Norms in my PLC

This year I am a "PLC of 1" but thinking about norms in my educational communities made me think of the norms in my previous geometry PLC. 

In my PLC for the last two years we had the following norms:

• Be student centered
• Seek out and be open to newness and feedback
• Maximize productivity

We were a brand new PLC when we formed these norms and we did it very intentionally.  I tried using post-its to do this, BUT got too much push back.  I do wonder how if I over-pushed for some of these norms because two of them are "Target-isms" from when I worked at Target.  So at the very least, I put my language into these.  HOWEVER, I truly believe that these norms helped our group accomplish things that I don't think most PLCs did in our building.  I think we really were student centered and maximized productivity.  I even think we did a great job of seeking out newness.  We probably needed to think about feedback more and put some structures in place to encourage that, BUT, again, when I think about what our PLC was able to do - our norms facilitated that.  

I wonder what my other PLC-mates think about our norms?  Do they think they played a big role?  A small role?  Do they think we had the same strengths and opportunities as what I saw?

From my perspective, in a lot of ways my experience with norms in my PLC foils that of my school/department so well.   Maybe it is just because I can name the norms of my PLC and with my school/department, I don't know where to start!  So, with that I am excited to get back to school and think about this more!

Other posts on norms:

1. Norms at KSTF
2. Norms in my classroom
3. Norms in my educational communities

Norms in My Educational Communities

So far, I've got:

1. I love KSTF's norms.  They are fantastic!  
2. I have control over the norms in my classroom, therefore I am going to ensure that there are positive norms in place.

And now, I've got norms in my educational communities.  This is the one I have probably thought the most about, and feel like I know the least about.  I am eager to understand the "what's going on here" of norms in my educational communities.

First off, I am a part of lots of educational communities, code.org, MTBoS, KSTF, CSTA-MN... and for the most part I am a part of all of these communities because I appreciate the norms in those communities.  I choose to participate in those communities because of their norms.  

But the biggest educational community I am part of is in my school.  Even within my school there are tons of sub-communities: PLCs, departments, committees.  Furthermore, the norms in each of these sub-communities impact each other.  In short, it is complicated.

I know there are the 7 norms of collaboration that every educator has seen in a power point at some time - and they are great norms.  There's absolutely nothing wrong with them.  But putting a list of norms in front of someone and actually having those norms valued and practiced are two different things.  Norms exist regardless of if they are stated or written down somewhere, which made me think, what are the norms that my department and school has? 

One of my goals this year is to better understand the norms already in place at my school and department. I wonder how I can tackle this.  Are there ways to think about different types of norms?  There are norms around communication, collaboration, and decision making.  What other categories of norms exist out there?

Even when thinking about communication, collaboration, and decision making, there are a lot of questions to be considered!  For example...

Communication:

• How do we communicate? In person? Via e-mail? How often?
• When do we communicate?
• What do we communicate about?  What is "worth" sharing?
• Who talks and who listens?  Who is invited?
• How do we know when people are listening?
• What do we expect interactions to look/sound like during meetings?  During lunch?  In the hall?

Collaboration:

• What transactional collaboration is taking place? Who is doing it? What are their motives?
• What transformational collaboration is taking place? Who is doing ti? What are their motives?
• What types of collaboration is sought out? Tranactional vs. transformational? Between courses?  Between departments?
• What time is provided/created for collaboration?
• Who decides who collaborates?
• How does collaboration in one layer of an educational communities impact collaboration? 

Decision Making:

• What decisions are made about curriculum, instruction, policies? How and where are they made?
• Who is invited into the decision making process and who invites them?
• What decisions need to be made by the whole department/building and what decisions are left to be made by other sub-communities?
• What happens when someone disagrees with a decision?

Moving forward, I wonder what other norms our department has around the values of our department or the propose of teaching in general (and math specifically).  I keep thinking back to Taylor Williams (@MrWilliamsSTEM) who shared one of his school's documents on "What is Math at our school?" which explained values of their department.  I have long wondered what such a conversation like this would yield in my department.  Furthermore, after reading Why School? by Mike Rose for KSTF, I have wondered what our building would say the purpose of school is.  How would having these conversations help us better formulate norms for our educational communities?

