We made it safely home from L.A, as many of you found out TWO MONTHS AGO. Yes, it has been many moons since I saw the loveliest math teachers in the world, and all I can think of is just how inspiring you all were. I have had this post brewing in my head this whole time, and it is not going to win any Pulitzers, but it is true. These are my thoughts (if anyone is reading this ghost town of a blog) on TMC 15.

If Fawn wasn't your favourite you are objectively wrong! Yes, I am being facetious; you are allowed to have other favourites, but seriously, Fawn made you laugh; she made you cry; she made you cry because you were laughing, and then I think she even made you laugh because you were crying! Fawn reminded us why we are teachers, and also why we became a part of this crazy MTBoS community. It was inspiring, and only solidified my love of her and all that she does. #forthenguyen

What an incredible group of people we have to interact with. This was my first experience of TMC, and I was just floored by the number of incredible conversations and minds that were in any given direction. What really got me was just how many more people there are who are contributing and engaging in this group than I ever expected. We can be secluded in our own blogs, and even the close knit mini groups of friends we have made, that we forget about the whole. Never have I seen so many teachers gathering all together to learn during their summer. I feel that bears repeating many times. Hundreds of teachers took time from the resting, relaxing, to fly, drive, probably bike, and I bet some weirdos were kayaking along the way, in order to engage in what we are apparently taking a break from. The reality is this group of people do not break from being teachers. It is what we do. It is what we live and breathe. Summer does not end that, in fact it only gives us time to dig even deeper than we can when the school year begins, and we have to worry about all the other non-teaching specific responsibilities we have.

My next favourite people were definitely Hedge and John Mahlstedt. Hedge is my sister from another Mister, so I knew she was awesome but it was great to meet John, and see how two great minds came come together to plan something so awesome as a mathematical zombie apocalypse. I realised just how awesome these two when they had us in teams planning which cars we would steal, hot wire, and take to safety. It was pure inspiration, and I hope one day I get to use it. My current context might not work yet, but I am looking how I can fit it in.

Besides the general inspiration, my one big thing that I am taking on this year is Number Talks. Chris Harris (my other new favourite person) led the discussion and really inspired me to start getting my kids to do more mental math. They are engaged, and I cannot wait to see how the whole year progresses. I can already see how it will enhance many of the topics that I will be teaching. The fact that kids are forced to talk, and discuss in mathematics, means that they are becoming stronger mathematicians every day! I love it.

This is still the aspect of the MTBoS that still blows my mind. You are actually my friends. I don't know how that happened. I remember reading about it and thinking, "Yeah right," but you truly are! I especially hung out with Mr. Matt Vaudrey (FYI his family is the bomb), but there were so many others that I cannot even begin to count.

There is so much more that I could express, but I did not want this to drag on. You have inspired me to be a more devoted blogger. I miss the engagement that I once had, and I am trying to jump bank into this amazing world. I can't wait to see you more #mtbos!

If you want a more detailed, but possibly harder to follow version, you can look at my notes. I am not sure if they are helpful to you, but maybe they are.

I dread terrible professional development. There is nothing worse than having to sit through hours upon hours of useless information.* It was with great trepidation that I went to a conference on Love and Logic. Even the name gives me shivers. There was very little description of what was actually entailed with this session, but we were required to go, and I was not too excited. That changed.

The gist of the program is that in management we have two options: (1) fear mongering and punishment, (2) empathy. Seems like a simple choice. Do I want to be a raging Hulk teacher, or do I want to be a calm Dalai Llama/Bl. Mother Teresa hybrid? I want to be the nice guy. We know that, but we always have that nagging feeling in the back of our head that "being nice" will mean students walk over me, so I need to bring some sort of hammer to the classroom management knife fight.

Luckily, empathy doesn't mean "niceness." It doesn't mean I have to sing Kumbaya at the beginning of class. It doesn't mean I have no expectations for the class. What it does mean is I must show care for students and help them to take responsibility in all that they do.

We all have expectations in our classrooms. Maybe we want the class to be so quiet you can hear a pin drop. Maybe you hope that students can work productively in groups for 15 minutes minimum. Something that you may have noticed in your years of teaching is that students at times do not always meet those expectations. What is your gut reaction to that? At the very minimum we might say "Stop doing that" or "Start doing this." At the worst we can tear our students apart: "I can't believe you are doing that!" or lap out the punishments: "Get out now!" Our tone and words vary, but often times we are at the end of our rope, frustrated, and not really ready to treat this student like a human (they actually are human! I researched it and everything). 

