Monday, October 29, 2012

Transformations Unit

Last year, I shared the transformations matching cards I used with my Advanced Algebra 2 students. With teaching transformations for the first time to all Algebra 2 students, I have revamped my lesson and cards. Thanks are due to @druinok for her help in hashing out what I was doing with this unit.

I'm working with F.BF.3:
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

After discussions with both @druinok and our pre-calculus teacher, I decided to hold off on the f(kx) portion. @druinok shared that in her state, they don't do the horizontal stretches and compression in Algebra 2 and our pre-calculus teacher said that until you are working with a periodic function, the horizontal and vertical appear to be the same. So I will wait to bring in the f(kx) part until we get to graphing sine and cosine later this year.

I began very similarly to what Rebecka Peterson did by introducing parent functions to my students on day one. Here is what I gave my students:


(I don't know WHY the graphs keep showing up wrong, but they do. It looks right in Word but I can't get it to show correctly.)

It went way quicker than I anticipated - it only took about 20-25 minutes from start to finish. I haven't decided if in future years I will start into the notes following this or what to do to not leave so much open time on day one.

The second and third day, we worked through this packet:

 (Like the last one, still having issues with the graphs. Not sure why.)

The second day, we got through the first two pages of the packet. I had students work through the three graphs and descriptions and we did the summary piece together.

The fourth day, I had a meeting. I left an activity that their Algebra 1 teacher called "Around the World." I've done this as a scavenger hunt before. Here are the pages I used:

I had a brainstorm for my fifth day activity. I didn't feel real comfortable coming in after being out the day before and having them start into the assessment activity. So, after going over questions from the practice problems and the Around the World activity, I had students make "appointments" like in the Appointment Test Review activity that Mrs. H blogged about. Then I had students make up 1 or 2 equations for functions that they transformed (depending on how much time was left in class). The only guideline I gave them was that each equation had to have at least 2 transformations. Then, when they met with each appointment, they exchanged equations and had to find the transformations. This went pretty well for many students, although some still had some difficulty coming up with the transformations after they made up their equations. Most students went with two transformations. I collected their cards at the end of the period.

On the sixth day, I had students do the Transformations Matching Cards as their assessment for the activity. I had them work in pairs and allowed them to use the note pages. Rather than have them complete 5 sets like I had last year, I had them work through 3 sets. Students are matching pictures of the graph with the description of the transformations and the equation of the graph. I had students work with the five parent functions they graphed on the first day. Many of the equations came from what they generated on the 5th day. Here is the what I gave them:


They did very well with the assessment - I am sure part of that is that I allowed them to use their notes and their cards with the parent functions. Possibly next year I would allow them to work in partners but without notes, but still with the parent function cards. Overall, i am pleased how this unit went.

All of the files I used are shown through box.net - they are in docx format and you are welcome to download and adjust them as needed. If you are having trouble, feel free to email me at lmhenry9 at gmail dot com and I'll be happy to email you a copy directly. I hope this helps someone out.
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Sunday, October 28, 2012

My Weekly Diigo Links (weekly)

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Friday, October 26, 2012

The Current State of Teachers


I am not one to espouse politics or be "rah rah teachers" in public, but I have to say that I am getting sick of being put through the ringer. As I have been reading blogs and taking stock of my own situation at the moment, it seems pretty clear to me that most teachers I know seem to be more strapped for time and stressed than ever. I have taught over 20 years now and I am barely a day ahead in my planning. Even when I was a first year teacher, I don't think I was this close in my planning. I have noticed that many teachers who have been blogging a while have a lack of blog posts, or a lack of posts of stuff that is going on in their classroom. I'm guessing that this isn't due to the lack of great things going on in their classes, but rather from a lack of time to blog about it.

Teachers have been under fire in the media and by politicians for some time. Granted, there are some who have been fighting it publicly. but for the most part, you don't see teachers fighting it. I don't think it's because we are willing to accept the additional work and stresses and criticisms we have been placed under. I think it's because we are conscientious workers who honestly try to do the best we can for our students and because of that, we are busy trying to make sure we are doing the best possible job in our classrooms. And with the remaining time, we are busy trying to keep things afloat at home and in our own lives. It's not that we don't care and that we like being criticized - we don't. But we are just too busy trying to do the best we can to stop and comment.

