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In-service program documentation
Reflecting and sharing on the on-going field experiences (D6.6)
Set of journals from the weekly support team meetings of one group during
the implementation of the first illustrative unit
The following set of "shared journals" are from the weekly support team meetings of one team as two of the participants, Linda and Julie, were implementing an illustrative unit for the first time. This set of artifacts comes from Implementation A of the field experiences since, for several reasons mentioned in the "logistics" for this section, we only required "shared journals" for the support team meetings during this implementation. However we continue to believe that, whenever possible, "shared journals" should be a requirement. The set of journals provided here show clearly that having such a journal requirement provided all the team members, including the facilitator, with an additional opportunity (over an above the actual support meeting) to give and receive support, to raise issues for further discussion, to continue a dialogue on a topic of their choice, and to reflect on personal experiences.
In order to give the reader a sense of both how the support team grew as a "team" as well as how the journals provided additional support for Julie and Linda as they implemented their first illustrative unit we have grouped the journals by week and within each week we put the two "new" inquiry teachers first (Julie and Linda), the "experienced" inquiry teacher next (Deb), and finally the team facilitator (Barbara).
Note: In order to provide a complete image of the role of the support team and the journals we chose to include Julie and Linda's reflections on their unit here, since they both submitted them as support team journals. These reflections have also been included in Section 6.7 as examples of participants' written reflections on the implementation of one of our illustrative units.
| SCROLL TO READ ALL OF THE JOURNALS IN CHRONOLOGICAL ORDER, or click an item to read the set of journals for a specific week. |
| Week 1 (Julie and Linda begin to implement their unit has begun) |
| Week 2 (issues are raised and support is offered) |
| Week 3 (issues are raised and support is offered) |
| Week 4 (issues are raised and support is offered) |
| Week 5 (the implementation is complete) |
| Week 6 (Julie and Linda submit overall reflections on their experience) |
| Week 7 (the school facilitator responds to the reflections) |
Week 1
Yeah!! Deb just called to say that we did not have a meeting on Saturday. Nothing personal, but I need my weekends to catch my breath; besides, some of the meetings tend to become overkill!!! On a happier note, things have gone well for Linda and I no far this year. We are working well together. I know that we were both unsure of what this blended class would be like. I'm glad that we can just go with the flow. We don't plan who will say what each day, we just get up there and start talking (and it seems to work). The class itself is going O.K. We are not too far into it yet, but I am experiencing more negativism than I thought I would. I know that I'm probably expecting too much. The students may be a little confused by the entire situation. There are 3 adults in the room (sometimes 4), and we haven't done any traditional math yet!! My other classes are going well. The students like the journals and other writing I've asked them to do. They are also very curious about the tessellation "stuff" that is displayed in the room. I just read this entry so far and boy did I ramble. Well I just finished correcting 90 quizzes, so that may be it. I'm looking forward to our get together.
NSF Journal
Linda
9/13/93
With all that has been going on with the beginning of the school year, I've found it nearly impossible to get up here to this computer to make an entry. Actually, I forgot for the first couple of days. It was only when Debbie reminded me at one of our team meetings that the light began to dawn. That must have been on Thursday or Friday of last week and here it is Monday...
There are so many new things going on all at once! I think I finally have a system for most of my classes that just might work. At least it's beginning to look a little more like something I might be able to manage. I've been leaving the house at 6:30am and school at 4: 30pm then working until 10:30 or so every night. WOW! (I finally unpacked the last of the moving boxes today. Now I just have to make sure that everything is filed so that I can find it again.) The funny thing is I'm noticing a lot of us seem to be keeping these same hours.
I really am pleased with the way our blended class has been going. So far we have met with the kids 3 times. It's a little difficult to learn their names...I'm not sure why. They seem like a good group. We have 15 students, mostly boys. We spent the first 2 classes going over some housekeeping kinds of things including getting acquainted activities, class rules, and a journal entry on their math autobiography. The Tessellation unit was started today. You should have seen the looks on their faces when we gave them the definition. We tried to reassure and encourage them. I can't wait to see what they come up with.
I have the feeling that Julie and I will make a good team. Even in the first few days of class, we seem to be completing each others sentences and filling in the gaps for each other I found it particularly difficult to sit still and observe today, and jumped in before the class ended to help explain the tessellation definition assignment. I did begin my observations and documentation of the classified kids. Julie and I went over their IEP's last Friday. So far, in class, they are functioning at about the same level as their non-classified peers with a few exceptions. I had to use proximity to discourage off-task behavior by one student who felt it was OK to talk to his neighbor during the lesson. Amazingly enough, one of the kids who had a really hard time staying on task during a self-contained class last year seems to be doing remarkably well so far in this blended situation. Another student who very seldom had anything to say last year actually volunteered a thought today.
It was interesting to see the students' reactions to viewing a video in math class. Apparently this was a totally new experience for them. They seemed to enjoy the show but had difficulty gleaning the information we hoped they would from it. We talked about this a little during our planning period (we have 3-4 per week!) and kind of came to the conclusion that maybe this was just something so new for them coupled with the fact that it was a pretty difficult thing we were asking. Most of them have really never been asked to broaden their concept of what mathematics is nor have they done much in the way of small group processing in this particular subject area. It may also be that the video we used "Math Who Needs Its" or the questions we asked were not focused enough to obtain the desired results. I think they did get something from the activity but maybe not enough. We thought about using the NCTM video but felt it was aimed at adults more than kids.
I guess the question that is beginning to nag me now is what do we do once this unit is over? We have set the stage for a new way of teaching mathematics and somehow we have to weave these techniques throughout the rest of the year. One step at a time..
It sure seems strange not to have the Thursday rush to Norman Howard School...not that I am complaining, but I do miss it in many ways. It seemed, while we were in the middle of it, that it would never end. For me, the end of the weekly meetings seemed to come pretty abruptly. I feel like I am just beginning to understand the whole concept of the grant, and now I am supposed to help others?? It feels so strange--I feel like I have so much to learn myself. But, as Linda mentioned one day, the grant may talk about a couple of units, but everything else we do is now affected! I know exactly what she means...you begin to question every single day you meet with your students...wondering if you are doing all you can...is there some better way...something you haven't thought of....
One difference that I've noticed this year is that I have labeled kids in my average classes. This seems a bit different, but I think better, since I really wish the modified class would be abolished, for many reasons.
I feel like I see one or two classes all the time, yet others not at all! Maybe it's just that two of my classes are more noticeable. One class--my smallest, but FIRST period (you know what a morning person I am)--is going to be my most difficult to deal with. There are MANY apathetic people in the class, and chronic homework abusers! One other class has some personality difficulties, but this seems better than the first day, I guess.
