July Challenge – TMC 1st day

All right, I have not done well this week at blogging at all. I have truly enjoyed the time with my sister, however, and have been doing some sightseeing and learning. We spent one day in Coffeyville, KS and learned about the Dalton Gang and their demise. We also visited the Precious Moments Chapel and museum and learned the story behind the creation of those wonderful figurines and paintings, and spent a rainy afternoon in Groves, OK perusing antique shops. It has been very interesting and enjoyable, and has definitely left me not wanting to blog.

Today was the first day of Twitter Math Camp, however, and I do feel that I need to write a little. First of all, what an incredible experience, being in a room of 150+ math educators who are all seeking information, collaboration, and interaction with other math educators seeking the same thing. The workshops and presentations are completely given by classroom teachers and coaches and people interested in creating better math education at all levels. There is an energy that just can’t be explained in words, you have to experience it yourself.

The morning session I decided to attend is a group workshop facilitated by Elizabeth, who had several ideas for creating a working relationship for groups, as well as activities to encourage students to become group participants. After lunch we heard from Steve Leinwand, who is well know in the math community, NCTM, and an author of “Principals to Action” the newest publication on the CCSS. He is a dynamic speaker, had us laughing, problem-solving, and reflecting on our own math learning, as well as how we introduce topics to our students. It was very enlightening.

The afternoon session I attended was led by Chris Luzniak, again a discussion on class discussions, and how to encourage student justification of their ideas and claims. It was a wonderful extension to the morning session with Elizabeth, and gave me some good insight into the work I will be doing with teachers, PLNs, and coaching. The final session for the day was Jason Valade from Tech Smith discussing Snagit, and it’s uses for classroom teaching and enhancing lessons.

I only wish I could have attended everything, there were so many great workshops and sessions going on. It was very difficult to choose one per time slot. I will definitely be collaborating with others who attended sessions I was unable to attend, and sharing information with them from mine. This is definitely a great professional collaboration opportunity, and I am grateful to be here this year. I highly recommend it, and give a might shout out to the people who spent the time and energy to put it together! Great job.

This evening before dinner a group of teachers who will be teaching geometry next year met to create a list of blogs, discuss a twitter chat time, collaborate and meet each other so that they will have a PLN to work with during the school year. Ideas were exchanged, blog sites compiled, and a list of possible guest speakers for Global Math Department’s webinars which air on Tuesdays at 6pm PST. I love twitter and the MTBoS! There is no better way to teach and learn!

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July Challenge – Vacation and TMC

Sunday morning my husband and I will be leaving for Oklahoma. My sister and her husband live there, and this year I am attending TMC, TwitterMathCamp, for the first time. This has been my first year on twitter and after meeting quite a few very creative and innovative educators, I decided that this would be a great way to spend a few days in the summer. I am excited about meeting so many of the teachers I have been interacting with and learning so much from. I am also excited about seeing my sister and her husband again, this time at their home, to which I have never been. 

I’m also looking forward to getting back on my feet after having a difficult year and finding myself all but frozen this summer. A couple of times I have attempted to start some lesson planning, looked at a couple of things, then lost interest. This is not like me, and I’m hoping that TMC will help me get back on my feet. 

I had one last interview this morning. I was a little anxious going to it. I have heard several times that I did a great job interviewing, then not been offered the job. I really don’t want to hear one more time that I have been “edged out” of something. One of the interviewers this morning was the superintendent that I worked with last year, which made me feel better. I did some good work last year for the district, preparing math teachers at the middle and high schools for the change to CCSS this year and changing to the Integrated Math pathway. Two other teachers and I wrote lessons, assessments, and activities to help teachers introduce geometry to algebra students and see what integrated math would look like at that level. The teachers I spoke with afterward said that the work we did was so helpful, and reduced their anxiety quite a bit. They feel better about moving to integrated mathematics this year because of the work we did. Another teacher and I were also able to come up with some resources, one of them being Mathematics Vision Project, so that they had something to work with until we could pilot some materials and get an idea of what we feel will work best for our district. We also previewed quite a few materials and narrowed down the amount of material the other teachers needed to look at and make decisions about. It took quite a bit of time, but I do believe it was worth it in so many ways. I’m just finding myself concerned that my work and skills won’t be recognized, and on the other had, concerned that they will want me for this position and I will have to explain to the principal at the school I just transferred to why I won’t be teaching there. Either option feels very uncomfortable at the moment. 

