Trying to be More Japanese

I had the wonderful opportunity to attend the CMC-Central Symposium in Bakersfield this weekend and *especially exciting* - I finally got to see Phil Daro speak IN PERSON! And... as always, his message(s) just rang so true.

There were so many great nuggets of information, challenges to how I think about teaching and learning, and possibilities for how I could improve my practice. I was thinking about what would be ONE thing I could really focus on and do right now, and because I want to document for myself now (and return to process later) I am sharing that with you :)

He talked a lot about practices and beliefs of high performing countries that differ from those that are common here. Many of those that seemed to really resonate with me came from Japan - here are the ones that I am focusing on right now:
 - All students start a lesson "all over the place" - in America we think students who do not grasp grade-level material immediately have a mathematical illness called "gaps" while in Japan, they focus on the future mathematical health of students by connecting lower grade level methods of approaching the problem to the grade level methods and exploring how/why it works.
 - Student work (approaches) is presented in a progression from easiest to understand to highest level mathematical approach. Solving a problem does not mean getting an answer, it means explaining in depth how they arrived at their conclusion(s) to prove that their answer makes sense in a way that is understandable to the students in the class (audience is not the teacher).
 - The teacher solicits information about the connections between different methods from students, asking students who used one method to relate to/explain/show connection with another.
 - Teacher summarizes progression of approaches, focusing on leading students to grade level (or beyond) approach.
 - THIS is the point where teacher might do "direct instruction" (because all students have necessary prior knowledge to connect to grade level approach to problem).

Apparently, much of how math is taught in Japan has been shaped by writer's workshop. I thought that was interesting too.

Anyhow, there was WAY more stuff packed into that talk, but gotta process!

So here's my plan for the next two days:

Monday: Focus is on gathering evidence of student understanding (this is technically review, but I am doing it because I know it is an area of need still and also pretty much the point of 8th grade).

• Give student Dominoes Pizza prompt (I went to the online ordering tool and put a two topping medium pizza and a 4 topping medium pizza, then took a screen shot). This idea is totally based on a Mathalicious lesson, by the way. You can find that here.
• Do Notice/Wonder
• Pick some good "wonderings" to answer (I imagine we will predict the price of some other medium pizzas with different amounts of toppings, and I will push them to work towards an equation - it would be CRAZY cool if a kid asks that as a wondering... we'll see). 
• SILENT independent work for 1:30 (2 minutes is still too hard! LOL)
• Continue working but discussion is permitted (I will float around room, ask questions, see different processes being used, start to pick who will present and in what order)
• Full explanation of process and why it makes sense is required. All parts of any equations must be identified and explained. (I will check in with students who I want to share to let them know so they are prepared and there won't be drama when I call them up)
• Selected students will present solutions. Audience will be looking for the best thing that student did to help them understand, and the one aspect that was the most confusing/unclear. Random select for feedback.
• As each new student presents, I will ask audience about connections from one solution strategy to the next.
• At end, I will summarize, focusing on how the different strategies are related to the equation, then ask students to add reflection on the summary to their own explanations

Tuesday: Focus is really on the explanations, giving and getting feedback, revision.

• Give students Me N Eds prompt (A sentence stating that Me N Eds charges $9.50 for a 1-topping medium pizza and $0.75 for each additional topping. The equation m = 0.75t + 9.50 is given, but variables are not defined). Students are asked to prove that the equation represents the situation. They must identify what every piece of the equation means/represents and give examples to back up their reasoning. 
• Time limit for completing draft explanation (I'm starting w/ 10 min, but willing to extend some - will have to see how things go)
• Break students into pairs - one student presents to the other. The watcher chooses best thing that helped understanding to praise and suggestion for one area that was vague or confusing. Then they switch roles. 
• Students have opportunity to update drafts using feedback from partners
• Selected presentations
• I will summarize and do a quick mini-lesson on extracting y=mx + b from situations, using student examples as evidence. 

I am nervous about many aspects, but also hopeful that I may have finally found a way to address concept development AND reasoning/communication at the same time. 

