Last week I had to stay after school for a 3-hour PD on Assessment. And as you can imagine it was not one of the things on the “to-do list” that I was looking forward to. But I am the kind of person who can ALWAYS get something out of a PD (bad or good). I am easily motivated and willing to implement changes in my classroom when I am convinced they will make a difference. That is, in fact, what made me choose Carnegie!!
Anyway, after the 3-hour PD was over I was already beginning to rethink the slope quiz I was planning on giving to my students this week. I knew for a fact that several students were still struggling with using the formula (because they had either not finished their assignments or hadn’t done them without the assistance of their friend’s papers) and I also knew that most of my other students were a little fearful of the threat I had given a few weeks ago that if they failed the quiz they would be staying after school for Extended School Services until they got it!!
So, I decided to do things a little differently this time. What if the quiz itself was actually a tool for teaching as well? What if the assessment was also a way to give my fearful students confidence and “catch up” the students who were behind….WHILE I got a clear picture of who gets it and who doesn’t? Why do I think a quiz always has to be 10 questions on a half sheet of paper?? Couldn’t assessment be MORE than that?
Here is what I did!! I typed up 7 different scenarios similar to the ones we have experienced in the text so far as a group ($8 an hour, US Shirts, Rent-a-Car, Moving a Sandpile, etc)….each of these on it’s own page. Also on each page were instructions to write an equation, construct a table, use two points to find the slope, graph, and find the x and y intercepts of their scenario. I handed each student ONE scenario so that no one would have the same one as anyone around them (that’s why I made 7). This way EVERY student had to do their OWN work. (I gave them two class periods to work so they could not take it home either.) I began to circulate and what I found was exactly what I thought. Some students finished their problem beautifully with the occasional need for a confidence booster (“Mrs. Bratcher, am I doing this right?”) which I provided. And other students I had to guide through almost every step. If they needed my help using the formula on their scenario, they first had to use the formula on ten generic sets of ordered pairs (with my guidance). (Like shooting practice shots, before the real game.) Then they could go back and do their “assessment” problem on their own. The results of this “assessment” were profound. Not only did I get a clear picture of who DID and who DIDN’T understand how to use the slope formula; I also got to teach, one-on-one, those who were struggling.
I didn’t even have to grade them because EVERYONE had to have it right before they were allowed to turn it in!! Formative assessment at its best!! Who knew a 3-hour PD could have such an immediate positive impact on my classroom!
Saturday, February 27, 2010
Thursday, February 18, 2010
Really Using Student Reports
I don’t know about you, but I LOVE the detailed student report (well, “detail per section” technically). I use it bi-weekly to give my students a grade for their work in the lab. The rubric that I use gives them points for the total time they have logged during the four days they spent working as well as the number of problems they completed, the number of units they have completed and their ability to stay on task during their time in the lab. Every four days I print their detailed report, attach a rubric and highlight the boxes in the rubric where they’ve earned points from their work. It may sound like a lot of work, but it’s much easier than grading a test!!
By the way, the rubric is available in the TeacherShare portion of the resource center, but it’s not what I want to talk about today. (We’ll talk about grading the lab in another post!)
What I thought about today as I was preparing myself for tomorrow’s cognitive tutor report scoring frenzy was how often I actually examine each report to see what’s going on with each student and better yet, how often I allow my students to examine their OWN detailed student report. Yes, I give them a grade and I hand their report to them every four days, but do they really know what they are looking at? Then it hit me, what a GREAT way to have students self-reflect. What if they took a look at the number of errors or hint requests that they were incurring per problem? And even correlate that to whether or not they had looked at or completed the interactive example problem? Or what if they figured their rate of time spent per problem during the four days? What would that tell them about their work ethic in the lab? And what about their mastered skills? What if they figured the percentage of skills they had mastered and not mastered? What if they compared the total time it took them to complete a unit or section to a friend’s time on the same unit or section? There are SO many things they could dissect.