For KSTF this year, I am looking at norms in my educational communities and as I explore what norms already exist in my department/school, I wonder what norms other people see.  I wonder if I am too close to the data to really be able to make sense of the data.  I wonder what assumptions I already have.  I wonder how an outsider would make sense of the same data. 

Norms in my classroom

The last two years I have been thankful to have one day to set norms in my classroom.  Part of the not-so-fun part of PLCs at my school is that you really need to be lock-step so I either needed to convince a PLC that taking more time would be beneficial to our classes or be thankful for what I already had.  I choose to be thankful.

This year, I am a "PLC of One" so - I need to convince my self of what the right thing is to do this year.  It is a little exciting!  Top on the list of important things I will be doing my first week is setting up classroom norms.

The last few years I have distinguished classroom norms and group work norms.  My classroom norms were 1) Be respectful, and 2) Give 100% effort.  I am sure I got these two from the MTBoS at some point but they summarize everything that I need to make my classroom run on a basic everyday level.  I have a poster of these in my room and reference them occasionally.

For group work norms, I spend a little more time getting student buy in.  I took my one day for norm setting and did an activity from Designing Groupwork.  Then students were given post-its and individually wrote down things they did that helped them be successful in the task.  Then, they shared these with their group and synthesized their norms onto one post-it.  Realistically, I wanted my KSTF CI norms to come out of this so, when I synthesized all the norms, I got 1) Take Risks, 2) Communciate Productively, 3) Work Persistently.  This year, my goal is to spend more time on norm setting, and get students to reflect more on those norms the first week (and beyond). 

My goals in norm setting is to set a culture in the classroom where students: 

• Take risks
• Collaborate
• Communicate
• Learn to take turns - share air time
• Invite others to participate
• Are curious and question things
• Respect eachother (and me) and the materials

At first, I was concerned that I would need different norms for my math and CSP classes but really, these are characteristics that I want in ALL of my classes.  The difficult thing will be to develop these norms with 5 different sections of students and somehow arrive at the same set of norms.  One year I had a different set of norms for each class but, really that is unsustainable when I have 5 classes.

In order to get this culture in place, my hope is to do the following

1. Choose tasks that encourage each of these actions
2. Acknowledge when students demonstrate any of my "desired" norms during the task - especially "taking risks" since that is one that students in my school REALLY struggle with
3. Have students develop the norms themselves through post-it note thinking and small group conversations.
4. Review norms the next day AFTER doing another task
1. Begin the conversation with "How did these norms help you be successful with the task?, What norm was difficult for you personally to practice?  Which norm do you think your team could have practiced more?"
2. Revise or simplify norms if needed
5. Start the next day with reviewing the norms
6. Intentionally review the norms periodically throughout the school year, especially for any tasks that require collaboration
7. Survey students on the norms 

I particularly struggle with "reviewing the norms" - I think it is important to come back to the norms and reflect on them but I struggle getting students to do that.  In the past, many of their responses to "How did these norms work?' ended in a shoulder shrug.

I am wondering if being more explicit about what these norms look/sound like and how to address when norms aren't being followed if students will be able to be more articulate about enacting these norms.  I suppose ultimately, if these norms are being practiced, that's the true goal, but being able to articulate when the norms are being practiced (or ignored) I believe can help our class operate more effectively together. 

Norms at KSTF

At summer meeting this year, our cohort spent some time checking in with our cohort norms.  I don't know exactly what our norms are, I would have to look them up, but I do know that the norms work.  Another fellow mentioned that when he imagines his "ideal" interactions at his school, those interactions look very similar to the interactions he has at KSTF.  Norms are what help determine how these interactions develop.  For my #MTBoSBlaugust post over the next few days, I am going to share a bit about norms at KSTF, norms in my classroom, and consider how norms impact my educational communities.

Norms at KSTF were not determined over night.  In fact, I believe our first summer meeting was entirely devoted to developing norms.  Think about that... we were all flown in and spent 8 hours wrestling with norms.  I'll admit, there were one or two times I was a little "over" the norm discussion.  I felt good about them and didn't see the need to change them, or I felt indifferent to the changes proposed.  The fact that others felt the need to further discuss was indicative that more time was necessary to get everyone on board with norms.