I really like my modified class, so far. They seem to work much better together than last year's modified class. Also, we discussed what "modified" meant, and soon after, I told them that I wanted to call them my 'orange' class, since I was color-coding all my classes. They seemed to like that.
I know that I talked to some of you about the interview exercise I gave all my classes, but I want to write about, so that I don't lose it for next year. I think it worked out pretty well:
I gave the assignment to:
Interview 5 people (self, 2 adults, 2 kids), asking:
1. What is math?
2. What does it mean to do math?
Then I put them into cooperative groups next day, with directions to summarize each answer to #1 in no more than 3 words. My thoughts were that kids interviewed would give the standard "number-crunching definition. The adults gave mostly thought-provoking answers (did they feel they would be tested?. Summarizing these forced the kids to look at the key components of a more sophisticated definition. They listed these key words on newsprint.
When finished, they were to write a answer to the What is math?" question by using all (or most) of the key components on their newsprint. I'll share a few of these in a minute. First, while I'm remembering it, I want to admit that I had decided against doing this activity with my 'orange' class, since I couldn't fit it in at first. But, really, I figured it might turn into a waste of time. After thinking about it, though, I figured that they may NOT get as much out of it as the other classes did, but they would benefit from it to a good degree.
So, I assigned them the activity, and we did the cooperative group work today. In general, their interviews were not as good as others, but all but three had their homework when they came in (even these 3 did it, I think, but forgot it--I asked them to jot down what they remembered, and they did this). I think each group benefited from the task of having to summarize, having to take turns and then having to integrate and reach consensus about a definition.
These are a few of the definition (not orange class, since they are posted on my wall):
"..a subject that you learn about different systems and numbers
and concentrate on multiplying and dividing.:"
"...is a fun, likable way to use numbers in learning and problem solving."
"....is work!"
"...a tool that we need everyday of our life."
"...the method using number relationships, shapes and sizes, word problems,
+,-,X,and -. Math also is a complicated puzzle that slowly needs to be pieced
together."
See ya!
Journal Entry - September 16,1993
Barbara
I know I didn't send this up to school like I said, but I am writing it before I read any of your journals. Then I can write another entry after I read yours. Let me first say how much I am enjoying working with all of you. It is a pure pleasure. You are fine professionals and very nice people besides!! I have been very impressed from the start at how well Julie and Linda are working together. Unless they are putting up a front when we're together, it looks to me like they complement each other very nicely. You both have good ideas, you bring your experience to any discussion we have and try to think through what you are thinking in light of what you know about students and the way they learn. You are good sports in going ahead with things even though I imagine there are times when you wonder what in the world you are doing mixed up in a project like this. If you're anything like me, there are times when you wish you could just go on and do the same old thing. It would take less time, less emotional and physical energy, and less stress. Just teach and pretend that the students are learning. In fact, don't ask for feedback because then you might find out that they aren't learning what you had expected or hoped for. (I'm not saying you're like that, but that's what I feel like doing and probably do more of the time than I wish for) So, it is rewarding to see you willing to take risks into something new. It only verifies that you truly care about students and their learning, beyond what is comfortable to you. And Deb. Oh my! From what I can tell, Deb was always good. But I have seen Deb change in many ways. All for the good. She is better than ever. Do you want to hear some of the ways sometime? Meanwhile, I can feel a positive tone in your group, but also genuine and realistic. You are not afraid to "do your own thing" and make decisions that are appropriate for your students and your own personality. So for starting a year with everything changed and different, you are all great troopers, because things seem good when one like me just comes and visits class. I always do things differently for every class I teach, so I am going through many of the same feelings and frustrations and experiences with my students that you are with yours.
Let me list some of the things I observed in class on the 14th and 16th. When I first came in the class, I immediately saw the MATH IS LIKE quotes on the bulletin board. I was impressed! At what the kids said and how quickly you got them up there. There was also the newsprint about what math is and what it means to do math on the front board. That served the purpose of both valuing what the kids came up with and having it visible so they could look at it, think about it further, etc. The tessellation definition was up, so I could tell that it was already before them to think about it. In other words, math was all around the room. The kids were quiet and cooperative. I wondered whether they would be like that all year or whether they were still checking it out. I also noticed a very comfortable way that Julie and Linda worked together in the class. It was obvious that both were teachers, as opposed to the Aid (what's her name?) Julie interacted with Linda several times in a very natural conversational way and Linda also felt comfortable to move around the room and interject comments or questions. It looked to me that the two of you were already finding your way regarding how the two of you would both operate in the classroom, separately and together. It seemed very natural and complementary to me. In fact, it further gave examples to the students of what it means to do math, because you two had conversations and could be seen modeling the way we come to know and make meaning of what we are studying. Here are some of the other things that I saw that worked very well: modeling the learning experiences and then giving students an opportunity to engage in the activity urging students not to be worried about right or wrong answers materials well organized structure provided by having a place to organize their thinking and their work (charts) more structure by giving clear but brief directions to the activities group processing (several times engaging the whole class in dialogue about what they are thinking and learning, causing them to both generate new thinking and synthesizing what is going on/what they have already learned) being responsive to student questions and comment (as opposed to proceeding through teacher agenda without regard to where students are and what they're thinking) varied formats during the class - teacher talking/modeling, large group discussion, small group work, sharing with whole group by small group, and journal writing, teacher probing and prompting students, instead of telling them the "right" answer, teacher validating students by acknowledging both their oral and written contributions, students seem to be having a good time, students really are thinking.
As I looked around the class the first day I was there, I had no idea who was LD. One student at the beginning of class said, "Are we going to write in our journals today?" And it was said with enthusiasm. Students have to "grow into" many of these new things, like group work, writing, thinking in new ways. It doesn't happen automatically and immediately. Students produce more good thinking, especially at the beginning, when they are prompted. For instance, when they are in groups and one of the adults comes around and gives them a mental nudge, prompt, etc., they come up with more stuff I think things are going very well, especially for the beginning, and you should be encouraged with their involvement and thinking.
Week 2
NSF Journal September 22, 1993
Julie
I've decided that rather than trying to recap the week, I'll just take pieces from my daily journal to share with you.
9/16/93 Well, well, this tessellation unit seems to be getting better each day. There are still questions here and there, but I fell like we are getting somewhere. It's funny because Ted had me "petrified'' of these MODIFIED kids (discipline, intelligence, jail!!??), and now that I've met them, I find it hard to believe. They're good kids, and so far they've come up with good ideas. Mark in particular has really impressed me. He has appropriate, thoughtful, comments and questions and he is not afraid to make them. Many of the times that I've been afraid that The "desired response" would not be drawn out, Mark has been there to save me!! Miraculously, the students are bringing up the same questions we did. (gaps, overlap, background) I know we were assured over and over that this would happen, but seeing is believing!!
