have polynomials, rational expressions/functions, radical expressions/functions, and exponentials/logarithms to do with them and I don't think we'll have enough time. After talking to the Pre-Calc teacher, I think I'm going to postpone polynomials. Of the remaining topics, it is the one I am most certain that the Pre-Calc teacher will go into more depth with them.
As the year is headed towards the end, I am a little apprehensive about our switch to the Common Core. We have been told we are to be teaching Common Core next school year. Although I am certain that next year's Algebra 2 students will have a stronger Algebra 1 foundation, since this year's Algebra 1 students weren't taught under Common Core, it will be a bit of a challenge to make the full leap to Common Core. Having said that, I do think we'll be able to get a decent start into Common Core. I have to look at Algebra 2 more in depth, but at first glance, it appears that all linear and some quadratic material has been taken out of Algebra 2 and put into Algebra 1 (or in some cases, 8th grade). My present thought is that I will end up starting with quadratics and try to fill in the gaps along the way. We'll have to see how things develop....
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