Our norms officially are:

• Strive for equitable participation and sharing.
  
• Hold ourselves (individually and others) accountable to tasks and people.
• Seek meaningfulness in our work.

One fellow mentioned that, while she couldn't recite the norms herself, she felt like norms had been internalized by our cohort - we didn't need to know the "list of norms" to be able to participate in discussions because we had internalized them.

This was brilliant. This made me wonder, how can I get norms to be internalized by my students? Also, what norms are already internalized in my educational communities that perhaps aren't stated in a list of norms?

Additionally, while we had internalized these norms, re-visiting them each meeting was important to explicitly state the norms.

While I had to look these up, they were important for us to revisit and consider the impact of these norms. Specifically, we thought about how our norms helped us to work together successfully as a cohort and what areas do we want to strengthen our norms this year.

Being able to have scheduled time for these discussions are essential to the work we do at KSTF but I think it falls under the "important, but not urgent" work that teachers do. Moving forward, I am wondering how my school's meetings focus on "important" topics versus "urgent" topics. Is there a space to discuss norms in our department? OR how do PLC norms impact department norms?

Next up:

• Norms in my classroom
• Norms in my educational communities (MS)

4. 
   

New School Year Goals and Resolutions

In an effort to try to write something a little more cohesive, I am adopting a MTBoS prompt from Teaching Statistics because... well... it was what I came up when I googled it.  There were many that I liked but I am going with "What are your New School Year Goals or Resolutions?" because it seemed easy and very relevant.  For some context, next year I am teaching a "Concepts of Advanced Algebra" class and 4 sections of AP Computer Science Principles.

I've got 6 things here for my goals and resolutions:

1. Bring enthusiasm each day. It can be tricky when students (or teachers) are tired and frustrated but If I am not enthusiastic and interested in what students are doing in class, there is no way I can expect students to be excited.  In CS50 they do this by playing energizing music as students walk in every day - I can certainly do that this year.  Also this year for CS I am planning two events - a puzzle-a-thon for first semester with a little SWAG and food, and then a hack-a-thon which will also have food but also allow students to get a solid head start on their AP CSP projects.  In addition to events like these, I am planning to do a field trip in each class.  Last year these trips really energized the class and were highlights for students.  While these events can bring enthusiasm, I also want to be "head cheerleader" for students in my classes. 
2. Create a family in my class. I suppose this is an extension of "bring enthusiasm" but Jose Vilson talked about using the words "love", "care" and "respect" on the first day to start explicitly building a community culture.  Next year, I am planning on doing the first week of school with culture building activities in all classes to start ensuring everyone gets to be part of the family.  In my math classes, I have always done grouping myself but in my CS classes this year, I told students they could pick one person to work with... I hope I don't regret that.  For the most part, in my math classes students have always been reluctant to switch groups because they "love their group" but then find that there are other "groups to love" out there too. Hopefully giving students a little more choice here doesn't create too many cliques in the class.  If it does, I can always try out Sarah DiMaria's "draft" technique! 
3. Be a teacher leader.  I am hoping this happens through a pending leadership grant with KSTF by doing a "lunch and learn" series this year.  If not, I will need to consider different ways to do this.  This year I am in a "PLC of 1" which means that leading in my PLC isn't really going to happen (since I am the only one in my PLC).  In KSTF we have also talked about "educational communities" and I know that this year I might want to consider leading in other ways outside my school/building such as contributing to MTBoS more, step up in the MN-CSTA, or with code.org.  I would love to do more with alignment with our middle school in CS, but I am not sure if that is really something that is desired in my district.  I also think I would need to do a lot of research about K-12 alignment in CS to be able to start this conversation.
4. Facilitate better wrap-up discussions/reflections.  After reading the 5 practices, I felt like I was getting pretty competent at facilitating these conversations for math tasks.  But in CS, I had a hard time transferring the same process to the discussions.  So here's the plan:
1. I think I can still use the same process as a teacher, but I need to think more intentionally about ANTICIPATING and SEQUENCING protocols that students develop.  
2. Observe other teachers who use Socratic seminar or other discussion techniques to try to learn from them.
3. John Dewey said "We do not learn from experience, we learn from reflecting on experience".  Between code.org and my own math curriculum I have spent time developing, I have a fair amount of good experiences for students.  Now I need to get students to reflect more on these experiences.  I am interested in doing this through exit tickets and through weekly reflections. I also want to do more re-learning in my CS classes and will need to figure out a way to make these re-learning experiences valuable (rather than busy work) for students. 
5. Expand my own understanding of CS.  I need to wrestle with some CS ideas further myself to be able to teach them better to students.  Once again, here's the plan:
1. One way I hope to do this is to go through Harvard's CS50 course more myself.  With any luck, I will have a student go through the course simultaneously which will help hold me accountable to this goal. 
2. Take on Eric's challenges after code camp.  At code camp, our leader, Eric, gave me a challenge to create a list manager for myself in JavaScript and HTML.  These kinds of challenges should help me be a more proficient programmer AND also learn some HTML/CSS since I know that is the next extension for my students after we learn JavaScript on studio.code.org
6. Be open to newness.  Being open to newness has never really been an issue for me... I really should have this read "Implement new ideas well and share out what I learn".  This year, I want to do these "new-to-me" things in my classroom.