9/17/93 O.K. Maybe I went a little overboard. I know we were only going to test 12 examples, but when I was compiling them this morning I was finding such good stuff, that I put together 18!!! Needless to say, we did not get to finish testing them today. The students found the most difficulty in asking questions. They really needed to be pushed to do this (or at least to ask questions with meaning). Tomorrow we will complete the testing, do a journal entry and try to start compiling this info. Till then...
9/20/93 Today was a good one!! Groups finished at all different rates, but the large group processing was fantastic. Linda and I commented on how the students you least expected to do well, or to even care, were the ones offering the most comments and questions. Paul was especially involved with good arguments and observations. Niki asked the question, "Can you change the object to make it T?" Linda and I almost fainted. How amazed we were. We were prompting them toward changing the definition but they haven't reached that point yet...
9/22/93 Today was a little more like pulling teeth. I'm not sure if they were just tired of reviewing the examples, or if the day off took away some of the momentum, but it took us a longer time to get them going. We finally got around to changing the definition when Mark pointed out that we only had 1 example that was definitely a tessellation. Linda and I decided to change the work stations after the experience she had in her self contained class. So, I'm looking forward to tomorrow. I hose they are not getting tired of this (I sort of felt that today) and that working with the different shapes will be fun!!
NSF Journal
Linda
9/21/93
It seems this week has been one of ups and downs...one class I'm totally convinced that this tessellations unit is going nowhere and the next I see a glimmer of hope. I think it was on Monday that Julie and I both noticed that the kids actually seemed to engage themselves in the lesson. Questions and insights began to emerge. Things clicked. It was really exciting. Then...I took the same lesson back to my self-contained class and became very discouraged. Maybe it's just that there isn't enough stimulation from other kids in the group to keep things moving. I feel that I have to direct, prompt, goad too much to keep things going. Even then, they just are not "getting it". They become bored quickly with work stations and seem to be missing the point completely. I did hear a few geometry terms today when we did the stations using "traditional" shapes, but still, I feel, they are not asking the questions, seeking the answers, or understanding the point of it at all. I worry about the "targeted" kids in the blended class also. I'm just not feeling comfortable. But then I think, if I had to estimate, we are reaching 4 of 6 to some degree in that class and about 50X of the self-contained class. Is that enough? Is that better than could be done the "traditional" way? Are they really feeling a need to learn and making it their own or are they completely lost? At this point, I just don't know.
I have to say that I think we are really lucky to have each other!! I spoke with Connie Smith in the last couple of days about the meetings in Brockport (which I have still not been able to attend!). It is very difficult for them, I think, since their phase one teacher isn't at the school. More than that, I think our success can be greatly contributed to the fact that you, Julie and Linda, are so dedicated! You spent time developing a general philosophy and got to know each other...and you are both bitten by that 'let's perfect this teaching thing' bug!!! It has been great watching your successes and your near successes, and your growths
My 'orange' group has been plugging along. I gave them some unusual word problems today (things like the handshake problem, the task of getting a fox, corn and a duck across a creek). I figured that they needed to be interested by giving them challenging type of puzzlers. Then, tomorrow, we'll discuss some of the methods they used to solve the problems.
It was especially interesting to watch one group in my 'pink' class (nicknamed the 'algebrats' by one student in the class). One out of the four boys was doing all the work on the handshake problem. He had a list from A...F and was going through the process of determining the number of shakes. He had 11. Another boy started doing a similar list, only slightly different. The first, Brian, got irritated by this questioning of his answer. But, when Jeff found an omission in Brian's list, he didn't mind. The other two sat and daydreamed. I prompted them to come up with another solution--that I was grading them on their own thinking. Jared began a similar list, but Adam drew 6 dots and started connecting them (hexagon), then drew in the diagonals, coming up with the same answer. We then discussed how great it was that they came up with the same solution, using a different method. I was happy that they all finally began buying into the activity.
Does a 48 minute class seem any longer?? To me, it doesn't!! I like the variety, but I don't feel like the classes are flowing yet...I don't have a mental image of when I met last...if there is class tomorrow...etc....
Journal Entry - September 23, 1993
Barbara
I realized after I wrote that last journal that I didn't say anything about Deb. Sorry Deb, it's not that there is nothing to say about you, but since I haven't been in any of your classes or talked about your units much, I didn't write anything about you. But I do want to say that your presence is greatly felt. You are such a positive force among us! I mean that, really. The fact that you have been through this and can give encouragement, advice, suggestions, etc. is really an asset. Your experience in very valuable and your model of growing and learning yourself is inspiring. So it will be fun to hear from you week by week, in the journal and in the meeting, about things in general and about your units. BREAK!
Now that the water break upset my plans and caused me to not get this journal done before the meeting, I will finish it and send it to school tomorrow. The composite of the journals is so interesting to read. Do you notice how we talk about different things each week, and some weeks one person is up more than another, but taken together, they give a whole picture of the current situation. I thought we had a good meeting today. I think Deb is right on when she says that the Spencerport team may be pulling together better because of 1) Linda and Julie got to know each other and planned together before the workshop and year began; 2) they had a common set of goals and the outline of a unit plan before they started; and 3) they have time during the week for planning built into their schedule (even though they may not yet know their schedules!!). I think Linda's and Julie's ability to anticipate and plan ahead (both in terms of the whole unit and the day to day adjustments they make) is very good. They seem realistic about what the kids can do in a day and have good time management in the class to stay with the plan but be responsive to what the kids are saying and doing and make appropriate adjustments. I will be interested to see how you think the teams are working after more time has passed. I would like to hear you talk about the basis for putting the LD kids in pairs and then what you see happening to them. In other words, did you take a particular LD need and pair it with another student because of some characteristic of that other student? Did you have time to know all the students well enough to make some educated guesses about what they might contribute to pairing with an LD student? I will be interested in hearing what particular kinds of activities Linda thinks LD students are benefiting from in the mainstreamed classroom. And what Julie thinks about as any disadvantages to the other students of having LD students in the class. There are so many variables changed all at one time this year, that from my researcher background it is hard to know what comes from what. But it is fun trying!!
Deb, I was really interested in the activities you did with your students, both in the orange class and in the others. Can I come visit someday? I miss you.
The kids were really engaged in class today. I didn't see anyone goof off, look like they were bored, or display any antisocial behavior. Even when one of the partners was done and had to wait for the other, they were good. See you Tuesday.
Week 3
NSF Journal
Julie
September 29, 1993
I'd like to begin by thanking Barbara for her kindness and hospitality last week. What a beautiful setting for our meeting, not to mention the delicious homemade bread and of course much needed use of the facilities!!! (especially for the coffee drinker in the group - DEB) The blended class has only met three times since our last journal, so I don't have too much to report.