I can't quite put my finger on why everyone is so busy/stressed/strapped. Is it because of Common Core? Well, not everyone is transitioning yet. Is it because we are all trying to be really awesome teachers and incorporating all of the great stuff we have found in blogs and on Twitter? Well, even my colleagues who are not reading blogs or tweeting are busy and stressed. Is it because we have had more stuff added to our plates? Possibly - I can say that is true at my school since we are doing more with less staff, but I'm not totally convinced that we have had that much added to our plates (but we have had stuff added). Is it because of increased family responsibilities? Maybe. Is it a combination of all of these things? Well, for me it is, but I'm not sure for everyone else. But something has changed this year.

I wish there was some way to promote, convince, make our case public or something. I think a lot of people still think that we have an 8 - 3 job and have summers off plus other vacations during the year and we have it easy. The reality is, we don't. I spend from 6:45 am until 3:15 pm in my school most days, plus usually at least an hour or two each night in planning or grading or researching for lessons as well as an additional 2-3 hours (minimum) on Sunday getting ready for the week ahead. I'm sure that many of you do the same. Don't even get me started about summer. Although we're not at school and working, I am still thinking about and reading and researching for my classes next year. Yes, I do get time off, but it's not as much as people may think. I think the worst thing for me this year is that I am stealing time when my kids are playing together (and not arguing or tearing the house apart) trying to get stuff ready for the next day or two. All of this adds up. It wears on your mind and eventually your body. It's a minor miracle that I haven't gotten sick yet this year - I'm just waiting for it to happen given the pace I have been keeping.

So, what am I going to do about it? Well, I guess I'm continuing to try to get more than 2 days ahead in my class planning. I keep telling that once I reach that point that I'll feel a bit more comfortable. Haven't gotten there yet, unfortunately. I'm going to try to do nice things for my fellow teachers, even if it's something as small as sharing a kind word or a small gesture. But beyond that, I can't really say what I'll do. I feel so helpless to get off this darn hamster wheel I am on. Try as I may, I just can't seem to get into the planning groove I have had in years past. I am striving to get there, but failing. So, I'll do what I know I can do: try to get ahead and try to be as positive as possible. Maybe at some point, I'll feel like I have the energy and the time to defend my choice of profession as we continue to be attacked. But for now, I am going to do what I know best: affect change where I can make a difference.
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Sunday, October 21, 2012

What a difference a year makes

I am going to be brief, but I have to say I am amazed at how well my Algebra 2 students did with functions so far. We had an assessment Friday over operations, composition, inverses, and piecewise functions (including absolute value). Traditionally for me, this has been a section that students have struggled with. I am pleased to share that they did well on their assessment. Most scores were 3's, 4's, and 5's - most of them in the 4-5 range. 

When I taught these concepts and checked how they were doing with it, they were doing fairly well. I was trying to figure out what was different - why they were doing so well. I know I shouldn't look a gift horse in the mouth, but I needed to know what went RIGHT after so many years of struggling. I can only pinpoint a few things:
  • this group of kids has been under the old curriculum a longer time (not buying this one... last year's group only had one less year and they did horrible)
  • I've been highly influenced by the Math Twitterblogosphere and I finally figured out how to explain it well. :-)
  • We had a different Algebra 1 teacher for the first time in 5 years.
In reality, I know that a good part of it is due to the 3rd bullet point. I'd like to think that I've made a lot of good changes since last year, but the reality is, the only major change I made was in how I did piecewise functions and maybe in some of the questioning and wording that I did of explanations. These students have come to me knowing much more than previous years' groups. Now, again, part of that may be that this group of kids may have had teachers who have taken the curriculum we were under seriously and pushed these students to learn the material well. But I think a good part of it is due to their previous teacher.