1. Try blogging in the classroom with CS - Right now I want to have students do one blog per quarter.  Initially I was thinking about having students subscribe to ACM's list of articles about CS/tech developments in the news.  Then students would need to choose one each quarter to summarize, research further, and discuss impact of the technology.  I want to give students more choice in my class as well so I might expand this to include a list of 5-10 different prompts that students could write about in a class blog.  These might include having students reflect on an activity in class in an articulate way, have students talk about CS vs. coding, research a career in technology, talk about the impact of a feild trip, etc.
2. Use the Fab Lab/Maker Space with microcontrollers.  Last year after seniors were done we did a little with the maker space in our school.  I am hoping to expand that even further next year and add a project that uses microcontrollers. So, here's the plan:
1. I went to a SparkFun conference on microcontrollers and saw a lot of extensions for coding with physical computing.  Students are always freaking out about if they are learning the right "language" or not.  At SparkFun, I saw how the language doesn't matter - it is the big ideas (recursion, logic, loops, arrays...) that students need to know that can transfer to nearly any language.  In the end I am going to have students make a kinetic light sculpture with the micro controllers and possibly other FabLab equipment
2. I am still having trouble understanding what the "vision" is for our school's Fab Lab/Maker Space, but I am determined to make sure that all of my students have access to these tools.  So, after the AP test, I really want students to see how all of the FabLab equipment works AND make something with the equipment.  Last year I had students make their own monopoly pieces with the 3D printer.  Although we ran into some hardware issues, it went well!  I am hoping to repeat that next year.  I also hope to use what I learned as a FundForTeachers Fellow to have students create their own designs and cut them out of paper with our laser cutter.  
3. Rock a new Concepts of Advanced Algebra Structure.  I have really struggled with what I want to focus on this year in math since I have a math class to teach all by myself.  I wanted to Exeter math, Desmos Activites, Project based learning, abolishing grading, portfolio assessments... the list is probably longer than that.   What I landed on was the following:
1. Incorporate more social justice into math class.   Again, this is something I have always been interested in but have never found the energy to convince others to do it.  So, this year, I think doing social justice is my best chance I have at hooking a class of traditionally struggling math students.  While Exeter is interesting to me, that would be a BIG reach for my students.  They aren't going to be doing homework at night so if I went the Exeter route, I would have needed to have students do the problems in class (one work day, one group day???) but I think this group could sit and do nothing for 50 minutes.  I think a little more structure with Social Justice and interactive notebooks is a little more do-able.
2. Commit to Interactive Notebooks.  I haven't really committed to these in the past - I have done some here and there but next year I want to go big or go home with these. 
3. Use more Desmos Activities in math.  Desmos activities really got going last year but I was teaching geometry so it was difficult to implement.  Also, next year I'll have chromebooks which will be easy for me to implement. 
4. Do 2 lessons that integrate computer science.  I will be using Bootstrap for the first time during first semester.  Still trying to think about what I will do second semester to integrate CS into math. 
5. Do number talks.  Did them last year, love them. 
6. Make it a no-hands classroom (without cold calling - more on this later)

While doing this, it has dawned on me that I have never stopped thinking about school since summer started AND at the same time haven't begun to think about school since the summer started.  Doing this forced me to get a little more practical with all of the hypotheticals for next year.  While these 6-ish things seem like a lot... some of them are new and others are just a re-commitment to what I have been doing in year's past.  Hopefully I can keep these up next year!  I am wondering what other resolutions teachers have out there for #Blaugust!