9/23/93 - The students really enjoyed the work stations. It seemed slow to start to me, but Linda assured me that it could have been much worse!! They did just find with tracing, making tessellations, and deciding if the shapes tessellated or not, but they are still having difficulty with questions.
9/28/93 - Today was a large group processing day. We talked about vocabulary, and questions and statements that students could make. Linda and I agreed to omit the "fun" tessellation day, anticipating that it might not be fun for some students but rather overkill. It was a good decision.
9/29/93 - I'd like to call this my "go with the flow" day because I actually told a student in class that I like to go with the flow. Needless to say, Linda almost passed out in the back of the room. The funny thing is I didn't even think about saying it, it just came out. Maybe this research project has taught me something. (cough gag cough) Anyway, it was a productive day. We reviewed vocabulary, questions and observations. We also asked the students what we should do next. Many of them came up with the idea to answer all of the questions. So, we started to. We'll see how it goes. PS Many of the responses I read in the journals about the unit were positive. (read attached)
Just as a footnote, I'm very pleased with the direction that my other classes are taking. The students seem a bit happier than they were at the beginning. (knock on wood) Their journal entries have been positive and I personally feel good about the way I'm teaching things. Let's face it, you just caught me on a "I like being a teacher" day. (as opposed to a "Can I really do this for the rest of my life?" day)
I just got the awful feeling that I am not writing in this thing often enough. I hope this is OK. It seems like there are just so many things to keep straight that I'm not sure if I'm really doing everything I'm supposed to. At any rate, last week's nasty little water main break turned into a very pleasant meeting at Barbara's house. Thanks for your hospitality. It was greatly appreciated - and your house is terrific!
Back to the unit...I have to wonder if we haven't reached the point where we need to start thinking about winding things up. There comes a time when even what's new can be over done. The kids seem to be feeling it too. We canceled the second day's "fun shapes" workstations because both kids and teachers seem to be ready to move on. We decided to consider the "what happens next" part of the unit and get into the choosing and testing of tessellation statements. We tried to summarize vocabulary today and will, hopefully, concentrate more on content regarding triangles tomorrow. We also decided to give the kids a short "quiz" along with another journal entry just to see what they have picked up so far and to bring home the point that they are accountable for what is happening in class. That will happen later in the week. We'll be sure to let you know how it turns out.
I was impressed with the vocabulary they came up with today. They really do know more than we give them credit for sometimes. It was also interesting to see that our targeted kids seem to be making just as many contributions to the group as the others.
Barbara wanted to know how we chose what groups to put the LD kids into. Truthfully, I think our guiding principle was simply not to have more than one classified kid per group, if at all possible. After that we just kind of "poked and hoped" seeing as we really did not know most of the class at the time the groups were set up. I knew most of the LD kids but we knew none of the others. We first divided the class into groups of four and watched how they worked together. Then we subdivided into teams of two based on observations of those first few days of class. So far, things seem to be going fairly well. I have noticed that some groups work better than others but the targeted kids seem to be doing just as well, if not better, than their non classified peers. Maybe I'll end on that note - it does seem rather positive...
I can't believe that I was talking to Julie on the phone last night, listening to her typing away, and I never thought about a journal entry. I had it in my head that we had another day. Wrong!
So, here it is...6:30 a.m....and you know that I am NOt awake....
I gave my 'orange' class (by the way, they want to be the purple class--just what I NEED is another color to master!!!) their chapter one test yesterday. I haven't graded them, but I know that they didn't do as well on the test as they have been on the work in class. I am worried about one of the mainstreamed kids. No, he isn't another Mike, but he is not taking the class seriously--either that or he in misplaced--but I think it is the first.
Also, I have noticed very few 'shining stars'. Most of them seem to be very weak in their skills. The skill that I see as MOST lacking is just plain old common sense. There is one kid in the class named Bob who is such a nice kid--I can't explain it, but he seems so at ease talking to adults and is respectful etc. I think he is a repeater. Could I be missing the eighth graders???? I'm in need of some serious help...ha ha
Yes, Barbara, I would love to hear what changes you've seen in me! It is very difficult to voice changes in yourself, I think. You're always right in the middle of change, it seems. Sometimes, I don't feel that I have changed much at all. I frequently feel that I am not good with modified kids. I have the rapport down. But, for instance, take this year's class...(please! Ok, an old joke, but remember I am not awake!!)...they seem to be getting squirrely on me. They've come in the last few days quite LOUD and boisterous--like they are going to lunch. I think all the teachers on our team are experiencing this 'kids are out of control' feeling.
I plan to start my Tessellation unit on Monday...and Julie and Linda are DONE!!! But, I am looking forward to it more this year--no video tape, which is great! I feel that so many people made such great modifications to our unit, that I don't want to miss doing them. I feel a bit overwhelmed lately...see you!
Journal - September 30, 1993
Barbara
I am sorry that I was unable to make the meeting today. I hope Julie told you the situation. It was totally unanticipated and unexpected until early this morning. Anyway, I am finally back after 10pm Thursday night and will bring this up to school on Friday morning. Thank you for bearing with me. (How do I know you did?)
After today's class, I am anxious to hear what the students said in their journals that they wrote on Wednesday and find out what they said on their quizzes. I have heard some disappointment by you in the past that maybe things weren't happening as fast or students weren't producing as much as you had hoped, but I think it takes time for them to learn new ways of thinking. Students are so used to "doing mathematics" in a teacher controlled and fairly computational classroom that it takes getting used to when you try to implement the standards. I think, first all, that Julie and Linda are doing a great job with the unit. It is organizes and well-thought out, yet class time is responsive to students and seems relaxed and fun. It is truly an example of what we were calling "invisible structure" this summer. And I think the students are producing some good stuff I was surprised at how much vocabulary they generated on Tuesday and how much they collectively came up with regarding definitions. Then today they got right into their triangles and were talking with each other and teaming to get the job done. It was interesting to me that as I was watching the two pairs that were closest to me that on the worksheet, they skipped down first to the last question about drawing the tessellation before they measured and labeled it. It was the same last year when Deb gave them the final exam. They immediately went to the tessellation and manipulation part before they did the more traditional stuff on definitions, etc. So no matter what they say, their actions say that they like this tessellation stuff and would rather do it than more traditional math.
Let me just put in writing some information about Saturday's meeting. Linda, Dana would like to meet with the LD consultants from 8:00-8:45am to talk about LD issues. Then the entire group will meet from 8:45am-1:30pm. We will start by going around the group and every 1st and 2nd-year teacher will say something about the classroom/kids that has surprised them or they are please with and something they are concerned about or have a question regarding. After we have generated these from everyone, we will have an open large-group discussion about the issues. We will also discuss later any concerns/suggestions/questions you have about team site-based meetings, the planning process for your unit, shared journals, documentation issues, what to do next, etc. So you might want to be thinking of things you might want to share during these sessions.
