I've had two or three blog posts started in my head, but then they fly off to wherever half-thought-out blog posts go. I'd love to figure out where that is.

The last two weeks have been okay at school. I think giving my students a review of the concepts being tested a couple days before the quiz is working. My students seem to be doing decently on their quizzes. The questions that are feedback only, they aren't doing as well. I guess I should qualify that - my (regular) Algebra 2 students aren't doing as well. My Advanced Algebra 2 students are doing okay on those portions - again, not perfectly, but strong enough that I feel that they got the concepts in the first place (for the most part).

In my last post, I was (and still am) pondering how to get my students more actively involved with math. I think they do better if they are involved in the mathematics and those of you who commented concurred. We are starting systems of linear equations in Algebra 2 - a concept they have not had before. The previous Algebra 1 teachers have not taught it - they have never gotten to it. When I looked at the suggestions I got from Twitter, I decided to go with an introductory activity from Kristen Fouss that had three problems set up in words. Students then figured out values for a table, graphed it, and came up with equations. They also answered questions about the information.

My Advanced Algebra 2 students worked through it Friday and my regular Algebra 2 students worked through them today. My Advanced Algebra 2 students did rather well with the problems, which I expected. They were able to come up with the equations successfully and were engaged with the material. My Algebra 2 students also were mostly engaged with the problems. Students tended to shy away from creating the graphs, especially in my second and third classes. Once my first class saw how the graphs worked, they were willing to try the graphs. They were also able to answer the questions (for the most part) and worked for the majority of the period.

So, what do I learn from today? I was very pleasantly surprised that my students were engaged with the material. I expected them to do the first and for their interest to wane as we did other problems. I guess I didn't give them enough credit. I hope that they feel like they got more actively involved in the mathematics. I definitely need to find ways to get them involved with math. I'm still not totally sure how to ensure that happens. Tomorrow we are starting with solving systems of equations by graphing. From their most recent quizzes, some of them are still struggling with graphing using slope-intercept form. I did put together a note page with the examples and graph spaces provided with the hope that students will complete the examples along with me. I'll have to see how that goes. I don't really want to get in the habit of providing them note sheets for each concept, however, if that will encourage them to take notes and engage somewhat with the material, it will be worth it.

Stay tuned...

## Monday, October 24, 2011

## Tuesday, October 11, 2011

### An epiphany, which leads to questions

Yesterday in my Algebra 2 classes, we finished the notes on graphing using slope-intercept form. As I have stated before, this particular group seems to have not absorbed much from their Algebra 1 experiences. I had assigned 10 problems for them to practice last night. My original intention today was to use the random word chooser in SMART Notebook (thanks Kate!) to choose a person, allow them to choose their partner and problem and have them copy their work for that problem from their homework and graph it on a graph whiteboard. I had intended to have students do a Gallery Walk after that. Oh, the best laid plans...

During my second class, it hit me. After having them work out the problem, I had given them a worksheet to work on (two of those lovely Marcy Math Works worksheets with the great puns) and had stopped to check on a group of 4 boys who really weren't working on the problems. I asked them why they weren't working and they said they didn't understand how to do it. So, we worked through 2 of them together, step by step. They continued working and I overheard one of them say something to the effect of "Now I get it! It seems so easy now!" Then it clicked in my head - many of my students aren't really actively involved as we go through the notes portion of the lesson. Some do copy notes down, but they don't know what to do with it.

It goes back to the Confucius quote: "I hear and I forget. I see and I remember. I do and I understand." My students aren't

I guess the bottom line of my realization today is how I am teaching my students isn't helping them learn or understand the material. I guess I kind of knew that but I am now stuck in trying to figure out how to change and adapt so that my students can have a better understanding of the mathematics I am teaching them. I know I can explain the material to them fairly well. How do I change what I am doing so they

**Very few**of my students did the homework. The ones who did were the ones who most likely took notes and/or got it pretty well in Algebra 1 and remembered it. Sigh. I scrapped the Gallery Walk portion, I spent most of the time they were working on their problem (which they*were*actually working on it) trying to help students who had no idea what to do or where to go from wherever they were.During my second class, it hit me. After having them work out the problem, I had given them a worksheet to work on (two of those lovely Marcy Math Works worksheets with the great puns) and had stopped to check on a group of 4 boys who really weren't working on the problems. I asked them why they weren't working and they said they didn't understand how to do it. So, we worked through 2 of them together, step by step. They continued working and I overheard one of them say something to the effect of "Now I get it! It seems so easy now!" Then it clicked in my head - many of my students aren't really actively involved as we go through the notes portion of the lesson. Some do copy notes down, but they don't know what to do with it.