Pattern Finding in Spain

I am currently in Granada which is home to the Alhambra - a fortress from the Moorish times in Spain.  Today I did a bike tour of the city and walked around the old town, snapping some photos along the way of patterns I saw.  Here are a few of my favorites:

Check out that symmetry!

How many different polygons can you find here?

When does this pattern repeat?  

What types of symmetries do you notice here?

While I had initially planned on using this in geometry next year, I found out that I will not be teaching geometry this upcoming school year.  Now the question is, how can I implement what I have learned in my classroom starting this year?

Here are some ideas in no particular order:

1. Math history: Math has a great history - a history that is actually shared with students who are under-represented in my school.  I can do a better job of incorporating that history in my classroom.  There is a great TED talk about why we use "x" to represent the unknown that I can certainly use in my classroom. 
2. Math "Excursions": There are fun things to do in math that maybe aren't in the MN math standards.  These fun topics can certainly be tied back to common core math practice standards (which MN doesn't know about/acknowledge) and they are worth while to do because it give students another access point to high level mathematics.  I would like to do a 2-3 day excursion on Islamic Patterns
1. Start with a little slide show action - incorporating the images I have taken here in Spain and with a little history/culture about why these patterns are in Islamic art.
2. Give students a pattern and ask them to re-draw it using some scaffold (like a circle, maybe a circle with other circles on it to give them a type of grid. 
3. After they struggle with it, give students a compass and a ruler and walk them through the process of creating the pattern. 
1. I think it is important here to bring back the vocabulary - definition of a circle, equilateral triangle, hexagon, regular shapes, bisect, etc. 
2. You could also relate it to fractals and show students how to keep putting shapes inside a shape.  This could be a good arithmetic sequence problem (when will you have 100 stars on your paper)
4. Provide students with a pattern and allow them to be creative.  At one point in the class our instructor asked us to "see what we could do" with a pattern we had created.  It was really challenging to think of what makes sense to try to do and what doesn't make sense. We also were asked if we were to make a tile that would repeat itself, what shape would you need to make that tile - how big would it have to be?  Also, a brain teaser!

I would be interested in other people's thoughts on culture in math.  How much do you try to incorporate others' cultures in the math?  

What does it mean to be a professional in teaching?

While in my Islamic Art class, I met two art teachers who were taking the class as well.  They were interested in using it in their own art and in their classrooms.  It was fantastic talking with them about collaboration across content areas and what it means to be a professional as a teacher.

This made me think about what it means to be a "professional" in the field of teaching and how you "advance" in the career.  We have been talking about this at the KSTF summer meeting as well.  At KSTF summer meeting, several fellows mentioned that things they do in their school are seen as "leadership moves" - essentially moves that they are doing to show competency as a future admin, rather than authentic things that they think are will bring upon educational improvement.  Many of these teachers, like myself, have no interest in going into admin, but do want to improve education outside their classroom.  I am wondering is there a space for this type of action in my school or in other educational communities I am a part of.

MTBoS seems like an excellent example of teacher leadership - these are teachers who for the most part want to stay in the classroom but do extraordinary things to invite others into their classroom.  By inviting others in (though blogs, twitter, etc.) they are really impacting education far beyond their classroom.  I am a better teacher today because I follow Sam J Shah, Kate Novak and the like.  By participating in #teach180, I was able to open up my classroom and was certainly more involved in the larger STEM teacher community as a result.  I don't know if I impacted others outside my classroom but I do know that I learned a lot from participating with this educational community.