The first step in Love and Logic is to turn these moments into opportunities for compassion. A student who is distracted we could ask "It looks like your having trouble with this, can you tell me what's difficult?" Giving the student a chance to respond is no longer a defensive position, but a conversation not a fight.

The next key is turning our wishes, "Don't do that," to enforceable statements, "We can do this, only if this happens." It is not about making consequences so much, but having logical outcomes that put the onus on the student to complete before they can continue participating in the class. What I love about this is classroom expectations are still apparent, but they are made clear to students, and worded in a way that doesn't degrade their dignity, but simply says, "If you want to be a part of what we are doing, this is how you can be ready for that." Here are some of the examples I can think of, off the top of my head.

Obviously, these cannot simply be canned responses. Obviously some work with particular students and not with others. Number three works great with my class this year; it was abysmal with my class last year. That is the nature of students and teaching in general.

The last bit of icing on the cake was the conversation on controls. Please do not be mistaken; this does not mean "How can we control kids?" Controls are just like those in an experiment. What variables, do we as a teacher control, in order to motivate, and move our students toward our expectations, hopes and dreams for their lives. This is what sold me on this philosophy because they made great mention how our curriculum is one of our most important controls. One of the greatest classroom management devices is simply GOOD TEACHING! This was affirmed, and has always been my belief. Like all humans, though, even in the best lesson in the world, management struggles arise, and power struggles are never the solution.

I encourage you to think about how you interact with students and management issues. Do you lash out? Do you do nothing? I think both of those answers are wrong. We as teachers do need to teach our students responsibility and how to be citizens, but not by means of punishment, or fear but by restorative empathy. I'd love to hear from you. What are your wishes? How can we turn those into positive enforceable statements?

* It is in those moments I feel most connected to how our students must feel (may that be a reminder to you all).

There was a time in my life when I looked down on board games. I had some happy memories of board games, but for the most part I remember playing Monopoly for seemingly eons and ending the game by sheer boredom.  I never understood the draw to them.  That is until I got married, and my sister-in-laws family introduced us to European board games. Now I am a full fledged board game geek, and my wife and I are known as the board game people. We found that there were games that were fast (usually 30  to 90 minutes), fun, and involved more strategy than, "I sure hope I get boardwalk!" They are interactive, and just really fun to play.

If you have never played Settlers (the way the hip cats say it), you should find someone who plays board games, because they have played it.  You should then proceed to play multiple rounds of it with them.  The game has been out for almost twenty years but, considering that, it is relatively unknown (though that is changing for sure).

The premise is that you are settlers on this new island and you are trying to farm and negotiate resources to build your settlement and be the reigning leader of the island.  It involves dice rolling, building and development, and the most fun part, negotiating. It is really a teacher's dream.

I first got the idea to use Catan from this excellent post. It really is a great tool to get students starting to think about trading and commerce in the context of building a society or civilization.  I was excited last year that I would get a chance to teach a humanities class where I could put this to use. The game can be played with six players (if you have an expansion), and I had 24 students, so all I needed were 4 copies.  I looked to get them and this happened

It doesn't take a Dan Meyer lesson to figure out that's a lot of money.  I tried e-mailing the publisher, Mayfair Games, who was awesome and did send me some free games (not strictly Catan), and since I really needed Catan itself that was not going to work with my budget of precisely $0. I needed to do something about this.

When I was in my university history class, my proff, Dr. C.S. Morrisey, set up a game of Diplomacy, where we played one turn per class.  We had the chance to negotiate with a team of fellow students, and we made strategic advancements over the course of the semester.  I wanted to create a version of Catan that was like this.  So I did.  I offer to you my adjustments for classroom Catan.

I went about creating my board in PowerPoint.  It is important to know (because I researched it), that copyright wise you are allowed to use the mechanics of a game as you want.  The visuals are what is copyrighted, so I had to scour for other images.  If you see anything here, that you know for sure is copyrighted, please let me know, and I can change it.  I tried to find creative commons, but I am unsure about absolutely everything. 

The basic rules of Catan stay very much the same. I will not repeat them all here, but if you are completely unfamiliar you could look at the pdf rules.

The following revisions I have made are to make it work in the classroom. Each day the following happens:

1. Development Cards are to be played before the round, in order of first team, second team, third team, etc.
2. Auctions for Buildings these take place if two teams try to build in the same spot. For ease of auctioning all resources are equally valuable during this phase. 
3. Resource Gathering takes place by one roll of the dice per number of teams.  Each country keeps track of their resources for the round, and the teacher divvies them out at the end of the round.  On a roll of seven, countries must subtract one resource from what they have (or will) earn that round.  If a seven is rolled and a country has not received any resources that round, they must subtract from their resource reserve. 
4. Building Requests are submitted by the building request form (see zip file S=Sheep, W=Wheat, L=Lumber, O=Ore, and B=Brick).  If more than one country wants to be build in the same area, they must pay up front, and then settle the debate next round in the auction.
   

