Sunday, April 29, 2012

My Diigo Bookmarks (weekly)

Posted from Diigo. The rest of my favorite links are here.

Tuesday, April 24, 2012

Review Worksheet Twist

I decided to give my Algebra 2's one more review day. After some deliberation, I decided to give them a review worksheet - partially because they would have a copy of all the problems I wanted them to practice so they could practice on their own, partially because I didn't feel like trying to put together another review activity for them that they wouldn't put a whole lot of effort into. On the way in to work, I came up with a plan that I hoped would help get questions answered. I think part of this inspiration came from @druinok.

I handed out the worksheet and told the students I would project the answers on the SMARTBoard once I was done giving directions. They were to work on the worksheet problems and check their answers. If they were correct, they were to continue working on problems. If they were wrong, they were to try to figure out what they did wrong and fix it. If they couldn't figure it out, they could check their notes or with the neighbor, or they could find the card with the worked out problem that was posted on my wall:

If they still were stuck and none of the above helped them, then they were to sign up for help:
I had them do this so that when there were several of them who needed help, I could keep track of who I needed to get to. I also told them to ask about one problem at a time so that I could help as many as possible and not have someone monopolize my time.

Did it work? Well, not as well as I would have liked. I did see several students going and checking their work against mine on the wall. I had a couple of students who just went and flat out copied what I had on the wall onto their work paper. I did not have a rush of questions that I had anticipated, which I'm not sure if that's good or bad at the moment. I suspect that it's not good because I don't think they took the work time as seriously as I think they should have.

I do like that the onus was on the students to check their work against something that was correct before asking questions. I was trying to get them to not only work on the problems but to figure out what they did wrong before automatically running to me with questions and this did help the students who took advantage of it. Would I do it again? Maybe not this school year - but I think it was helpful for those students who did the activity in the right spirit.

Monday, April 23, 2012

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?

Sunday, April 22, 2012

My Diigo Bookmarks (weekly)

Posted from Diigo. The rest of my favorite links are here.

Wednesday, April 18, 2012


I have generally been a calculator proponent as long as I have been teaching. I have been hot and cold on graphing calculators - for a while, all of our Algebra 2 students had them but in the last few years, we have backed off and required only our Advanced Algebra 2 students to have them. Part of this is financial (remember - just over 50% free and reduced lunch)and part of it has been to have our Algebra 2 students concentrate more on learning the content rather than learning the technology and letting the technology do it for them. I want to make sure students understand what the technology is doing for them and over the years, I have watched students pretty much just let the technology do it and not really get what's going on. But as far as (scientific) calculators, I've pretty much given my students carte blanche. I guess that I've always felt that by the time they're in high school, they should be able to do the operations and letting them use the calculators expedites the process. And as far as fractions go, at this point, it's just easier to let them use the calculator so that we can move past that there are fractions in the problem and do the problem.

As I have mentioned a couple of times, I am on a committee with both high school and higher education faculty that is working on lessening the number of students who require remediation when they enter college. We were talking about how students end up in the "remedial" mathematics classes and one of the college faculty made the remark that if a student couldn't multiply a 2-digit number by another 2-digit number by hand that he or she would automatically end up in the lowest class. In my mind, that seemed rather harsh, especially since calculator use is highly encouraged in our classrooms and have been since middle school. Why in the world would a 4th grade skill automatically preclude a student from progressing to a higher level math course when technology is so readily available and expected to be used? So, I asked. The college faculty member replied that it has to do with transferring from numeric to algebraic. If a student can multiply a 2-digit number by another 2-digit number, he or she can use the same process to multiply a binomial by a binomial - it is the same process. It has to do with number sense.

Later in the meeting, a different college faculty member made some of the same points. (He didn't come in until later in the day, so he had missed the earlier comments.) He mentioned fractions, signed numbers, and decimals as the basic skills that students should have and that students needed to understand the concepts behind them. Like with multiplying, these are concepts that resurface in mathematics. I have certainly seen this as we have worked with rational expressions. If students don't understand how to work with numeric fractions, how are they going to transfer that to algebraic fractions?

So now I am sitting here this evening starting to rethink calculators. On the one hand, I have students who have struggled with basic facts and are (mostly) able to work with algebraic concepts using the calculator to handle the computation. But am I doing my students a disservice by providing them the calculator? What if I didn't allow them calculators at all at the beginning of the year and tried to remedy the issues that came up? Would I even get anywhere? Maybe what makes more sense is as I am introducing the concepts that tie into those earlier concepts - introducing multiplying polynomials, for example, that I begin with the number sense concept that preceded it. It would take some research on my part - although with the Common Core State Standards, the progressions have been fairly well-documented. By taking the time to (briefly) review the numeric concept, maybe students would have a better handle on the algebraic concepts. It's a thought. I need to think a little more on this one.