Their previous teacher was a first year teacher last year. Sadly, he is no longer with my district. He and his new wife have settled in a different area based on where she was able to find a teaching job and he was able to find a job closer to her. I totally get that - I was there once also (took me 5 years to get in the same place as my now-husband). Family has to come first. But I am still sad that he isn't my (direct) teaching colleague anymore. Now, don't get me wrong, he was not perfect. But, he did a great job with teaching the students I have now. His classroom management was quite good for a first year teacher. He held his students to high standards and they achieved them, and retained a good part of the information he taught them. Did they all remember the information right away? No, but with a little reminding, they remembered pretty quickly that they had been taught functions and they understood the notation. 

Quadratics are up next for us and I had hopes before finishing grading papers that I may be able to skip the multiplication of binomials and polynomials. I still have quite a few students struggling with it. However, I am confident with a little more practice, they'll get it again. It is amazing what a difference a year makes. A different teacher, who truly cares about teaching and teaching mathematics to the best of his ability, makes a considerable difference. I am hoping that his successor is as good of a teacher as this first year teacher was. I'll be curious to see how my former colleague develops as a teacher. I am confident that if he continues on the track he began as a first year teacher, he will be a great teacher. I am grateful that my students had him last year and that his students came to me well-prepared.
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My Weekly Diigo Links (weekly)

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Monday, October 15, 2012

Piecewise Functions

Piecewise functions have been something my students have always struggled with. They don't always get they are taking parts of the function and graphing them on the same graph. They'd like to graph the whole graph of all functions on the same graph or they don't have an idea where to get the points to graph. So, I am changing up piecewise functions this year based on some suggestions from the Math Twitterblogosphere.

The first thing I did was introduce piecewise functions via Mathalicious' Domino Effect lesson. (shameless ad - I've met Karim and had wonderful conversation with him. He and his company are doing some great things to help teachers. It is worth the money to subscribe and have access to the lessons. Go check it out. I'll wait. :-) ) I had used this at Hedge's suggestion - she had used it in her Algebra 2 classes to introduce piecewise functions.

On the second day, I adapted what Maggie has done with her PreCalculus students when introducing piecewise functions. She created an investigation where the students graphed the individual functions and cut out the pieces needed and put them together on a graph. What a great idea! Granted, right now we are working with piecewise linear functions, but the idea is fantastic. So, I took her idea and modified it to fit what we were doing with piecewise functions. Here is what I came up with:


I should add here that the graph is larger and has the printed axes on it - for some reason, I can't get it to show correctly when uploading to either box or scribd. If you want the file, try the updated post or send me an email at lmhenry9 at gmail dot com.

We only had time to work through the first two functions, We did the first one (mostly) together as a class, so that students would understand how to put them together. Once the first one was complete, we talked about what a piecewise function is and how it is created. We discussed the domain restrictions and why we cut out the individual pieces. On the second function, we talked about how to determine which x-values to use in the table and they walked through the process. When it came time to cut out the functions, students asked how to determine where to cut the graphs and we discussed the domain restrictions again. Here are some samples of what my students did:

When the kids returned on Monday, we went over the last question and discussed how to deal with the more open-ended domain. I then went over 2 piecewise examples with them without doing the formal cut-and-paste. With the remaining 20 minutes, I had students work on 5 problems in class. Most students got through all 5 problems and I was surprised that not only did they have very few questions on how to start, but that they were working successfully on the problems they attempted.

What a difference compared to previous times I have taught this concept! In the past, I have not even broached this topic with the regular Algebra 2 students, only the Advanced students, and even then, they have struggled with it. What a huge difference - students actually seemed to understand what parts to graph and to put it together on one graph. I am really pleased with how this turned out. Thanks Hedge, Mathalicious, and Maggie for all the great parts to this lesson!
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Sunday, October 14, 2012

My Weekly Diigo Links (weekly)

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Sunday, October 07, 2012

My Weekly Diigo Links (weekly)

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Wednesday, October 03, 2012

What would YOU do??

I have 4 sections of Algebra 2. My smallest section has 17 students, but it also has the largest gap. I have the brightest students in there - students who want to learn math, are enthusiastic about it, and do well with mathematics. They are extremely motivated. I also have students who are not very motivated, who complain I am going too fast (even though I am actually going at a much slower rate that I probably should be), and who are not as strong as other math students. The students who aren't as motivated actually seem to resent the students who do well and are motivated.