It goes back to the Confucius quote: "I hear and I forget. I see and I remember. I do and I understand." My students aren't

*do*ing. They are hearing and seeing and it isn't sticking with them. How do I get them to the*doing*stage? I could certainly give them copies of the slides with a space for them to take notes, but that doesn't necessarily help them, does it?

I guess the bottom line of my realization today is how I am teaching my students isn't helping them learn or understand the material. I guess I kind of knew that but I am now stuck in trying to figure out how to change and adapt so that my students can have a better understanding of the mathematics I am teaching them. I know I can explain the material to them fairly well. How do I change what I am doing so they

*do*and eventually*understand*?## Saturday, October 08, 2011

### Giving it away

Thursday I did the Dan Meyer Stacking Cups activity with my Algebra 2 classes. My intention was to give some motivation to linear functions, plus it's a fun activity and it would get them thinking. Or so I thought.

My first two classes did a nice job with the activity. Of course there was some playing around with cups and what not, but the pairs came up with good guesses and we had a nice discussion about them afterwards. I specifically told my 1st two classes to not tell the answer to my later classes and my first class honored that rather well. By the time I got to my last class, I knew something had to be up since there were about 4 pairs that had an answer rather quickly. The activity went rather poorly since they seemed to think they had a correct answer (which some did and some didn't) so they weren't engaged with the activity at all.

In the discussion phase, it did come out that two of my 2nd class students had told the answer to another student in the last class. They had blatantly volunteered the answer without even being asked about what we did. It totally ruined the activity. I wasn't in school Friday to talk to the two students about this and I was still trying to figure out what I wanted to say to them. The two students are both 9th graders - they took Algebra 1 in 8th grade but did not take the advanced class (I can't remember if it was because they weren't recommended or that they just chose not to). Both young people are pretty bright. Not having talked to them, I would guess that they were just being smart-aleky freshmen boys and trying to be better than the teacher.

After reading this post by @hillby258 at "Math is a Shovel" - it really clicked in my head why what they did ruined the activity. These students robbed my last period class of having the experience of figuring it out for themselves, of having the satisfaction of coming up with the correct answer on their own. But then I asked myself, how is my providing students the answers to their practice problems any different? If I am giving them the answers to the problems at the beginning - what's different than those two students giving the answer to the Stacking Cups problem? At the moment, I think it's different because it's in a different situation - I am giving them the answers so they can make sure they are practicing the problems correctly, whereas Thursday students were given the answers to a singular problem they were to figure out on their own with little information (but enough) provided.

And I'm also asking myself how can I continue to try these types of activities with my classes to provide context to the mathematics? There are students who are volunteering the easy way out to others and robbing them of the journey to get there. I have students who have little desire to go on the journey. How do I proceed with a similar task for my classes? I really felt it went well with one of my classes, okay with another one, and not well at all for the other class. I don't want to rob my students of the experiences of seeing the mathematics in a different context - not in the "here's the math - do the problems" structure of class. I thought I had made clear to my earlier classes in the day why it was important to not share the answer - and it was followed by all by two students, who wrecked the activity for my last class. How do I keep that from happening again? Or better yet, how do I adapt so that I deal better with it if it does happen again?

My first two classes did a nice job with the activity. Of course there was some playing around with cups and what not, but the pairs came up with good guesses and we had a nice discussion about them afterwards. I specifically told my 1st two classes to not tell the answer to my later classes and my first class honored that rather well. By the time I got to my last class, I knew something had to be up since there were about 4 pairs that had an answer rather quickly. The activity went rather poorly since they seemed to think they had a correct answer (which some did and some didn't) so they weren't engaged with the activity at all.

In the discussion phase, it did come out that two of my 2nd class students had told the answer to another student in the last class. They had blatantly volunteered the answer without even being asked about what we did. It totally ruined the activity. I wasn't in school Friday to talk to the two students about this and I was still trying to figure out what I wanted to say to them. The two students are both 9th graders - they took Algebra 1 in 8th grade but did not take the advanced class (I can't remember if it was because they weren't recommended or that they just chose not to). Both young people are pretty bright. Not having talked to them, I would guess that they were just being smart-aleky freshmen boys and trying to be better than the teacher.

After reading this post by @hillby258 at "Math is a Shovel" - it really clicked in my head why what they did ruined the activity. These students robbed my last period class of having the experience of figuring it out for themselves, of having the satisfaction of coming up with the correct answer on their own. But then I asked myself, how is my providing students the answers to their practice problems any different? If I am giving them the answers to the problems at the beginning - what's different than those two students giving the answer to the Stacking Cups problem? At the moment, I think it's different because it's in a different situation - I am giving them the answers so they can make sure they are practicing the problems correctly, whereas Thursday students were given the answers to a singular problem they were to figure out on their own with little information (but enough) provided.