Then, after having them ask themselves these self-analyzing questions, what if I had them assign themselves a fair grade for their work? I wonder what would happen? I wonder if they would be more tough on themselves than I am. I wonder if the self-assessment would motivate them to do better the next time around and to become a little less reliant on the hint button and a little more reliant on the interactive example! Or to become a little more conscious of the time they may be wasting talking to a neighbor as opposed to doing an extra few problems the last three minutes of class.
Well, tomorrow is the test! Tomorrow they WILL examine their own reports (with a little guidance from myself) and I promise to let you know what happens after that!!
By the way, the rubric is available in the TeacherShare portion of the resource center, but it’s not what I want to talk about today. (We’ll talk about grading the lab in another post!)
What I thought about today as I was preparing myself for tomorrow’s cognitive tutor report scoring frenzy was how often I actually examine each report to see what’s going on with each student and better yet, how often I allow my students to examine their OWN detailed student report. Yes, I give them a grade and I hand their report to them every four days, but do they really know what they are looking at? Then it hit me, what a GREAT way to have students self-reflect. What if they took a look at the number of errors or hint requests that they were incurring per problem? And even correlate that to whether or not they had looked at or completed the interactive example problem? Or what if they figured their rate of time spent per problem during the four days? What would that tell them about their work ethic in the lab? And what about their mastered skills? What if they figured the percentage of skills they had mastered and not mastered? What if they compared the total time it took them to complete a unit or section to a friend’s time on the same unit or section? There are SO many things they could dissect.
Then, after having them ask themselves these self-analyzing questions, what if I had them assign themselves a fair grade for their work? I wonder what would happen? I wonder if they would be more tough on themselves than I am. I wonder if the self-assessment would motivate them to do better the next time around and to become a little less reliant on the hint button and a little more reliant on the interactive example! Or to become a little more conscious of the time they may be wasting talking to a neighbor as opposed to doing an extra few problems the last three minutes of class.
Well, tomorrow is the test! Tomorrow they WILL examine their own reports (with a little guidance from myself) and I promise to let you know what happens after that!!
Wednesday, February 10, 2010
Pacing (part 2)
Well, we’ve been out of school almost ALL week for snow. Let me be the first to say that I LOVE snow days, but after about the 8th one, I begin to start panicking that I will not get everything covered before my students are tested. Anyone else feel me? With that said, what an appropriate time it is to give myself (and all of you out there reading) part two of my pep talk on pacing!
As you already know when I first started teaching with Carnegie I immediately became overwhelmed with getting through the textbook. Each lesson was taking two to three days and after spending the other two days a week in the lab I felt like I was only getting through one lesson a week. How would I ever get through everything by the end of the year?
Thank goodness there were several Carnegie veterans nearby that I wasn’t afraid to ask for help!! Here are three secrets they shared with me right off the bat that eased my mind and made “getting through it all” so much easier.
#1 You don’t have to do EVERY single part of EVERY single problem in the text. You would NEVER make your students do every single problem in any other Algebra textbook so why would you feel the pressure to do that with this text? When you are planning your chapters, first choose which problems your students cannot learn without, which ones you’d love for your students to try out and which ones are not as important for whatever reason. Next, work the problems you are going to ask your students to work. And as you work them choose which parts they need, which parts would be good if they got to see and which parts might not be as important for your classes. Throw out the stuff that’s not important to you and be flexible with what would be “nice” for them to see. If you have time, do it and if not, keep on trucking!
#2 Don’t stress over getting through the entire textbook. The Algebra I textbook wasn’t written in a way that if your students don’t get through the whole thing they won’t have learned Algebra. And the same goes with the Cognitive Tutor. Figure out which parts are parallel with your state standards and don’t worry about the rest. If you get there; great! Your students will be exposed to more, but if you don’t; that’s ok too.
#3 Most Carnegie lessons SHOULD take more than one day. I really wish someone had told me this before I had completed a whole year of teaching with it. I was so relieved to hear that it was ok that my lessons were taking longer than one day. So often the easiest thing for teachers to cut short because they feel the lesson is taking too long is student presentation. PLEASE don’t do that. I’ll talk to you more later about why student presentation is so important, but trust me, cutting that part out because you think you’re wasting time is a big mistake.