In addition to MTBoS I am beyond excited to be part of code.org's team this year!  I will be teaching AP CSP this year using their curriculum again and am excited to (hopefully) implement it with a little more confidence and with the ability to provide more extensions for students this year. Additionally, I am a facilitator for their CSP program which has given me access to the community of AP CSP facilitators as well as the ability to provide support for other CSP teachers through workshops and in an online community.  This feels like a more traditional path to leadership, but what I love about code.org is that their PD model asks facilitators to do just that, facilitate learning - not dictate it.  I appreciate the PD approach where you put teachers in the role of a learner and ask them to reflect on that process.  Seeing that reflection focus on engagement and equity is powerful for me to see since in my school community, I have not seen PD take this approach in the past.  ALTHOUGH, now that I have seen it done (and semi-facilitated it myself) I am wondering how (and if) I can bring that to my school community.

Finally, while in London, both of the teachers I met in my classes were exhibitionist artists in addition to teachers.  One of them mentioned that as a professional art teacher, she has decided it is important to be an exhibiting artist since she is teaching students to be artists, she needs to be an artist as well.   However, this individual felt like that being an exhibiting artist was not valued by her peers or by administration.  They thought of it as a "side thing" rather than an essential part of her professional development.  I wonder how being a mathematician, historian, or writer can be an act of teacher leadership.

In my first year of KSTF we did a lot with the different types of knowledge that teachers needed.  There was a diagram of an egg.  It kinda looked like this.

Now that I think about it, there were a lot of versions of the egg that we saw, BUT the point is that there are a lot of different things you need to know and be able to do.  Somehow, the knowledge of content seems to get pushed to the background at times.  Shouldn't it be important that people teaching math also practice math - that they put themselves into the position of actually LEARNING math.  Every time I take a math class after a while, I gain a new appreciation for what we put our students through in math.  When I had to take a college level geometry class after two years out of grad school I didn't understand 2/3 of what the professor was writing on the board!  Additionally, taking a math class helps me practice thinking like a mathematician and talking with other math students helps me practice communicating mathematically.  I wish our culture valued having teachers further their own content knowledge more - I think there is a perception out there that anyone who took high school algebra can teach high school algebra.  Even fellow math teachers have said that they don't use Abstract Algebra to teach Algebra 1.   Which, might be in part true, BUT that sounds awfully like what our students say ("When are we ever going to use this?") - a complaint that is often dismissed.  The point is that doing math at any level grows your brain and gives people new tools to look at the world and solve problems.

As far as my time in Europe goes, my time is London is done for the time being and I headed to Madrid yesterday and Cordoba today.  Cordoba has a lot of tiling everywhere!  I went to a synagogue that was originally a mosque where saw some more original tiling but I took pictures with my camera so I cannot post them here.  Then we went to some ruins at Medina Azahara .  While a lot of the decoration had deteriorated, the museum gave a good idea of what the palace was originally like.

A problematic proof and more fun with tiles!

How a week flies when you're thinking hard!  My week at the Art of the Islamic Pattern class is coming to an end.  I thought a week would be enough, but MAN do I wish I were staying for week 2!  I feel like we are barely scratching the surface of this.  Thankfully I will have some more time to look at this in Spain.

One of the many interesting things we did this week had to do with this image.

Essentially, our teacher said that to evenly divide the perimeter of a circle into 10 parts, you needed to pack 2 circles into your original circle, and then take another (third circle) tangent to the 2 you just packed in.  The radius of the third circle is what gives you 10 congruent parts. Here's a better picture of what's going on:

It seemed a little too good to be true.  THAT's where math comes to save the day.  I wrote up a proof that it works.  I was really proud of it.  Just a little trig, Pythagorean theorem and BOOM.  Proof done.

Then after class I went to do more art with some peeps where Riswan (another student) also expressed surprise about the same division problem.  Luckily I had my proof in my (pocket protector-ed) proverbial pocket and pulled it out.  While I was pretty proud of it, I knew it wasn't THAT satisfying.  Yeah... it was an accurate algebraic proof, but the geometric proof would get to the WHY behind the concept.  It is too weird that you magically use this new tangent circle (the third one) and it just works out to be one tenth of the circumference... Riswan wasn't satisfied with it either.  So, we went back to the drawing board.  Hopefully I will have an elegant proof of it at some point.  OR maybe someone in the MTBoS wants to take a stab at it.