And I'm also asking myself how can I continue to try these types of activities with my classes to provide context to the mathematics? There are students who are volunteering the easy way out to others and robbing them of the journey to get there. I have students who have little desire to go on the journey. How do I proceed with a similar task for my classes? I really felt it went well with one of my classes, okay with another one, and not well at all for the other class. I don't want to rob my students of the experiences of seeing the mathematics in a different context - not in the "here's the math - do the problems" structure of class. I thought I had made clear to my earlier classes in the day why it was important to not share the answer - and it was followed by all by two students, who wrecked the activity for my last class. How do I keep that from happening again? Or better yet, how do I adapt so that I deal better with it if it does happen again?

## Tuesday, October 04, 2011

### Math Scavenger Hunt

So what I did today was set up a scavenger hunt of sorts for my Algebra 2 students. I wanted students to spend time working through the problems and comparing answers with their partners and hopefully learn from each other. (Remember from the last few days that my Algebra 2 students are still struggling with solving equations properly.) I paired the students so that a stronger student was working with a weaker student. I gave each partner group a letter to start with. Around the room I had construction papers with an answer at the top and a problem below as you can see pictured here.

Each pair began with the letter that I gave them and then worked their way through the problems. I had students work out the problems on my

As each class worked through the problems, each had its own character. My first class worked at their seats in pairs. They did not get up and move around to each problem. I think this group did the best job of working in pairs and helping each other. This class has truly been a pleasant surprise for me. I had many of these students in 7th grade and they have done quite a bit of maturing since then (especially the boys). They worked diligently throughout the period and I think they really got a lot figured out. My second class did a lot more moving around. They tended to move from problem to problem, which was more of my original thought when setting up this activity. However, of my three groups, this class worked in partners the least. I saw a lot more individual working out of the problems and much less consulting with partners. My third group, which is probably my lowest group ability wise (this class also has the largest amount of juniors - who are students who did not start with Algebra 1 as freshmen which is considered the "normal" path) actually surprised me. Although they were middle of the road as far as how well the partnerships worked - some worked well, others did not, they were engaged the whole way through the activity. When we did the test corrections yesterday, this was the group that seemed to do the least and it is also the group that has the fewest students doing reassessments.

I liked this activity because all three classes were engaged for the class period. Students were doing math and I think they feel better about their understanding on how to solve equations and inequalities. Next up are a couple of days with bringing in some word problems. Tomorrow, I have set up some number tricks (the ones where you start with a number, do several things to it and you are able to tell what number was the final answer) and we'll work through why the number tricks work.

I do need to give a shout out to @misscalul8 and @jreulbach for the inspiration for this activity - I think they discussed something similar to this back in April or May but I couldn't find where either had blogged about it. Thanks ladies for the inspiration!

**new**$12 set of (30) 12" x 12" whiteboards (thanks Frank Noschese for the directions on how to get them!) and had each pair record which order they worked the problems so I could check how they were doing on paper. By the third class, I had figured out that if I provided the paper with the first letter on it and the pair's name, it was quicker to get them started and then as they got through the problems, I kept the papers so no one could go and copy the order. A little further down the page on the right is one of the papers from my last class. Some of the groups decided to write the answer along with the problem which helped keep them on track. If they did it right, they would have worked through all of the problems without repeating any of the problems. I had intended to have 15 problems, but in my haste this morning, I managed to leave out the letter k and ended up with 14 problems. My larger classes had 12 pairs working through problems.As each class worked through the problems, each had its own character. My first class worked at their seats in pairs. They did not get up and move around to each problem. I think this group did the best job of working in pairs and helping each other. This class has truly been a pleasant surprise for me. I had many of these students in 7th grade and they have done quite a bit of maturing since then (especially the boys). They worked diligently throughout the period and I think they really got a lot figured out. My second class did a lot more moving around. They tended to move from problem to problem, which was more of my original thought when setting up this activity. However, of my three groups, this class worked in partners the least. I saw a lot more individual working out of the problems and much less consulting with partners. My third group, which is probably my lowest group ability wise (this class also has the largest amount of juniors - who are students who did not start with Algebra 1 as freshmen which is considered the "normal" path) actually surprised me. Although they were middle of the road as far as how well the partnerships worked - some worked well, others did not, they were engaged the whole way through the activity. When we did the test corrections yesterday, this was the group that seemed to do the least and it is also the group that has the fewest students doing reassessments.