Yesterday I was at Normal Howard for a meeting and picked up a big notebook Ann has put together for each team to keep all our materials organized. I was going to bring it to the meeting today, but since I wasn't there I will bring it on Saturday and then again next week for you to see. It is the school-based documentation notebook to systematically keep things like my field notes, our meeting notes, our shared journals, the unit plan, the assignments, etc. (I always forget to take notes at our meetings. The meetings are so interesting and we get so involved that I forget to write notes. I think I also forgot at the last meeting to tape it. OF course it was here, that's why. Could you remind me next meeting to take notes and to turn on the tape recorder? Do one of you have or know where the tape recorder is? Thanks). There are some class assignments I need to get from Linda and Julie to fill in the days. I will bring this notebook so you can help me determine what we need to round up for it. The purpose is to file the stuff as we go so that when we are done, everything will be in one place and it will be easier for us to refer back to things when we need them and also everything will be available for others in the future when they want to get an image of what the unit looked like.
If you have your reflection on the summer institute done, you can turn it in now. But if you don't have it done yet and would rather spend the time keeping up with the unit, you can wait and do it when the unit is over.
I will be out of town next week on Thursday and Friday. Is there any time on Monday or Tuesday for next week only that we could meet? Think about it and we'll touch base about it on Saturday.
I have to say that we had a NSF staff meeting on Tuesday and I am so glad that I am working with the best team there is. Don't tell the others I said that, but you guys are far and away the best. Deb, I still haven't even been in your room yet this year. I don't have a good mental image of you. I can't squint and see you. Can I come visit you sometime soon. I miss you.
See you all tomorrow. Have a good day.
Week 4
NSF Journal
Linda
10/4/93
I wasn't sure whether or not we would be exchanging journal entries this time since it seems we just did that, but here goes anyway. I came away from Saturday's meeting with more questions than ever. How to assess this unit is probably the most pressing as the five week marking period comes to a close. I've come up with a few ideas. I'll be happy to get your input when we meet on Monday.
The LD meeting was especially valuable to me Saturday. I think what I came away with was probably not what was intended but was none-the-less extremely important to me. As I listened to others talk I began to tune back into some of my original beliefs about kids and teaching that I had come close to losing (or at least forgetting for a while) with the pressures and chaos of change and overloading that the beginning of this school year has represented. There are reasons for the way kids behave in a class and for the problems they experience learning. It is up to us to find out what those reasons are, modify to fit their needs, and teach them how to work with their learning differences. Maybe I needed to think about that more for my self-contained kids than our blended class. (The 7th graders are a very needy group and can sometimes push me close to the edge!)
At any rate...as I listened to the discussion later in the day, I could not help but get the feeling that our team meetings were running considerably smoother than some others. Maybe we just have an easier set up, or maybe we are just fortunate to be able to be more flexible, or maybe it's because we are all in the same building, or maybe, Barbara, you make all the difference. Thanks!
The documentation also has me concerned. I'm still not comfortable that what I am doing is what needs to be done and maybe we should talk about that a little before any more days go by.
It was a rather humbling experience to have our little quiz scrutinized. I keep encouraging my kids to take risks and telling them that it's OK to make mistakes because we learn best from them. When I'm the one in the arena, however, I see that this is not such an easy thing to do, not that anyone was super critical (well, OK, maybe someone was). I hope they helped.
I'm looking forward to our meeting. I have to quit for now. It's 9:00 Sunday night and I still have about 2 hours of work to do.
Week 5
NSF JOURNAL
JULIE
OCTOBER 13, 1993
Let me just start by saying TGIFO (Thank God it's finally over!!!). At this moment (day we gave the unit test) I can honestly say that that's how I feel. I know that just thinking back over the activities we did and all the information we drew out of the students, I am pleased that we did the unit. And without planning it, Linda and I are already discussing the changes we'd make next year. (We actually caught ourselves talking that way several times!! Please do not reveal that information to anyone else).
Okay, now for the final wrap up. When last we met, we had given quizzes that had a few downfalls; therefore, we were in the process of planning to repair the situation...
10/5/93 We gave the students new quizzes and allowed them to work in pairs. Bad move!!! Linda noticed that in many cases, only 1 student was doing the work. Deb suggested that next time we give each student a copy and then let them compare answers after completing the quiz. (We discussed with Deb the timeliness of her suggestions) Students started work on their projects. They seem to be going well.
10/12/93 The students made their presentations today. Their work was excellent, but they didn't have much to present. I'm not sure of how to make that better next time. (Oops! There I go again with that next time business!!! ) We also played a review game ''Jeopardy"'. The kids enjoyed it and seemed to do very well. I'm not sure if it prepared them for the test though!?...
10/13/93 The big finale!!! The test took the entire period for 2-3 students, but most finished early. Linda and I corrected them and 6 students failed. 5 were LD kids. We (especially Linda) are concerned about this. Is this a result of the T unit, or would the same kids perform this way with a "traditional" format?? We also discusses regrouping so that equal ability students are paired up. And last but not least, we are thinking about how to carry some of these ideas over into the rest of the year. We also feel pressured for the time to start planning this... HELP!!
Linda
Reflections on T Unit
10/17/93
I guess you could call this a reflective response to the tessellation unit. I'm not exactly sure that's what it will turn out to be or even if anyone will be able to make sense of this at all. My goal is simply to write down what I am thinking and feeling now that I have finished teaching this unit to two separate classes. I'm afraid that the form may not be what is expected but...the response will be honest.
My initial reaction to the end of the unit was "Thank God! It's over!" Although I realize that it will never really be over because of the "trickle down" effect into my "everyday" teaching, at least that particular unit is DONE. Why I feel that way is difficult to put into words. I guess I just felt like it was overkill or something. Julie and I kind of came to the conclusion on our own that it might be better to take "traditional" math and try to put new vision into it rather than take a whole new thing and try to extract traditional math. I might be wrong, but who knows? It may have been because it was our first time through this thing (although, I did use it and modify even more with my self-contained class), but it seems that both teachers and students tired of this unit about half way through We needed more large group processing, fewer back to back days of small group work, fewer workstation types of activities, more closure both for us and the students.
You might ask, "How did you modify for the LD kids?" Well, we did and we didn't. Obviously, what we did was not nearly enough. The unit exam was a disaster for these kids. One out of six passed. (In my self-contained class, three out of thirteen passed). Something is terribly wrong with those statistics. Modifications included a slower pace, what we thought was strategic grouping of students, directions written as well as given orally, use of the overhead and newsprint, repetition of key concepts, preferred seating, one to one monitoring) questions read to students, extended time, use of manipulatives, and use of journals and large group processing. What resulted seems, at least at first glance, to be a vast majority of "lost" students. The higher ability kids did well; the LD students did not.