Well, I feel better already, don’t you! And whether we have another snow day tomorrow or not, we’ll get through the important stuff; no doubt!
As you already know when I first started teaching with Carnegie I immediately became overwhelmed with getting through the textbook. Each lesson was taking two to three days and after spending the other two days a week in the lab I felt like I was only getting through one lesson a week. How would I ever get through everything by the end of the year?
Thank goodness there were several Carnegie veterans nearby that I wasn’t afraid to ask for help!! Here are three secrets they shared with me right off the bat that eased my mind and made “getting through it all” so much easier.
#1 You don’t have to do EVERY single part of EVERY single problem in the text. You would NEVER make your students do every single problem in any other Algebra textbook so why would you feel the pressure to do that with this text? When you are planning your chapters, first choose which problems your students cannot learn without, which ones you’d love for your students to try out and which ones are not as important for whatever reason. Next, work the problems you are going to ask your students to work. And as you work them choose which parts they need, which parts would be good if they got to see and which parts might not be as important for your classes. Throw out the stuff that’s not important to you and be flexible with what would be “nice” for them to see. If you have time, do it and if not, keep on trucking!
#2 Don’t stress over getting through the entire textbook. The Algebra I textbook wasn’t written in a way that if your students don’t get through the whole thing they won’t have learned Algebra. And the same goes with the Cognitive Tutor. Figure out which parts are parallel with your state standards and don’t worry about the rest. If you get there; great! Your students will be exposed to more, but if you don’t; that’s ok too.
#3 Most Carnegie lessons SHOULD take more than one day. I really wish someone had told me this before I had completed a whole year of teaching with it. I was so relieved to hear that it was ok that my lessons were taking longer than one day. So often the easiest thing for teachers to cut short because they feel the lesson is taking too long is student presentation. PLEASE don’t do that. I’ll talk to you more later about why student presentation is so important, but trust me, cutting that part out because you think you’re wasting time is a big mistake.
Well, I feel better already, don’t you! And whether we have another snow day tomorrow or not, we’ll get through the important stuff; no doubt!
Sunday, February 7, 2010
Pacing (part 1)
I really struggled with what topic to start the blog with. There are so many relevant things I want to share with you all, but my classes on Friday pretty much decided for me!! I think one of the most stressful things for teachers when they first start using Carnegie’s curriculum is pacing. When I first started using the curriculum, we had gotten a grant for the textbooks and software and I didn’t even get started with it until mid-September. Already over a month behind, I stressed every day about how long each lesson was taking. As much as I knew that this new way of thinking about and discovering mathematics was right for my students I was still completely overwhelmed with covering the content. By Christmas break we hadn’t even gotten through Chapter 3! We were STILL solving equations in January...I was petrified.
Despite my apprehensions, I pressed on. And as I did I started to notice something interesting…the farther we got in the content, the quicker the students figured out the deeper things and the deeper they connected with them.
This week we have been developing the concept of slope as well as “discovering” slope-intercept form. On Thursday, my students (in groups) were each given a different scenario (similar to one they had seen in the lab) to write an equation, make a table of data, graph the data, find the x and y intercepts and use their data to find the slope. The next day the groups made posters of their scenario and we ended up with ten different posters with a wide variety of slopes and y-intercepts. After that, they did a gallery walk recording the equation, the x and y intercepts and the slopes of each different scenario. Before I could even ask them questions they were already figuring out that the slope was always the number before x and the y-intercept was always the “extra” number.
The discussion following the gallery walk about WHY that was always true was so valuable!! The students themselves talked about how slope is just the “rate” in the problem and it makes sense that that’s why they are multiplying it by the variable. They talked about how the y-intercept was always their starting point and they came up with a “formula” for writing almost all equations; b + mx = y. I think it’s cute that they write it “backwards”….I learned it y = mx + b, but their way is so much more practical; the starting value (b) + (or –) the rate, multiplied by your independent variable will give you your dependent variable. Duh!! Or at least it was duh to them at that point!!