Although I do try to do grouping with them, unlike most of the students in my other classes, when the groups are of mixed ability, the students who struggle don't necessarily want help from the students who know what they are doing. We did a relay in class to review this week and I said that all students had to have the problem worked out before I would check their boards (and that I would be checking all of the boards) and I had students who would not even copy down what was on the other boards. Now, as a veteran teacher, I do recognize that is a two fold issue - not only is it an issue of not learning, it is now a discipline issue. I would like to deal with it from the not learning aspect rather than the discipline side first, with the hope that I can avoid the discipline issue.

Any suggestions? Please leave them in the comments. Thanks. :-)
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Monday, October 01, 2012

Change is Hard

(Warning - rambling and ranting ahead) I don't feel like I am a very good math teacher. I can explain the concepts fairly well so that many students understand it. I can structure the lesson so that it makes sense. But, I am pretty much a traditional teacher. I have made no bones about that here.

But then I start reading Mathematics Formative Assessment and we had a Waiver Day last week where a lot of the discussion was around formative assessment and now I feel like I suck as a teacher. As it is, I have been stressed and barely on top of stuff and it is extremely easy to revert to my old, established ways of just teaching and students watching, taking notes and then having to work out the problems.

During the Waiver Day, one of the speakers was talking about making formative assessment part of the daily culture of your classroom. I wish I could remember what exactly she said or what triggered the thoughts in my head, but I got to thinking that maybe I didn't need to do my lessons the same way each day. Right now, I still pretty much start with a warm up, go over homework problems, then teach the lesson. As it is right now, I don't have time to do an exit slip - I am pretty much filling the period. I want to do exit slips - I know I need to, and to be honest, I'd like to get to a point that I could try Socrative with my students. But if I don't have enough time in class to get to a paper exit slip, how am I going to have time to get to Socrative?

Another thing that was discussed, albeit briefly, was flexible grouping and differentiation. This is something else that I haven't done before and probably ought to be doing. It was presented to us as a part of using formative assessment to form the flexible groups. They didn't give us a ton of information about it, so I suppose that I will have to go do some research about it in my ever-growing shrinking free time.

One small good thing that I have done in the last week is I did put together a Google Form to survey my students as to what they know/remember about functions, which is our next unit. In the past, I have just taken for granted that they remembered (or guessed what they wouldn't remember) what was previously taught. I did do a pre-test at the beginning of the school year the last couple of years, but I wasn't happy with it. So, this is what I came up with while mowing the lawn Sunday:


(Hopefully this will continue to show up after my students are done with this)

I did like doing the pre-assessment this way. I very quickly got an idea after the first 5-10 responses where my students stood because I had a fairly good representative sample of students with varying abilities. What I did find out that they didn't know a whole lot about functions and function notation. I didn't ask them about the idea of one-to-one and based on what I saw in their responses, I'm pretty sure they don't remember much about it if at all. I am rethinking how I am going to teach functions. Originally I was going to start right at operations with functions, but I think I am going to have to spend a day reviewing what functions are beforehand. At least I know that now. :-)

Back to the original reason for posting... I still pretty much feel like I am totally sucking as a teacher. I am still pretty much teaching the way I was taught and the way I have taught for the last twenty years. I am looking at some of my students and seeing that they are not engaged. I already see a couple of my lower-ability students already not putting forth much effort and one in particular who is starting to become rather challenging - not participating in group activities and bringing down his group in the process, which happened today. He and I will have to have a conversation here shortly I can see.

I am looking ahead to functions and trying to figure out how I'm going to help my students learn the material. I wanted to type "teach" there, but as I was about to type it, I thought that if I said "teach," I already knew what to do. I know how to explain to my students how to work through the procedural stuff. But that doesn't help them learn the material. I'm trying to figure out how to help them learn the material. Me teaching and them sitting and getting isn't going to work. I have been telling myself that for 2-3 years now. The problem is, I haven't done anything about it. Compounding that, I don't really know what to do. What do I do differently? How do I structure class so that my students are learning and I am aiding them in their learning rather than imparting information to them?

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