Oh... and by the way... we are having walk throughs during this too. Wish me luck! ;-)

Am I Crazy? Ok... Silly Question. Are You Crazy Enough to Join Me? :)

Ok - been thinking about all the great things I've discovered through the MTBoS and how it could impact my teaching for the future. 

I find that I get some cool lesson ideas as well as teaching strategies, class structures, and other independent pieces that are all awesome from the MTBoS, but I feel like what I have as a product for my students right now is rather disjointed and doesn't really flow in the way I wish it would. I am going to go on an analogy tangent here - bear with me... It's like we all have this huge 5000 piece puzzle to build (curriculum). No one actually has the picture on the box (example of pre-made perfected curriculum... because let's be honest, it doesn't exist - but besides the point for the analogy), but there is this basic instruction that says the goal is that our puzzle will be a representation of the Golden Gate Bridge (standards). We have to go find the puzzle pieces and, while it is possible to force all the pieces we find together, in reality, they are all to different puzzles. So the trick is to figure out which pieces match your idea of the "representation of the Golden Gate Bridge" and try to put them together so that it makes sense in the end. I feel like we are all frantically trying to put the pieces together into our own puzzles separately, although we do shout out to our neighbors when certain pieces seem to go, or seem to go together in a theme (MTBoS sharing). At the same time, it is such a huge amount of man-hours going into all of us separately trying to do essentially the same thing. 

So... Here's the idea: What if I could find a handful of teachers who match my content and would be willing to REALLY collaborate. Like not just make a lesson myself, teach it myself, then share afterward. I mean the long hours of hashing out what is the point of the curriculum, what are the pieces that need to be included, how to include them in a way that actually fits and then work together on making that happen. Like open source curriculum design - true "global math department." What I wish I had was a team of people that could work together to actually make units that incorporate all of the awesome stuff we are all trying to do but in a way that is more seamless, more thought out, and with a support system of other educators where we could try, discuss, tweak, etc. Does this just sound way too Pollyanna and ridiculous to you? 

Like... I'm not totally naieve. I know the input of work would be CRAZY. But seriously? It already is! If I had three people and we all put in the kind of hours I already know we all do, but were working towards a common goal, we could have something really worth all that time. I also know that we would probably disagree. And since most passionate educators are also driven and stubborn it would probably be a lot. But at the same time, wouldn't the resulting conversations be extremely fruitful in terms of pushing us all towards better pedagogy? 

I mean... it sounds cool to me. Am I crazy? If so... tell me and I'll keep playing the rat race game. But if not, go sign up on my interest form: http://bit.ly/8mathUnitDesign  and be a part of the insanity! I promise I won't really bug you too much until the end of the school year (since I don't even have time to sleep right now...). 

Anyway... That's where I am right now. Let me know what you think. And... I'm not kidding - if this is just a total ridiculous waste of time, please tell me. I don't have spare time to waste on something that is pointless. But, if you think I have a chance at making this work somehow, I'd love to try. Even if it isn't perfect, the possibility for awesomeness would be too good to pass up :)

Thanks!

Back to My "Roots"

Well... Somehow I made it through all of the blogging challenges (almost) on time, which means that in the last month I have blogged the same amount as I had over the past two years before that. So I guess that is a good thing, right? If nothing else, it has proven that even if my digital musings aren't stellar and I decide to post them anyway, no one is going to die! :)

This week, my poor chicken-scratch-covered remains of a pacing calendar had me covering simplifying radical expressions. Now, last Friday, I went to a fantastic PD by +Robert Kaplinsky where we talked a lot about HOW to bring problem-solving to life in the classroom and I was totally all about it! So I went home and hunted around for something that would relate and it was seriously like staring into a void. Now... I didn't search exhaustively because let's be real people...

At least, not in the middle of the school year.

But I am NOT KIDDING YOU - I was convinced that the #MTBoS would save me every time and I just didn't find something that I thought would build understanding of how and why we simplify imperfect square roots the way we do (then expand that to other radical expressions). 