Never, in my years of teaching before Carnegie (and even in my years of learning in high school and college) did I ever understand slope-intercept form that deeply!! I realized quickly as I kept pressing on that first year of Carnegie that my students weren’t behind in the curriculum. They were getting ALL of the curriculum ALL of the time and when it was time to develop a concept, they understood it at such a deeper level that just “here’s a formula and here’s how you use it.” What more could a teacher ask for?!?!!
Despite my apprehensions, I pressed on. And as I did I started to notice something interesting…the farther we got in the content, the quicker the students figured out the deeper things and the deeper they connected with them.
This week we have been developing the concept of slope as well as “discovering” slope-intercept form. On Thursday, my students (in groups) were each given a different scenario (similar to one they had seen in the lab) to write an equation, make a table of data, graph the data, find the x and y intercepts and use their data to find the slope. The next day the groups made posters of their scenario and we ended up with ten different posters with a wide variety of slopes and y-intercepts. After that, they did a gallery walk recording the equation, the x and y intercepts and the slopes of each different scenario. Before I could even ask them questions they were already figuring out that the slope was always the number before x and the y-intercept was always the “extra” number.
The discussion following the gallery walk about WHY that was always true was so valuable!! The students themselves talked about how slope is just the “rate” in the problem and it makes sense that that’s why they are multiplying it by the variable. They talked about how the y-intercept was always their starting point and they came up with a “formula” for writing almost all equations; b + mx = y. I think it’s cute that they write it “backwards”….I learned it y = mx + b, but their way is so much more practical; the starting value (b) + (or –) the rate, multiplied by your independent variable will give you your dependent variable. Duh!! Or at least it was duh to them at that point!!
Never, in my years of teaching before Carnegie (and even in my years of learning in high school and college) did I ever understand slope-intercept form that deeply!! I realized quickly as I kept pressing on that first year of Carnegie that my students weren’t behind in the curriculum. They were getting ALL of the curriculum ALL of the time and when it was time to develop a concept, they understood it at such a deeper level that just “here’s a formula and here’s how you use it.” What more could a teacher ask for?!?!!
Thursday, February 4, 2010
Stretching
Welcome to the ranting of a small-town algebra teacher whose perception on teaching has been completely transformed by this 21st century curriculum called Carnegie Learning!! If you want a snapshot into a real-live classroom that has truly adopted the philosophy “learning by doing,” this is the blog for you. Over the next several months, I will be posting each week about the everyday things that happen in my Carnegie classroom.
In my seventh year of teaching (third with Carnegie) I still feel like I am just beginning, but there is one thing I know for sure; no matter how many years I teach, I will always have room to learn. This blog is my way of sharing with you what is working and even sometimes what isn’t working in my Carnegie classroom in hopes to encourage you in yours.
And there is so much to talk about!! From setting up your classroom and establishing class norms, to how to grade the lab, to the importance of student presentation, keeping groups on task, grouping, planning, pacing, and on and on we will talk about it all!! And if there is anything you want to know about my classroom that I haven’t shared, just let me know. I truly want this to be interactive and I anticipate to learn as much from you as you do from me.
My goal for this blog is simple; to stretch you with new ideas for your classroom! Because a wise man once said, “Man’s mind stretched to a new idea never goes back to its original dimensions” (Oliver Wendell Holmes).
In my seventh year of teaching (third with Carnegie) I still feel like I am just beginning, but there is one thing I know for sure; no matter how many years I teach, I will always have room to learn. This blog is my way of sharing with you what is working and even sometimes what isn’t working in my Carnegie classroom in hopes to encourage you in yours.
And there is so much to talk about!! From setting up your classroom and establishing class norms, to how to grade the lab, to the importance of student presentation, keeping groups on task, grouping, planning, pacing, and on and on we will talk about it all!! And if there is anything you want to know about my classroom that I haven’t shared, just let me know. I truly want this to be interactive and I anticipate to learn as much from you as you do from me.
My goal for this blog is simple; to stretch you with new ideas for your classroom! Because a wise man once said, “Man’s mind stretched to a new idea never goes back to its original dimensions” (Oliver Wendell Holmes).
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