HS/HE Conference

I need your help, dear readers. I am on a committee that has 4 school districts and 3 institutions of higher learning represented. Our task is to facilitate the closing of the gap between high school and higher education. In Ohio, 41% of students entering college need to take either remedial Mathematics or English courses. One of the things we are looking at is putting together a conference (probably on a Saturday) that would bring together high school teachers and higher education faculty. I'm not sure what it's like where you are, but there is very little contact between high school teachers and the content faculty in higher education.

So, this is where you come in... If you were attending a conference with higher education faculty and had the opportunity to be in sessions with them, led by them, led for them by high school teachers, what would you want to see in sessions? What types of sessions? What would be interesting to you? What would help promote conversations between high school and higher education faculty? By the same token, if you are a higher ed person reading this, what would appeal to you? Ideally this would lead to something with some sustainability. Please comment with any thoughts you have - I'm just looking for ideas right now. Thanks so much!

Sunday, April 15, 2012

My Diigo Bookmarks (weekly)

Posted from Diigo. The rest of my favorite links are here.

Saturday, April 14, 2012

Flowers in the Garden (follow up)

I did go through and do the Flowers in the Garden activity with my Algebra 2 and Advanced Algebra 2 students on Friday. It is based on Ghosts in the Graveyard from Math Tales in the Spring. I felt that it went better than it did with my first class on Thursday. Students had a better idea of what they were doing. I had put 2 problems per card instead of three. They earned a flower for each problem they successfully completed, rather than the whole card. I think that kept them moving, plus since they were adding and subtracting rational expressions, each problem took some time. If I do this one again, I think I would only put one problem per card if they take that long. In my Advanced Algebra 2 class, it was actually good to see that the team who completed the most wasn't the winner - I like that each "garden" got assigned a random number of points. Rather than do 25, 50, 75, and 100 points, I did 1, 2, 3, or 4 points. I think this activity works better if the students have a pretty good grasp on what they're doing. If they don't have much of an idea, it's harder to keep them moving.

In my Advanced Algebra 2 class, there were a couple of students who commented that "Mrs. Henry has the best games ever" or something along those lines. It was gratifying that they enjoyed the activity and seemed to get something out of it. I have to remember that even though they will do the work outside of class or the worksheet in class, they like to do these kinds of activities too and it's worth the effort to put it together for them. Just because they're compliant with what needs to be done to learn the material doesn't mean that they should get left out of the "fun" activities.

Thursday, April 12, 2012

Post Spring Break Blues

We have 37 days left with students (yes, I finally counted) and I'm real concerned on how the rest of the year is going to go. We returned from Spring Break yesterday and I started into adding and subtracting rational expressions. I did the guided notes thing I've been doing and I really felt like the lesson didn't go well. I had planned on doing the Ghosts in the Graveyard activity to have students practice and after my first class, I scrapped it until tomorrow. I called it "Flowers in the Garden" because it's spring and I used post-it flowers instead of ghosts. I had put 2 problems per card and most groups only got through 2 problems in about 30 minutes. They had no clue. For my second and third classes, I gave them the Pizzazz worksheet I planned to do tomorrow and sat down with some students for some one-on-one (or small group in some cases) tutoring. Their work ethic (as a whole class) pretty much sucked.

After some reflection, there are a few conclusions I have reached:
1) I think I could have better designed the lesson and set up the examples better. I do like how I started out the lesson, but I am going to revisit what examples and in what order they are in. Here is my note page - feel free to offer comments.

2) It is harder to get students to put forth effort in class when you haven't been doing it all year. When I set up smaller group activities (here is what I have tried in the last few weeks), I still have students who blow it off, but for the most part, they are more engaged. When I went back to a worksheet today, maybe a third to half worked on it, but of that group, not all of them stuck with it. Less structure at this point means less effort.

3) It takes a lot of work on my part to set up these activities. @druinok's post on practice has been a big help in giving me some ideas of what to try. However, it takes some significant work to set up these activities. I know that once I've done it, I have them and can use them again. However, I am incredibly busy both inside and outside the classroom and I feel like my energy and time to put this stuff together is waning fast. (I'm on two different committees for work and both have me out of the classroom on the average of once a week between late March and mid-May, not to mention all the other stuff going on in my life.) I wish I had half the creativity that my fellow blogging math teacher do with coming up with these practice activities. I am happy to use what they have shared, but I'd love to come up with something myself.