I guess it won’t hurt me to take this time off. The courses I am scheduled to teach are familiar to me, I haven’t taught Pre-Calculus in a while, and will definitely need to do some work planning for inquiry and modeling, but I know I can do it. There’s also a lot of people and resources available to help me get my ideas flowing, I’m just so used to having a lot of it done by now. 

 

July Blogging Challenge and Start/Stop/Continue

Well, here we are, the 1st of July. Our last day of school was June 6, but it seems like I really haven’t stopped since then. I was at a Transformational Geometry workshop one week through the UC Berkeley Math Project. Henri Picciotto presented for three days, and it was wonderful. The last two days we looked at using transformations in higher level classes and saw some inspiring Pre-Calculus applications along with other math subject areas. I attended PBL World in Napa for one day and heard some great stuff from Paul Curtis and Kentaro Iwasaki about Critical Thinking and PBL in Mathematics.

I still am unsure about what I will be doing next year. I have just completed another interview and have one more to go before I can say that I have done all that I am supposed to do about finding my path and waiting to hear. I know if nothing else comes through that I will be teaching Math II and Pre-Calculus at American Canyon High School, a New Tech Network high school, which is exciting in itself. I have applied for some other opportunities in coaching and developing, planning and implementing PD within our district so there is still much up in the air.

With that in mind, I will work on my Start/Stop/Continue topics knowing what I know at the moment and reflecting on last year’s teaching assignment.

3 things to Start:

  • Because American Canyon is a New Tech school, I need to work on implementing more of my assignments and topics utilizing technology, I need to work on how to assign, and monitor work on-line, utilizing the echo program. I also need to become familiar with a Promethean board, and plan to go to the school site to work on this.
  • I want to work on writing more activities and lessons myself. I started doing this toward the end of last year and really liked the way they went. I have utilized other’s lessons also, and appreciate the work that is out there, and am inspired to attempt to create some good things myself.
  • Desmos and Geogebra as regular programs  for research, inquiry, and modeling of mathematical ideas. I’ve begun interacting in the Geogebra chat and am hoping to work with others in learning to do some coding with the Desmos API app.

3 things to Stop:

  • I need to stop being so strict about what and how students do their learning. I want to plan my units as more open, knowing what topics need to be covered and allowing students to have more say in how we cover or learn those topics.
  • Utilizing only tests and quizzes to do most of my assessing. I want to do more activities and search out other ideas for assessing student knowledge and assigning proficiency and understanding.
  • Assigning HW problems on a regular basis. I want to work on more of a “flipped classroom” idea, where students are researching or gathering some information on their time, and we are working together in class on problem solving. Haven’t quite figured this one out yet.

3 things to Continue:

  • One thing I do quite a bit of in class is insist upon discourse. This is a very important part of learning and I want to continue this, along with finding new ways to encourage students to engage in important problem-solving discussions.
  • Greeting students daily at the door and making sure to interact with each student every day, even if just to say hi or let them know I notice them. It helps students to see that I care, and that I’m interested in their success.
  • Blogging consistently. This year was my first year of blogging, and I really like the reflective practice and being able to share my practice with others. I’ve appreciated the comments and ideas shared with me, and hope to be even more consistent this year in my blogging practice.

Thank you for the challenge, and I will work hard at keeping up.

Tessellations and Love of Geometry

I had my geometry students work on a tessellation project while I was in New Orleans at NCTM. A colleague had done this with her students a year or two ago and said they really enjoyed it. I thought it would be good for them while I was gone, it would give them time to research and maybe really put some effort into it. I had them research about tessellations and art for extra credit on this, for the tessellation itself they had to create stencils to create the tessellation and then color it. I thought they would enjoy this, and I hoped to get some decent results. I had no idea. They loved this! I had some wonderful research and many of them included me in the section about contributions saying, “Mrs. Ryan has contributed to my understanding of tessellations and improving my understanding and appreciation of geometry.” I really loved hearing this.