So... I made something:

Here's a link to the entire document for those who are interested. I was having issues getting the word doc to show up correctly, so I had to convert to PDF, but if you want the word doc because you want to edit please just let me know and I can email it to you directly :)

Here's the rundown of what I was going for, how it went, and what I would do to make it better:

My Goals:

1. Build understanding that we can distribute roots over multiplication 
2. Extend understanding of equivalent expressions to include radical expressions
3. Use a specific progression of problems to demonstrate the pattern of "factoring out" perfect squares to simplify imperfect squares
4. Create "fertile ground" for students to develop the "rules" for simplifying roots without me explicitly teaching the procedure at the start. 

The Lesson Run Down:

1. Stood at the door and informed students that their warm up was the first two questions on the paper (we usually do a lot of our warm ups on whiteboards, so this was a change in procedure). I told them there was NO right or wrong answers, but they HAD to have their thinking written there. 
2. I asked what they noticed about the table of numbers. I was hoping they would see that they could multiply the numbers inside the radicals on the right to get the number inside the radical on the left. I was also hoping they would ask (or maybe even assume) that they were equal. *How it went: My first class got there and that was about it, but over the course of the day I had some really fantastic "noticings" - for example, I had students notice that the right side was always made up of a rational number times an irrational number but the left was all only irrational numbers (yay for some generalization!). I also had kids predicting what the next number(s) on the table would have been and passionately trying to convince peers who disagreed at first... it was glorious. And I didn't take a picture of our list. Because apparently I am forgetful and not quite as glorious as I wish. But you can imagine it, right?  Anyway...
3. I told them we were going to try to prove whether the two columns were equal. The students were set up in pairs today already, so I explained that each partner would use a calculator to find the value of the radial expression. We talked about order of operations and different calculators, and they set off. The DID complain when I told them that YES, in fact they did have to write that whole decimal number, but I also told them they only had to do their own column (they would compare with their partner's column after calculating). They were also to move on to the bottom two questions after comparing (so the whole front of the paper would be complete). *How it went: There were a couple of kids during the day who did weird things on their calculators and had to go back, but it was something like 3 out of 75, so not too bad there. Right away they saw that the two columns were equal, which was a blessing and a curse. That was kind of the point, but at the same time, many of them decided to stop there and turn off their thinking - like that was the pinnacle and they were done now. I had a hard time getting the early finishers to extend thinking at all and think about why I had chosen to break down the numbers on the right so that it was always a perfect square as a factor. I think perhaps I should add a question about this (i.e., "Why do you think Mrs. Aoki chose the numbers on the right the way she did?" or maybe, "Could you write another equivalent expression for the following?                            (imperfect square root) = (factored square root) = ____(fill-in-the-blank)___"   
4. I brought them back together again and took their noticing again as well as predictions for simplifying. I then had them flip over the paper and look at the example on the back. *How it went: At first, there was a lot of, "Wait, what the...?" but a lot of them started to see how it fit the pattern after a few seconds. Of course, there were also a lot who just looked confused. So we talked about how the example related to what we did on the front and it seemed like it wasn't too crazy of a leap. I do think I confused some of them because they wouldn't normally jump to 16 and 5 as their first choice of factors for 80. Most of them would have said 8 and 10. Perhaps I should have chosen a problem from the list that was a little more intuitive. Also, having the decimal approximation at the bottom was misleading. We covered approximating square roots before this lesson and I really wanted them to keep connecting that idea and practicing, but I decided it made more sense to actually do that at the top first (to the right of the original square root) and then go into simplifying. We discussed through a few and then I turned them loose again. Most got close to finishing before the end of class but didn't quite get there, so timing was pretty good. 

Overall: I was actually pretty happy with the result. I used to teach simplifying radical expressions in my Algebra I class four years ago, but having taught 7th grade Common Core for three years, it wasn't part of my duties any more. I feel like this little exploration really set them up for a stronger understanding so that when I went into more complex expressions (messier numbers and variables) students had the foundation and seemed to catch on a LOT faster than I remember in the past. 