Assessment is also an issue. When the exam was taken as part of the whole, what resulted was the vast majority of students passing the unit ( in the blended class; in the self-contained). The only problem with that is - at this point, this form of assessment (portfolio) does not match the "standard" expectation. What is going to happen to these kids when they take the grade level final exams or SAT's? What will happen when they move on to the next level of math? Does this kind of teaching really prepare them to move within the system that exists I have some real concerns - especially for my students.
I keep asking myself, what else could I have done to modify; teach to their needs. There probably was more that could have been done. Maybe it would have been better to give these kids copies of the overheads, let them highlight the notes, rather than try to copy them and process all at the same time. If one of your problems is eye/hand coordination, then copying from the screen can be a real concern - to the point that when I went back and looked at notes after the exam (should have been done before!) I was amazed to see just what they didn't have. How could they possibly do well?
But, the other nagging concern, was what to me was a lack of focus and closure. One of the key strategies used with these kids in traditional classes has been overreaching - clear, concise expectations and lots of practice. Many times I will give a "procedure" or step by step process, connect visuals and manipulative to the lesson, monitor them through a guided practice, then assign independent practice. I try to involve them in the learning process by allowing them to act as peer tutors and class presenters. Something is missing for the LD kid in this new method. For them to be successful, I feel I should have met with each kid individually and reinforced concepts using the "old" methods. What good is that? Why not stick with those strategies and allow for more problem solving type lessons based on this newer method. We need to connect to real life and problem solving. We need more open ended types of questions and a honing of problem solving abilities. We need to help kids see the need and importance of being involved as mathematician. But I do not feel that five weeks on a tessellations unit is the way to do that!
At this point, I am having a very difficult time with inclusion at all. My instinct and my training, as well as my experience, tell me that these kids need to be included and accepted as part of the student body. We need to create a learning environment in which each one s individual differences are accepted, celebrated, and used to the fullest. But, the fact remains that these kids do learn differently than the majority of the others in the room. Why is it wrong to tailor make a class to fit those needs? What's so wrong with a system that, over the past 25 years or so, has shown itself to be very valuable to the success of thousands of students? If the point of this grant it to examine supporting the LD student in the mainstream classroom, then maybe what we need to do first, is take a step back and think about this one most basic assumption. Then, to my mind, we need to focus in on this special population and how best to help them learn math.
11/3/93
I was very tempted to erase the previous paragraph or two but decided not to. Maybe there is value in noting an evolution of thought. I am still having problems trying to sort out all the questions raised but not with such an emotional edge.
I will stick to my initial skepticism, however, regarding teaching methods and LD students. While I can see benefits, in my mind, there still needs to be more processing and drawing to closure for these kids. Maybe I will write more later on.
Journal entry Deb 10/13/93
This is a combination journal entry reflection of today's class in my purple tessellation class.
We spent yesterday and part of today looking at about twenty examples both the students and I brought in for tessellation samples. I had the students working in pairs, and they worked well overall. One student is not working well in groups, and a couple of the boys are letting their partners do most of the work. But, after a quick review of the key points in the definition and modeling of two samples, the students took off by themselves. They came up with the following good questions:
Does color (size, border, numbers or pictures) matter?
Hearts can't fill up the paper.
Do the spaces in between matter (are lines gaps?)?
Why do the hearts go in different directions (they were reflected).
Do you count the top and bottom of the calendar?
Can something be a T and not a T??
What is a six sided shape called (a 12?)
Do rectangles and squares make a T?
Still, after yesterday's class, I felt somewhat disappointed about some of the kids questions and statements. So today, we discussed their role as mathematicians who are inventing or creating a new area of math. We've discussed what it takes to understand a new definition (this is similar to Kate's activity and we have the results on newsprint). I emphasized that they needed to consider what questions they would ask if they were actually in a job as a mathematician--what do we have to study to completely understand tessellations?
Today, I had the samples grouped and I had the kids rotate to each station if they needed to go to that area. I actually think this would work better--they seemed to like being up and around and were very quiet--staying pretty much on task. It may be a good idea to do this right away--the first day. Although, perhaps they just liked it because it was new and slightly changed the activity from yesterday.
We have a vocabulary list started (on newsprint, and in their notes)and I graded their charts out of 15 points from yesterday--giving them back today--with notes on how to up their grade in finishing up their charts.
I had them write a short reflection on the 'samples' activity, but I haven't read them yet. We don't meet tomorrow and then Friday is school pictures (taken during math class!). We may have a short amount of time on Friday to do some large group processing. I hope so!
Boy' Barbara it was sure great having you and Karen in last year. I feel okay about everything--I mean we had discussed how this unit could be done alone--but it takes a lot of energy, planning and organization! But, Julie knows that my absolute strength (HA!!!) is the LOOK of organization!!!
Also, it is interesting that Julie and Linda are GRADING their tessellation unit test, as my unit is JUST beginning. Anyway, it sounds like it went pretty well.
See you! Barbara, perhaps you could come in next week--when we do our work stations? That could be Tuesday, I think! It will be an A day, if I am not mistaken--I will check....
Journal Entry - October 14,1993
Barbara
I wish I could have been in class for the final days, but I am anxious to hear how it went and see the tests, etc. Before I even know any more about the unit, I want to remind us all that both our learning and our students' learning in developmental. When we try new ways of learning, we can't expect that instantaneously things will be different. I'm trying right now as I write to think of a metaphor for this developmental process. It's not coming!!! Anyway, whatever the results of the test, don't be overly disappointed in the students' performance. The test will not measure many of the goals of this unit. It is much more difficult to measure attitudes, comfort ability with working in groups and sharing in large group processing, thinking in new ways, looking for math around them, etc. For instance, I think I told you back at the beginning of school that I did this unit on the area of the circle with one of my classes. They were the ones that were quietly, politely moaning and groaning about taking the area of the circle and finding it in at least 3 ways. They were saying things like "When are we going to do real math?" "When are we going to start using the book?" I had them write an assessment piece recently, in which I asked them to "Reflect on your own learning in this unit. What did you learn? How did you learn it? How do you know you learned it?" I couldn't believe they were the same students. They said good stuff about seeing math in a new light, having to finally think for themselves, feeling good about math, etc. It may be that 8th graders will not recognize and articulate changes like college students do. But I really believe that they are probably there (the changes) even if we can't find ways to assess them. So how would we assess the more subjective, affective, and even cognitive goals we had for these students. Can the students understand what happens to them and then convey that in some form? And when? During the process, half way through the year, later in high school? So, we've only just begun. What can we learn from this beginning? What needs to be changed and what should stay the same? And what just needs time? I know that I am always under construction. I am not the same teacher I was last year and last week. And I learn new things about mathematics all the time too. Like this morning. I was finding all the ways I could to do 14x23. I used to just do the regular algorithm and think it was the way. The one and only. In fact, I didn't even know to think about it because I had just always done multiplication automatically. So this morning it hit me that one way to do it was by area. Make a grid with 14 units on one side and 23 units on the other side. Then break the 14 into 10 and 4 units, and the 23 into 20 and 3 units. That would make 4 smaller rectangles that I could easily find area for. (Diagram below). So find the area for each rectangle--80,, 200, 12, and 30--and add them up to get 322. Then it hit me that what I was doing was just a picture of the distributive property. I probably sound goofy to you, but I had never thought of either the area or connected area to distributive before. It was really neat!! How can I make my students feel neat about mathematics? And how would I measure "neat"? So, we are all under construction, both students and teachers alike. I hope I never forget that.