4) I really feel like I am busting my can and my students don't care/appreciate it. It's not like I went into teaching for the recognition, but sometimes it would be nice to see genuine effort and to overhear comments like "that was fun" or "I learned that better" or something positive rather than comments that could very well be sarcastic. One of my students after one of these activities (and I can't remember which one) made the comment on the way out the door "that was fun" and from his tone, it was difficult to tell whether it was sarcastic or serious. When I asked him, he said "both" and added that he did learn something during that class period. It's not like I live for positive comments from my students, but I could really do without the sarcasm. It's hard not to take it personally when I spent a lot of time getting the activity set up in the hopes that they would actually practice and learn the concept since other methods weren't working.

Well, what's next? Next week I am out Monday and Wednesday (scheduled doctor's appointment and committee meeting, respectively). I would be ready to begin solving rational equations on Monday, but since I won't be there, @druinok suggested that maybe reviewing how to solve equations with fractions in them without a calculator would be good practice. This is the worksheet I came up with:

On Tuesday, hopefully they'll be ready to go with solving rational equations and it won't be so horrid. Since I'm out again on Wednesday, I am going to have a practice Pizzazz worksheet for them, We'll see how that goes.

Sunday, April 08, 2012

My Diigo Bookmarks (weekly)

Posted from Diigo. The rest of my favorite links are here.

Friday, April 06, 2012

How Much is Enough?

When I first started teaching 20 years ago, I was happy that my textbook had a guide to let me know what problems (and how many) to assign my students. I had no real idea how much was enough. Of course, at that point, most of the assignments were like #1-39 odd. I learned that it was a good idea to look at the problems before just assigning #1-39 odd carte blanche.

Fast forward to now, 20 years later. Assigning 20-30 problems a night doesn't work. I'm struggling to get my students to complete any outside assigned problems at times. So, as I was mowing the lawn today, I was wondering, how many problems is enough practice? Can you put a number on it? What practice do you assign on a regular basis? I look forward to reading your comments.

Thursday, April 05, 2012

Common Core Concerns

I am starting to become concerned about teaching Common Core next year. After having done the Gap Analysis between what I currently teach and what I will be teaching, there is a lot that I haven't taught either in a few years, or ever. It's not that I am concerned about teaching it - I am pretty flexible, content-wise. I am concerned with how my students are going to adjust to the new expectations.

My Advanced Algebra 2 students had a quiz Wednesday. Rather than knockin' it out of the park, there were a lot of ground outs, and some pretty ugly ones too. These are supposed to be the best of my current students and lately, they've been pretty awful with their work ethic and drive.  As we were working through the review colored folders, I could tell that they have not been putting forth the effort to really learn the material until before the test. They were asking questions and as I was listening to their questions, it was apparent to me that it was as if they were learning it for the first time. They did not seem to have much recollection of the lesson and even though they had their (guided) notes they had filled in, it seemed like some of them didn't know how to follow them. How is it that my "brightest" students can't figure it out for themselves?

And as far as my "regular" students - their work ethic isn't stellar either. I've been struggling with getting them to even practice what we're learning as of late. Even though there have been improvements, it still isn't where it needs to be and I'm finding I'm doing a lot of work to set up in class practice.

I understand that there are going to be a lot of changes with Common Core. I am going to be teaching different things and I am going to need to approach it differently. Having said that, I feel rather unprepared for this shift. I get that we will need to incorporate rich problems/tasks into our classes. I am not sure how to go about doing this. Do I just put the rich task in front of them and say "Here it is - have at it?" I'm pretty certain if I do that most of my students will give up within 3 minutes. When do I incorporate these kinds of problems and tasks into my classes?

I am used to teaching the material in a certain unit, preparing some sort of review and then testing them on what they have learned from the unit. From what I can tell, I am still supposed to think of my class as being comprised of units. How does my day-to-day business of teaching change? What is it that I will need to be doing differently? How will my assessments change? Will I be giving projects or tasks instead of traditional end of unit tests? Or will it be a combination of traditional unit tests infused with projects or tasks? How do you really determine if a student knows the material if he or she is working with other students? What about using resources to help them along (notes, the internet, etc.)? I've been mainly of the mindset that students have to be able to recall the information, but in the "real world," they'll use Google and others to help them figure out the solutions to whatever problems their work presents. How does that fit into how I assess? I know I've posed some of these questions before, but I still feel like they, and many more, are unanswered.

