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.

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. :-)

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?

Thoughts on Retention

Why is it so hard for students to retain information? I know this is a question that has been popping up for me almost daily as we are working through the rational expressions unit. Students have to factor as a part of the process and I still have students with issues factoring. There is multiplying binomial times binomial and they don't remember how to do that either. Both concepts I have taught this year.

I think I have some of the answer. It is in our culture of how we teach our students. My dad and I had a conversation about it. He shared with me his adult learning experiences and how he was more successful than other students who had just left college. My dad's approach involved asking questions and tying the new material to his experiences and prior knowledge. The students in the course who had recently attended college tended to "study" the material the evening prior to the test and memorize it. Their scores weren't as high as his.

@RobertTalbert tweeted a link to a commentary on the Chronicle of Higher Education's webpage that discussed why telling students to study for exams wasn't really a good idea. What David Jaffee is getting at is similar to what my dad shared: encouraging students to memorize for a test doesn't really help them to learn the material.

Jaffee says:

An indication of this widespread nonlearning is the perennial befuddlement of faculty members who can't seem to understand why students don't know this or that, even though it was "covered" in a prior or prerequisite course. The reason they don't know it is because they did not learn it. Covering content is not the same as learning it.

Then he proceeds to discuss why formative assessments are important to good instruction. Right now, in K-12 education, formative assessment is a buzzword. I only mention this because in the comments, it seems like it is an "utopian" ideas to the people commenting.

Now, I'm not here to debate or comment on what college faculty feel about this. However, I do see relevance to my own situation. I would have a better idea of where my students are at with a particular topic if I did some formative assessment (i.e. exit cards) on a regular basis. Students would have done at least one problem themselves in class and that may give them the confidence to do more on their own. It is not something I have done regularly enough in the past and I know I should do it more often (and I intend to).

As far as my lessons go, I guess this is the direction the Common Core State Standards are taking us. I have 2 units left this year - radicals and exponentials and logarithms. I am thinking I am going to try to set up my exponentials and logarithms unit as I should for Common Core. I have a little bit of lead time to do it, however, with it being my last unit of the year, I am a little hesitant (especially since student focus tends to decrease as the number of days left decreases). But I have to start somewhere and some time. No time like the present, right?

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.

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.