I asked them to use two different shapes to tessellate and create their design. Most did this, some used three or more, and some created some pretty spectacular designs from one stencil. I have a very creative and talented group of students, some I would have never known. They don’t do much in the class, but for this they pulled out all the stops. The assignment I gave them is here. The grading sheet I used is here. And I will stop talking now and just let you see for yourselves what they created.

Image

Student Questioning

I annoy students terribly. I love teaching geometry and teach it the way I love it. To me, geometry is the foundation of questioning, exploring, extending thinking, inquiry. I think Algebra should be, but for our students it seems, at least at this point, geometry is where that begins. Until now, Algebra has been taught procedurally, like their previous math classes. Then comes geometry, with Mrs. Ryan. Oh no!

The first thing my students learn is that I never run out of “why?” I also rarely answer questions, but respond with a question. When they say they don’t understand a problem, I ask them what they do understand about it. I guide them to find an entry point, I push them to figure out what they know and what they need to know. I walk away when they shrug their shoulders at me and tell them to call me back when they figure out where they are. I make them explore, inquire, dig, re-read, look at examples and re-answer the same questions until they go, “OOOOOOHHHH.” I get calls from parents telling me their son or daughter has told them I don’t teach them anything. They accuse me of refusing to show students how to solve problems. I try to explain what I do, but they don’t get it. It doesn’t look like math has looked for their previous 10 years in school.

Some years my students begin to see and understand in the first semester. Usually this occurs about November. I’ve had a couple of years when this has occurred near the end of October. Some years it takes to the second semester, January or February. This year, it still is not occurring. I had a parent-teacher conference yesterday where I heard once again from the parent that her daughter says I refuse to answer her questions. When I responded that I always answer, I just tend to answer with a question, the daughter starting laughing hysterically. We all looked at her and she said, “that’s exactly what she does.”

After the conference, I had a geometry class. We were working on solving some trigonometric problems and students were asking questions about HW problems. I always ask them to tell me what they tried and where they got stuck. They have to have tried something, in fact that’s one of my chants, “try something.” We worked together on creating a visual model on the board, labeling values and making sure that we had a right triangle in the model to work with. I solved the problem the way they told me to solve it, then asked, “are there any problems with what we’ve done here?” They all looked at me like I had lost my mind. The problem started with a plane 10,000 feet off the ground, we were looking for the angle of elevation for the plane to get to 20,000 feet. They used 20,000 feet as the opposite leg of the triangle. When we finally figured that out, and changed the values, students began to solve again. One student asked, “can’t we just divide the angle measure by 2?” I said, “I don’t know, can we?” He responded, “I guess not.” I said, “why do you guess not?” He said, “because you just asked me if we could like I had asked a crazy question.” You’d think they’d be used to me by now! I said, “I asked you because I thought it was a worthwhile question and thought we should figure it out.” After a few more questions, a few more changes in values to test conjectures, determining what types of values we needed to test to determine if the conjecture worked, we came to a conclusion. And they understood the relationships between the ratios and the sides and angles of the triangles better. We didn’t get to what I had planned for the day, but I think we got a whole lot more mileage out of what we did do.

When will they learn?

Right Triangle Trigonometry

Monday was our first day back from spring break. We had started looking at right triangles, pythagorean theorem and special right triangles before the break. After a week off, I was sure they had forgotten some of it. I wanted to move on to trigonometry, so I began searching out some ideas for how to present this. I have learned in the past that just trying to teach them the ratios and show them how to use them rarely resulted in good understanding of the ratios or how to determine which one to use when. I wanted to do something that would really drive home that these were related to the acute angles in the triangle and the ratio of specific sides in relation to the angles.