Week 6
NSF JOURNAL UNIT REFLECTION JULIE
OCTOBER 20, 1993
I'm simply writing this reflection off the cuff, so bear with me. When Barbara suggested that we write a '"final" reflection of our unit, I thought ... "No Problem''. Now that it is over, it will be easy to sit back and think clearly about the body the bad and the ugly of the past few weeks. Well, I was wrong, I feel that Linda and I have less time to discuss and think about the Tessellation Unit now than when we were doing it. We are so busy getting used to the "tradition!" curriculum an-d the methods we want to use to teach that curriculum, in the aftermath of our innovative unit, that we just finally caught our breath today.
I think it is the hardest, but I will start with the changes that I've seen in myself since this whole thing began. I think that considering all of the differences that I faced from last year to this year, I've done a pretty good job adapting. I am VERY pleased with the way that Linda and I have talked, planned, taught, laughed and yes sometimes cried together. We seemed to have clicked and are still kicking even after the tessellation unit. I am also happy with the way I've worked at modifying my teaching in order to meet the special needs of learning disabled students both in and outside of the blended class. I KNOW that I have a way to go in this area, but at least I'm on my way...
Now to Linda, I've seen many more changes in her throughout this unit. Maybe this is because it is easier to concentrate on someone else. Linda seemed to be thrown into all of the changes she has faced this year unwillingly. I'm not saying that she wasn't interested in teaching a blended class or that the grant was not right up her alley, but all combined, it must have been an overwhelming challenge. She has met that challenge head on. She is not afraid to ask for help when she feels she needs it or to offer her suggestions when I need them. I know that she still has many doubts about what this project is doing for and to the LD students, but many good things have happened already. We have discussed the possibility that eventually all LD students will be blended into regular classrooms, and even if all we get out of this is a first hand experience as to what that will be like and how to adapt to it, we are ahead of the game.
And last, but definitely not least, the students. This is a difficult area to see change in. With a new bunch of students we have no baseline to refer to. I guess if I go from my expectations of what a modified class would be like, we've made some changes. The students seem open and willing to try different things. Although they don't even know it themselves sometimes, they'll say that math is OK this year, or at least better than last. And their parents had nothing but good to say to us at open house. So maybe some of that is transferring home.
As for the unit in and of itself, Linda and I have already discussed changes we would make next time, or at least the willingness to make changes, we felt were necessary. I'm not trying to say that we were told we Cadets do anything a - , specific way, but because we were new at this, it was easier simply to follow suit. Evaluation is a big part of that change. I can see the changes that Deb is making in her evaluation already this time around. Linda and I did-not evaluate soon enough or enough period. -We also were not up - front with the students about what would be expected of them' during the unit. (probably because we did not know this yet ourselves.) I think we recovered pretty nicely thanks to Linda's efforts at putting together a 'portfolio assessment" system to use for the unit. We are both a little more at ease with the final results now. In addition, we saw need for more of a variety between cooperative and individual work. And a big need for very specific closure, especially to clarify key points for the LD students. I'm sure that this is something that will come with time, experience and a more concentrated effort.
Overall, I think this experience will help everyone involved to continue to work towards finding better ways of teaching. Whether it's in our next innovative unit, or simply in our day to day class, we are now constantly thinking about change and how to keep it happening.
NSF JOURNAL
Linda
10/20/93
Well, we've finally finished the Tessellations Unit. Alleluia!! I sat down at this computer earlier in the week to try to down load my initial reactions and found myself becoming more negative than usual. Maybe it was just my gut response to the fact that only one of six LD students in the blended and three of thirteen in my self-contained class passed the unit exam. Something is terribly wrong with those statistics. This prompted me to start asking myself lots of questions - about the way we taught, about the nature of these kids, about the effect of our new time schedule, and about the grant. Both Julie and Deb were subject to my venting sorry, guys...but I can feel it coming on again!
I really do see merit in this way of teaching) but I also see problems. Part of it was my own "green-ness" in teaching this unit for the first time(s). I needed to incorporate more of what I know to be tried and true into the framework of our plan but did not because I wasn't sure how much license I had to do that. I will do things differently the next time around. For one thing, there needs to be more large group processing and drawing to closure both for students and teachers. For another, we need to vary the type of activity so that students do not overdo the small group work and become bored with it. Note taking is a major concern as is the ability to focus in on the most important parts of the lesson and what needs to be held onto. Groupings need to be more homogeneously done with similar abilities put together so that one student is not tempted to sit back while the other does all the work or one become extremely frustrated while the other struggles. At least this is what I think...
Assessment is also a problem. We worked up a points system in the end that seemed to work fairly well. It took into account much more than just paper and pencil tasks. 98% of the kids passed the unit using this form of portfolio assessment. The only problem with that is that they did so poorly on the only form of assessment that is currently being used for standardized and district wide testing. What is going to happen to these kids on the grade level unit exams, the SAT's, and next year's RCT's? What have I done to help them prepare to deal with those instruments and the evaluation that is done based on them? Something is not quite right...
And just where does the piece about special ed students fit into this whole thing? I see us trying to conform to and implement the new standards...and I can see the value...but where is this piece called "supporting the LD student in the mainstream middle school math class". Is that my minuscule contributions Where are the guidelines? Where is the discussion of the needs of this population? I don't quite see how it all fits together. Something is not quite right...
But there is value. As we begin our next unit, I am already seeing the influence of the grant. We have worked in journal writing, working in partners (new and more compatible groupings, we hope) and asking kids to think about what they are doing and why. There is more note taking (but we are also offering a copy of the overheads to any student who wants them - after the fact - to help fill in the notes they may have missed). Things seem a bit more focused, class is progressing pretty well and we are already beginning to think about the next grant unit. Julie is great to work with and somehow, through it all, I feel we are learning to be better teachers.