Talking to one of the art teachers there, I realized that really when we skip constructions OR just do them on the computer, students are missing exploring these in space.  I would LOVE to take 2-3 days at the beginning of the semester and try making some of these with students.  We could really develop some good vocabulary around geometry (perpendicular, bisect, vertical angles, interior/exterior angles, congruency... UNDERSTANDING circles, angles, arcs, chords...) MAN the possibilities are endless!  I still think moving on to geogebra is the right thing to do from there - geogebra allows for a lot more exploring AND I think with the background of having done constructions by hand, students will not be quite as frustrated by geogebra.  Also, maybe students will be more willing to draw out diagrams if they have a lot of experience drawing them in class as "art" rather than math diagrams.

ALSO in class we did THIS massive drawing.

The tessellation of this was a lot of fun too with a lot of manipulatives.

Ahem... check out those wooden tiles!  Those are totally what I would love to do with my Ss.  Pick a tesselation and we will cut one out on the laser cutter.  Maybe this can be a CS thing later in the class...

ALSO, in my inbox today, I got this article about using art in CS.  It made me realize that I can use what I learned in my CS class to talk about recursion.  These patterns require a lot of precision... and computers are good at precision - especially doing precise things over and over again.

The Beauty of Math and Art

I arrived in London at 6:00 AM and my class started at 10:00 AM - just enough time to get through customs, tube it across town to my hotel, check in, throw my stuff in my room and get to class.  I have never really had an issue with jet leg before - maybe it was the fact that I only got 4 hours of sleep the night before and probably only slept 4.5 hours on the plane but the last few hours of class were rough. I have been in that situation before and it is a good reminder to be sensitive to students who are tired in class - especially at our school when we start at an unhealthy hour for teenagers.  Any way... on to the fun stuff. 

I love teaching geometry and learning about Islamic Art and its origins is making me love the topic even more!  I think we have lots of great options to make the subject students favorite; Sheila Orr does some fantastic things with social justice and I have seen Stephanie Woldum us art an anchor throughout her geometry classes.   There's a lot of potential. What I love about Islamic Art is how it brings an alternative culture into the classroom.  

A lot of geometry (an honestly, a lot of other math) was developed in ancient Egypt.  Even when we look the word "Geometry" broken down "geo" and "metry", we see that the subject was made to measure the earth. Big problems were solved with geometry, like what the circumference of the earth was.  As a Fund For Teachers Fellow, I am looking at how geometry and Islamic art are connected.  Today in class we discussed if the artisans that actually created the art knew about the complicated math behind it.  While our instructor argued that they probably just did things they though were beautiful and worked to tile a space, I think an argument can still be made for the value of understanding the math behind these topics.  For example, when we look at what regular polygons can tile a plane, we've got only three shapes triangles, squares, and hexagons.  An extensions for this might be:

• Argue that each of these shapes will tile a plane
• Argue that there aren't any more shapes that will do that
• What if there are two shapes that you could use together?  Then what could tile the plane?

This could all connect quite nicely to a unit on quadrilaterals to practice using interior an exterior angle measurements.  Moreover, really "arguing" (which students love) is a trick to motivate "proof" (which students... don't love). 

In addition there is a lot of constructions being done:

Hexagons are AMAZING!  These were divided up into kites.  I would love to do an "exploration" in math topics where we create tessellations, vote on the favorite, and then cut them out of wood on our laser printer.

A great example of radial symmetry. This is actually made out of the same core pattern as the hexagon above, just divided up another way.

And the dreaded "weave" - getting the over/under right on this was a doozy... especially with so little sleep! 

That's all for now from the class but more to come tomorrow!  As a side anecdote, in an interesting situation in customs, when asked what I was doing in London, I said I was taking a class on Islamic Art.  The customs officer didn't hear me or didn't understand and asked me to repeat what I was doing.  To be honest, I hesitated because I wasn't sure if simply saying the words "Islamic" would get me an "additional screening".  While it was all fine in the end, I cannot help but wonder if people who dress a certain way or look a certain way also feel uncomfortable in those situations.  I wonder if I would feel this way before the current political season where there is such a hateful rhetoric around the "other".  All the more reason to explicitly value ALL backgrounds in the classroom.