I liked this activity because all three classes were engaged for the class period. Students were doing math and I think they feel better about their understanding on how to solve equations and inequalities. Next up are a couple of days with bringing in some word problems. Tomorrow, I have set up some number tricks (the ones where you start with a number, do several things to it and you are able to tell what number was the final answer) and we'll work through why the number tricks work.

I do need to give a shout out to @misscalul8 and @jreulbach for the inspiration for this activity - I think they discussed something similar to this back in April or May but I couldn't find where either had blogged about it. Thanks ladies for the inspiration!

## Monday, October 03, 2011

### Surprises abound

A surprising thing happened today as I had my students working on correcting their quizzes today. (See here for the original plan.) As my first period students were working on correcting my quizzes (and wanting me to answer questions as opposed to asking peers), several students asked to reassess. I had forgotten to say anything about wanting to re-quiz them on Wednesday and after seeing that several students were motivated to reassess on their own, I opted to not give a re-quiz to my Algebra 2 classes. For two of my three classes, my students were rather motivated and worked hard on correcting their quizzes. I think I have between 10 and 15 students coming in for reassessments between my three Algebra 2 classes (that's out of about 70 students). I am pleased to see them taking initiative.

I chatted with my principal during my planning period today. As I continue to reflect on my students' quizzes, I am really disturbed with the errors they made. These are things that should have been corrected/caught and fixed in Algebra 1. I had a brief discussion with my fellow math teacher with many years experience before talking to the principal and he is seeing the same things from his students (the ones I had last year in Algebra 2). It's as if the students aren't retaining what they have learned. As I talked with my principal, she made the point that they may have learned it wrong and continue to make the same mistakes because that's how they practiced it. This, for me, reaffirmed the importance of giving the students the answers when I give the practice problems so they can confirm that they are doing the problems correctly.

My principal is also about incorporating the real world where possible. As we discussed the situation, I expressed that I am almost afraid to put a real world situation in front of them, especially given what happened last week. It's almost as if my students don't know how to think. Put something even a little challenging in front of them and they freeze. But I also know that the real life situations can help motivate them. I started to look through the Math Forum Problems of the Week to see if I could find anything that caught my attention, but I didn't find anything right off the bat. I also looked at YummyMath but I didn't have a whole lot of time to dig through to see if I could find something that specifically had one variable equations. So, I'm still looking with a short time frame (for Wednesday!) to find something real world to help motivate solving equations.

I also have to figure out how to teach them to think - how to work with these types of problems. But I suppose that's a post for another day. For now, I'm off to bed. As always, comments are welcome and appreciated. Thanks for taking the time to read my ruminations. They help me sort through it all.

I chatted with my principal during my planning period today. As I continue to reflect on my students' quizzes, I am really disturbed with the errors they made. These are things that should have been corrected/caught and fixed in Algebra 1. I had a brief discussion with my fellow math teacher with many years experience before talking to the principal and he is seeing the same things from his students (the ones I had last year in Algebra 2). It's as if the students aren't retaining what they have learned. As I talked with my principal, she made the point that they may have learned it wrong and continue to make the same mistakes because that's how they practiced it. This, for me, reaffirmed the importance of giving the students the answers when I give the practice problems so they can confirm that they are doing the problems correctly.

My principal is also about incorporating the real world where possible. As we discussed the situation, I expressed that I am almost afraid to put a real world situation in front of them, especially given what happened last week. It's almost as if my students don't know how to think. Put something even a little challenging in front of them and they freeze. But I also know that the real life situations can help motivate them. I started to look through the Math Forum Problems of the Week to see if I could find anything that caught my attention, but I didn't find anything right off the bat. I also looked at YummyMath but I didn't have a whole lot of time to dig through to see if I could find something that specifically had one variable equations. So, I'm still looking with a short time frame (for Wednesday!) to find something real world to help motivate solving equations.

I also have to figure out how to teach them to think - how to work with these types of problems. But I suppose that's a post for another day. For now, I'm off to bed. As always, comments are welcome and appreciated. Thanks for taking the time to read my ruminations. They help me sort through it all.

## Sunday, October 02, 2011

### And the saga continues...

I have been in a posting flurry the last week (check here and here for the ones that will relate to this post). Here is the quick update....