Journal Deb 10/20/93
Well' well, well...is it Friday yet?? I am not sure whether we are really meeting tomorrow...but, I guess I can do a quick journal entry anyway.
I am a bit down about the fact that the mainstreamed kids in Julie and Linda's class didn't do well on the tessellation test. And I am more concerned that Linda is wondering why...why WHY??? And I am sure wondering whether the grant is worth it if the kids don't do well. I've really given this quite a bit of thought, since talking to her the other day. I know that I come from a different perspective, so I am sure I react differently to the whole situation.
For example, the first time I had mainstreamed kids in my modified class, I didn't even know it! I wondered WHY the h---Dawn Murphy-Bruton was asking me how one of my students was doing in math, of all things!! She said, "Well, she's one of ours, you know." Okay, who is 'ours'??? Maybe I was just a bit more dense than other professionals, but I don't think so. It took the rest of that year to realize just what was really happening, and why she would periodically ask me. The student went on to take a regents course, passing it with no problem...
Well, since then, I have realized a great deal more about mainstreamed kids. Part of this learning is from teaching modified for that last 5 or 6 years. But, much of the learning is a direct result of the grant. So, as a regular ed teacher, I have had the chance to work with LD specialists, and get ideas. about how best to meet their needs.
I have to be honest, though, my chief goal is to get as many mathematics teaching ideas as I possibly can--the grant giving me an opportunity to do this--to work with the best in the field. I realize that kids will be mainstreamed into my classes, whether I am in this grant or not--whether I WANT them to be or not ( and you know that I DO!). But, the grant gives me the opportunity to ask questions--and pursue answers to these questions...when have we even been allowed to really investigate what's best for them???
I also realized early on (much to my dismay!) that there was no secret information that someone had knowledge of, as to what the answers to my questions were. That, in fact, I was part of the group of professional people (scary!) that would come up with these answers.
I guess that I view success in different ways. Last year, Staci was mainstreamed. She was absent the day of the test, and when she did take it, she didn't do very well (in the 501 range). This made me wonder if the tessellation unit was such a good idea for mainstreamed kids. Then I remembered the changes in Staci that continued for the rest of the year. She had become a leader in her group during the unit (previously never said one WORD), coming up with some very intuitive thinking. But, even after the unit, Staci had changed. She seemed to be more social, more self confident, happier. Now, in NO way, am I attributing all of these changes to a simple unit. But I think her success in math and English classes did help contribute to the change.
Another factor that plays a part, I think, is the change for the better) in kids' attitudes toward math. When they are finally able to get away from the number crunching stuff of grade school, they get excited about things like tessellations and algebra. That, to me is worth every minute I spend in the grant.
Linda, please don't take any of this personally--this is not really meant to be any message to you. I just needed to sort out in my own mind why I have spent almost 2 years on a project that isn't always successful. There were many times when Kate and I questioned our place in the grant...what was the purpose in the grant...how did we fit in--where could we contribute...where was the focus on LD...why wasn't there more of it....It took some time, and the above is pretty much what I came to realize, in time. I think the power and success of reaching all kids--LD or non-LD--is in our working together...people like you as an LD professional...people like me as a mathematics teacher....
Week 7
NSF JOURNAL
Linda
10/27/93
I just realized that I needed a journal entry for this week; it's 10:00 o'clock at night and I am totally uninspired. One thing though, since my ranting last week, I have been trying desperately to be more positive.
Our classes seem to be going along quite well. I think we're both feeling like maybe we're rushing the kids a bit to try to "catch up" to where the other section of eighth grade is. We really don't want to be unfair to the kids though, so we're trying to monitor ourselves closely.
I am experiencing one definite "spill over" from the Tessellations unit. The kids are so used to working with a partner that they naturally slip into that pattern even when the directions do not explicitly say to do so. I have these kids for both math and English. The funny thing is, they are using the same technique in both classes even though it was only really emphasized in math. Interesting... And, by the way, they are working well together.
I had another student make a comment about how something we were doing in class that day "was just like that tessellation stuff". This was in reference to a word problem that had to do with figuring out the area of a floor in order to purchase new carpet. When I asked him how it was like tessellations, he replied that the carpet had to completely cover a flat surface. OK, so he missed a few major parts of the definition, but at least he was thinking on his own - and this was a student in my self-contained class.
We will probably start trying to get our documentation re: the T unit together some time next week. It is still hard to think about it and even harder to find the time to do the work. But, we are getting closer. I'll see you all tomorrow. Good night for now.
Journal Entry - Barbara
October 28, 1993
It seems like a long time ago since the unit with Julie and Linda! Now we support Deb! As I have said before, I think you should be encouraged about the unit. Sure, there are some things you would want to change, some disappointments, some lessons to be learned. It is difficult, I think, to sort out all the dynamics and issues of any unit. Education and learning are so complex, with so may interrelated aspects. At this point, I think it is important to reflect back on the unit and consider such items as the following: What worked well in the unit? What process skills were observed to be working? Pairing? Small groups? Large group processing? The variety of methods used in any one day? In the unit as a whole? The structure of the unit? Too much, not enough? For LD students, for modified students? The relationship between the content/process goals and the mechanics/structure used to accomplish them? The writing? Which types of writing produced the greatest quantity and quality of reflecting, thinking, questioning, giving feedback, etc.? How did the placement of LD students with others work and how could it have worked better? What problems did LD students have specifically that could be addressed in future units? What problems/issues of LD students were addressed and worked in this unit? Are there any points of "carryover" from the unit to the units now? How did students respond to the Tessellation unit, both during and after it? How does their reaction compare to other classes you have had in the past or present? How do you feel about the unit, from both your affective and cognitive sides? Your heart and your head? Which of the goals of the unit were met, partially or totally? Are there other goals that were met that were not originally specified? What is the most important thing from the unit that students gained? What was the biggest disappointment? What modifications are you now making that you learned from the T unit?
I am not trying to put pressure on or anything, but have you started thinking yet about the next unit? Just wondered. I have been thinking lately about "drill." You know all the slogans. "Drill and kill." 'monkey see, monkey do." I gave a presentation this last Saturday in New York City and someone raised the question of the value of drill in learning mathematics. What is the value of drill? What is the role of drill? How much, when, and where should drill occur? Then I got a new publication from the University of Rochester and there was an excerpt from Sharon Carver's work with students and she said you could drill students to know their multiplication tables, and if successful they could end up knowing their multiplication tables, but that would not necessarily be thinking. What is the connection between "memorized facts" in mathematics and "success" in mathematics. What do we mean by success? These are interesting questions to me. What do you think?
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