I found a couple of activities that others had done, but was not quite satisfied with the way they were written or convinced that they would really drive home what I was hoping to help students understand. I decided to write something myself expanding on some of the ideas I had seen, and as I worked on it I realized that we needed two days to do this. Monday was a pre-discovery activity, mainly to refresh what they knew already about right triangles and to begin to encourage them to start relating the angles and sides. They worked on this in groups, discussing and writing out their conclusions together. This went well, better than I had expected, and I gave them a problem to work on after finishing it, which I thought they would need to take home and finish. A large portion of the students finished in class and were able to clearly explain what they were thinking and how they found an entry into the problem. I was pleasantly surprised at the work.

Tuesday I had a trigonometry discovery activity for the groups to work on together. Unfortunately, my planning was not quite as organized as I would have hoped. Tuesday’s are our short days, our PLC teams meet for an hour in the morning, so we start school one hour later. This shortens our periods approximately 10 min, which doesn’t seem like much, but this can be crucial for an activity. It definitely was for this one. I tried to get the students started right away, but kids will be kids. Several groups did not make it to the 3rd problem, and I even told them to skip the second, explaining that it was to verify that the results of the first problem would be consistent no matter what type of right triangle they used. I gave them some homework problems to work on identifying trigonometric ratios in several right triangles in both fraction and decimal form, but I felt uneasy about what might happen.

Today I decided that we would go back to the 3rd problem in the discovery and discuss it as a class. It turned out more students that I had anticipated actually did understand what they were seeing, and we went over a couple of the homework problems and the class really did have a vision of how they should be setting up the ratios. We looked at a couple of problems where they had to find the angle measure using the inverse functions and made sure everyone’s calculators were set properly to use the trig functions.

All in all, a good activity and the students are really verbalizing understanding of the functions better than I have ever seen in the past. We will work on application problems tomorrow and friday, which will give me a better idea of how well they are truly understanding this, but I feel better about it right now that usual.

Refresh, Reflect, and Reinvent

I’m on spring break this week and have spent quite a bit of time perusing web sites, looking at lesson ideas, and trying to be thoughtful about how I am going to proceed for the next two months. I have just been notified that I will have access to a cart of Chromebooks to be shared with another teacher. She would like to alternate days with them, giving each of us 1-1 time on alternating days. I have been thinking about this and have a concern with that. Because we are in our last eight weeks of the year, and my students have not had any access to technology to speak of this year, I am concerned that we will not have any time to do anything of value if we alternate. The other option is for each of us to have access to 18 computers every day. This would allow me 1-2 access in class, and with smart phones and a couple of ipads that students bring, I could be nearly 1-1. I have to be sure that students have gmail accounts, and that they have knowledge of how to use the computers and any programs we might want to use. It seems like alternating days might make this difficult.

On the other hand, I knew it would be a different ball game to plan lessons with technology in mind, but I am beginning to realize how different it is. I am feeling a bit overwhelmed looking for lessons, thinking about how to alter them for my classes, and how to focus the lesson so that all students feel they are able to access the material. I guess I won’t really know until I try, so I’m starting on Monday with a simple lesson that includes both pencil and paper, and a portion on-line to evaluate students ability to jump in and become comfortable with the technology part. I guess until I do that it will be difficult to know where to go next. I’ll try to have a couple of ideas ready for each day until I know.

I really wish we would have had access to these earlier in the year. Our district has four high schools, two are 1-1 computing schools and two are not. We are piloting the SB test this year with our sophomores, and the district has been frantically attempting to implement technology at the two sites which have not had the tech strength. It has been a furious implementation that has taxed the tech personnel as well as the teachers and administrators. I am grateful that our administration has given us the opportunity to try some things with the time we have left, it’s just been quite a year of change and I guess I’m a bit tired. We have had to switch our curriculum from traditional to integrated to prepare our students for full implementation of the integrated pathway next year, which has been challenging. We are still searching for books and resources also.

I guess I’m feeling a bit inadequate at the moment, and wondering if I can continue to have the strength to implement new ideas, try to incorporate the technology and finish teaching the students the topics they need to know to move on to Integrated III or Pre-Calculus next year. Somebody please tell me I can get through this somewhat gracefully. I am still not well versed in geogebra myself, how can I teach students to use it?