Ok. If you are still with me - I seriously APPLAUD you because that was a long post. Thank you for your time and your eyes! If you want to really be awesome and go above and beyond, please share any ideas/improvements you might see so I can be better next year!

Questioning My Questions...

So, apparently, I am incapable of just following a prompt - I guess I just like to do things my own way! :)

I was supposed to talk about good questions, which made me think about what questions I have used that have the biggest impact on student learning, as well as where I see the most issues with misconceptions. I think the idea is meant to be more like those "HOT" (higher-order thinking) questions that have been buzzing lately, but I am going to swerve and head a TOTALLY different direction...

Here's what I've noticed in my time as a math teacher - the issue for most kids when they "don't get it" in math isn't really centered on all those things that most of us complain about (imprecision, lack prerequisite skills, etc.). The issue I see the most is that kids literally do not comprehend what the problem means - they don't know how to relate what they are presented in math class to any kind of recognizable context. 

For example, if a student is doing the following problem: 2.80 + 7, and they do the following:

   2.80

 +     7

   2.87

Does that student really understand what 2.80 means? What 7 means? So if we extend this line of questioning, does this student understand place value? 

It seems to me that this student is just performing a memorized procedure for addition, without thinking about context or meaning. If we asked this same student the same question, but put dollar signs in front of the numbers ($2.80 + $7) would he/she make the same mistake? This could tell us a lot in terms of where to go to help fill in the gaps here.

It seems crazy to me that there is SUCH a huge focus on reading comprehension with students, especially early in elementary school, but there isn't that same idea being carried over to create "math comprehension." I have so many kids that are bright and capable but just don't know what certain numbers or symbols really mean. They get so caught up in jumping into a procedure that they often don't even use the correct values (see above example), or maybe they just write down all the numbers in a word problem and add them up because they see the words "all together" somewhere near the end.

So... Here's the point. The number one question that seems to help kids when they are struggling? I simply point to something and say, "So, what does this mean?" (or if they are looking especially unsure, perhaps, "What do you think this means?")

Then follow up with things like: 

"How do you know that/Why do you think that?"

"Could you write it out/show me/draw it/make a model?"

"What do you notice?"

.... Etc...

Now... I don't start with "What does this mean?" if I am teaching something brand new. Usually I do noticing and questioning first (my kids are too "cool" to call it wondering - so lame... LOL!), and "What do you notice?" is like my go to question when we are exploring, so I think it is probably a tie in terms of both usage and impact on student learning with "What does this mean?" but, seriously, everyone is already on the boat with noticing and wondering. I feel like math comprehension needs some love now! :)  Who's with me?

My Favorite Things

So... Technically this post is late, so in order to make it up to you, I decided to do a sort of combo of last week's and this week's assignment, but seriously people, my life is crazy! First of all, I am a teacher, I play in two symphony orchestras, I have ridiculous food allergies so I have to cook most of what I eat from scratch, and I attempt to exercise when possible. Let me just show you what my week has been like (kinda like "a day in the life" from last week)... BUT, I will highlight my favorites (from this week) along the way :)

Monday: Day off - Woo! I can "catch up," right? Wake up, exercise, shower, shove food in my face while I grade, cook, do a TON of laundry, and try to clean up the kitchen after my cooking escapades. At 5:30 I head out so I can drive an hour to my symphony rehearsal which gets out early (yay!) at 9:30pm, drive an hour home, see hubby for like 5 minutes, get all my crap materials for the week gathered at the door, go to bed around 11:30pm

Favorite Thing: Car audio jack for my phone so I can listen to podcasts (some teacher-y stuff, radio lab, cooking shows...). Keeps me alert when I put hours in on the road. And I learn cool stuff :)

Tuesday: Teach all day (duh), help kids at lunch and after school, shoo said kids out around 4:30 so I can drive to the gym, exercise for an hour, go home, cook dinner (I made pressure cooker braised pork short ribs, cut up a pineapple to throw on at the end, and roasted some broccoli), go to target with my hubby since he is leaving tomorrow for a big conference and this might be the only time I see him this week, prep my lunch, clothes, trombone, etc. and get ready for bed (I think I made it in bed before midnight, but I'm not really sure...)