Between classes students are allowed to make deals and trades as they see fit.  They get really into the bartering mode between these rounds.

My goal for this was to create an anchor for our discussions of civilizations. I didn't have any grand assessment come out of this (I think I pulled a Mr. D journal entry).

It wasn't my goal to have anything large scale from this; it was a conversation starter, that I could use when we talked about civilizations.  It does not mean however that I don't want it to grow this year. I can see this being useful in more than just a humanities context.

I see this as useful in at least the following contexts.

• As stated above history and humanities: What are the resources that we see in X? How did those resources affect their culture? What happens when one country becomes too powerful? What happened in our game? What are the benefits and advantages of trading? (Send me more in the comments)
• Math: STATS?! This is one of the best games for figuring out the probabilities of dice (in the actual board game they are clearly labeled).  You may want ore more than wheat, BUT the ore is placed on a 12, but the wheat is on an 8! I can see keeping logs of the rolls as the game is played, to figure out what is producing the most to show experimental probability, and then discuss the theoretic probability of the game. Take a break from the game to roll HUNDREDS OF DICE, and let them know that it is your team's research and development. 

What would you do with it? Let me know...

Hello, I am Timon Piccini.  You may have heard of me before, and mispronounced my name in your head as you read one of my blog posts. Where have I been though? I have left my blog alone over the last year and been a relative ghost on the Twitterverse-sphere-munity. I don't like that, not at all. It took a little bit of guilt

and some encouragement

to really inspire me to get back in the game, and I hope that over this next year I find more time to write posts to keep you in the loop, share some ideas, and hopefully get some well needed help.

So what have I been up to in the last year?  Well here is a quick break down...

I took a leap this year, and taught elementary.

I know, I can hardly believe it myself, but it was incredible to try my hand at teaching students how to write, give speeches, learn about ancient cultures.  I felt completely out of my depth, but it was fantastic and I loved it.  Difficulties were had, and it really kept from being able to have the math lessons and ideas that I have been trying for so long, but I also learned to adapt some of the great inquiry based methods I have learned from this excellent community in other contexts.

I know it is somewhat a trend to have students do programming, but after watching my students create video games from scratch, using Scratch, was  a real joy.  I essentially stole (errr I mean utilized) this unit verbatim, but I am all right with that.  Students loved it for the most part, but they really had to fight and struggle with programs that wouldn't quite work.  Basically it was mental weightlifting that they had never really attempted until this point.  There was brainstorming, editing, trial and error, research, and great results.  Did every students work have all of this? No, but as I plan on doing this again, I can foresee more of the needs that students will have.

I love technology.  I love using it.  I lover sharing it. I also love helping people use it better.  At both schools I have worked at I have become a welcomed helper.  Teachers would contact me before our official IT provider, and it was a task I truly loved.  As I was rehired this year I am now being given two afternoons a week (give or take) to devote to helping teachers incorporate tech.  Whether it is preparing Pro-D for our Friday mornings, or just helping people get PowerPoint to work, I get to help with that.

As I have thought about this new role, I have realised the greatest form of tech integration I have experienced is this community.  You all have taught me, encouraged me, and challenged me to be a better teacher.  I hope that this year I can continue to grow with you, and share some of what I have been doing, because even though I dropped off the earth a bit, I know that this community is worth investing in, and I hope to continue in that, and show my colleagues the value of Blog-o-twitter-verse-sphere-munity-dom. See y'all soon.

At some point kids learned that algebra is hard, confusing, or some other description preceded usually by an expletive, and followed by a sigh.  As a lover of Math, I never understood that algebra was difficult, and it became stunningly obvious the first time I tried to teach basic equations that I was not "normal."  I stood in front of the board, and told my grade eights "Just do the opposite operation, that's it!  If you see adding just subtract."  It seemed so obvious to me.  No stress, just tell them.  We see it all the time. It just didn't work for my students, and it didn't work for me.  So I thought long and hard, and this is what I came up with.

With my mind on 3 acts so often, I wanted to boil down my problems to a simple question.  I began to ask my students "How many pennies are in that cup?"

If you ask students how many pennies were in that first cup (assuming I divided the pennies equally), they will have the answer before the video is finished.