I can't say that these changes are necessarily bad. It will certainly step up the rigor and, given time, I think that our students may enter college more prepared than they are now. But there are going to be some growing pains, and I think they will be huge. When we changed currciula in Ohio 10-11 years ago, there was grumbling then that our students weren't going to be ready for the "rigors" of the new curriculum. I think what happened is that most of us continued to teach what we have been teaching and made the indicators fit what we were doing. (For those of you not familiar with our standards - we had indicators at every grade level and there was never any specification what got taught in what course.) Given that we are going to have assessments that reflect the course structure from the Common Core, we won't be able to do that again. We will have to adjust what and how we teach. I am really hoping for some guidance as we shift.

Wednesday, April 04, 2012

Practicing in Class Update

Over the last few weeks,  I have been complaining about my students' lack of practice and being able to work on their own. I did want to give a quick update, but first I need to give a shout-out to my great twitter friend @druinok for her blog post on practicing that she put together after my complaining. I have tried some of her suggestions and I am grateful to have had a one-stop resource to start looking for ideas.

My Math 1 students had a test today and I used the colored folders activity from Mrs. Graham's Math with them on Monday. I took some 12" x 12" card stock and cut it into 4 6" x 6" squares and wrote review questions on them. Each color had the same type of problems on them. With my Math 1 students, I put the answers in the folder they would get next so they wouldn't just copy the answers. I felt my students worked very well with this review activity. Almost every student was engaged and some of them were helping each other. This is my inclusion class and it allowed both me and the aide in class to get around and help students. My only complaint (and it's my own fault) is that some problem sets didn't take as long to do as others did, so there was a little too much down time. I think if the problem sets took around the same amount of time, this would work well. I did Speed Dating with them again (they did it before the previous test) and also did fairly well with it. The one thing I have found with them is they tend to take the problems they are comfortable with rather than challenging themselves to work with one they are not as sure of. Overall, it's been a successful week with them and I think I'll be looking to do more of these type activities with them.

My Advanced Algebra 2 students also had a test today. Instead of giving them a review sheet like normal, I broke it up and used the same colored folders activity I used with Math 1. I did put the answers in the same folder as the problems because they like to know they are correct as they are working on it. I think they were a little more engaged than if I had given them the worksheet to do the problems, however, their test scores today were not good. I'm trying to figure out if they didn't learn the learning targets very well when they were taught and it's catching up with them or if the different way of reviewing is the issue or what. More on that in another blog post, perhaps.

My Algebra 2 students did the notecard activity that Mimi blogged about on Monday - I had originally planned this for last Friday but didn't have time. We did a new lesson Tuesday and since today was our last day before Spring Break, I put together a relay activity similar to what @druinok mentioned in her practicing blog post. I set up 6 sets of cards and made duplicates so I had 12 sets of cards. I used the Random Word Chooser to have students choose partners (or in one class - 1 group of 3) and had them get whiteboards. Once they were settled, I explained the rules: They would each begin with a card (face down to begin) and work out the problem on the card. When they thought they had the correct answer, one team member was to bring the whiteboard up with their card and I would check it. If it was correct, they would get the next card. If it was wrong, they had to go back and fix it. (In most cases, I gave them a hint as to what was wrong to keep them moving along.) The first 6 teams to successfully get through their cards (I did 9) would get to pick a plastic egg from my basket (they all had candy in them).

At the start, most of my students were engaged. When they got stuck, some of them got really stuck. (The first 2 problems had GCF factoring in them -  I have no idea why they don't "see" it, but that's another story.) In all three classes, there were 2-3 groups that basically seemed to give up after struggling for a while with the problems and those groups got through maybe 2 problems each. However, most of the classes were engaged and working - and it was the last day before Spring Break!

Here's what I am struggling with: although I am seeing more students who are engaged with practicing the math when I do this in class, it takes a lot of work to set these up, even when I am taking problems from worksheets (and not creating them from scratch). I probably have about 2 1/2 hours invested in the set up of the relay activity. Right now, I don't have a lot of extra time to give to keep setting up these kind of activities. However, it does mostly pay off since the students are doing the math and seem to be somewhat enjoying it. I am still seeing an issue in terms of them not completing homework or worksheet/book problems. How do you get the students to realize that they still need to do outside work, especially now when the weather is nicer and we are getting near the end of the year? I'm not sure what that answer is right now.

Sunday, April 01, 2012

Unnamed (weekly)

Posted from Diigo. The rest of my favorite links are here.