Favorite Thing: Instant Pot! I am not kidding you - this thing is AMAZING. My hubby got it for me for my birthday and I use it probably twice a week. If you are busy and trying to still eat at home, this is a life saver. If you have food issues like me and can't eat out, well... just go get one. Like now. My page will still be here for you to read once you do ;)

Wednesday:  Head to school for a minimum day (we have staff meetings on Wednesdays). This sounds like it should be easier since classes are shorter, but we have ALL our classes (8 periods) in a row (until 12:50) then go to lunch at the end of all that, so I am always exhausted. Then after lunch (1:45) we went to a staff meeting that didn't get out until 5 or 10 minutes to 4pm, so I rushed back to my room to grab my stuff and had to jump in my car to drive to symphony rehearsal again. This time, we didn't get out early, so I didn't make it home until 11pm. I then had to make my lunch for the next day (Greek salad with marinated roast beef), get ready for bed, etc... Didn't see my bed until after midnight this time :-/

Favorite Thing: iPads in the classroom. When I found out my new school site was going 1-to-1 iPads this year, I was actually pretty nervous. I've heard plenty of stories about the challenges that arise in these situations, so I wasn't sure how I felt about it. Now, I am so grateful. After having to jump in my car and leave school after that meeting, there was no way I would have copies for the following day, and the copy machine is ALWAYS busy in the morning. Now I can send and track assignments digitally, so no copies means a little more sleep. By the way, if you haven't checked out Desmos yet and you are teaching math, go now. The classroom activities are especially cool, and you can edit or create your own. SO COOL! Again... I'll wait :)

Thursday: By now, I am feeling fatigued. I love my sleep and I have had a LOT of days in a row where I'm running on a deficit. I didn't think I was in a bad mood or anything, but a number of my students asked me if I was okay/upset/having a bad day - I must've looked like hell. LOL! We had an all 8th-grade meeting in the morning to discuss rolling out iPads, then went back to have class during the rest of the day. I had kids working in my room during lunch, and a number asked to stay after school again, so I said that was fine. A couple of the girls who asked to work with me came in after school and I helped them with classwork and homework, but lost track of time and had to shoo them out at 4pm so I could race back to town to teach trombone lessons (4:15 - 6:30 pm). Then, I had a moment where I considered going to the gym, but decided that sounded too exhausting and went home to cook dinner and get things ready for tomorrow. I actually made it into bed just a little after 10pm. SUCCESS!!!

Favorite Thing: Working with students 1-on-1 or in small groups. I have tutored people in various subjects since I was in 4th grade, which is probably why I fell into teaching, but there is just something special about the interactions you have and connections you make with students when there isn't a whole room full off them. One of the reasons I lost track of time and had to scramble out was because, even though we were working on past-due work (a frustration for me) and a subject that wasn't the students' favorite (a frustration to them), we were actually having fun. We wound up having a semi-deep life lesson conversation at one point, and one of the girls came back and told me how she went home all excited and talked to her mom about it. Pretty sure that's never happened with ANYthing I have ever said during class!

Friday: Finally! Teach teach teach, help kids, pack up all my stuff to grade, try to clean off at least a corner of my desk so it isn't a total disaster, and head off to symphony rehearsal again. Back home by 11, cart in all my stuff from the car (it took me two trips), get ready for bed, and crash.