The thing that arose as the difficiency of this method, is that the problems became so easy in this case, that students couldn't see the connection between the algebra and the cups.  I worked for a while on a basic set of work that would bridge the gap between the visual and the abstract.  My process for my students went as follows:

1. Student views visual and solves.
2. Student develops visual from words and solves.
3. Student views equation, develops visual (if necessary), and solve.

To see a copy of what this looks like just click on the link below.

I hummed and hawed about how to bridge two and three, but I found by the time students had finished step 2, they could complete step three without any hesitation.  It was fantastic! As soon as students get a bit stuck on the equation, I tell them, "Let's draw it on this lovely whiteboard."

To really hammer home the connection between them we play lots and lots of Algebranary!

There are a number of downfalls with this method, that I am still trying to work through, and I would love any critique that you can give.

• When kids can do it in their head, they feel no need to draw anything; when the numbers are too large drawing is cumbersome, and inefficient (the necessary breaking of visual models to get to the abstract I guess).
• Visually subtraction is impossible (very hard?) to show in a static image, so in my slides you will see I resort to number lines (I save the visual of that for last), since students will have a hard time drawing on their own.
• Though students are able to UNDERSTAND the steps of solving equations, this set up does not create the desire FOR algebraic knowledge like some of the awesome projects we often see on the blogosphere.

It is not perfect, but this has all been incredibly valuable for student understanding the basics of solving linear equations.

I have always imagined this would also work great for inequalities (unbalanced scales and ask "What is the minimum number of pennies to do this?"). Dig through the slides, and the pictures, and the videos, take what you like, tell me where you would go, and hopefully enjoy.

I started to organize the video files, then I got lazy.  If you want to deal with the raw files however, you can download this mess of files. Otherwise see how I organized them in my PowerPoint.

How do we inspire a curiosity in number sense?  I think one way is by having awesome internet colleagues who make ridiculously great resources, but I have been noticing one spot on the Youtubes that continuously shows some outlandish, beautiful, and yet humorous representations of things that we normally wouldn't think about.  I want students to learn in my class that math is not so much about "using in the real world" as if we are to know that a particular concept is used in scenario A, but rather to use it with your own impetus. I think Buzzfeed (and possibly more specifically Ze Frank) strikes this magnificent harmony between beauty, humour, and number sense. Check out these videos, and share anything else that you have seen.

Also if you haven't seen it yet go to Math Munch NOW!  The spirit of their posts is very much in line with how I feel about these particular videos, but definitely at a more mathematically sophisticated level.  Enjoie.

In case you were wondering...

As you can see over the past two months I have been quite busy.  Some of you may have seen that I went in for an interview, and I am happy to say that I am now getting ready to be a grade seven teacher! It is going to be a HUGE growth opportunity, as this is not a strictly math position.  Heck it is not even my usual math, science, and French.  I am going to be responsible for PE, social studies, and even English (eek!).

I've had a huge amount of support from you guys, and I just wanted to thank you all, and I hope to see you on here a lot more (I know I need to share more of my stuff, and I'll try).  Right now I just have to get ready for this wild world of Elementary teaching.

Here's to the drawing board!

Over the past months I have been slightly invisible.  This makes me sad, but I know that blogging, tweeting etc. is an ebb and flow process for me.  My mind is not constantly bursting with new ideas, and when I have new ideas these days, I have not been in the space to bring them to fruition. I am also right now at a difficult point in my career.  This year I have suffered for the first time the dreaded "cutback." The school that I have lovingly served for three years has gone down in enrollment, and as such they needed to bring the budget down by one full time teacher; I'm on the lowest rung, and therefore I had to say good bye.  

I am surprisingly at peace with this, because I do feel I am now given a chance to pursue my passions, especially in regards to teaching math as I truly want to devote myself fully to the discipline of math (many of you know that I have been teaching science, and French as well).  I am looking forward to seeing what is next in store for me, as I know something will show up; I just don't know what that will look like yet!

For awhile I have wanted to hop on the Virtual Filing Cabinet Bandwagon and as I see myself in a spot of not really knowing what to plan for in the next year I decided to plan for EVERYTHING. This is partially a way of practicing  for my future, but also to prepare for the possibility of having a position at the end of summer, and having no resources.  I also want to give a Canadian spin (because we all know I play that card ALL THE TIME) on the virtual filing cabinet process.  You can see the first efforts here.  I will be updating throughout the summer.

I have separated the topics in subjects based on British Columbia's IRPs and curriculum.  I have lifted (plagiarized?) the standards as they are written in our government documents so that anyone (me mainly) may go directly to the assessment standard and see resources for that specific standard.  I am not sure how much they link to the other provinces, but hey, I'm from BC I can't make everyone in Canada (no matter how nice they are).