I gave quizzes Friday in my Algebra 2 class - I graded the learning targets on solving and graphing inequalities, solving and graphing compound inequalities, and solving absolute value equations. I have not finished grading the quizzes - I still have feedback only to give on solving absolute value inequalities, determining if a pattern is linear, and finding slope. On the portions that I graded, the solving equations and inequalities was not looking good. I still have students trying to subtract the same quantity from the same side of an equation or inequality. There are other errors (not distributing well, computation errors, and dividing both sides by different numbers to name a few), but that one is the one that bothers me the most. I did some quick analysis and I found once I took the time to look that it wasn't as bad as I thought, but it's still not where it should be.

Here's my plan for the start of the week -

Tomorrow (Monday), I am handing back their quizzes. I will give them the answers as I have been doing, but before I do so, I am going to direct them to take 3-5 minutes and really read the feedback that I have given them. After giving them the answers, I have marked 6 students in each class as "experts" - there were 3 concepts, 2 quizzes so 1 student for each quiz on each concept (that means 2 experts per learning target). The remaining students I am going to direct to work on correcting their quizzes and if they are struggling, they need to see the "expert" for their trouble. I am hoping that this will get them really looking at their quizzes to see what they're doing and that the peer help will help get them in a better place with the material.

On Tuesday I am going to pair them up and set up a "scavenger hunt" type activity - answer at the top of the page, new problem to work on the bottom of it. Students will work on the problem and go find their answer to find their next problem. I am going to pair them deliberately - a student who has a stronger understanding of solving equations with a student who does not have as strong of an understanding. Each student will need to work out the problem. Hopefully this will help strengthen the weaker students while putting the stronger students in a mentoring role. I am going to mix equations and inequalities.

On Wednesday, I am going to give another quiz on the same learning targets (those students who have already mastered the learning target obviously will not need to redo) - my goal is two-fold: I want students to see what reassessing will do for them and I want them to feel some success (which I am hoping will happen!).

I really don't want to spend the extra time at the moment, but I feel that if I don't have 95% of my students with solid linear equation solving skills, I am going to have an incredibly difficult hill to climb with them. I'm really not sure what else to do - I have about 50%+ of my classes who don't have (in my opinion) a solid enough grasp of the skill, so we need to make sure they've got it. There are other issues I'm concerned with (mainly their lack of willingness to "think" and work at stuff), but this is the most pressing thing at the moment. I hope this is the right decision....

I gave quizzes Friday in my Algebra 2 class - I graded the learning targets on solving and graphing inequalities, solving and graphing compound inequalities, and solving absolute value equations. I have not finished grading the quizzes - I still have feedback only to give on solving absolute value inequalities, determining if a pattern is linear, and finding slope. On the portions that I graded, the solving equations and inequalities was not looking good. I still have students trying to subtract the same quantity from the same side of an equation or inequality. There are other errors (not distributing well, computation errors, and dividing both sides by different numbers to name a few), but that one is the one that bothers me the most. I did some quick analysis and I found once I took the time to look that it wasn't as bad as I thought, but it's still not where it should be.

Here's my plan for the start of the week -

Tomorrow (Monday), I am handing back their quizzes. I will give them the answers as I have been doing, but before I do so, I am going to direct them to take 3-5 minutes and really read the feedback that I have given them. After giving them the answers, I have marked 6 students in each class as "experts" - there were 3 concepts, 2 quizzes so 1 student for each quiz on each concept (that means 2 experts per learning target). The remaining students I am going to direct to work on correcting their quizzes and if they are struggling, they need to see the "expert" for their trouble. I am hoping that this will get them really looking at their quizzes to see what they're doing and that the peer help will help get them in a better place with the material.

On Tuesday I am going to pair them up and set up a "scavenger hunt" type activity - answer at the top of the page, new problem to work on the bottom of it. Students will work on the problem and go find their answer to find their next problem. I am going to pair them deliberately - a student who has a stronger understanding of solving equations with a student who does not have as strong of an understanding. Each student will need to work out the problem. Hopefully this will help strengthen the weaker students while putting the stronger students in a mentoring role. I am going to mix equations and inequalities.

On Wednesday, I am going to give another quiz on the same learning targets (those students who have already mastered the learning target obviously will not need to redo) - my goal is two-fold: I want students to see what reassessing will do for them and I want them to feel some success (which I am hoping will happen!).

I really don't want to spend the extra time at the moment, but I feel that if I don't have 95% of my students with solid linear equation solving skills, I am going to have an incredibly difficult hill to climb with them. I'm really not sure what else to do - I have about 50%+ of my classes who don't have (in my opinion) a solid enough grasp of the skill, so we need to make sure they've got it. There are other issues I'm concerned with (mainly their lack of willingness to "think" and work at stuff), but this is the most pressing thing at the moment. I hope this is the right decision....

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