Favorite Thing: Objectives/Standards Based Grading. I FINALLY could switch my grading system this year (at a new site and after pitching my principal, he said go for it!). While I have had a few newbie-type issues (educating kids and parents about it in a way that makes sense to them, progress reports always look way worse than they would if I were grading assignments, the fact that I can't easily change grades from past grading periods when kids do learn the skills that were a part of that grading period, etc), overall this has made a huge impact on my ability to provide feedback to students. Since I don't grade every paper, I can spend that time on giving feedback instead. Of course there are some kids who don't like the fact that their grade is entirely dependent on their ability to perform or produce with quality, but I feel like I am able to track students' knowledge and needs much more easily :)

Saturday: Get up, go to the gym, head to Costco, back home, eat leftovers because Costco took longer than planned, jump in the shower, try to make myself look at least passably nice, drive back to symphony rehearsal, eat dinner, then back to play the concert. The piano soloist was amazing, by the way. There was a reception afterwards at the ONE place where I can actually eat the food for the reception, but I was so tired that I decided to just hit the road. Home around 11. I tried to just crash but I could NOT sleep. I hate when my husband is gone, especially this long. For some reason, even though I have the WHOLE bed to myself and I can be in whatever position I want and hog all the blankets, I have a really hard time sleeping. I'm pretty sure the last time I frustratedly tossed and turned and looked at what time it was, it was around 1:45am. Ugh...

Favorite Thing: MTBoS. I KNOW that, with the fact that I now have ONE day (tomorrow) to grade, plan, cook a ton of food, do laundry, blog, and FINALLY see my hubby, there is no way that I could actually make awesome engaging lessons for the whole week. I have an outlined idea of what I'm doing for the week as well as an activity for Monday, but the rest of the details will be filled in based on ideas that I shamelessly steal from the army of fantastic and generous teachers who digitally enrich my life. Thank you for sharing ideas, uploading resources, and making me think about, question, and improve what I do every day. :)

On that note... if YOU have any favorites that have to do with radical expressions, rational/irrational numbers, etc. please let me know in the comments so I can go steal those too since that is where we are heading next :)

One Good Thing

Okay, so I think I might be stretching the assignment a little here since the "one good thing" I am going to write about actually happened before break, but I think it's worth bringing up!

Anyhow, my mom had to have a somewhat sudden surgery and I am the only family member who's even in the state, so when they said she needed a solid week of round the clock care it was obvious that I would be jumping in to take care of that. They wound up scheduling the surgery on the last day of school before winter break, which meant I had to miss that day.

I like to prepare my kids for sub days so I can put more responsibility on THEM, so of course I told them what was going on. There are always about a million questions ("Who's the sub? What are we doing? Will your mom be ok? Do I have to do the work? What if a chicken ate a taco? etc...), but as those questions died down, I figured that would be the end of it. Then one of my students (who tends to be easily distracted and goofy) stands up and says, rather passionately, "We have to do something." The rest of the class was already moving on to the next thing, so I went over to talk to her. She was determined that they (the students) do something for my mom. She was also gathering a steadily increasing crowd of kids who were in agreement. 

I didn't want to spend my precious instructional minutes on an art project for my mom, so I grabbed some butcher paper, put it on my back table, and told the class what assignments they had to complete in order to have time to sign during class. 

I did offer the opportunity to my other classes as well, but essentially, they had to really want to sign it because they had to be on top of it with their work. 

I was amazed at how many of my tougher kids, as well as those who tend to have a harder time in math wanted so badly to write messages to my mom - who they've never met. 

By the end of Thursday, when I gathered the poster up to take home, I read through everything to make sure no one "tagged" anything or wrote inappropriate messages (I do teach 8th graders). It was seriously one of the sweetest things I've ever seen from kids this age. There were lots of positive encouragements, a surprising number of "I love you's", awesome artwork, and a fair share of funny yet sweet, honest, and heartfelt messages (these last came mainly from my boys, who totally surprised me by wanting to participate in the project so much). 

I'm so glad I caved and begrudgingly allowed my students to make this happen - I have a feeling it's a memory that will stick with me :)

MTBoS Blogging Initiative

Ok - I've had this blog for over two years and I've posted a whopping 4 times (5 if you let me count this one). I realized that if I want to actually be a contributing of the MTBoS community I needed some help getting going here. So... I joined the January Blogging Initiation hosted by Explore MTBoS!

This means that I actually have to post stuff - and I have a mentor who will force help me to stay accountable :) 

You, too, could join in on this exciting adventure. All you have to do is dust off your blog and get ready for the first prompt to arrive January 10th!