You can read, enjoy, and hopeful put to use this collection, but what be even BETTER is to help me out.  At the end of each page I have a small form that you can fill out.  If you see a topic that is missing an awesome activity, or has NO activity (designated by the TBA), fill in the form and let me know.  We are a gift culture on here, and I am not ashamed to ask for a showering of gifts in the form of links!  So please, help me out if you can, and maybe we can get an awesome resource going for the Canucks!

Language is a funny thing.  I have talked about it before but the use of language and our ability to reason numerically is so interesting.  I had a conversation with a student today where he told me about his dogs. It was one of those off topic conversations.  He was describing the size of his dogs and he said "I have two hundred ten pound dogs."  Now I have intentionally left out any dashes, because I want to let you in on what I understood.  When he said that I thought of this massive group of hundreds of these ten-pound puppies.  He meant he had two dogs that were 110 pounds.

Which brings me to my thought.  In one sentence we can have three different meanings, the likes of which are such.

I have:

1. I have 210 pound dogs
2. I have 200 10 pound dogs
3. I have 2 110 pound dogs*

What does this tell us about the nature of quantity?  They all sound the same but all produce different quantities.  In scenario 1 we have 210x pounds of dogs. We do not know how many dogs I have, but they are all around the same size.  In scenario 2 I have 2000 pounds of dogginess, and in scenario 3 I have 220 pounds of dogs.  In some weird linguistic sense, these seem like they should all be similar in some sense, but they all produce different images, and different quantities entirely.

I do not know why this particular quantity pun amuses me so much, but I feel there is something here.

* Ya, I realise that mathematically we should say two one-hundred-ten pound dogs, but conversationally we rarely say that.

**Another fun quantity pun to ask kids especially is would rather have one and a half million dollars or one million and a half dollars? Something seems eerily the same about those, but they are screamingly different.

Well Geoff and Michael have been bugging me, and I  was also really inspired by Stadel's recent post on exponents that I wanted to quickly share my little intro to exponent rules for my grade eights this year. They (and I) really enjoyed it, and I think it touches a bit on what Dan Meyer is trying to get at with Tiny Math games.  In Grade 8 students do not need to know exponents, but our school wants them to be familiar with them, before grade nine, so I concocted this little activity.

Nothing too fancy here, but basically I printed out this sheet multiple times

I sliced each section, and put them in envelopes at the front of the board titled "Product Rule," "Quotient Rule," "Power Rule," and a^0=?  I told students a few simple directions

1. Follow the directions on the first slip of paper.
2. Complete all directions on your large whiteboard.
3. When you think you have it figured have me come and take a picture.
4. Practice that rule with some basic worksheets.
5. Move to the next rule.

If you can't tell or don't recognize the questions, I was inspired by Exeter.  Reading their problems I realise they have a knack for assessing, and teaching within the context of a clear and concise question.  The question itself pushes students to work through the problem solving in a natural way (even if it is pure math not applied). I worked on these questions for awhile, to make sure that they put the students through the algebraic clarity but they also had a chance to play and punch numbers in their calculator.

(aside) This in my mind is also a less rigorous version of David Cox's fantastic lesson.

Students had a concept of repeated multiplication.  They knew how to evaluate exponents within whole numbers and could hit the "equals" button on their calculator a repeated number of times.  They were not instructed how to find the exponential form of a number (for example they can find 2^3=8 but they had never tried 8=2^3).

Since this only needed to be an overview, and we just needed to touch on these concepts I felt that I didn't need to make sure that everyone learned every rule.  Most students were very proficient with the product rule and quotient rule, and figured that the power rule would somehow involve multiplication of the exponents.

What students LOVED is that they could work through it "at their own pace" (KA buzzwords I KNOW, but still!).  Students struggled through it, but it was set up in a way that was just out of their intuitive reach!  The students who arrived at a^0=1 were very easily convinced of that fact, and because of that, I knew I had a winner.

Sure they know the rules, and that is fine and dandy, but do they know the reasons behind the rules?  I do not teach associative property in grade eight, and therefore reasoning through WHY these concepts work (at this stage, rather than because my teacher said so, it is kind of because my calculator said so), but I think this is only a small drawback, because students are convinced of these rules, and they feel they are natural because they found them.  The rigour can come later.

I will do this again with students, especially as review.  I think it puts them in a state of problem solving that is not to laborious, but also not rote procedural notes.  Tell me what y'all think!